Home

Extended SCEPTRE Volume 1 User`s Manual

1. HE DERIVATIVE OF E VARIABLE SOURCE XXX HAS NOT BEEN SUPPLIED GTCODE CAN T ENCODE THE ILLEGAL TERM XXX PROGRAM ERROR NUMBER OF HEADING CARDS EXCEEDS MAXIMUM THIS CARD IS IGNORED SIMUL8 DATA GENERATION HAS BEEN DELETED FOR THIS RERUN NO STOP TIME HAS BEEN SPECIFIED ILLEGAL INITIAL CONDITION VARIABLE NAME XXX IMPROPER VALUE SPECIFICATION ON CARD PRIOR TO GROUP CARD ILLEGAL VALUE SPECIFICATION ILLEGAL TABLE SPECIFICATION EXTRANEOUS X IGNORED FOLLOWING VARIABLE NAME TRUNCATED TO SIX CHARACTERS XXX INCORRECT DELIMITER FOLLOWS VARIABLE NAME XXXXXX AN HAS BEEN SUPPLIED INCORRECT DELIMITER FOLLOWS VARIABLE VALUE EEEEEEE EEEEE X HAS BEEN SUPPLIED ILLEGAL RUN CONTROL SPECIFICATION RUN CONTROL DATA MISSING INITIAL CONDITIONS WERE NOT SPECIFIED FOR THE ORIGINAL RUN EXTRANEOUS X IGNORED INCORRECT DELIMITER FOR FOLLOWING RUN CONTROL SPECIFICATION XXX AN EQUAL SIGN HAS BEEN SUPPLIED INVALID NUMBER OR INTEGRATION ROUTINE SPECIFIED NO ENTRIES IN RERUN DATA LIST ILLEGAL VARIABLE NAME XXX ILLEGAL TABLE NAME SPECIFICATION XXX TABLE XXX RERUN TABLE EXCEEDS LENGTH OF ORIGINAL TABLE ILLEGAL CONTINUE SPECIFICATION ILLEGAL RUN CONTROL SPECIFICATION RUN CONTROL D
2. 3 IF TIME GE Z TP T0 GO TO 2 X TIME Z 1 TP TO IF TIME TO 4 4 5 2 Z Z 1 TE 220 1 ee Ay A 4 FGEN VO RETURN 5 IF X LE TR GO TO 6 IF X GT TR AND X LE TR TD GO TO 7 IF X GT TR TD AND X LE TR TD TF GO TO 8 IF X GT TR TD TF GO TO 4 6 FGEN VO X V1 VO TR RETURN FGEN V1 RETURN F R GEN V1 X TR TD V1 VO TF ETURN The value of El will be computed in the function subprogram FGEN at each time step of the transient problem The user may change any of the parameters given in figure 2 7 to create variations in waveshape It is the users responsibility to avoid format errors in the body of any included subprogram since they will cause the entire run to be aborted Subprogram functions on S 360 must be typed double precision In the above example the function FGEN card would be replaced by DOUBLE PRECISION FUNCTION FGEN A B H Also variables such as A B H in the argument list for subprogram functions must be typed double precision The appropriate entry may be REAL 8 A B H 57 or IMPLICIT REAL 8 A H 2 7 1 Subprogram insertion 7090 94 only Once the subprogram cards are generated they are inserted in the second half of the SCEPTRE Program Control Deck behind the IBJOB card PGMC1970 see figure Assuming that a source deck is to be submitted the proper sequence
3. x IB WO x A CO UO OWrR oOo x These entries reflect the situation shown in figure 2 12 The independent variable values of the original table 0 1 2 4 are replaced by 0 1 3 5 for both reruns The original corresponding table values 0 10 27 1 47 are replaced by 0 3 4 7 for the first rerun and 0 5 8 4 9 for the second rerun If both reruns are intended to use tables in which the independent variables differ form each other another proce dure must be used Instead of one RERUN DESCRIPTION card with N 2 two such cards may be used each represents one rerun The sequence of subheadings could appear as 50 Master run First run Second run Independent Table Independent Table Independent Table variable value variable value variable value 0 0 0 0 0 0 1 10 1 3 1 5 2 27 1 3 4 3 8 4 47 5 7 5 4 9 Table 2 12 Tables In Rerun ERUN DESCRIPTION UNCTIONS ERUN DESCRIPTION UNCTIONS do Mer j a Each new table is given separately under one of the FUNCTIONS subheadings The length of any table in a rerun must be equal to its counterpart in the master run RUN CONTROLS Under Rerun Any of the quantities except Automatic Termination messages that were defined under the RUN CONTROLS of a master run may be changed in any rerun The Automatic Termination messages of the master run apply to all reruns If three reruns are to be made in which
4. Note that decimal points are required for the constants 1 and 30 No further description is required under FUNC TIONS The designation DIODE TABLE N is used when any diode or transistor junction is to be represented in tabular form The independent variable will automatically be taken as the voltage across the current generator Therefore the required entry is simply J18 10 3 DIODE TABLE 1 The tabular entries for DIODE TABLE 1 must be entered under the FUNCTIONS subheadings subsection 2 2 6 Examples of typical component descriptions that appear in the ELEMENTS group are shown below R7 4 5 11 5 El GND 1 6 JA 0 4 98 J18 E12 C 7 0005 VRC JA is a secondary dependent current source JK and E12 are linearly dependent sources EQUATION 15X ILX3 TIME 7 MODEL 2N7479AA Reference to the FUNCTIONS section Section 2 2 6 is never required for a given entry when the expression format is used The rules for the mathematical definition become specialized only in the case when a table is to be used as an argument For example if it is desired to enter capacitor C1 as 10 80 TABLE 7 where TABLE 7 is a function of VC1 an appropriate entry would be Cl 7 8 X314 10 80 XTABLE T7 VC1 Note that in this special case the word TABLE is preceded by X and that both the table name in this case T7 and the independent variable of the table VC1 must be included in
5. VCET1 3 3818865E 01 VCET1 3 3696571E 01 VCCT1 8 9376695E 00 VCCT1 8 9570427E 00 VCET2 4 4221916E 01 VCET2 4 4077602E 01 VCCT2 8 8226781E 00 VCCT2 8 8603292E 00 RESULTS OF INITIAL CONDITION COMPUTATIONS RESULTS OF INITIAL CONDITION COMPUTATIONS PEC 5 3007344E 00 RERUN 2 PEIN 2 7598821E 04 PEC 5 0340188E 00 VR3 6 5620879E 01 PEIN 9 2654405E 04 VR4 2 1082735E 01 VR3 6 4422545E 01 VR4 2 0044292E 01 I C TRANSIENT VALUES AT TIME EQUALS ZERO I C TRANSIENT VALUES AT TIME EQUALS ZERO VCET1 3 3626101E 01 VCET1 3 3769191E 01 VCCT1 8 9679012E 00 VCCT1 8 9456210E 00 VCET2 4 3993970E 01 VCET2 4 4163421E 01 VCCT2 8 8813264E 00 VCCT2 8 8381601E 00 RESULTS OF INITIAL CONDITION COMPUTATIONS RESULTS OF INITIAL CONDITION COMPUTATIONS RERUN 3 RERUN 1 PEC 4 8854795E 00 PEC 5 1910074E 00 PEIN 1 2915639E 03 PEIN 5 4289718E 04 VR3 6 3752024E 01 VR3 6 5128728E 01 VR4 1 9466077E 01 VR4 2 0655488E 01 SIMULATION PROGRAM HAS TERMINATED Figure 4 6 Example 3 Output Listings PEC X1 EC IEC PEIN X2 EIN IEIN OUTPUTS PEC PEIN VR3 VR4 RUN CONTROLS RUN INITIAL CONDITIONS ONLY RERUN DESCRIPTION 3 DEFINED PARAMETERS PETIS 96 23 39 The RUN INITIAL CONDITIONS ONLY entry ensures that no transient computatio
6. R1 1k R2 19k 1 fig 10V o Figure 1 1 Sample Circuit To give the uninitiated some idea of the input data required to accommodate a simple but practical problem consider the electrical schematic of an inverter circuit shown in figure 1 1 A SCEPTRE version of the circuit appears in figure 1 2 under the assumption that a transistor equivalent circuit named 2N914A has been stored at some previous time The stored model also includes a primary photo current generator The sample listing given below will be sufficient to compute the initial conditions that hold before the radiation transient is applied as well as the complete transient solution itself up until 500 nanoseconds of real time Both printed and plotted outputs of VR1 VR3 and VCX a capacitor in the model will be obtained plus any other outputs that were requested in the stored models CIRCUIT DESCRIPTION ELEMENTS R1 1 2 1 R2 2 4 19 R3 5 3 1 5 EL 1 5 10 ET 4 1 10 2 fig Figure 1 2 SCEPTRE Version T1 2 1 3 MODEL 2N914A PERM OUTPUTS VR3 VR1 VCXT1 PLOT RUN CONTROLS STOP TIME 500 RUN INITIAL CONDITIONS END The detailed rules will be given throughout this manual for generating circuit descriptions such as the one above 2 SCEPTRE use The DC transient or AC solutions of large electrical networks are computed on request when the circuit description langua
7. The following RUN CONTROLS are legal on a rerun only if INITIAL CONDITIONS were calculated on the master run otherwise the run will terminate RUN SENSITIVITY RUN MONTE CARLO RUN WORST CASE RUN OPTIMIZATION RUN INITIAL CONDITIONS RUN INITIAL CONDITIONS ONLY The following RUN CONTROLS are illegal on rerun but will not terminate the run SCEPTRE will merely ignore them and process whatever other requests have been entered under RERUN DESCRIPTION NO ELEMENT SORT PUNCH PROGRAM FULIST 7090 94 only PUNCH BINARY CARDS 7090 94 only 52 RITE SIMUL8 DATA ECTOR EQUATIONS RITE DEBUG RINT B MATRIX LIST NODE MAP IC FOR RERUNS USE DIFFERENCED JACOBIAN USE SYMBOLIC JACOBIAN EXECUTE SET UP PHASE ONLY USE FIXED AC MATRIX IN RERUNS IMPULSE RESPONSE BUFFER INPUT FUNCTION BUFFER U S lt 3 The following RUN CONTROLS are reset by the program prior to a rerun Therefore if they were in the master run and are desired in the rerun the user must reenter them I I MONTE CARLO DETAILS OPTIMIZATION DETAILS CH OPTIMIZATION RESULTS PTIMIZATION RANDOM STEPS RINT A MATRIX RINT EIGENVALUES PRINT EIGENVECTORS INIMUM FUNCTION ESTIMATE INITIAL RANDOM NUMBER RUN AC RUN SENSITIVITY RUN MONTE CARLO RUN WORST CASE RUN OPTIMIZATION LIS LIS Pp Z
8. PIVOTING OF THI E 7090 94 only If the analysis phase is aborted by any of the error messages indicated above the following messages will also appear IBFTC CARD WITH CORRECT DECK NAME NOT FOUND This message is printed following the Program Control Deck card labeled PGMC 1960 T LOADING HAS B EN SUPPRESSED This message is printed following PGMC 2300 65 3 Equivalent circuits and associated notation A prime objective in the development of SCEPTRE was to permit the users as much freedom as possible in their choice of equivalent circuits The result is that almost any combination of the allowable elements R C L M E or J may be used to represent any active device This is true whether the user relies on the stored model feature or elects to enter each component of the equivalent circuit individually under ELEMENTS A complete discussion of equivalent circuits is beyond the scope of this manual but a few pertinent points that will be given in this section may prove useful to the user 3 1 Diodes A general diode model is shown in figure 3 1 in which C represents the sum of the junction and diffusion capaci tances of the diode the RB and RS refer to the bulk and shunt resistances of the diode respectively The heart of the model is the perfect diode the current of which is given by the diode equation which in turn is dependent upon
9. RUN WORST CASE and or RUN OPTIMIZATION See subsection 2 2 7 for more detailed discussion of the Sensitivity Monte Carlo Worst Case and Optimization Run Controls Any one or more of the above five entries will cause Initial Conditions to be found by the Newton Raphson method If it is desired that the DC solutions be run using the Implicit technique include the extra entry RUN IC VIA IMPLICIT See Appendix A 3 for a discussion of the Implicit Method of computing Initial Conditions Notes 1 The entry RUN IC VIA IMPLICIT will cause all requested DC solutions to use the implicit methods If this card is not entered all requested DC solutions will be by the Newton Raphson method 2 DC solutions are accomplished in the order shown in this table See text 3 Transient only is the default mode of analysis 30 The user should note that the method he chooses either Newton Raphson or Implicit for finding Initial Conditions will be used in all DC solutions he requests on the same run Thus the choice of the method for a particular problem can have a sizeable effect on running time when several DC calculations are involved The user should thus exercise care in the selection of the Initial Conditions method The user should also note that the DC runs are performed in the order Sensitivity Monte Carlo Worst Case and Optimization regardless of the order in which the cards are entered Thus if the user desires to use the re
10. Rerun Mode of Analysis A master run may consist of the combination of solutions discussed in subsection 2 2 7 A general rule is that no rerun may contain more than its master run did If the master run was an AC or transient solution only all associated reruns must be the same If the master run was initial conditions only all associated reruns must also be initial condition or other DC solutions Thus the Run Control RUN AC is illegal on reruns if it was not used on the master run and will terminate the run if used If the master run was an initial condition solution plus a transient solution there is some leeway The user should determine whether the changes in the network will affect the initial conditions Usually only changes in resistors or batteries will have an effect If 1t is decided that the initial conditions will not change the initial condition run that was made for the master will suffice for all reruns In this case no special entry is made for the reruns If however it is decided that a new initial condition run is required for each rerun the user must request this with the entry under RUN CONTROLS under RERUN as RUN INITIAL CONDITIONS The single entry will allow for re computation of initial conditions for all reruns in that group The user may ask for new initial condition solutions for each rerun even if the master initial conditions are valid However this action 1s wasteful of computer time and should be avoided
11. A time derivative of an AC source means simply a multiplication by jw SCEPTRE will detect this situation and will automatically handle it A complex defined parameter W cannot be used as a value specification Convolution models are either series combination of voltage source and resistor FCONVE or parallel combination of current source and resistor FCONVJ See Appendix A 8 The constants in the Convolution Model Call are arbitrarily assigned integers identifying the impedance or admittance functions stored on Disk 12 as explained in Appendix A 8 Examples of variable element entries using EQUATION TABLE or EXPRESSION descriptions are as follows El E2 JM RA LZ 1 2 ABLE 3 TIME 1 6 EQUATION 47 1 4 EQUATION 47 3 4 LESS VC1 TABLE 2 ILO 36 Vele Pop 152 oa ABLE 5 TIME EXPRESSION 7 10 ILZ 20 The tabular entries for TABLE 3 and TABLE 5 as well as the analytical expression for EQUATION 47 must be entered under the FUNCTIONS subheading subsection 2 2 6 A good general rule to follow throughout the program is that all constants inside parentheses must include decimal points A more convenient form that always may be used is to replace the word EQUATION by Q the word TABLE by T and the word EXPRESSION by X El JM LZ T3 TIME O47 YE 1 Body LS 47 10 ILZ 20 12 1 4 1 5 10 The second and third
12. B C EQUATION 1 10 400 TABII J1 B E DIODE TABLE J2 B C DIODE TABLE 2 J3 C B P1 J1 DEFINED PARAMETERS P1 98 OUTPUTS VCE VCC Jl PLOT FUNCTIONS EQUATION 1 A B C A B C DIODE TABLE 1 007 370 007 6087 DIODE TABLE 2 0 0 58 0 62 4 64 1 CIRCUIT DESCRIPTION A023 ELE 66 2 ENTS 1 1 2 TABLE ERIVATIVE E2 1 4 20 CZ 2 3 1E3 CX 5 6 1E3 R1 4 3 30 R2 3 1 20 R3 5 1 2 R4 4 6 240 R5 4 7 3 3 R6 9 1 1 8 T1 3 5 4 MOD T2 6 1 8 MOD L1 7 8 100 L2 9 1 900 1 TIME E1l TABLE DE1 j o m q 2N9999AA 2N9999AA PERM 3 LOT Sy transformer coupled amplifier PERM CHANGE EQUATION 1 5 40 TABLE 1 VCE 2 VCC shpe Ops Lap ay Lopere Tps pe AAN 22 O Td V2 P1 975 82 M L1 L2 299 7 OUTPUTS VR6 VL1 VL2 FUNCTIONS ABLE 1 0 0 50 5 100 5 ABLE DE1 0 01 50 01 50 0 100 0 RUN CONTROLS STOP TIME 500 COMPUTER TIME LIMIT 5 RUN INITIAL CONDITIONS MAXIMUM PRINT POINTS 3000 END VL1 0 ee A A A A A ee See VL2 0 i i fi i fi fi fi 50 100 150 200 250 300 350 400 450 500 TIME Figure 4 4 Example 2 outputs 4 3 Example 3 DARLINGTON PAIR A03 The schematic of a Darlington pair appears in figure 4 5 The problem is to determine the d
13. Chase Stability Properties of Predictor Corrector Methods for Ordinary Differential Equations Journal A C M 9 October 1962 pp 457 468 17 R J Kuhler Application of Generator Analysis Methods AFAPL TR 77 31 NTIS AD A042071 18 Wm C Davidon Variable Metric Method for Minimization AEC Research and Development Report ANL 5990 REV 1959 19 M J Box A Comparison of Several Current Optimization Methods and the Use of Transformation in Con strained Problems The Computer Journal 9 pp 67 77 1966 20 M J Box D Davies W G Swann Non Linear Optimization Techniques Imperial Chemical Industries Ltd Monograph No 5 1969 21 Variable Metric Minimization SHARE Routine No 1117 AN Z013 A3 SHARE Inc Suite 750 25 Broadway New York NY 10004 22 J C Bowers J E O Reilly G A Shaw SUPER SCEPTRE A Program for the Analysis of Electrical Mechanical Digital and Control Systems University of South Florida Tampa Florida 33620 May 1975 NTIS AD A011348 23 W A Cordwell Transistor and Diode Model Handbook AFWL TR 69 44 NTIS AD 862556 24 Y C Liang V J Gosbell A Versatile Switch Model for Power Electronics SPICE2 Simulations IEEE Transactions on Industrial Electronics vol 36 no 1 February 1989 p 86 25 Lawrence J Giacoletto Simple SCR and TRIAC PSPICE Computer Models IEEE Transactions on Industrial Electronics vol 36 no 3 August 1989 p 451 26 F Javier Gracia
14. EXECUTE SETUP PHASE ONLY PLOT INTERVAL 2 2 4 Used with composite Plots Omission results in deletion of Composite Plots Table 2 6 Additional run controls Allowable dependent variables are listed in table 2 7 Allowable independent variables are listed in table 2 8 The Sensitivity Worst Case and Optimization solutions use Adjoint Calculations as discussed in 2 Adjoint calculations give the partial derivatives of dependent variables with respect to a list of independent variables There is no specific limit on the total number of dependent variables or independent variables The limit is on sets of variables A set is a list of dependent variables together with its list of independent variables The total number of all sets entered for Sensitivity plus Worst Case plus Optimization must not exceed one hundred Also four times the total number of dependent variables plus the total number of independent variables must not exceed four hundred The total number of Monte Carlo sets must not exceed forty Four times the number of Monte Carlo dependent variables plus the total number of Monte Carlo independent variables must not exceed one hundred An example of valid Sensitivity input data cards is SENSITIVITY IL3 PX JX EY VR1 IR1 VCX P1 E1 In this example the following partial derivatives would be calculated 0IL3 0IL3 OPX OPX VRI OVR1 IRI IRI OVCX OVCX OJX OEY OJX OEY OP1 OF1 OP1 0El OP1 OF 1 A
15. Fernando Arizti F Javier Aranceta A Nonideal Macromodel of Thyristor for Transient Analysis in Power Electronic Systems IEEE Transactions on Industrial Electronics vol 37 no 6 December 1990 p 514 27 Vineeta Agrawal Anant K Agarwal Krishna Kant A Study of Single Phase to Three Phase Cycloconverter using PSPICE IEEE Transactions on Industrial Electronics vol 39 no 2 April 1992 p 141 28 H A Nienhaus J C Bowers M S Ziemacki A Computer Model for a High Power SCR AFAPL TR 75 106 NTIS ADA 022375 4 Air Force Aero Propulsion Laboratory 133
16. If the phenomena connected with each pulse is such that it affects some network parameter say transistor current gain that in turn affects the quiescent point of the network it may be advantageous to run the entire problem as a master run with a series of associated reruns The state variable values that exist at the end of each individual transient run will be transferred to the beginning of the next run without any intervening analysis The required language is identical to that given in the preceding section If the master run final values are to serve as the starting point for all associated reruns enter under RUN CONTROLS IC FOR RERUNS MASTER RESULTS If all runs are to begin with the final values of the previous run enter IC FOR RERUNS PRECEDING RESULTS There is no danger of ambiguity that may be implied by the identical language The feature in the previous section is distinguished from this one by the fact that it will also contain the statement RUN INITIAL CONDITIONS ONLY A 4 Specified print interval The basic output format of SCEPTRE supplies printed output at every successful step taken by the integration method up to a default maximum of 1000 points If more than 1000 steps are taken that number is divided by the smallest integer n such that every nth step is printed out and no more than 1000 points would be output If a given run took 2115 steps n here is 3 705 points or every th
17. J2 VJ2 e Any element value as C17 e Any transient state variable derivative as DC4 DL13B e Any Defined Parameter as P12 e Any Complex Valued Defined Parameter Wname in AC Calculations e Any Defined Parameter derivative as DP12 if the user has supplied one e Any internal parameter as defined in table 2 11 All requested outputs in SCEPTRE will be supplied in printed tabular form The general format for requesting printed outputs is variable variable variable and or variable variable variabl 0 Note that no output request card ever ends with a comma 17 Plotted Form In addition the user has the option of requesting plotted outputs for any or all quantities If plotted outputs are desired the word PLOT is used as the last entry on each output request card for which plots are desired The general format is variable variable PLOT and or variable PLOT variable PLOT Some typical output requests follow VR3 IR3 VR2 VR5 VC29 VRY VCl ESUP PLOT IC8 Note that more than one output can be requested on a single card The third card indicates that three quantities are required and that all three are to be plotted as well as printed The quantity IC8 the current through capacitor C8 would be output in printed form only If the word PLOT is used no other dependent variable may follow it on that card All indicated variables in the above example will use time as the inde
18. Pname value Some possible combinations are PWR EXPRESSION 69 IE 3 E3 P2 TABLE 1 VC7 PX7 EQUATION 2 VC7 VR1 For the special case in which the derivative of a quantity is supplied the first two letters must be DP followed by no more than four alphanumeric characters or in general DPxxxx value Real Valued Defined Parameters with Bounds Real valued defined parameters with bounds may be used as independent variables in DC calculations under the MONTE CARLO WORST CASE or OPTIMIZATION subheadings of CIRCUIT DESCRIPTION see subsection 2 2 8 When independent variables are used in this manner they must be specified with bounds under DEFINED PARAMETERS The format is Pname number number number or Pname number number The first form gives two numbers in parentheses SCEPTRE reads the smaller number as the lower bound and the larger as the upper bound The second form has one number in parentheses In this form SCEPTRE reads the number as the percentage variation allowed in the nominal value of the independent variable For Worst Case and Optimization calculations the nominal value must not lie outside of the region defined by the upper and lower bound 15 Real Valued Defined Parameter Total Differentials The user must specify the closed form differentials for each defined parameter that is used as a dependent variable in adjoint calculations Optimization Sensitivity and Wor
19. Ze VCET2 PITI 1 04334237E P1T2 2 66473139E R3 7 88042611E R4 1 11083071E VCCT2 PITI 2 44690518E P1T2 1 09869936E R3 1 84816183E R4 2 06232105E PEIN P1T1 1 49908934E P1T2 1 24411528E R3 1 14882427E R4 7 18255438E VR4 P1T1 6 81772684E PE 1 74127029E R3 5 14946906E R4 3 94163071E RESULTS OF INITIAL CONDITION COMPUTATIONS VCET1 3 5123970E 01 VCCT1 8 9126370E 00 J1T1 2 1824751E 02 VCET2 4 3874672E 01 VCCT2 8 9197511E 00 J1T2 4 6675032E 01 VR3 6 3104773E 01 VR4 1 8670015E 01 01 02 06 00 01 05 01 02 06 01 01 06 01 01 06 02 02 07 02 01 00 05 01 02 03 07 03 02 01 06 01 1 34086834E co Ul oO w Figure 4 18 Sensitivity Example Output 98 NORMALIZED SENSITIVI TY 11299797E 11288150E 14092110E 33163490E 57951394E 51498104 368114861 63192979E 98134165E 54500777E 70617891E 00294086E 27350752E 12760299E 28288587 83056702 59224392 01273074 63351403 1 18248970 14397623 24833451 64935209 36882044 63328717 29271044 50563074 95349841 51629887 44483683 E 02 E 02 E 04 E 02 E 02 E 01 E 04 E 03 E 01 E 00 E 02 E 00 E 01 E 01 E 03 E 01 PEC EC IEC and its total differential is EC d IEC IEC d EC Since EC is constant and is not one of the independent variables it is not necessary to include its differential
20. a complex valued defined parameter W cannot be use to define elements that is it cannot appear in an equation expression table or function The acceptable entries under the heading DEFINED PARAMETERS are Wname real value defined parameter Wname TABLE name Wname EQUATION name see subsection 2 2 6 for the correct way to distinguish the real and complex valued arguments Also 16 Wname EXPRESSION name see subsection 2 2 6 for a list of the more general FORTRAN complex operational functions available Also Wname external function It is the user s responsibility when writing FORTRAN programs to insure the correct declaration and usage of complex valued quantities Alternatively the format allowed for specifying AC sources can be used This format is Wname entry entry type where the details are described in subsection 2 2 2 2 2 4 Outputs Tabular Form Any output must consist of some dependent variable which is a function of some independent variable SCEPTRE outputs consist of printed tabular listings of requested dependent variables as functions of time and or plots of the dependent variables as functions of time or some other independent variable In SCEPTRE the following general quantities may serve as either dependent or independent variables e The voltage or current associated with any passive element as VR1 IL6 e The voltage or current associated with any source as El IE1
21. and the function re minimized each time The smallest value resulting from the random motion and re optimization should be accepted as the true minimum If the Run Control RANDOM STEP SIZE CONTROL number is used the independent variable steps an amount estimated to increase the value of the function by 0 5 num ber 2 above its minimum at each random displacement If this Run Control is not used the value 0 2 is used The formulation of the Davidon method requires that the objective function minimum value be positive Since this is not always the case provision has been made within SCEPTRE to effectively maintain the objective function positive by addition of a suitable positive number However if the user has some estimate of the true minimum value he may enter his own reference value and thereby improve the performance of the optimization The correct form of this Run Control is MINIMUM FUNCTION ESTIMATE number Note however that the value entered will apply to all objective functions specified under the OPTIMIZATION subheading Convolution Run Controls The insertion of one or more Convolution Model Calls under ELEMENTS see table 2 2 causes SCEPTRE to request the Convolution Option as part of a transient run Four Run Controls are used to regulate the Convolution option These Run Controls are in addition to those described above for the transient run proper Of the four Convolution Run Controls two regu
22. ru al WO U If either of the following RUN CONTROLS IC FOR RERUNS MASTER RESULTS or IC FOR RERUNS PRECEDING RESULTS has been entered for the master run see subsection 2 2 7 Initial Conditions for reruns will be taken from the source indicated without another request In this case if RUN INITIAL CONDITIONS RUN INITIAL CONDITIONS ONLY or RUN IC VIA IMPLICIT is entered under RERUN DESCRIPTION the run will terminate Any of the other DC options may be requested however 53 Rerun with Stored Models Many users will probably apply the rerun option to networks in which stored models appear If network changes leading to rerun occur in the body of the stored model a slightly different format is required To illustrate assume that a model has been stored with the following card sequence MODEL DESCRIPTION ODEL XXXX PERM 1 7 8 9 ELEMENTS Rl 1 2 1 Cl 2 3 TABLE 1 VC1 El 9 1 20 Jl 8 7 EQUATION 1 VCl Pl DEFINED PARAMETERS P1 2 7 OUTPUTS VR1 VOL IC1 PLOT INITIAL CONDITIONS vcl 10 FUNCTIONS TABLE 1 o Oe Be O EQUATION 1 A B 3 A B Assume that this stored model is designated as T8 under CIRCUIT DESCRIPTION To change the constant ele ment R 1 under the rerun option the entry should
23. the user may supply initial conditions data himself as entries to a Transient or AC run without the help of the DC options One of the DC options called Initial Conditions takes part in all DC solutions It may be called separately and if any other DC option is called that option uses two or more passes of the Initial Conditions calculation to produce its results The Initial Conditions solution and thus the other DC options may use either the Newton Raphson or implicit method Table 2 5 shows the entries under RUN CONTROLS used for each mode of analysis If it is desired to run only DC solutions the proper entry is RUN INITIAL CONDITIONS ONLY plus the selected DC option for which the entries are RUN SENSITIVITY and or RUN MONTE CARLO 29 Mode of Analysis RUN CONTROL Required RUN CONTROL Optional Notes Desired DC Solutions RUN INITIAL CONDITIONS ONLY RUN IC VIA IMPLICIT 1 only RUN SENSITIVITY 2 RUN MONTE CARLO 2 RUN WORST CASE 2 RUN OPTIMIZATION 2 DC Plus Tran RUN INITIAL CONDITIONS or one or more RUN IC VIA IMPLICIT 1 sient of the following RUN SENSITIVITY 2 RUN MONTE CARLO 2 RUN WORST CASE 2 RUN OPTIMIZATION 2 plus STOP TIME number DC Plus AC same as above plus RUN AC RUN IC VIA IMPLICIT 1 Transient only STOP TIME number 3 AC Only RUN AC Transient Plus This combination is not possible AC Table 2 5 Run controls for specifying mode of analysis and or
24. volution can be performed with either type or with a mixture of types The following illustrates the appropriate card entry for each model Consider the situation shown in figure 4 10 Assume that a larger network circuit was partitioned and an interface created which requires three impulse response functions Further assume that the three functions KH have previously been obtained and are given as tabular functions of time and that they reside on Disk 12 in the proper format 4 6 2 Convolution impedance mode The three functions KHAB KHBC and KHAC given in figure 4 10 represent impedance functions They are identified with the arbitrarily preassigned integers 1001 2002 and 3003 see figure 4 11 NOTE That integers are written as constants i e followed by decimal points when used as arguments in function statements The appropriate entries are KHAB A B FCONVE 1001 KHBC B C FCONVE 2002 KHAC A C FCONVE 3003 1Disk 12 has been preassigned for this purpose and the required format and preparation instructions are given in Appendix A 8 89 Y Ho KHAB SCEPTRE CIRCUIT B SCHEMATIC KHAC A ee d a DY l Figure 4 10 Convolution Mode Interface KHAC 44 fig C O Figure 4 11 Convolution Representation Using Series Impedance Elements The order of these entries is immaterial Each entry is
25. 10 Impedance Model The V1 term involves only previously calculated values of current and can be represented as a variable battery El The V2 term when expanding using equation A 14 becomes V2 I Ty 1 pz Tn 1 pan mr ATy_ 1 1 Ty a ty 4 Ey ad Aca A 19 The terms comprising V2 can be considered to result from a series combination of another variable battery E2 and a variable resistor R Thus V2 E2 I Ty R A 20 and letting E El E2 Vag Tyn E 1 Ty R A 21 SCEPTRE can handle equation A 21 At each step it evaluates E and R solves for Tn and then calculates Vap Tn see figure A 10 A 8 6 Admittance model If we regard the H function as an admittance function then the current of a particular time Ty is Tn Tap Tn f Yans T V r dr A 22 0 Similar to the procedure of the paragraph entitled Impedance Model we separate this integral into two terms Lar Ty 11 12 A 23 where Tn 1 MN J YasB Tyn T V T dr A 24 124 and Tn I2 J YaB Tn T V T dT A 25 TNn 1 Il is represented as a variable current source J1 and 12 is expanded to yield I2 V Twn 1 a Tni ma a ATN 1 V T a H Tyn an ATy 1 A 26 Then I2 can be considered to be associated with a parallel combination of a variable current source J2 and a variable conductance G Letting J J1 J2 we can get Tap Ty J V Ty G A 27 In terms of circuit element
26. 2 Source Derivatives The time derivatives of sources must be supplied as input data when certain network configurations are encoun tered These situations occur whenever a variable voltage source is connected in a loop containing only capacitors and other voltage sources and whenever a variable current source is connected in a cut set containing only induc tors and other current sources see figure 2 3 If the sources in question are constant the zero derivative will automatically be supplied and the user need not be concerned If the user fails to supply a source derivative when one is required the run will be terminated with an appropriate diagnostic message The general form for a source derivative entry is 1Except for AC Analysis See Table 2 2 note 8 12 Capacitor Voltage Source Loop Inductor Current Source Cut Set L1 L2 E7 _ C2 Ji L3 5 fig Figure 2 3 Configurations That Require Source Derivatives DEname value DJname value where the name is that of the appropriate E or J source An example would be DERIVATIVE E7 TABLE 2 or more simply DE7 TABLE 2 Elements with Bounds Three of the DC options Monte Carlo Worst Case and Optimization require additional information in the entries under ELEMENTS For a Monte Carlo calculation it is necessary to specify parameters for distribution of the variable elements For Worst Case and Optimization calculations minimum and max
27. 3 4 7 fig Figure 2 5 TABLE ERIN Values as a Function of Time pairs that may constitute any table is defined Only single value functions are allowed It is permissible to supply two consecutive independent variable values that are equal but which have different dependent variable values This may be done to produce step functions as illustrated in figure 2 5 When the table values are updated at each solution time step linear interpolation is used between the points supplied For independent variable values falling outside the range of values supplied in table linear extrapolation is performed to determine the correct table value and therefore proper termination may be necessary For example in figure 2 5 for any value of TIME in excess of 3 the dependent variable ERIN will be assigned the value zero because of the use of the point pair 4 0 When the independent variable takes on a value exactly at a step point the ordinate used depends upon the direction from which the step was approached TABLE ERIN 05 30 o 2 1 2 1 5 3 1 5 3 0 4 0 or TERIN 0 Or ly Ly 2r ly 2 Lib Se dior By 07 Ay 9 In situations where the same table will serve to define more than one quantity the user need only explicitly define the table once A common situation occurs when two current generators in the network are defined by the same tabular data differing only in the independent variable In this case the
28. 8 THE MAXIMUM OF 100 DEFINED PARAMETERS HAS BEEN EXCEEDED 9 DEFINED PARAMETER LACKS A D or P PREFIX 10 DEFINED PARAMETER DERIVATIVE CANNOT BE A CONSTANT 11 IMPROPER DELIMITER SEQUENCE FOUND IN NODE STRING 12 NODE DESIGNATION MISSING 13 LIMIT OF 25 MODEL NODES HAS BEEN EXCEEDED 14 NODE STRING IMPROPERLY TERMINATED 15 PRECEDING MODEL IS NOT IN THE MODEL LIBRARY 16 ABLE NAME OR INDEPENDENT VARIABLE EXCEEDS 6 CHARACTERS 17 ABLE VALUE OR ARGUMENT EXCEEDS VALUE LIMIT 18 ABLE INDEPENDENT VARIABLE IMPROPERLY SPECIFIED 19 RIGHT PAREN FOLLOWING TABLE INDEPENDENT VARIABLE MISSING 20 EQUATION ARGUMENT STRING MISSING 21 NO OUTPUT REQUESTS SUPPLIED RE OUTPUT HAS BEEN DELETED 22 INCORRECT DELIMITER OR INSUFFICIENT DATA ON CARD 23 THE LIMIT OF ONE HUNDRED OUTPUTS HAS BEEN EXCEEDED 24 ISSING COMMA SUPPLIED BY PROCESSOR 61 UTPUT VARIABLE OR LABEL EXCE LOT NAME OR LABEL IS MISSING RECEDING UNRECOGNIZABLE CARD IGNORED T DS SIX CHARACTERS T E MAX OF 100 DEFINED PARAMETER DERIVATIVES IS EXCEEDED EDUNDANT DEFINED PARAMETE R DEFINED PARAM DERIVATIVE X p po QO OF TEN TERMINATE IF R ONTROLS HAS BEEN EXCEEDED PROPER RUN CONTROL FORI LETE SPECIFICATION Z T RIOR TO GROUP OR MOD UP G E CARD PAREN MISSING FOR TE Ea INATION CONTROL
29. Carlo run is selected by use of one of the controls DISTRIBUTION GAUSSIAN or DISTRIBUTION UNIFORM If neither is specified the Gaussian distribution is used The initial random number is specified by use of the control INITIAL RANDOM NUMBER number The number used should be a nine digit positive odd integer If no initial number is specified a suitable number is provided by SCEPTRE If it is important to have all reruns start with the same random number the statement INITIAL RANDOM NUMBER DEFAULT may be used If this entry is not used SCEPTRE will select a different initial random number for each rerun Optional printed information from each Monte Carlo iteration is obtained by inclusion of the statement 34 LIST MONTE CARLO DETAILS The Worst Case calculations will be executed if one of the Run Controls WORST CASE LOW WORST CASE NOMINAL RUN WORST CASE HIGH is provided The word following the equal sign determines the set of values to be left in the elements voltages currents and defined parameter tables at the conclusion of the Worst Case calculation for use as initial conditions in a subsequent transient calculation LOW and HIGH refer respectively to those table values which produce the smallest and largest value of the last objective function requested in the list entered under the WORST CASE subheading of CIRCUIT DESCRIPTION see subsection 2 2 8 If t
30. Model Feature of SCEPTRE o o e 45 P lse sirali 2 A ee a a AS AA lt te A pon 57 General Diode Model iio cc maoe a aow ee Se Ser Re gE e a pogo 66 SCEPTRE Diode Representati0d a 67 Alternate SCEPTRE Diode Representation o o oaa e a 67 Basic Ebers Moll Transistor Equivalent CircuitS o e 69 SCEPTRE Ebers Moll Representations 0 2 0000000002 eee 71 Alternate Ebers Moll Representation 2 2 0 0 000000000000 eee 73 Low Frequency H Parameter Model e 74 SCEPTRE Representation of H Parameter Model o o 74 Voltage Dependent Primary Photo current oo o 75 Capacitor Radiation Equivalent Circuit o e 77 Example 1 Schematic Diagram SCEPTRE form 2 2 ee es 79 Example LiGutputs y 2 os DA o A E RA a ogi AA 81 Schematic of the transformer coupled amplifier transistor model 82 Example 2 outputs gent da eee tek betes ad ie Sed ae Shae ed 83 Schematic of the Darlington Pair e 84 Example 3 Output Listings 2 200 000 0000 0000200000 00 4 85 Schematic of Example 4 Low Frequency h Parameter Equivalent Circuit 86 4 3 Plot of VRE versus TIME oca Ge ee bh Sobek Oe a i we wh lees Be eS 87 4 9 Plotof VRL2 versus TIME 88 4 10 Convolution Mode Interface e 90 4 11 Convolution Representation Using Series Impedance El
31. PCMC0500 and PCMCOS510 A 9 Notes to the SCEPTRE User SCEPTRE contains several features which when properly used can save the user computer time money and or analysis time A 9 1 Specification of dependent sources SCEPTRE is designed to handle only certain types of dependent sources All other types of dependencies are ignored in the formation of the mathematical model and are used only to evaluate the source It is therefore important to use wherever possible dependent sources which will be treated as such by SCEPTRE There are 4 types of such dependent sources 126 1 Resistor dependent voltage sources Exx node 1 node 2 constant VRyy 2 Resistor dependent current sources Jxx node 1 node 2 constant IRyy 3 Diodes Jxx node 1 node 2 e DIODE O a b e or DIODE EQUATION a b e or DIODE T xy e or DIODE TABLE xy 4 Diode dependent current sources Jxx node 1 node 2 variable Jyy where Jyy is a diode current source Such sources must be specified exactly as shown Variations in forms such as Exx X1 3 VRyy will not be identified as type 1 sources by SCEPTRE and may lead to a computational delay Correct specification of dependent sources will in general produce a larger step size in transient runs and faster more reliable convergence in initial condition runs leading to a decrease in running time in both cases This is particularly importa
32. Restrictions on AC transient and initial condition solutions 109 A 1 2 Restrictions on initial condition solutions o o e e 109 Computational delay m s st RA A E E RA 110 Special options in initial conditions computation 0000000 110 A 3 1 Initial conditions computation via transient analysis o o 111 A 3 2 Reruns with the DC algorithm e 112 A 3 3 Optional initial conditions for transient reruns o e e 114 Specified print interval Viloria sn Syl E Ae Se GaP Bek iria 114 Composite plots cbr pl e ed ee td ge th id e 115 Nodal listings vw o A A Oo A A A es 117 Differential equation identification ee ee 117 Convolution analysis sec RR eR EE e 119 A S InttOducnon tic ewok Ss a ee a ey Aa A i eh eo te ae a oy 119 A 8 2 Mixed domain approach a 120 A 8 3 Network situations for which the convolution analysis may apply 121 A 8 4 Integration routine lt o ss ke ek oe ee Sh ee So BR ee Sees 121 A 8 5 Impedance modelia ue bees a wed a a a rs 123 A 8 6 Admittance model omiso Bee Pe a ee oe wes 124 A 8 7 Storing impulse response functions 00 00 00 000000048 125 Notes to the SCEPTRE User e e 126 A 9 1 Specification of dependent sources oo aa 126 A 9 2 Proper use of dependent SQUICEsS a 127 A 9 3 Avoiding computational
33. a name to each circuit element Assume arbitrary current flow directions in each passive circuit element Parameter Unit Resistance kQ Capacitance pF Inductance y H Current mA Voltage V Frequency GHz Time ns Table 2 1 Units for High Speed Transistorized Circuits a ia 3 fig Figure 2 1 Circuit in SCEPTRE Form e Indicate the direction of positive current flow in each voltage and current source e Choose and record circuit values in a consistent set of parameter units Figure 2 1 shows a circuit diagram prepared in the recommended manner 2 2 Preparing the SCEPTRE input data The SCEPTRE circuit description language is a structured free format language the syntax of which is easy to learn and remember The language consists of descriptive statements constructed syntactically from user derived component names parameter names node names and value specifications These are delimited by special char acters such as comma dash parenthesis and equal sign thereby allowing the program to interpret the statements properly Thus the statements themselves can be punched anywhere on the input data card columns 1 72 with any desired spacing In general several complete statements can be punched on a card separated only by a comma The rules for continuing a statement from one card to another generally require that the discontinuation be made immediately after delimiters with the delimiter appearing as
34. be R1T8 number Note that the circuit designation for the model has been appended to the element name In the same way changes to P1 and TABLE 1 may be effected by the entries P1T8 number and TABLE 1 T8 number number All changes must be made under the appropriate subheading For rerun changes may be made to EQUATION 1 of the stored model only by changing the defined parameter which appears in the equation Therefore the user is advised to use the DEFINED PARAMETERS section liberally if frequent recourse is expected to both stored models and reruns 2 5 CONTINUE feature The purpose of this feature is to allow the user to continue transient runs that have been run previously and have been properly terminated Without this feature the user would be forced to begin the problem again This would waste computation Most continue runs will consist only of an extended problem duration time but the user has much more flexibility with the continue feature 2 5 1 General usage This feature is intended primarily to extend the time duration of transient runs The only changes permitted under this heading are most of the changes allowed under RUN CONTROLS No changes are allowed to the network under this heading so the subheadings ELEMENTS DEFINED PARAMETERS OUTPUTS INITIAL CONDITIONS and FUNCTIONS can never appear under CONTINUE The following representative sequence is appropriate for the case where an original run is carried to its spe
35. calculation would take a form like those above under a WORST CASE subheading 2 2 9 Program limits 7090 94 only The standard core memory capacity available on the IBM 7090 94 data processing system is 32 000 words which imposes certain program limits on the capacity of the SCEPTRE program Two factors that establish these limita tions are program storage and data storage The program storage requirements have priority over data storage and must be satisfied first The entire SCEPTRE program would require approximately 64 000 words of core storage but this capacity is not necessary if the overlay feature of the IBSYS monitor system is used This feature breaks up the program into several segments called links which are executed sequentially Each segment overlays or occupies the portion of core storage used by the preceding segment Therefore the amount of program storage required is equal to the largest program segment 40 The storage capacity that remains after the program storage requirements are satisfied is available for data In the SCEPTRE program there are about 10 000 words of storage available for this purpose Within this area the program data are limited by FORTRAN dimension statements which allocate specific amounts of storage Although these limits are usually considered fixed they can be changed somewhat by a programmer However increasing limits in this manner usually is accomplished by decreasing one
36. circumstances One is to specify the element as one of SCEPTRE s special dependent sources see A 9 1 and A 9 2 When this cannot be done the user should rerun Phase I only specifying WRITE SIMUL8 DATA under RUN CONTROLS An examination of the SIMUL8 program generated may indicate a possible change of variables to avoid the computational delay For example if the specification L2 node 1 node 2 X1 P1 IR2 produces a computational delay and examination of the SIMUL8 program shows that P1 and VR2 have been calculated while IR2 has not L2 should be respecified as L2 node 1 node 2 X1 P1 VR2 R2 A 9 4 Overcoming restrictions in initial conditions runs The restrictions on initial conditions circuits described in the SCEPTRE manual 2 p 40 apply only to the Newton Raphson method of initial conditions solution They do not apply to the alternate initial conditions solution using implicit integration of the transient equations It is therefore advised that initial conditions for a circuit be found using SCEPTRE s transient model instead This is done by inserting in the RUN CONTROLS section the card RUN IC VIA IMPLICIT A 9 5 Error checking in IC VIA IMPLICIT Theoretically a circuit containing capacitor current source cut sets and or inductor voltage source tie sets i e loops has no DC solution This condition is detected by the default Newton Raphson SCEPTRE initial condition routines an error message is printed a
37. delay o a 128 A 9 4 Overcoming restrictions in initial conditions runs o oo aoe e a 128 A 9 5 Error checking in IC VIA IMPLICIT o o e e 128 A 9 6 Element Sorts lio a Gas BEARER Ge ee le A ee ee eee 129 ALO QUIPULTECUCHON z 204 5 Bares Gi Be bee Bid eR a be BR Se ee cee RA 129 A 9 8 Some frequenterrors soc oise ee 129 A 9 9 DC coupling capacitor in certain AC runs 2 2 2 ee 129 A 9 10 Convolution input 2 ee 129 A 9 11 Voltmeters and Ammeters 2 0 20 0 0 00 0002p eee eee 130 A 9 12 Avoiding redundant sensitivity runs 2 2 0 2 0 0 00000000004 130 A913 Ideal transformers seb eR a ee ee ew wed Be Sg ed eee 130 A 9 14 Semiconductor capacitance 2 ee 130 AS TS REUN cit Bees A Oe RS A PA tO ete NS AR ews As 131 lil List of Figures 1 1 1 2 2 1 2 2 2 3 2 4 2 9 2 6 2 7 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 10 4 1 4 2 4 3 4 4 4 5 4 6 4 7 Sample Circuit 2466 Swi Aa eRe REL EE eR Re a A 2 SCEPTRE Version 3 2 ra Gb yoke eee a Gel be o ah ae ee ed he 3 Circuit in SCEPTRE Form ooo a ee ee Ee ee Ree eS 5 Mutual Inductance Polarities ee 12 Configurations That Require Source Derivatives o o e o 13 Voltage Polarity and Current Direction ee 21 TABLE ERIN Values as a Function of Time o e 25 Example of the Stored
38. et al A survey of Computer Aided Design amp Analysis Programs AFAPL TR 76 33 NTIS AD A 026567 8 Soo Young Shin A Survey of Computer Aided Electronic Circuit Analysis Programs NTIS AD A 009185 9 H Spiro Simulation integrierter Schaltungen durch universelle Rechnerprogramme Verfahren und Praxis der rechnergestiitzten Simulation nichtlinearer Schaltungen Verlag Oldenbourg Miinchen 1985 10 J I Lubell Transmission Line Modeling for Use with Circuit System Analysis Programs AFWL TR 73 128 NTIS AD 913 800 11 P Krehl W R Novender A Graphical and Analytical Method to Determine the Transient Response for an Ideal Transmission Line Loaded by a Time Varying Impedance IEEE Transactions on Plasma Science Vol PS 13 No 2 April 1985 12 C B Frye Jr M J Apfelbaum Mixed Domain Transient Analysis of Large Non Linear Networks Tenth Annual Allerton Conference on Circuit and System Theory October 1972 13 W Kaplan Ordinary Differential Equations Addison Wesley Reading Mass 1958 Section 10 2 pp 400 401 14 eb da Section 10 4 Heun s Method pp 402 403 15 K G Ashar H N Ghosh A W Aldridge L J Patterson Transient Analysis and Device Characterization of ACP Circuits IBM Journal of Research and Development Vol 7 p 218 1963 2 Air Force Weapons Laboratory Kirtland AFB NM 87117 USA 3National Technical Information Service Springfield VA 22151 USA 132 16 P E
39. following example of the procedure tells how to permanently store the transistor of figure 2 6 The appropriate entries could be as follows MODEL DESCRIPTION PRINT ODEL 2N1734B PERM B E LEMENTS CE B E EQUATION 1 5 80 TABLE 1 VCE CC B C EQUATION 1 10 200 TABLE 2 VCC Jl B E DIODE TABLE 1 JA E B 1 J2 J2 B C DIODE TABLE 2 JB C B 98 J1 OUTPUTS VCE VCC Jl PLOT FUNCTIONS DIODE TABLE 1 Or Oz 137 0r Ep DD 275 6 e lAr bey 293 2r 4 74 p34 8 10 482 15 DIODE TABLE 2 0705 358 00 627 0 4 dr 1 O 2p 2 07 By 4695 70 oT 12 EQUATION 1 A B C A B C With the word PRINT on the MODEL DESCRIPTION card the program will generate a printed listing of all models including MODEL 2N1734B stored on the permanent library tape The word PRINT is omitted if no listing is desired The B E C nomenclature used to name the base emitter and collector nodes of the above transistor is not manda tory but it is recommended as a systematic and orderly procedure for storing transistor models The designation VCE refers to the voltage across capacitor CE and has no connection with the often used designation of collector to emitter voltage 45 After this model is stored permanently it may be called upon as often as required The user should use as few alphanumeric charact
40. for AC Analysis AC Analysis is called by use of the Run Control RUN AC Frequencies at which the analysis is to be carried out are specified in one of two ways If the response at a single frequency is desired the single entry under RUN CONTROLS FREQUENCY number is used Number in the above entry is the desired single frequency If however the response is desired over a range of frequencies the following sequence of three entries is used INITIAL FREQUENCY number FINAL FREQUENCY number 37 where number in each case denotes a frequency and NUMBER FREQUENCY STEPS number where number is the number of intervals desired one less than the number of calculations to be made This entry may be omitted The default value is ten eleven calculations If linear frequency spacing is desired the control TYPE FREQUENCY RUN LINEAR E may be used If logarithmic spacing is to be used the proper control is TYPE FREQUENCY RUN LOG if neither of these two entries is supplied the default value is linear If circuit ELEMENTS other than source values are not varied in reruns computation time for the eigensolution portion of the analysis can be saved by inclusion of the Run Control USE FIXED AC MATRIX IN RERUNS Additional Run Controls There are seventeen additional Run Controls in SCEPTRE which are not describe
41. functions in a way acceptable to SCEPTRE 6 Solve the remaining moderate size sub network containing the nonlinearities and include these impulse response functions using SCEPTRE with its convolution capability Step 1 is accomplished manually at the discretion of the user Step 2 may be accomplished using any auxiliary AC analysis program which is capable of providing the desired immittance functions Step 3 is done using any off line program which can process the AC outputs and supply the necessary inverse Fourier Transforms Steps 4 5 and 6 represent the convolution analysis portion of the overall approach The ability to do Steps 4 5 and 6 is the key to this method of analysis The problem of modeling the time functions and processing them in synchronism with SCEPTRE was solved by observing that these functions form the impulse response matrix for the removed circuitry as seen by the original network across the appropriate interface terminals Therefore in the impedance mode the time function of the voltage across any pair of interface terminals can be obtained by convolving the appropriate impedance function with the time function describing the current flowing through the two terminals Similarly in the admittance mode the current flowing through the terminal can be obtained by convolving the voltage function across the terminals with the appropriate admittance function SCEPTRE calculates currents and voltages for a given configuratio
42. generators of the Ebers Moll equivalent circuit and JX represents the primary photocurrent caused by the effects of the radiation on the transistor in the inverter A valid sequence of cards would be CIRCUIT DESCRIPTION A01 INVERTER CIRCUIT LOADED WITH RC NETWORK ELEMENTS El 7 1 10 E2 1 6 10 CE 3 1 EQUATION 1 5 70 J1 CC 3 4 EQUATION 1 8 370 J2 C1 5 1 500 79 Rip Lag S2 R2 2 7 17 R37 bonm AaS R4 5 1 18 5 RB 273 3 RE S74 4 015 J1 3 1 DIODE EQUATION 1 E 7 35 J2 3 4 DIODE EQUATION 5 E 7 37 JA 1 3 1 J2 JB 4 3 498 Jl JX 4 3 TABLE 1 TIME OUTPUTS VCE VCC VCL IR3 JI INITIAL CONDITIONS VGI 925 VCE 1 vec 10 25 FUNCTIONS TABLE 1 0 0 40 8 100 6 5 200 25 500 0 600 0 EQUATION 1 A B C A B C RUN CONTROLS INTEGRATION ROUTINE TRAP Original intgr routine INTEGRATION ROUTINE IMPLICIT 7 much more faster STOP TIME 800 RERUN DESCRIPTION 2 FUNCTIONS TABLE 1 0 0 0 40 1 2 4 100 75 sea 200 TOA 129 500 0 0 600 0 0 END The results of the master run indicate that the inverter turned on at about 48 nanoseconds base emitter junction forward biased and returned to the OFF condition at about 135 nanoseconds Since the degree of turn on was small maximum positive VBE 0 26V the transistor
43. in the RUN CONTROLS section of the SCEPTRE input data 2 9 Error diagnostics The free form input data format of SCEPTRE is intended to minimize formatting errors Other types of errors such as those of omission ambiguity inconsistency and violation of syntax program limits etc must be detected and diagnosed and the user alerted For this purpose the program possesses a comprehensive input data diagnostic capability A listing of the principal error messages in the input processor program are shown below As the input data cards are read in by the input processor each card is printed out and then scanned for errors If an error is found an error message stating the trouble is printed immediately following the detection of the error The severity of errors detected in this manner is also indicated There are three levels of severity 60 Level 1 warning only errors of this type are not critical and will be repaired by the input processor The error scan is continued and the analysis phase executed providing that errors of a higher level are not detected elsewhere in the input data Level 2 simulation deleted errors of this type are critical and thus prohibit execution of the analysis phase However the error scan is continued in order to detect diagnose and alert the user of any remaining errors in the input data Level 3 execution terminated this type of error will not permit the proper execution of the input processor and
44. is explicitly described as EQUATION 2 A B C A B C At each solution step C1 is evaluated in the program by replacing dummy variables A B and C by 10 80 and the ordinate value of TABLE 7 respectively C2 is then evaluated by replacing A B and C by 5 120 and the ordinate value of TABLE 4 respectively Note that two quantities of the same mathematical form have been accommodated by one equation The mathematical Definition may be any combination of the allowable operations functions or variables The following mathematical operations and corresponding symbols are included in SCEPTRE Operation Symbol Exponentiation sele Multiplication x Division Addition Subtraction The order in which operations are performed is indicated by the order in which the operators are listed The use of parentheses to denote clearly the intended mathematical combination is suggested to avoid ambiguity For example X Y Z should be written as X Y Z if X Y Z is not intended Any function of real arguments that is available in the FORTRAN IV Subprogram Library may be use in any EQUATION or EXPRESSION A few of the most widely used of these are listed below In addition the functions of complex Arguments listed in table 2 3 may be used The argument of any function may be any allowable mathematical definition In addition the user may supply subprogram functions that he has written himself see subsection 2 7 Wh
45. is familiar with computer programming may write FORTRAN sub routines and insert them in otherwise conventional SCEPTRE runs This option permits handling special situations even though these should be rare Program Language The program has been written entirely in FORTRAN IV to facilitate the task of adapting it to digital Computers other than the IBM 360 Automatic Termination Runs may be automatically terminated contingent on the behavior of specified net work quantities Flexibility Non conventional source dependencies and network i topologies can be accommodated Save and Continue Capability Runs may be terminated and then subsequently continued after examination Input Convenience Provision has been made for a free form format for input data 1 2 Handbook coverage This volume describes the means of utilizing all of the many SCEPTRE features This coverage includes in structions for preparing the circuit and input data and includes subsections on the stored model rerun continue reoutput and subprogram features There are examples of each type of analysis that SCEPTRE can provide and sections containing information pertinent to the use of SCEPTRE on the 7090 94 and S 360 Computers Back up information on some less frequently used special options appears in the Appendices of Volume I References to these appendices are made in the body text at the appropriate points 1 3 Input data example R3 1 5k o 10V
46. near the end of subsection 3 2 67 Conventional Ebers Moll equivalent circuits for NPN and PNP Transistors are shown in figure 3 4 This model is in wide use because it can accommodate all four regions of operation with a minimum amount of complexity and operates with conventional electrical quantities The currents through the perfect diodes and I e are represented by voltage dependent non linear current gen erators The expressions for these generators are as follows 1 Leo Oe V Tre Los e95 1 e2 vo 1 3 1 1 ayjan and V Leo V Tei e Veo 1 e Veo 1 3 2 1 AIAN The equation of the form J e 1 is the emitter collector junction current of a transistor with the collector emitter shorted to the base The equation Igo e 9 Voz 1 is the emitter collector junction current of a transistor with the base collector emitter junction open circuited Thus the short circuit junction current is greater than the open circuit junction current by a factor of 1 1 aray For alpha inverse equal to zero the open and short circuit junction currents are the same The current sources I e and Irc are defined in SCEPTRE as primary dependent sources and in order to achieve numerical convergence for the initial condition computation they must be entered in the general form JX B X DIODE EQUATION X1 X2 where X1 Ies or Ies and X2 O or O or if tabular d
47. never approached saturation in this environment The voltage excursion seen by the RC network was about 0 18 volt A reproduction of the plotter output for the voltage across capacitor CE or VBE is enclosed figure 4 2 The first rerun effectively included the effects of a 50 percent increase in I as reflected in the modified TABLE 1 The increased effects on the base emitter junction voltage are shown The second rerun effectively included the effects of a 50 percent decrease in pp and the corresponding reduced circuit reaction can be seen 4 2 Example 2 TRANSFORMER COUPLED AMPLIFIER A02 The schematic of an emitter follower common emitter combination driving an output transformer with a resistive load is shown in figure 4 3 80 A01 INVERTER CIRCUIT LOADED WITH RC NETWORK Co 1 AR AREA 0 4 bf 0 2 0 4 0 100 200 300 400 500 600 700 800 90C Sun Jan 11 11 40 49 1998 TIME Figure 4 2 Example 1 outputs The circuit will be driven by a ramp voltage input coupled through a capacitor For this example it will be assumed that the user wishes to permanently store a transistor model and to use this model for both circuit transistors The initial conditions will be computed along with the transient solution No reruns will be made A few remarks about this run are in order It happened that the stored model that was used for this run was also stored along with the run but it could as well have been stored at s
48. of DC results with the left side of equation A 2 set to zero The average network usually converges to a final solution in anywhere from 10 to 25 iterations It is usually true that when a series of DC only reruns are to be made the overall circuit differs just slightly in element value from one rerun to the next It follows then that the final solution will also not vary greatly from rerun to rerun In circumstances of this type it is often likely that convergence of a given rerun could be significantly speeded if the final results of a preceding run were used as the starting point Example A03 of the manual can be used again as an illustration When the master run and each of the three associated reruns were started at zero voltage all four runs converged in 11 passes The same problem was repeated with each of the three reruns begun with the voltages with which its predecessor finished Convergence was then obtained in four passes for each of the reruns and there was no difference in accuracy Other tests have been made with comparable results The attractiveness of this feature will of course be proportional to the number of DC reruns that are to be made Significant computer solution time will be saved only if a significant number of reruns are used Two variants of this feature are allowed The first is if all reruns are to begin with the final voltages of the master run In that case the required language is RUN CONTROLS RUN INITIAL COND
49. of elements that are implicitly defined as variables are specified in subsection 2 2 6 More than one element may be described on a card if the elements are separated by commas Some examples that illustrate proper entries under elements for the constant valued elements of the network of figure 2 1 are El 1 2 20 E2 1 6 20 JM 1 4 2E1 Note that any of these constant elements may be entered with or without decimal points or by use of the E format Note also that the proper reference direction for voltage sources p p correspond to the direction of current or positive charge movement within the voltage source NOTES to Table 2 2 Name Nodes Value specification see note 9 QHmrawD number TABLE name independent variable Defined Parameter name nodel node2 y EQUATION name argument list EXPRESSION name math definition External Function argument list name L namel L name2 see note 1 amp 2 and subsection 2 2 2 Linearly Dependent Sources E name nodel node2 constant VRname J name nodel node2 constant 1Rname Primary dependent Current Sources see note 3 amp 4 DIODE TABLE name J name nodel node2 DIODE EQUATION XI X2 Secondary dependent Current Sources see note 4 amp 5 J name nodel node2 value Jname gt Voltage and Current Source Derivations see note 6 amp 8 DE na
50. the diode junction voltage VJ The perfect diode itself is just a voltage dependent current generator and it is entered in SCEPTRE as such The general diode model is replaced by a form suitable for SCEPTRE as shown in figure 3 2 The only difference is that a current generator with the arbitrary designation JD replaces the perfect diode JD would be indicated under ELEMENTS with a diode equation designation This closed form representation of the general diode requires that the user possess accurate values of IS and for use in the descriptive equation The sequence of cards that could be used to describe the circuit of figure 3 2 under elements is C 1 2 20 RS 1 2 2000 RB 2 3 05 JD 1 2 DIODE EQUATION 1 E 7 35 12 fig Figure 3 1 General Diode Model 66 13 fig 14 fig Figure 3 3 Alternate SCEPTRE Diode Representation The description for current generator JD is based on the explanation given for current generator J18 in subsection 2 2 2 An alternate procedure figure 3 3 would be to obtain the terminal characteristics of the diode by measuring the diode current as a function of the voltage across it The current generator could then be described in tabular form which would include the effect of RB see figure 3 3 Either representation would permit the user to omit the shunt resistance RS The equivalent shunt capacitance is quite another matter There is nothing to preve
51. the last non blank character on the card 2 2 1 Headings and subheadings Networks are described in SCEPTRE language under the following major headings and subheadings regardless of which mode of analysis is desired MODEL DESCRIPTION INITIAL PRINT MODEL NAME PERM or TEMP NODE NODE NODE Comment or message cards if any up to 11 allowed EMENTS EFINED PARAMETERS TPUTS NCTIONS NITIAL CONDITIONS TRCUIT DESCRIPTION Comment or message cards if any up to 11 allowed EMENTS EFINED PARAMETERS UTPUTS NITIAL CONDITIONS UNCTIONS UN CONTROLS O ENSITIVITY NTE CARLO WORST CASE OPTIMIZATION R ERUN DESCRIPTION N Comment or message cards if any up to 11 allowed ELEMENTS DEFINED PARAMETERS INITIAL CONDITIONS FUNCTIONS RUN CONTROLS CONTINUE RUN CONTROLS RE OUTPUT OUTPUTS required s 360 only RUN CONTROLS optional In the IBM 7090 94 version no subheadings are permitted under this heading END The MODEL DESCRIPTION heading is used when it is desired to store one or more models The MODEL name card comment cards optional and any or all of the five subheadings listed can be used for each model for either permanent or temporary storage under the MODEL DESCRIPTION heading One or more models may b
52. the number of solution points may be precisely controlled and chosen more selectively The user supplies the desired time interval and only those solution points that fall on or immediately after integer multiples of the specified interval will be printed in this series The required entry is PRINT INTERVAL number This printed series will appear in addition to the normal printed output format If only this printed series is desired the normal printed output format may be suppressed by the entry MAXIMUM PRINT POINTS 0 For additional discussion of print interval see Appendix A 4 A discussion of the PLOT INTERVAL run control used to control the length of composite plots may be found in subsection 2 2 4 Automatic Termination of Transient Runs The user may often desire to monitor certain voltages or currents in a network to determine their relation with some predetermined quantity If the relations are satisfied there may be no further interest in continuing the run The run can be terminated at that point by the entry H ERMINATE IF XXXXXX relational operation XXXXXX The X quantities refer to any variable or constant The user frequently supplies some element voltage or current for this purpose The following relational operators may be used LE less than or equal to 32 LT less than GT greater than GE greater than or equal to EQ equal to NE not equal to NOTE Decimal points are req
53. the recommended input formats are used A 3 Special options in initial conditions computation Under normal operational circumstances the initial conditions for any transient run are either inserted as input data by the user if they are known or computed by the DC portion of the program if they are not Three separate and distinct alternatives have been provided that when properly used can add flexibility for special situations 110 69 fig p Figure A 4 Current Source Capacitor Cut Sets A 3 1 Initial conditions computation via transient analysis It is and always has been possible to compute the initial conditions for any SCEPTRE problem by using transient analysis The most practical motivation for the use of this option is the situation in which either the DC algorithm will not converge or the user would prefer not to alter the original topology to comply with the published DC re strictions no J C cut sets or E L loops Until recently there existed a series of obstacles that had to be overcome before the user could effectively utilize transient analysis to solve the initial condition problem The user either had to make one run to get the initial conditions and then a second submission to apply these results to the transient computation or had to somehow delay the network transient forcing functions until the initial conditions computa tions had settled down The latter course is feasible although often awkward in that t
54. the sample times involved We make use of these sample times in our selection of the sub divisions along the T axis by considering these sub division breakpoints to be the ordered set of points obtained by interleaving the two sets of time points which define the H and F functions respectively We also assume that the two time functions are representable between consecutive time points as straight line segments through these data points That is F T Aj r T Bi A 6 and H Ty 7 C r T D with T lt 7 lt Toa A 7 where PPT A gt Tiga Ti B F T 4 8 A T T A T T gene DO A9 Tigi Ti The ordered set of interleaved time points define the non zero subintervals which contribute to the overall integra tion The contribution from the ith general subinterval is Tay Si i H Ty 7 F r dr A 10 Ti Ti J Ci T Dill Ti Bijdr A 11 Ti Ti face T 4 Di ByC 7 Ti BiDi dr A 12 Ti The integrand associated with this subinterval is seen to be a quadratic expression resulting from the product of the two straight line segments characterizing the two functions over the interval The exact analytic integral of this equation is Si Tiy DY 42729 Tirar Ti BD Ti41 Ti A 13 122 Let AT Ti41 Th Then after substituting equations A 8 and A 9 into A 13 and simplifying we get S F T ae SS
55. 00000E 01 00000000E 02 1 24486175E 01 o DISTANCE 6 03034076E 02 ALONG GRADIENT PITI DISTANCE 2 01011359E 02 ALONG GRADIENT INDEPENDENT VARIABLE P1T1 WORST CASE COMPUTATION OBJECTIVE FUNCTION VCCT1 INDEPENDENT VARIABLE PITE 9 P1T2 9 R3 2 WORST CASE COMPUTATION OBJECTIVE FUNCTION VCCT1 INDEPENDENT VARIABLE P1T1 9 P1T2 9 R3 2 VR3 VR4 RUN CONTROLS RUN WORST CAS fl HIGH VALUE 8 89478115E 00 VALUE GRADIENT COMPONENT 80000000E 01 1 60698069E 00 57986132E 01 1 76735527E 01 00000000E 02 1 61045665E 05 LOW VALUE 8 95520062E 00 VALUE GRADIENT COMPONENT 00000000E 01 66041604E 01 00000001E 02 6 78924171E 01 4 67066273E 02 4 44565760E 06 1 23628942E 00 9 1 14951356E 05 1 LOWER BOUND 00000000E 01 00000000E 01 95000000E 02 UPPER BOUND 9 80000000E 01 9 80000000E 01 2 05000000E 02 LOWER BOUND 9 00000000E 01 OF UPPER BOUND 9 80000000E 01 OF Figure 4 19 Worst Case Example Outputs RUN INITIAL CONDITIONS ONLY END The output from the Worst Case calculation on one of the requested dependent variables VCCT1 is presented in figure 4 19 as typical of the The function value of 8 9126 for the nominal independent variable values P1T1 P1T2 is printed followed by entire set the gradient components of VCCT1 with respect to each independent variable 4 10 Example 10 USE OF OPTIMIZATION A10 The Darlington pair used for Ex
56. 1 2 8 Additional output and control Some additional output and control is available to the interested user This information will probably not be desired for most runs that are made but can be useful in special situations 58 2 8 1 SIMUL8 program data Normally the program outputs the results of initial conditions computations once after convergence has been achieved regardless of the number of iterations required However all resistor and primary dependent current source voltages may be output after each iteration of the DC program In addition all the formatted data that is used by the FORTRAN program SIMUL8 written by SCEPTRE is available This information may be obtained by the request WRITE SIMUL8 DATA in the RUN CONTROLS section 2 8 2 No element sort In the absence of any user direction the program forms the network tree by giving priority to the smaller elements within any passive element type Variable elements are considered to have zero value for this purpose If the instruction NO ELEMENT SORT is inserted in the RUN CONTROLS section tree priority is given within passive element types according to orders of appearance under ELEMENTS This instruction of course does not change the basic element type preference order of E C R and L 2 8 3 Matrix printouts 7090 94 only The network B matrix which gives the topological relation between all network links and tree branches is available i
57. 1 6 5705E 01 0 0000E 00 1 6454E 02 0 0000E 00 2 3 4296E 01 0 0000E 00 1 6454E 02 0 0000E 00 104 In particular he will be given the values of the replacement resistors used by the AC program The AC sources may be connected between any two nodes However since all AC scurces are set to zero in a DC run they should be decoupled from the circuit by a DC blocking capacitor or a sufficiently large resistor value as R1 in figure 4 21 Similarly all DC sources are set to zero in an AC run i e batteries are short circuited and current sources are open circuited 4 12 Example 12 TRANSFER FUNCTION SIMULATION An extremely useful method of applying SCEPTRE to true system problems has evolved that adds even more flexi bility to the program This method depends on the use of transfer functions that define the output input relationship of systems or subsystems Typically these transfer functions appear in the form of a ratio of polynomials as a Oe EX8 AGA aS eee Om 1 8 ams 4 1 E s a gi i bo bis bn 18 7 bns i As a practical matter it is almost always true that the order of the numerator is less than that of the denominator m lt n A procedure will be given by which any transfer function with m lt n may be readily and accurately simulated on SCEPTRE The case m n may also be accommodated while the rather impractical case m gt n is not discussed The first task must be to devise an automatic method o
58. 15 minutes of computer solution time can ever be lost in this way The user may change the save interval to any number of minutes of computer solution time by the entry COMPUTER SAVE INTERNAL number 33 Run Controls for DC Options This paragraph describes the Run Controls for the four special DC options Sensitivity Monte Carlo Worst Case and Optimization See subsection 2 2 7 for a discussion of the use of these options in combination with each other with the normal Initial Conditions calculations and with the Transient and AC calculations In addition to the Run Controls discussed below use of the DC options requires entries under the corresponding CIRCUIT DESCRIPTION subheadings SENSITIVITY MONTE CARLO WORST CASE or OPTIMIZATION listing the dependent and independent variables to be used in the calculations See subsection 2 2 8 Use of Monte Carlo Worst Case and Optimization also requires bounds on entries under ELEMENTS and DEFINED PARAMETERS See subsections 2 2 2 and 2 2 3 Sensitivity calculation requests are made by the entry RUN SENSITIVITY There are no additional Run Controls for Sensitivity The Monte Carlo calculation is initiated by use of either MONTE CARLO number or RUN MONTE CARLO The number specified is the count of Monte Carlo iterations to be performed If the count is unspecified it is assumed to be 10 The distribution to be used for random variables in a Monte
59. 2 2 2 000 000 00000022 eee 67 3 3 Transistors small signal equivalent e 73 3 4 Insertion of basic radiation effects 20 0000000000 eee eee 75 Examples of SCEPTRE Use 79 4 1 Example 1 INVERTER CIRCUIT LOADED WITH RC NETWORK A01 79 4 2 Example 2 TRANSFORMER COUPLED AMPLIFIER A02 80 4 3 Example 3 DARLINGTON PAIR A03 e 83 4 4 Example 4 USE OF SMALL SIGNAL EQUIVALENT CIRCUIT A04 86 4 5 Example 5 SOLUTION OF SIMULTANEOUS DIFFERENTIAL EQUATIONS A05 87 4 6 Convolution example amis at A eed St A A ee ees 89 A A eas ba interes ee tes ai ai at Almaty at abel Is aa R 89 4 6 2 Convolution impedance mode 20 0000 0000000000 89 4 6 3 Convolution admittance mode 0 000 000 0000 0000 90 4 6 4 Sample problem 0 0 a e eee ee ee ee ee 91 4 7 Example 7 USE OF MONTE CARLO A07 2 020 2 ee ee 94 4 8 Example 8 USE OF SENSITIVITY A08 o e e 95 4 9 Example 9 USE OF WORST CASE A09 oo o ee 99 4 10 Example 10 USE OF OPTIMIZATION A10 o e 0000000 100 4 11 Example 11 USE OF AC ANALYSIS All o o e 103 4 12 Example 12 TRANSFER FUNCTION SIMULATION o oo 105 A Appendices 109 A l A 2 A 3 AA AS A 6 AT A 8 A9 Topological restrictions on SCEPTRE a 109 A 1 1
60. 2 VRKCV3 EKCV3 OUTPUTS El PLO IRKCV1 IRKCV2 IRKCV3 PLOT PVOLT1 PVOLT2 PVOLT3 PLOT VR2 VR4 RUN CONTROLS INTEGRATION ROUTINE RUK WRITE SIMUL8 DATA PRINT B MATRIX STOP TIME 4 7 AXIMUM STEP SIZE 0 15 IMPULSE RESPONSE BUFFER 300 INPUT FUNCTION BUFFER 900 END Figure 4 16 shows the output voltage across the same nodes as were used for the reference circuit figure 4 13 4 7 Example 7 USE OF MONTE CARLO A07 The Darlington Pair used for Example 3 and shown in figure 4 5 is used also to demonstrate the Monte Carlo option While all four of the DC options Monte Carlo Sensitivity Worst Case and Optimization can be requested in a single run they are shown separately in this and the next three examples for clarity In each case the complete SCEPTRE input deck is listed and the output due to execution of the requested feature is shown MODEL MOD iw ESC 70 N RIPTION 6A TEMP B E 94 ELEMENTS CE 1 E Q1 5 70 J1 CC des 918s T 0042 RB B 1 3 RC C 2 015 Jl 1 E DIODE EQUATION 1 E 7 35 J2 1 2 DIODE EQUATION 5 E 7 37 JA E 1 1 J2 JB 2 1 P1 J1 JX 2 1 0 DEFINED PARAMETERS Pl 0 96 0 98 0 9 FUNCTIONS Q1 A B C A B C OUTPUTS VCE VCC Jl CIRCUI
61. 476900 2 3 2 N terminal model storage The storage of N terminal models differs from the storage of transistor models only in the number of terminal nodes program limit 25 nodes that are specified Storage may be effected by an entry following the MODEL DESCRIPTION card as MODEL name PERM or TEMP node node node As many internal nodes as desired may be included within the program limit of 301 nodes The remainder of the information will be entered under the appropriate subheadings Regardless of the number of terminal nodes that are supplied the user must take care that these nodes are referenced in the same sequence when called by the main program 46 2 3 3 Changes to a stored model The user who frequently makes use of the stored model feature of SCEPTRE will often encounter the situation in which the topology of his stored model is satisfactory but the size of some of the model elements must be changed Changes can be effected easily for any individual run but no permanent changes to the stored model are possible The user has the option of storing a second model which contains a different version of the original All changes must be indicated along with the statement that locates the stored model in the main circuit This will always be under the main circuit ELEMENTS subheading Changes in ELEMENTS or DEFINED PARAMETERS Consider that a stored model has been called out as T1 7 8 12 MODEL 2N1734B In
62. 5 200 lines or three pages plus two lines on a fourth page plus approximately three lines per variable for identification and scaling information The PLOT INTERVAL entry always appears under RUN CONTROLS and the format is simply PLOT INTERVAL number Only one PLOT INTERVAL will be recognized regardless of the number of composite plots that are requested For additional discussion of composite plots see Appendix A 5 Convolution Outputs The above discussion about outputs also applies to transient runs employing the Convolution option One precau tion is noted here When the user requests an element of a Convolution model as output he must prefix its name Kname see table 2 2 with a letter denoting the element desired The code is as follows E for the voltage source of an impedance kernel e g EKname J for the current source of an admittance kernel e g JKame R for the resistance value of a kernel e g RKname Additional prefixes I and V are required if the user is requesting currents and voltages of these elements e g IEKname IRKname VJKname VRKname See subsection 4 6 for a discussion of Convolution kernels 19 AC Outputs The results of AC calculations can be obtained as outputs in either tabular or plotted form The general rules for output requests given in subsections 2 2 4 and 2 2 4 apply equally to AC outputs except that AC outputs are not given as functions of time All AC tabular outputs and all but o
63. 5E 0 5616323E 00 8368401 2660595E 0 8157624 MEAN 9 4000000E 01 9 4000000E 01 7906312E 01 5900296E 01 E 0 E 00 E 03 E 0 PROP ds OBN OW 578234 892785 772682 364949 97738 318985 337242 25759 166474 727594 SAMPLE MEAN 538829 4255822E 01 SAMPLE MEAN SIGMA 1 3333333E 02 1 3333333E 02 6E O1 4E 0 7E 00 0E 02 3E 0 9E 00 2E 0 2E 00 8E 03 5E 0 3E 0 Figure 4 17 Monte Carlo Example Outputs 96 he DOBRNNWEWNHEA SAMPLE SIGMA 6480857E 02 1320930E 02 SAMPLE SIGMA 0157705E 03 2013686E 02 9307541E 03 4850834E 03 5350405E 02 2252503E 02 2675435E 01 3076374E 04 1793613E 03 9010012E 03 MOD MODI CI AO 3 N J 706 TS H O T 1 JA JB EFIN RC 8 P1 0 UNCTIONS Q1 A B UTPUTS VCE VC EL D EMENTS T1 A ESCRIPTION T EMP Q1 5 70 Q1 8 370 aS 015 B 1 B J1 132 DIOD E EQUA ION 1 E F DIOD a LITZ P1 J1 96 C C wW o o o RIP 0 i d AO GNE a D ET ERS A B C J1 UIT DESCRIPTION arlington pair S 10 1 20 5 200 4 1 T EQUA ION 5 E ENSITIVITY 5 7 ODE 2N706A ODE T 2N706A E NSITIVITY VCI VCI ET1 VC
64. 600E 01 1 700E 01 1 800E 01 1 900E 01 2 000E 01 2 100E 01 2 200E 01 2 300E 01 2 400E 01 2 500E 01 2 600E 01 2 700E 01 2 800E 01 2 900E 01 3 000E 01 3 100E 01 3 200E 01 3 300E 01 3 400E 01 3 500E 01 3 600E 01 3 700E 01 3 800E 01 3 900E 01 4 000E 01 4 100E 01 4 200E 01 4 300E 01 4 400E 01 4 500E 01 4 600E 01 4 700E 01 4 800E 01 4 900E 01 5 000E 01 5 100E 01 5 200E 01 5 300E 01 5 400E 01 5 500E 01 5 600E 01 5 700E 01 5 800E 01 5 900E 01 6 000E 01 6 100E 01 6 200E 01 6 300E 01 6 400E 01 6 500E 01 6 600E 01 6 700E 01 6 800E 01 6 900E 01 7 000E 01 7 100E 01 7 200E 01 7 300E 01 7 400E 01 7 500E 01 7 600E 01 7 700E 01 7 800E 01 7 900E 01 8 000E 01 ommno 000E 00 000E 00 500E 00 000E 00 ACB 400E 00 400E 00 100E 00 000E 01 800E 00 800E 00 700E 00 000E 01 onan uwao 200E 00 200E 00 300E 00 200E 00 uwao Figure A 5 Composite Plot Example 116 600E 00 600E 00 900E 00 600E 00 7 000E 00 6 000E 00 4 500E 00 2 000E 00 ES2 Figure A 6 Circuit to Illustrate a Nodal Listing A 6 Nodal listings A special capability has been added to assist the user in post run interpretation when either suspicious results have been obtained or a final check is desired before the analysis results are accepted This feature takes the form of a printed listing of each network node all attached elements and the other node associated with e
65. AT F Tiss A at AT A 14 Equation A 14 describes the general form of the convolution integral over a subinterval in terms of the width of the subinterval and the four data points defining the two functions at each end point of the subinterval Two salient features of this integration scheme are e It introduces no new time points That is it used only subintervals defined by known time points e It introduces no error of its own This is the exact integral based on the straight line assumption and there is no approximation to an integral involved Granted the original data points may be in error and the straight line assumption is an approximation A 8 5 Impedance model If we regard the H function as an impedance function between two nodes A and B then the voltage across A B and the current through A B are related by the convolution integral given in equation A 3 That is the voltage at a particular time Ty is TN Van Zw f Zan Tw Ind A 15 0 However equation A 15 cannot be solved by SCEPTRE as it is written because the present value of current I Tw is not known Examination of equation A 15 indicates that the only term containing I T is the nth subinterval Rewriting the equation in order to separate this term yields Vap Tnw V1 V2 A 16 where Tn 1 v1 J ZaB Tyn T T dr A 17 0 and TN V2 Zap Tn T T dr A 18 Tyn 1 123 AB us gt F 2 fig E E1 E2 Figure A
66. ATA MISSING INCOMPLETE RUN CONTROL SPECIFICATION ON CARD PRIOR TO END CARD ILLEGAL DEBUG CARD IGNORED THE NEWTON RAPHSON PASS LIMIT HAS BEEN EXCEEDED WITHOUT ATTAINING CONVERGENCE MATRIX XXX IS SINGULAR 64 UNABLE TO LOCATE DEPENDENT PLOT VARIABLE FOR INDEPENDENT VARIABLE XXX NO PLOT PTS HAVE EXCEEDED PLOT STORAGE BLOCK SIZE DERIVATIVE XXX FOUND IN THE TERMINATION CONDITION S IS NOT RESOLVED THE LENGTH OF HE FIRST SOLUTION BUFFER IS ZERO ORE THAN 9 OUTPUTS WERE REQUESTED ON PLOT NUMBER XXX ONLY THE FIRST 9 REQUESTS WILL BE HONORED PLOT REQUEST XXX WAS NOT SPECIFIED AS AN OUTPUT IN THE ORIGINAL CIRCUIT DESCRIPTION RUN FOR THIS SYSTEM AXIMUM PLO ENGTH 2000 LINES HAS BEEN EXCEEDED A TRACE ON ONE OF THE PLOTS IS DISPLACED FROM ZERO BY MORE THAN 10 6 TIMES ITS TOTAL RANGE OSS OF SIGNIFICANCE IS POSSIBLE IN THESE RESULTS TABLE CONTAINING IMPLICIT INTEGRATION DATA HAS OVERFLOWED SIMULATION HAS BEEN DELETED CONTAINING SPARSE MATRIX DATA HAS OVERFLOWED SIMULATION HAS BEEN DELETED TABLES CONTAINING SPARSE MATRIX DATA HAVE OVERFLOW ATRIX WILL BE DELETED bd TABL a
67. ATION EXCEEDS FOUR CHARACTI CHANGE VALUE IS VARIABLE E RS O Y 1 E LIMIT OF TEN SUPPRESSED OUTPUTS HAS BEEN EXCEEDED RECOGNIZABLE MODEL MODIFICATION DATA ORE THAN 250 TEMPORARY OR PERMANENT MODELS SPECIFIED N EQUATION 15 NOT A PERMISSABLE ARGUMENT ER ARGUMENT FORMAT ATION ARGUMENT OR VALUE EXCEEDS 1200 CHARACTERS N CIFIED LIBRARY ALTERNATE LIB SCAN STARTS O 4 H Z uN U RCE DERIVATIVE REFERENCES NON EXISTENT SOURCE P U D TUAL INDUCTANCE REFERENCES NON EXISTENT INDUCTOR U E INED PARAM DERIV REFERENCES NON EXISTENT DEF PARAM ODEL ELEMENT CANNOT BE A MODEL EMENT MUTUAL INDUCTANCE OR SOURCE DERIV IS REDUNDANT ODEL TABLE OR EQUATION CHANGE IS REDUNDANT EMENT IMROPERLY SPECIFIED T INT MISSING 1FERENCED TABLE EQUATION DEF PARAM OR ELEM E FOLLOWING OUTPUT REQUEST IS NOT VALID 62 77 NO PUT REQUESTS HAVE BEEN SUPPLIED 188 T OPER EXPRESSION FORMAT COMPUTATION DELAY
68. C 1 J1T1 PR3 PRR3 P1T1 P1T2 R3 ET2 VCC EFI ED PARA 2 PEIN VR4 P1T1 P1T2 R3 R4 ET ERS E P4 1 GPEIN P4 DIE PR3 PDR3 PDIR3 GPR3 PRR3 p X2 IEIN X4 EIN i R3 IR3 IR3 IR3 IR3 La FIRIFRI DR3 PDIR3 DIR3 IR3 VR3 PDIRR3 RR3 VR3 PDVRR3 XDVRR3 IR3 GPRR3 PDIRR3 DIR3 PDVRR3 DVR3 OUTPUTS VR3 VR4 RUN CONTROLS RUN SENSITIVITY RUN INITIAL CONDITIONS ONLY END The 22 partial derivatives calculated are tabulated with dependent and independent variables identified The output appears in figure 4 18 The problem shows the use of defined parameters as both independent and dependent variables Only those defined parameters used to relate primary and secondary current sources may be used for independent variables The defined parameters used for dependent variables must have their total differentials provided see paragraph 2 2 3 97 SENSITIVITY CALCULATION S SET DEPENDE INDEPENDENT PARTIAL NUMBER VARIABLE VARIABLE DERIVATIVE T VCET1 P1T1 2 23659125E P1T2 4 07175175E R3 3 75988248E VCCTI p1T1 1 23628942E P1T2 1 24486175E R3 1 14951356E J1T1 PLEI 1 70846451E P1T2 3 11028820E R3 2 87206067E PR3 p1T1 2 07019909E P1T2 5 27852161E R3 5 68080410E PRR3 P1T1 1 03764443E P1T2 2 64134241E R3 2 11814175E
69. CUIT DE SCRIPTION cards to illustrate how it is set up A transient run was first made on the reference circuit shown in figure 4 13 to obtain a typical output for later comparison CIRCUIT DESCRIPTIO AO6A CONVOLTION REFERENCE EXAMPLE DESCRIPTION FIG 47 ELEMENTS El 0 1 Q1 TIME R1 1 2 5000 Lily 273 25 C1 1 4 0 001 R2 3 4 3000 R37 3 5 20 00 R4 4 0 8500 C2 4 6 0 004 R5 5 6 11000 L2 6 0 175 C3 5 7 0 0025 R6 6 8 1000 RCV1 7 8 12000 ccv1l 7 8 0 001 LCV1 7 8 1000 RCV2 8 0 12000 91 original network terminations 46 fig L 3 Figure 4 13 Convolution Sample Problem Reference Schematic CCV2 8 0 002 LCV2 8 0 500 RCV3 7 0 12000 CCV3 7 0 0005 LCV3 7 0 2000 FUNCTIONS Q1 T 10 T DEXP 5 T Q2 A B C A B C DEFINED PARAMETERS PCUR1 Q2 IRCV1 ICCV1 ILCV1 PCUR2 02 IRCV2 ICCV2 ILCV2 PCUR3 Q2 IRCV3 ICCV3 ILCV3 OUTPUTS El VCCV1 PCUR1 VCCV2 PCUR2 VCCV3 PCUR3 VR2 VR4 RUN CONTROLS INTEGRATION ROUTINE RUK STOP TIME 4 7 AXIMUM STEP SIZE 0 015 END The output chosen for this problem VCCV2 is given in Figure 4 14 Next in order to establish the Convolution mode three blocks of circuitry were removed from this reference circuit Each removed portion had a known analytic spec
70. E 00 0 0000000E 00 0 0000000E 00 0 0000000E 00 1 0000000E 00 0 0000000E 00 0 0000000E 00 0 0000000E 00 1 0000000E 00 OPTIMIZATION RESULTS TERMINATION CONDITION OPTIMIZATION RUN COMPLETED OBJECTIVE FUNCTIO VR3 VALUE OF OBJECTIVE FUNCTION AT TERMINATION 5 65021325E 01 OPTIMIZATION PASS COUNTER 13 MAXIMUM PASSES SPECIFIED 40 INDEPENDENT VARIABLE VALUES AT TERMINATION GRADIENT TRANSFORMED TRANSFORMED VARIABLE VALUE COMPONENT VALUE RADIANS GRADIENT p1T1 9 00000002E 01 4 50846113E 01 2 86201981E 04 5 16132196E 06 P1T2 9 00000004E 01 5 48451029E 01 4 44554674E 04 9 75265843E 06 EC 1 00000000E 01 1 28031073 147 1 57079633E 00 6 40155365 148 Figure 4 20 Optimization Example Outputs 102 4 11 Example 11 USE OF AC ANALYSIS A11 This example is intended to illustrate the proper use of the AC program which is designed to conduct a small signal AC analysis around a circuit s DC operating points Figure 4 21 shows a circuit containing an active device in both schematic and SCEPTRE form Figure 4 21 Schematic AC Example Equivalent Circuit The DC operating point set up is either supplied by the user or is done automatically by the program The only response required by the user in addition to requesting the AC run by supplying the appropriate Run Controls is the inclusion of the cards for the DC mode he desires paragraph 2 2 7 Run Controls must be supplied if initial conditions are to be calculat
71. ELEMENTS as a direct math expression and its value is completely enclosed in parentheses see subsection 2 2 2 An equation could have been referenced for E1 and then subsequently defined under FUNCTIONS but this was not done for this run 4 5 Example 5 SOLUTION OF SIMULTANEOUS DIFFERENTIAL EQUATIONS A05 This example is intended to illustrate the flexibility of SCEPTRE through the special use of the DEFINED PA RAMETERS section Assume that the user has the problem of solving the following set of first order simultaneous 87 A04 small signal equivalent circuit 8 0 5000 10000 15000 20000 25000 Sun Jan 11 12 49 22 1998 TIME Figure 4 9 Plot of VRL2 versus TIME differential equations that may be entirely independent of any electrical network t 6x 5y 10 y 5x Ty 22 z 0 2y 0 2z 0 5 30000 350 with X O 6 Y O 5 Z O 4 as initial conditions Note since the derivatives of PX PY and PZ DPX DPY DPZ are entered PX PY and PZ will be updated at each integration step Only capacitor voltages and inductor currents are entered under the INITIAL CONDITIONS subheading The user may enter each of the derivatives under DEFINED PARAMETERS in explicit form A proper sequence would be CIRCUIT DESCRIPTION A05 Solution of simultaneous differential equations DEFINED PARAMETERS DPX EQUATION 1 PX PY DPY EQUATION 2 PX PY PZ DPZ EQUATION 3
72. EOUS DELIMITER IGNORED Hmm DENT SOURCE IMPROPERLY SPECIFIED OR INTEGRATION ROUTINE D I ATA FOLLOWS MODEL DESCRIPTION NG EL HAS BEEN SPECIFIED T D E OF 11 HEADING CARDS HAS BEEN EXCEEDED ABLE OR EQUATION SPECIFICATION EXPECTED C Q A UATION OR UNEVEN TABLE PRIOR TO NEW FUNCTION 1 TION PROPERLY SPECIFIED U ry ry INVALID CONSTANT S T D bd O E Hum UATION NAME EXCEEDS SIX CHARACTERS PECIFIED Q I QUATION IS REDUNDANT Q N Pp ABLE DATA EXCEEDS CAPACITIY OF THE INPUT PROCESSO pa AXIMUM OF 300 ELEMENTS HAS BEEN EXCEEDED E AXIMUM OF 50 UTUAL INDUCTANCES HAS BEEN EXCEEDED AXIMUM OF 50 SOURCE DERIVATIVES HAS BEEN EXCEE OMMA OR SIGN MISSING OR WRONG DERIVATIVE S URCE ELEMENT MISSING FOR TABLE OR DIODE EQUATION NCORREC ODEL CARD ELEMENT NAME INCOMPLET P G m E U tj U PROPER MODEL CHANGE SPECIFIED ONSISTEN ODEL CHANGE EQUATION AND TABLE ARE EQUATED IMIT OF 15 TABLE OR EQUATION MODEL CHANGES EXCEEDED NSUFFICIEN ODEL NODES SPECIFIED ODEL NAME EXCEEDS EIGHTEEN CHARACTERS ODEL CIRCUIT DESIGN
73. Extended SCEPTRE Volume 1 User s Manual David Becker GTE Sylvania Incorporated Revised and edited by Wolf Rainer Novender D 64625 Bensheim Germany Oktober 1999 Contents 1 Introduction 1 1 1 SCEPTRE capabilities coji le Sage Bee a Se ged te AS ee EYE eae 1 1 2 Handbook coverage asso e Se ee he SAS he a A le eee ap 2 1 3 Inpuit datarexample ocios a A a EELS is BRR AS Bk GOR BEES a n 2 SCEPTRE use 4 2 1 Circtut preparation por g o oY we pened bad ew gdh OR ee lk ee eee amp 4 2 2 Preparing the SCEPTRE input data 2 2 aa 5 2 2 1 Headings and subheadings 0 000000 00000000045 5 2322202 BICMENIS A Se hse ey Be Sree cee Baek Bade gh ew Are eh a NA 8 2 2 3 Defined parameters sa ita be ww pate eek foe eo ds wh Ee enh ee os 15 BRA SOUPIS ee ae ack Boas ye A ee TER See he SP Geo Bak ogee oe WAP ae Ee Oe A 17 2 29 Amtial Conditions e ns iy Bia gO e ae Woe ae amp E 20 232 606 FUNCION 2 0d Bite Serco hh Pete Bare ee ah ee Ae Bie eee dk cee 22 2 267 RUM CONTOIS y o a be we wR bee BARS A ee we Bebe Pw E 26 2 208 DE Options W226 en ew A OE A eee BO we SR EE Gs 38 2 2 9 Program limits 2 58 5 e Bae a Pee bee ee Bae es 40 2 2 10 Vectorized notation y face A tee o aS ee PE E ea 41 2 2 11 Internal Parameters ee 41 2 3 2 stored model feature ise ewe AIRS we OR OO oe Bowie we Le BW Sete isle 4 44 2 3 1 Transistor model insertion 0 a 44 2 3 2 N term
74. IS FUNCTION OF CAPACITOR XXX VOLTAGE FOR WHICH VOLTAG ee E isa RROR Gl SUBSTITUTION CANNOT BE PERFORMED INITIAL CONDITIONS RESISTOR OR INDUCTOR CURRENT SUPPLIED AS TABLE INDEPENDENT VARIABLE OR EQUATION ARGUMENT FOR XXX IS NOT ALLOWED FOR INITIAL CONDITIONS PROBLEM XXX UPON WHICH XXX IS DEPENDENT CANNOT BE FOUND IN THE CLASS 9 SECTION OF HE ELEMENTS TABLE AN INTEGER TO BCD CONVERSION ERROR OCCURRED IN A DIMENSION STATEMENT GENERATION XXX WHICH XXX IS DEPENDENT UPON IS NOT IN THE CLASS 2 OR 5 SECTION OF ELEMENTS PROGRAM ERROR THE VMUTUAL SUBROUTINE SUPPLIED XXX FOR TYPE OF MUTUAL TERM TO BE ADDED R F E TO V3P N or V6 N MUST BE IN RANGE OF 1 5 H D
75. ITIAL RANDOM NUMBER DISTRIBUTION RUN OPTIMIZATION MINIMUM FUNCTION ESTIMATE OPTIMIZATION CRITERION OPTIMIZATION RANDOM STEPS RANDOM STEP SIZE CONTROL INITIAL H MATRIX FACTOR RUN WORST CASE j None None 7090 94 600 min S 360 20 000 0 XPO 1 1078 STOP TIME xpo trap ruk 1 10714 STOP TIME implicit 2 107 STOP TIME 1 1078 STOP TIME xpo trap ruk 1 1078 STOP TIME implicit XPO TRAP RUK IMPLICIT 0001 00005 00005 0001 005 001 005 0002 0005 00005 005 01 005 Transient Only 100 0 001 0 0001 1000 15 100 transient 70 DC 10 5 LINEAR 10 3 Input Function Buffer 10 127263527 GAUSSIAN 30 0 1077 0 2 1 NOMINAL f Default value obtains when Run Control is entered without number If the Run Control itself is omitted the indicated calculation will not occur Table 2 4 Default run control quantities in SCEPTRE 27 or INTEGRATION ROUTINE RUK or INTEGRATION ROUTINE IMPLICIT Certain additional operations are required when implicit integration is used These are performed internally ac cording to a prescribed default mechanism but the user may exercise control over the default See 2 subsection 5 5 Two possible statements are available USE DIFFERENCED JACOBIAN USE SYMBOLIC JACOBIAN Use of the Convolution routine requires that the RUK integration routine be s
76. ITIONS ONLY I R C FOR RERUNS MASTER RESULTS ERUN DESCRIPTION N The second version of this feature allows all reruns to begin with the final voltages of the run preceding it The n 1 th rerun would start with the final voltages of the nth rerun The required language then becomes RUN CONTROLS RUN INITIAL CONDITIONS ONLY I R C FOR RERUNS PRECEDING RESULTS ERUN DESCRIPTION N Itis possible to combine this feature with DC via Transient feature described in the preceding section The language is 113 UN CONTROLS UN INITIAL CONDITIONS ONLY UN IC VIA IMPLICIT C FOR RERUNS either form ERUN DESCRIPTION N DHA DW DW Note that in all possible cases the necessary call is inserted under RUN CONTROLS of the master run and never under RERUN DESCRIPTION A 3 3 Optional initial conditions for transient reruns The third alternative for initial conditions is a method that has some of the characteristics of the other two It is similar to the method of subsection A 3 1 in that it utilizes transient analysis and is similar to the subsection A 3 2 technique because it applies to reruns only It offers the user the capability of starting any transient rerun with the state variable values that existed at the end of a previous transient run Consider the situation in which the effect of a series of pulses applied to a given network is to be ascertained
77. L2 M M L1 L2 M Figure A 13 Ideal Transformer A 9 11 Voltmeters and Ammeters A zero valued series voltage source which allows reference to a branch current i e acts as an ammeter may be used without disturbing conditions in the circuit Figure A 12a Similarly a zero valued parallel current source provides the voltmeter function without affecting circuit conditions Figure A 12b A 9 12 Avoiding redundant sensitivity runs It is not necessary to make a sensitivity calculation for variables listed in worst case or optimization Both worst case and optimization calculate partial derivatives for the listed variables at the nominal values A 9 13 Ideal transformers Ideal Transformers i e where K the coefficient of coupling is one will not be accepted by SCEPTRE How ever since SCEPTRE allows negative element values a T equivalent of the ideal transformer will be accepted by SCEPTRE see figure A 13 A 9 14 Semiconductor capacitance Semiconductor junction capacitance as given in the SCEPTRE manual often creates a problem The equation given for capacitance is Co C ae Rs A Vo diffusion C depletion or junction C 130 When the junction is forward biased the denominator of the first term in the equation becomes negative Since the value of n lies between 1 2 and 1 3 the first term becomes complex However according to the basic physics of semiconductors the first term of the equation
78. N CONTINUES AN ERRONEOUS TREE BRANCH EXISTS IN THE PATH OF XXX ERROR IN BCD CONVERSION OF XXX ENTRIES IS CLASS II THE REFERENCE INDUCTOR XXX FOR XXX CANNOT BE FOUND IN THE ELEMENTS TABLE PROGRAM ERROR IN WTEQTN ILLEGAL ARGUMENT TYPE CODE FOUND IN DEPENDENCY TABLE THE VARIABLE XXX COULD NOT BE FOUND IN THE VALUE LIST BY WTEQTN PROGRAM ERROR THE VARIABLE XXX IS DEPENDENT UPON ITSELF HE RUN CANNOT BE CONTINUED THE DEPENDENCY TABLE HAS OVERFLOWED IN WTEQTN PROGRAM ERROR THE ERM XXX WILL CAUSE A COMPUTATIONAL DELAY THE TERM XXX COULD NOT BE FOUND IN THE VALUE LIST BY EQFORM PROGRAM ERROR VALUE EXPRESSION FOR TYPE 6 IS NOT CODED YET THE RUN CANNOT BE CONTINUED THE VARIABLE XXX CANNOT BE FOUND IN EITHER THE LIST OF CIRCUIT ELEMENTS OR DEFINED PARAMETERS BY COMPCK 63 THE FOLLOWING INVALID PREFIX HAS BEEN SUPPLIED TO COPYDP X COPYDP IS BEING REQUESTED TO GENERATE THE FOLLOWING INVALID RESISTOR ERIVATIVE TERM IN AN EQUATION XXX THE FOLLOWING TER ILL CAUSE THE DEPENDENCY TABLE TO OVERFLOW XXX SCANEQ COULD NOT FIND THE TERM XXX IN THE ELEMENTS TABLE PROGRAM THE XXX ELEMENT COMPLETES A LOOP CONTAINING XXX WHICH WILL PROHIBIT AN INITIAL CONDITIONS SOLUTION THE VARIABLE ELEMENT XXX COMPLETES A LOOP CONTAINING AN ELEMENT OF THE SAME TYPE WHICH PROHIBITS AN IC SOLUTION CAPACITOR XXX REFERENCED IN TABLE OR EQUATION BUT NOT SUPPLIED AS ELEMENT ELEMENT XXX
79. N CONTROLS heading rather than the OUTPUTS heading Thus PLOT INTERVAL and PRINT INTERVAL are both considered RUN CONTROLS and should appear in that section of input A 9 9 DC coupling capacitor in certain AC runs The user is encouraged to insert a DC coupling capacitor in series with all AC voltage sources for AC problems which require initial condition solution During the IC solution the AC source is set to zero forming a short and allowing current through the source The capacitor prevents any current from flowing through that branch resulting in the correct IC solution Analogously an inductor should be connected in parallel with an AC current source This forces a short across the current source which has been set to zero open circuit for the IC run This prevents any voltage from appearing across the source In both cases the value of the element should be large enough so it does not load the source driving the AC run That is the capacitor should appear as a short circuit and the inductor should appear as an open circuit at the lowest analysis frequency A 9 10 Convolution input The input function h for convolution must specify h 0 See section A 8 7 page 125 In cases where there is no energy in the total circuit at t 0 any value may be given for h 0 since it has no effect on circuit behavior 129 ee a ae Haa a Ammeter b Voltmeter Figure A 12 Ammeter voltmeter elements L1 M
80. PY PZ PX 6 PY 5 PZ 4 88 OUTPUTS PX X PY Y PZ Z XSTPSZ FUNCTIONS EQUATION 1 A B 6 A 5 B 10 EQUATION 2 A B C 5 A 7 B 2 C EQUATION 3 A B 2 A 2 B 5 RUN CONTROLS INTEGRATION ROUTINE TRAP STOP TIME 100 END Note that the initial values of each of the variables X Y and Z have been entered as PX 6 PY 5 and PZ 4 respectively The differential equations themselves are entered under DEFINED PARAMETERS in the language given in subsection 2 2 3 The quantities X Y and Z will be treated in the same manner as would the state variables of the general transient problem and therefore these equations will be subjected to the same step size limitations in whatever integration routine is used These quantities are explicitly labeled as X Y and Z because of the format used under OUTPUTS see subsection 2 2 4 The step size is output through the use of the internal name XSTPSZ see table 2 11 4 6 Convolution example 4 6 1 General A transient run utilizing the Convolution mode requires that a single entry for each convolution kernel see Ap pendix A 8 be inserted under the CIRCUIT DESCRIPTION subheading ELEMENTS Each of the two convolu tion models is made up of two elements a variable source and a variable resistor The impedance model consists of a resistor voltage source in series and the admittance model consists of a resistor current source in parallel Con
81. S 124 A J1 Admittance Model coco ts a eee Oe eee a ee Ok eG 125 A 12 Ammeter voltmeter elements 0 00 00 0 E a a AARE ee 130 A 13 Ideal Transformer si a Sao ek Be a See ed a ed 130 List of Tables 2 1 Units for High Speed Transistorized Circuits 0 000 000 000004 5 2 2 Entriessunder ELEMENTS 3 ccs 4 soe ak ee a ee Ew ea g 9 2 3 Functions of Real and Complex Arguments 00 0000 000004 24 2 4 Default run control quantities in SCEPTRE o o e 27 2 5 Run controls for specifying mode of analysis o o e o 30 2 6 Additional run controls ee 39 2 7 Dependent variables in DC calculations o o ee 40 2 8 Independent variables in DC calculations o e e e e 40 2 9 Program data limits e c s Ae eee eee d 42 2 10 Maximum alphanumeric character lengths allowed Recommended 42 2 11 Internal parameter table lt a Pb ae ee Bee ob dd Se eh iy eee 43 2 12 Tables In Rerun 4 4 See Eh eee a he Dae ee ee ee ee ch A 51 A J Comparison of DC results cia sosse cer A e a BEE S 113 vi This manual is almost an identical copy of 1 The references to the IBM 7090 94 and S 360 computers have been left untouched for historical reasons The machine dependent chapters 7090 94 S 360 and CDC6600 System Information have been omitted references to them within this manual will look like wr
82. S MAY OCCUR 79 INVALID SYNTAX 80 ABLE XXX FORMAT ALTERED TO TXXX 81 IME SUPPLIED AS ARGUMENT IN XTABLE FUNCTION 82 HE MAX OF 100 PARTIAL DFPRAM DERIV HAS BEEN EXCEEDED T DO E J U 83 PART DFPRAM DERIV REFERENCES NON EXISTENT DFPRAM DERIV 84 INVALID OR MISSING DELIMITER IN A DC OPTION CARD 85 INVALID VARIABLE IN A DC OPTION CARD 86 MONTE CARLO DEFAULT 10 PASSES SUPPLIED 87 OPTIMIZATION DEFAULT 30 PASSES SUPPLIED 88 NOMINAL VALUE DOES NOT LIE BETWEEN BOUNDS 89 AC RUN REQUESTED WITH INITIAL CONDITIONS ONLY RUN 90 COMPLEX DEFINED PARAMETER GIVEN AS REAL CONSTANT 91 LIMIT OF 50 COMPLEX DEFINED PARAMETE 92 AC SOURCES PRESENT IN NON AC RUN 93 SYMBOLIC JACOBIAN WITH ADJOINT RUN MAY LEAD TO ERROR 94 INVALID OR MISSING DELIMITER IN A DIFFERENTIAL DATA CARD 95 INVALID VARIABLE IN A DIFFERENTIAL DATA CARD Da n x Q J J YU The program generator portion of the program also contains a diagnostic capability to inform the user of errors that can only be detected after the network topology is analyzed Such errors may or may not cause the execution of the
83. T DESCRIPTION A07 Darlington pair MONTE CARLO ELEMENTS EC 1 6 10 EIN 1 2 1 Ri 4 2 3 20 R2 6 5 eo R3 4 1 200 R4 8 1 4 ROD g 6 7 1 T1 3 4 5 MODEL 2N706A T2 4 8 7 MODEL 2N706A MONTE CARLO VCET1 VCCT1 J1T1 VCET2 VCCT2 J1T2 PEC PEIN VR3 VR4 P1T1 P1T2 DEFINED PARAMETERS PEC X1 EC IEC PEIN X2 EIN IEIN OUTPUTS PEC PEIN VR3 VR4 RUN CONTROLS RUN MONTE CARLO 10 RUN INITIAL CONDITIONS ONLY END In the Monte Carlo example Gaussian distribution was used since none was requested and Gaussian is the default mode and ten iterations were requested The independent variables are the defined parameter P1 as used in both model T1 and model T2 Since no initial random number was specified SCEPTRE supplied its own Details of each iteration were not requested If they had been the random element and defined parameter values and the requested output values would have been listed for each run The outputs provided shown in figure 4 17 are the statistical parameters of the independent variables plus a summary of the maximum minimum and mean and standard deviation of the requested output parameters 4 8 Example 8 USE OF SENSITIVITY A08 The Darlington Pair used in Example 3 shown in figure 4 5 is used to demonstrate the Sensitivity option For this case two sets of partial derivatives were requested the first with five dependent and two independent variables and the
84. TS See Appendix A 3 for additional information Convergence of the Newton Raphson Routine The Newton Raphson iteration method should produce convergence and hence d c solutions in less than 30 passes for most networks If convergence is slow or does not occur some realistic limit should be placed on the number of passes that are made Unless otherwise specified a limit of 100 passes is built into SCEPTRE To change this limit the proper entry is NEWTON RAPHSON PASS LIMIT number 31 Convergence is considered to have occurred if n Y n 1 lt A n B where Y refers to the vector of initial condition state variables n is the number of completed passes A is the relative criterion and B is the absolute criterion The values A 0 001 B 0 0001 are built into SCEPTRE The user probably will not want to change these values but if either quantity is to be changed the proper entries are RELATIVE CONVERGENCE number ABSOLUTE CONVERGENCE number x Output Control Some transient runs may require thousands of solution points and it is usually unnecessary to have every solution printed out SCEPTRE is processed to output a maximum of 1000 spaced points regardless of the number of steps taken The maximum number of printed output points may be changed for any particular run by entering MAXIMUM PRINT POINTS number An additional means exists by which
85. ach of those attached elements This listing is requested by the entry LIST NODE MAP under RUN CONTROLS A sample listing is provided in figure A 7 that corresponds to the network of figure A 6 A 7 Differential equation identification The purpose of the differential equation identification feature is to serve as a sophisticated diagnostic that will help the user to localize if not pinpoint any circuit conditions that cause a transient run to be aborted because of step size difficulties in any of the explicit integration routines The usual cause of this type of abort is either an input error or a very small time constant with respect to the required problem duration The four stage transistor circuit shown in figure A 8 illustrates the feature Reasonable numbers were chosen for all element values except for CE of T2 1 x 10 7 picofarads and a current source in parallel with CC of T3 JPP 1x 108 mA A problem duration of 100 ns was specified which automatically led to a starting step size of 0 1 ns see subsection 2 2 7 The error criteria of the integration routine XPO rejected the step size as well as all smaller attempts down to the default minimum which in this case is 0 001 ns see subsection 2 2 7 At that point the run was aborted with the diagnostic message STATE VARIABLES REQUIRING SMALLER MINIMUM STEP 1 3 This message indicates that the computed solutions to the first and fifth state variable
86. al initial voltage polarity agrees with the arbitrarily chosen reference direction that initial voltage is entered as positive if not it is entered as negative Proper statements for the example of figure 2 4 are under ELEMENTS L5 7 8 value and either of the following En 4 5 value Cc11 5 4 value Automatic Initial Conditions When the user requests that initial conditions be calculated by the program see subsection 2 2 7 he need supply no initial conditions himself To shorten the initial condition calculation however he may supply approximations of the voltages across diodes or transistor junctions The language must be VJ number 21 The iterative process will begin with any VJ entries that are supplied One practical application of this type of input would be to bias the ON and OFF sides of symmetric circuits such as flip flops in the desired state Approximate values could be supplied and the DC solution would then provide the correct voltages for the desired state The results of the DC solution would then carry over to the beginning of the transient solution if one is called for Appendix A 3 discusses special options in initial conditions NOTE If the user requests automatic initial conditions for a transient run and also supplies initial conditions for capacitor voltages and inductor currents per subsection 2 2 5 his supplied values can appear as impulses at the start of the transient run This
87. ample 3 shown in figure 4 5 is used to demonstrate the Optimization option For this case one set of optimization parameters was specified The set contained two objective functions and four independent variables MODEL DESCRIPTION MODEL 2N706A TEMP ELEMENTS B 1 E Q 100 CE 1 E Q1 5 70 J1 cc 1 2 Q11 8 370 lt 32 RB B 1 3 RC 6 2 015 J1 1 E DIODE EQUATION 1 E 7 35 J2 1 2 DIODE EQUATION 5 E 7 37 JA E 1 1 J2 JB 2 1 P1 J1 DEFINED PARAMETERS P1 0 96 0 98 0 9 FUNCTIONS Q1 A B C A B C OUTPUTS VCE VCC J1 CIRCUIT DESCRIPTION A10 Darlington pair OPTIMIZATION ELEMENTS EG Aao 1 6 LO Deo 065 EIN 1 2 1 Ri 7 253 20 R2 6 5 U5 R3 4 1 200 R4 8 1 4 ROD 6 7 1 T1 3 4 5 MODEL 2N706A T2 4 8 7 MODEL 2N706A OPTIMIZATION VR3 PEC P1T1 P1T2 EC DEFINED PARAMETERS PEC XEC EC IEC GPEC P3 DIEC P5 DEC P3 X3 EC P5 X5 IEC OUTPUTS VR3 VR4 RUN CONTROLS RUN OPTIMIZATION 40 RUN INITIAL CONDITIONS ONLY LIST OPTIMIZATION DETAILS END The two objective functions are minimized with respect to the four independent variables specified The output appears in figure 4 20 The problem shows the use of defined parameters as bo
88. analysis phase to be aborted as indicated by the error messages which occur A list of diagnostic messages that may originate in the program generator follows AN ILLEGAL PROCESSING SEQUENCE HAS BEEN REQUESTED PROGRAM CAPACITY HAS BEEN EXCEEDED XXX LIST OVER FLOWED IN FILING XXX WISPTP HAS BEEN ASKED TO WRITE XXX SOURCE STATEMENT CARDS THE LIMIT is x THE 111111 ELEMENTS TO BE PROCESSED EXCEEDS THE LIMIT OF XXX T XXX RESULTS IN A CURRENT SOURCE CUT SET XXX CAUSES J C CUT SE XXX RESULTS IN A VOLTAGE XXX CAUSES E L LOOP PREVENTING I C SOLUTION THE ELEMENT XXX FROM XXX TO XXX IS SHORTED OUT OF TRE CIRCUIT EXECUTION WILL BE TERMINATED AFTER COMPLETED ERROR SCAN D PREVENTING I C SOLUTION SOURCE LOOP E T WARNING ONLY THE XXX NODE OF XXX IS NOT CONNECTE TO ANY OTHER ELEMENT IN THE CIRCUIT EXECUTIO
89. andom Steps Remaining to be Executed XRNSSC Random Step Size Control XHHFAC Initial H Matrix Factor XMNFES Minimum Function Estimate XSAVIC Type of Rerun Initialization XMXERT Computer Time Limit Table 2 11 Internal parameter table 43 2 3 Stored model feature All active devices must be represented in SCEPTRE by combinations of R L C M E and J Most users will find that repeated use is made of certain models of active devices or of standard combinations of passive elements such as filter sections biasing networks etc These situations can always be handled by inserting the components one by one in a CIRCUIT DESCRIPTION under ELEMENTS A more convenient approach is to describe the model or network once and store it for future use The stored model feature is not free its use requires extra tape manipulation and hence more computer time However the time saved in circuit preparation and the added flexibility will compensate for the extra time The stored model feature of SCEPTRE is especially flexible since the user stores whatever models meet his specific needs A model may be stored permanently or temporarily If it is stored permanently the model may be called out for insertion in a main network as often as desired per run and for any number of runs The user might desire to reserve this type of storage for proven models that will see reasonably frequent service Temporary storage on the other hand store
90. ansistor models coded for SCEPTRE when closed form expressions for Ipe Iye and the junction capacitances are available Reference figure 3 5 For the NPN 70 Figure 3 5 SCEPTRE Ebers Moll Representations 71 ELEMENTS CE B E EQUATION 1 57 1 VCE CC B C EQUATION 1 10 8 VCC JE B E DIODE EQUATION 2 9 E 9 JC B C DIODE EQUATION 1 46 E 8 JI E B 534 JC JN C B 99 JE RB B1 B 1 RC C1 C 06 OUTPUTS VCE VCC VRB PLOT ICC ICE IRC FUNCTIONS EQUATION 1 A B C D E F G For the PNP ELEMENTS CE E B EQUATION 1 9 9 VCE CC C B EQUATION 1 11 6 VCC JE E B DIODE EQUATION 2 67 E 5 JC C B DIODE EQUATION 2 12 E 4 JI B E 2598 JC JN B C 985 JE RB B B1 1 RC C EL 005 OUTPUTS VCE VCC VRB PLOT ICC ICE IRC FUNCTIONS EQUATION 1 A B C D E F G Definition of terms Cj Cac Cj Cae QI fn TA a v o o D SM w o Inverse alpha Forward alpha Slope of In Jre versus Vie 43 189 JE 2 9 E 9 aL 7500 5 JC 2 246 E 8 36 7 28 2 A B C D E F G 55 7205 Es 2 67 E 5 34 1620 JC 2 12 ESA 36 7 34 A B C D E F G Junction capacitance associat
91. at cannot be accommodated in the Initial Condition solution using the Newton Raphson method that could be accomplished with IC via Im plicit which computes initial condition solutions using the transient portion of the program The Newton Raphson method is generally more efficient than the implicit method however See Appendix A 3 for detailed information A 1 1 Restrictions on AC transient and initial condition solutions E2 El E3 66 fig Figure A 1 Voltage Source Loop No run may contain a loop composed exclusively of voltage sources figure A 1 or a cut set composed exclusively of current sources figure A 2 If either configuration is presented to the program it will be rejected with an appropriate diagnostic A 1 2 Restrictions on initial condition solutions No initial condition solution will be performed if any loop exists that is composed solely of voltage sources and inductors figure A 3 Configurations which contain cut sets composed entirely of current sources and capacitors are also prohibited figure A 4 If either configuration is presented to the initial condition formulation it will be rejected with an appropriate diagnostic It is worth noting that any J or J C cut set may be easily broken up by the insertion of a resistor in the proper position For example the JC cut set in figure A 4 may be eliminated by the insertion of a resistor between node X and the network ground The size of this resistor should be larg
92. ata See also subsection 2 2 8 Maximum number Heading Cards Elements Nodes Source Derivatives Defined Parameters P Defined Parameters W Defined Parameter Differential Equations Mutual Inductances Arguments in Equation Value Specification Model Table Changes Model Equation Changes Model Output Suppressions Output Requests Supplied Initial Conditions Equation Functions 1 equation per card Cards per Equation Function Table Functions Optional Termination Conditions Models on Library Tape Combined Characters in Model Name Model Terminals External Nodes Model Internal Nodes Linearly Dependent AC Sources plus Secondary Dependent AC Current Sources Independent AC Voltage and Current Sources Maximum Convolution Kernels 11 300 301 50 100 50 100 50 50 15 15 10 100 100 80 20 x 80 10 250 18 25 301 50 50 50 Table 2 9 Program data limits Item Circuit description Model description Nodes Names 6 3 Element Names 5 2 Defined Parameter Names 6 3 Table Names 5 2 Equation Names 5 2 Model Names 18 18 Output Labels 6 3 Circuit Designation for calling models 3t Table 2 10 Maximum alphanumeric character lengths allowed Recommended 42 Int name Definition XSTOPT Transient solution duration STOP TIME XIR Integration routine TRAP 1 RUK 2 XPO 3 XTISSS Starting step size XMNISS Minimum step size allo
93. ata is to be used JB B X DIODE TABLE XXXXX and the DIODE TABLE is subsequently defined The current sources a y re and a 1 are defined as secondary dependent sources and should be entered as JS value JX where value represents ay or a and can be a number table defined parameter equation or math expression The total capacitance associated with the emitter junction is usually expressed as Coe Oe Ve Cr Ciunction Cdiffusion Voc Vor OeTelese t CP 3 3 or Coe Ces LO LA 3 4 Voe Ver which is an explicit function of the junction voltage In the forward region Iye gt Ies gt O and therefore Equation 3 4 may be written Coe Voe 4 Vor Ce X H OcTelre 3 5 68 b PNP 15 fig Figure 3 4 Basic Ebers Moll Transistor Equivalent Circuits 69 Note that Equation 3 4 must always have a positive diffusion capacitance even when Ipe lt 0 because Tes gt Ie when Vcg lt 0 in the diode equation but that a negative diffusion capacitance and therefore a negative total capacitance is conceivable in 3 5 Normally any negative contribution due to the diffusion term will be orders of magnitude less than the positive junction term and the total capacitance will be positive It is clear that if the current source I e in 3 5 is represented by a diode table that permits no negative current a negative capacitance is never possible The situation r
94. c output voltage and power requirements of this circuit under nominal conditions and after the first stage transistor alpha has been degraded to various levels due to the effects of a steady state radiation environment Assume that the transistor model has been permanently stored at some previous time 83 zal Q Figure 4 5 Schematic of the Darlington Pair MODEL DESCRIPTION MODEL 2N706A PERM B E C ELEMENTS CE 1 E Q1 5 70 d1 CC 1 2 0118 0437002 RB B 1 53 RG C2 015 Jl 1 E DIODE EQUATION 1 E 7 35 J2 1 2 DIODE EQUATION 5 E 7 37 JA E 1 1 J2 JB 2 1 P1 J1 JX 2 1 0 DEFINED PARAMETERS Pl 0 98 FUNCTIONS Q1 A B C A B C The Rerun feature will be used to accommodate the additional runs that are required for the degraded alpha ver sions A valid sequence of cards for example 3 would be as follows CIRCUIT DESCRIPTION A03 Darlington pair ELEMENTS ECs ay ELO 10 EIN 1 2 1 Rl 2 3 20 R2 6 5 10 R3 4 1 200 R4 8 1 4 R5 6 7 1 T1 3 4 5 MODEL 2N706A PERM T2 4 8 7 MODEL 2N706A PERM DEFINED PARAMETERS 84 I C TRANSIENT VALUES AT TIME EQUALS ZERO I C TRANSIENT VALUES AT TIME EQUALS ZERO
95. cal definition itself must be included in parenthesis and must be written in terms of A B C along with any constants and allowable subprogram functions that apply It is important to mention that there would be no need for the user to reserve quantities A B and C for equation 15X alone These dummy variables may be freely used in other equations to represent other circuit quantities As another example consider the equation mentioned in subsection 2 2 2 where it was desired to enter capacitor Cl as 10 80 TABLE 7 where TABLE 7 is a function of VC1 If under ELEMENTS the user enters Cl 7 8 EQUATION 2 TABLE 7 VC1 then EQUATION 2 must be explicitly defined under FUNCTIONS An appropriate entry would be 22 EQUATION 2 A 10 80 A At each solution pass the ordinate value of TABLE 7 would replace the dummy variable A and the computation 10 80 A would be carried out Note that decimal points are required for the constants 10 and 80 because they appear with an EQUATION designation Still another method can be used that is particularly efficient when more than one equation of the same general form is used in a given run Let it be desired to enter C1 as in the above paragraph in addition to C2 as 5 120 TABLE 4 where TABLE 4 is a function of VC2 Under ELEMENTS the user may enter two cards as 8 EQUATION 2 10 80 TABLE 1 EQUATION 2 5 120 TABLE and under FUNCTIONS Equation 2
96. cified duration and the user subsequently wishes to continue the run to a new duration of 2000 units of time 54 CONTINUE RUN CONTROLS STOP TIME 2000 END Other changes that are permissible under continued RUN CONTROLS are those described in subsections 2 2 7 2 2 7 through 2 2 7 and 2 2 7 2 5 2 Limitations on the CONTINUE feature This feature is intended for transient runs only and has no control over DC or AC computations including Initial Condition computations When the original run contains a number of reruns the continue option will apply only to the last run that was processed which will usually be the last rerun 2 6 RE OUTPUT feature The user may often desire additional copies of output from previous runs without the necessity of repeating the runs This can be done in SCEPTRE through the use of the Re output feature if the original run has been preserved on tape In addition to repeating the original output the Re output feature permits some degree of modification Any quantity that was originally outputted in printed form may be obtained in both printed and plotted form by the use of this feature If the printed output results of a previous run are desired without modification the appropriate entries are simply 7090 94 only RE OUTPUT Original output requests without the OUTPUTS subheading END If in addition to the printed results any of the same outputs are desired in plotted form rega
97. contribution to the total differential GPEC 4 9 Example 9 USE OF WORST CASE A09 The Darlington Pair used for Example 3 shown in figure 4 5 is used to demonstrate the Worst Case option The Worst Case request specifies one set of ten dependent and two independent variables MODEL DESCRIPTION MODEL 2N706A TEMP B E C EL TS CE 1 E Q1 5 70 J1 Cop Lee QU 3180 02 RB B 1 3 RC C 2 015 Jl 1 E DIODE EQUATION 1 E 7 35 J2 1 2 DIODE EQUATION 5 E 7 37 JA E 1 1 J2 JB 2 1 P1 J1 DEFINED PARAMETERS Pl 0 96 0 98 0 9 FUNCTIONS Q1 A B C A B C OUTPUTS VCE VCC Jl CIRCUIT DESCRIPTION A09 Darlington pair WORST CASE ELEMENTS EC 1 6 10 EIN 1 2 1 Rl 2 3 20 RZ y 6 5 5 R3 4 1 200 195 205 R4 8 1 4 0 35 0 45 R5 p 6 7 1 T1 3 4 5 MODEL 2N706A T2 4 8 7 MODEL 2N706A WORST CASE VCET1 VCCT1 J1T1 PEIN P1T1 P1T2 R3 VCET2 VR4 P1T2 R3 R4 DEFINED PARAMETERS PEIN X2 EIN IEIN GPEIN P4 DIEI P4 X4 EIN OUTPUTS 99 WORST CASE COMPUTATION OBJECTIVE FUNCTION VCCT1 INDEPENDENT VARIABLE PITI 9 P1T2 9 R3 ae LOW VALUE LOCATED AT INDEPENDENT VARIABLE HIGH VALUE LOCATED AT NOMINAL VALUE 8 91263697E 00 VALUE GRADIENT COMPONENT 60000000E 01 600
98. d in figure 4 22 Note that here m 2 n 4 The entire SCEPTRE input will be given in upper case followed by appropriate commentary in lower case type 4This practice is identical in principle to that used in analog computer programming where the highest derivative is fed into a series of integrators 5Nodes 2 and 8 may be common without loss of generality 6 For the special case m n this relation must be revised to EO am DPm am 1Pm a P2 aoP1 106 Q Jl EO e oe a b Figure 4 22 A Transfer Function Block and the Equivalent SCEPTRE Representation ELEMENTS JI 1 2 0 EO 8 7 X1 DP2 7 P2 10 P1 from equation 4 7 DEFINED PARAMETERS DP4 X2 VJI 2 P4 10 P3 200 P2 from equation 4 8 1000 P1 1 DP3 X3 P4 from equation 4 9 DP2 X4 P3 DP1 X4 P2 Pl 0 these establish initial values P2 0 They may be omitted and the only P3 0 consequence will be a series P4 0 of warning messages It is clear that if a particular system requires two or more transfer functions of the above type the user must repeat the procedure for each one If there are very many transfer functions involved or if those that are involved are of higher order the input task becomes a bit tedious and error prone The remedy for this of course is the stored model of SCEPTRE It is suggested that the user store on his permanent tape one model for each degr
99. d in subsection 2 2 7 These Run Controls either have semi diagnostic roles or are best explained within the detailed discussion of functions they control Table 2 6 lists these Run Controls and the paragraphs which describe them 2 2 8 DC options Subheadings under the CIRCUIT DESCRIPTION heading are provided for the user to identify the variables he wishes treated in the Sensitivity Monte Carlo Worst Case and Optimization calculations The input data consists of the appropriate subheading SENSITIVITY MONTE CARLO WORST CASE or OPTIMIZATION followed by the appropriate parameters Each set of parameters is enclosed in parentheses The objective func tions or dependent variables are listed first followed by a slash and the list of independent variables Individual variables in the list are separated by commas Each set must name at least one dependent variable and at least one independent variable The form is dependent variable list independent variable list 38 Run Control See Subsection Remarks PRINT A MATRIX 2 8 5 AC Diagnostic PRINT EIGENVALUES 2 8 5 AC Diagnostic PRINT EIGENVECTORS 2 8 5 AC Diagnostic LIST NODE MAP 2 8 4 Network Diagnostic X PLOT DIMENSION Y PLOT DIMENSION SOLUTION TIME LIMIT NO ELEMENT SORT 2 8 2 PRINT B MATRIX 2 8 3 PUNCH PROGRAM FULIST PUNCH BINARY CARDS WRITE SIMUL8 DATA 2 8 VECTOR EQUATIONS WRITE DEBUG 2 8 6 Prints Internal Program Data
100. designations in the SPECIAL VALUE list are intended to accommodate the class of linearly dependent sources that are encountered in small signal transistor equivalent circuits see subsection 3 3 The fourth designation was designed for the class of secondary dependent current sources that always appear in the large signal Ebers Moll transistor equivalent circuit see subsection 3 2 The capability of specially processing these sources has been built into the program and should always be entered directly in the ELEMENTS section without parentheses Examples of these appear in this subsection The last two designations in the SPECIAL VALUE list are reserved for primary dependent current sources that represent diodes or transistor junctions DIODE EQUATION X1 X2 would be used when any diode or tran sistor junction has been entered and the user wishes to employ the conventional closed form representation J I e 7 1 The value of X1 must correspond to I in the diode equation and the value of X2 must correspond to O The program will automatically use the voltage across that particular current generator as the independent variable and for that reason this voltage need not be specified If for example a current generator that 1s named J18 and is connected between nodes 1 and ground is to be described by the conventional diode equation as 1 1077 e30 V7 1 the appropriate entry would be J18 1 GND DIODE EQUATION 1 E 7 30
101. differential equations were forcing the step size below the minimum allowable In addition to the above diagnostic the program always prints out a numbered state variable derivative sequence whether the particular problem at hand aborts or not For the network of figure A 8 the following sequence would be output 117 THE CIRCUIT TOPOLOGY IS GIVEN HERE AS AN AID IN CHECKING THE INPUT DATA NODE ATTACHED COMPONENT ADJACENT NODE 3 ES1 0 RBIAS 2 0 ES1 3 ES2 5 EIN 1 CI 2 C2 4 CEMQ1 BPO1 JD201 BPO1 JREQ1 BPO1 5 ES2 0 RLOAD 4 1 EIN 0 RIN 2 2 C1 0 RIN 1 RBIAS 3 RBBO1 BPO1 4 C2 0 RLOAD 5 CCOQ1 BPO1 JD1Q1 BPO1 JEWO1 BPO1 BPO1 RBBOL1L 2 CEMQ1 0 CCOQ1 4 JD1Q1 4 JD201 0 JEWO1 4 JREQ1 0 Figure A 7 Nodal Listing requested by LIST NODE MAP 118 DCE DCE DCCT DCE DCCT DCE DCCT DCCT J OAarATNA OBWN FE NOP BP WWE PDN From this numbered sequence the user can immediately determine that the difficulty is associated with CE of T2 and CC of T3 As far as the first named element is concerned the difficulty is the size of the element value itself and this is obvious The second element is not in itself a problem but the user can readily establish that the current source is parallel with it JPP is a problem This feature is built into the program and no special entry is required to activate it Figu
102. ditional SCEPTRE entries under ELEMENTS JP1 5 6 EQUATION 2 C1 VC1 4 E 9 PF1 under DEFINED PARAMETERS DPF1 EQUATION 3 TABLE 1 TIME PF1 9E3 PF1 0 77 under FUNCTIONS EQUATION 2 A B C D A B C D EQUATION 3 A B C A 1 E 9 B C The factor 1 E 9 converts TABLE 1 to nanosecond time units as in EQUATION 1 78 4 Examples of SCEPTRE Use This subsection presents various examples which the user may use for checkout or as sample entry forms Consid erable effort was expended to make these examples as practical and therefore as useful as possible 4 1 Example 1 INVERTER CIRCUIT LOADED WITH RC NETWORK A01 Figure 4 1 shows a schematic of an inverter circuit loaded with an RC network It is desired to analyze the effects of a transient radiation environment on this circuit The forcing function will be the primary photocurrent appropriate to the environment Two reruns are to be made and these differ from the master run only in the magnitude of the photocurrent effectively applying an upper and lower tolerance to the Ipp The stored model feature will not be used and the initial conditions will be supplied as known quantities therefore the mode of analysis will be transient only Figure 4 1 Example 1 Schematic Diagram SCEPTRE form Here J1 and J2 represent the transistor junctions JA and JB represent the conventional current controlled current
103. e MODEL DESCRIPTION MODEL SS1 TEMP B E C JEMENTS EA E X 0005 VR2 R2 C E 2000 Rl B X 3 JB C E 50 IRI CIRCUIT DESCRIPTION A04 small signal equivalent circuit ELEMENTS El 1 2 X1 001 DSIN 000628 TIME El 2 3 5E6 C2 4 5 5E6 RB1 3 1 100 RL1 1 4 1 RB2 5 1 100 RL2 1 6 1 T1 3 1 4 MODEL SS1 T2 5 1 6 MODEL SS1 OUTPUTS VRL1 VRL2 VC1 VC2 RUN CONTROLS STOP TIME 30000 86 H TEGRATION ROUTINE TRAP TERMINATE IF VRL2 GE 20 END A04 small signal equivalent circuit 9 04 O4 0 03 0 02 0 01 0 01 0 02 0 03 0 04 0 5000 10000 15000 20000 25000 30000 350C Sun Jan 11 12 48 04 1998 TIME Figure 4 8 Plot of VRL1 versus TIME Since the frequency of the input sinusoid is 100 kHz its period is 10 000 nanoseconds The problem duration has been set to 30 000 nanoseconds to accommodate three cycles of the input wave Output plots for the voltages across the two load resistors are shown in figures 4 8 and 4 9 The latter waveshape peaks at about 6 6 volts which indicates that this circuit has an overall voltage gain of 6600 at this frequency The automatic termination condition was never activated since VRL2 remained below 20 volts throughout the run It is worth noting that the input sinusoid El was entered directly under
104. e 1 An all current source cut set is recognized by the presence of one or more nodes which cannot be connected to all other network nodes without traversing current sources 109 J1 J2 Ji Ry J2 67 fig i i Figure A 2 Current Source Cut Sets enough so as to preclude significant effect on the network but not inordinately large to avoid possible introduction of numerical error A value of about one megohm will usually meet both requirements 68 fig Figure A 3 Voltage Source Inductor Loop A 2 Computational delay The user may note that a wide selection of network quantities are allowed as arguments in equation and table construction It is sometimes true that the use of certain quantities can cause a computational delay in transient runs That is computation at the nth time step will begin with independent variables that are valid at the n 1 th step The amount of error will be proportional to the degree of non linearity exhibited by the functional dependence Computational delay will not occur if the independent variables are time capacitor voltages or inductor currents There is no problem with the use of resistor currents or voltages as independent variables if they are entered according to subsection 2 2 2 The validity of the use of other independent variables cannot be unambiguously stated the status is topology dependent The program will always print out a warning message if a computational delay occurs provided that
105. e Value Current Source DIODE TABLE or DIODE EQUATION X1 X2 Variable Denotes any of the following e The voltage or current associated with any element as VR1 VJ7 IE4 ILM etc e Any source or source derivative as J17 DJ17 E4 DE4 etc e Any defined parameters as P7 DP7 etc e Any element value as R17 CA M12 etc e Time as TIME e Frequency as FREQ e Any internal parameter see subsection 2 2 11 V Element Name or Element Name Denotes the element voltage or current of ELEMENT NAME For ex ample the voltage across capacitor CAB1 would be referred to as VCAB1 and the current through inductor LCHOK would be referred to by ILCHOK TABLE Name Independent Variable Used when a variable circuit quantity is given in tabular form The table used must be given a unique name prefixed by TABLE or simply T and followed by a single indepen dent variable in parenthesis The name may consist of up to five alphanumeric characters The independent variable may be any of the quantities defined under VARIABLE such as TABLE 1A VC1 If an indepen dent variable including the enclosing parenthesis is not supplied then TIME will automatically be chosen EQUATION Name Argument List Used when a variable circuit quantity is given in closed form The equa tion must be given a name prefixed by EQUATION or simply Q and followed by one or more arguments separated by commas and enclosed in a parenthesis The EQUATION name may cons
106. e entered under one MODEL DESCRIPTION heading The CIRCUIT DESCRIPTION heading is always used when any network is presented for analysis Any or all of the ten subheadings listed under the heading may be used The RERUN DESCRIPTION heading is used whenever the rerun feature is exercised All changes to the master network must appear under this card Any or all of the five subheadings listed under this heading may be used The CONTINUE heading is intended for use only when continued computation is desired after a problem has been originally run The only subheading permitted under this heading is RUN CONTROLS The only other heading that may appear together with CONTINUE in a run is END The RE OUTPUT heading is used whenever the user desires output from a previously completed run without repeating that run No subheadings are permitted under this heading on the 7090 94 The only other heading that may appear with RE OUTPUT on the 7090 94 is END On the S 360 the OUTPUT subheading is required and the RUN CONTROLS subheading may be used see subsection 2 6 The END heading is used to terminate every input data deck submitted to SCEPTRE This heading is the only one that must always be used without subheadings The data supplied within each of the subheadings consists of descriptive statements which are constructed as properly punctuated sequences of symbols The group heading subheading and subsequent statements may be punched on a card with arbi
107. e in the INITIAL CON DITIONS ONLY mode as illustrated in example 3 If the transient aspect of beta degradation must be examined the alpha term may be made a tabular function of time To illustrate consider the transistor equivalent circuit that is used in example 4 1 Since a constant alpha of 0 98 is used the simple entry JB 4 3 0 98 JI suffices If a variable alpha which is a function of time is desired that entry could be JB 4 3 TABLE 8 TIME J1 where the data for TABLE 8 is supplied under FUNCTIONS The user should always keep in mind the fact that comparatively long beta degradation and partial recovery times which run into many microseconds can lead to long computer solution times The most pronounced radiation effect in capacitors is the change in the conductivity of the dielectric material This effect can be represented by a voltage dependent current source in parallel with the capacitor This current source can be approximated by the following relationship a t ilt CV KD CV Kan i D A exp t A Tdn dd 3 7 n 1 0 where m is the appropriate number of delayed components for a given dielectric C is capacitance V is the voltage across C K are empirically determined coefficients D is the gamma exposure rate in R sec as a function of time A is a dummy variable of integration Td are empirically determined time constants The first term in this expression represents t
108. e made for the sake of simplicity For example if the inverse alpha azr of a transistor is judged to be negligible then generator JA may be omitted In either version it is always true that diodes or transistor junctions must always be represented as current genera tors by the designation DIODE EQUATION X1 X2 for closed form representation and the designation DIODE TABLE for tabular functions The current generators that are functions of other current generators must always be represented as a SPECIAL VALUE see subsection 2 3 1 3 3 Transistors Small signal equivalent There exists a family of transistor models known as small signal equivalent circuits These are composed of H Y Z and R parameter circuits that differ from one another only slightly in configuration and technique of parameter 73 18 fig 19 fig Figure 3 8 SCEPTRE Representation of H Parameter Model measurement These models are all alike in that they are intended for operation at some particular operating point in the linear region of operation Saturation and cut off cannot be accommodated and large signal swings are subject to error As a consequence small signal equivalent circuits are not nearly as versatile as the Ebers Moll model but for some applications the user can legitimately make use of their inherent simplicity Voltage sources that are linearly dependent upon resistor voltages and current sources are handled directly If voltage sources dep
109. e referenced on the right hand side of the changed expression or in the main circuit descrip tion must include the model designation as a suffix VCC T1 J2T1 VCX is the voltage across a capacitor CX that is not in a model and therefore uses no suffix Changes in OUTPUTS The sample stored transistor model of subsection 2 3 1 called for the output of three quantities VCE VCC J1 Normally any run that uses this stored model will produce these three outputs without further instruction from the user If some other quantity in the stored model is desired as output e g J2 it must be requested under the main circuit OUTPUTS subheading e g J2T5 if the circuit designation T5 were used to call the model under the main circuit ELEMENTS subheading Output requests in the stored model may be inhibited as well If any quantity is not desired as output for a given tun e g J1 even though a stored request for that quantity exists that output may be inhibited in the statement that locates the stored model in the main circuit The proper format is 47 T1 7 8 12 MODEL 2N1734B PERM SUPPRESS J1 If it is desired to suppress more than one output the format is T1 7 8 12 MODEL 2N1734B PERM SUPPRESS Jl VCE All output associated with a stored model may be inhibited by entering T1 7 8 12 MODEL 2N1734B PERM SUPPRESS ALL The normal output routine will produce a listing of the ent
110. e responses rather than network elements This capability allows the com bination and simultaneous solution of subsystems represented in different forms It also allows SCEPTRE to handle significantly larger networks by partitioning and reduction followed by convolution Rerun Multiple case rerun based on a single master run may be carried out automatically The user supplies only the changes that apply from the master run for each repeated run Defined Parameters A special section has been created to enable the user to define quantities that may be out put other than sources or passive currents and voltages The user may enter systems of first order differential equations that may or may not have anything to do with a particular electrical network Output In addition to the conventional output format which allows all sources and passive currents and voltages at each solution increment the user may request as output any defined parameter from item 1 1 He may also select any element value step size and pass count Time is not the only independent variable for these outputs the user may select others from a fairly large list Linearly Dependent Sources Voltage and current sources that are linearly dependent on resistor voltages and currents respectively can be accommodated without computational delay This feature permits the extensive use of the family of small signal transistor equivalent circuits Subprogram Capability The user who
111. ed or the subheading card INITIAL CONDITIONS must be included followed by the IC data if the user is supplying the initial conditions A valid sequence of cards would be MODEL DESCRIP MODEL 101M ELEMENTS RBC B RC Cc RE E elon CE E JA B JB B Jl E J2 C FUNCTIONS Q1 A B Q2 A B OUTPUTS VCC VC CC CE JA JB Jl J2 CIRCUIT DESCRIPTIO Example A11 ELEMENTS EAC 1 R1 B R2 225 TION B C E R B 50 BR 2 4E9 BR 5 7E8 BR Q1 5 5E 12 8 VCC 3 2 88E BR 02 3 5E 12 17E 9 Jl R E 332 J2 RoC S986 TL BR DIODE EQUATION 60E 9 38 4 BR DIODE EQUATION 54 3E 8 38 4 C D E F G A B C D E F G C A B C E NYQUIST PLOT DEGREES RADIANS PLOT small signal AC Analysis around a circuit s DC operating point Bre Os25 D 2 25E4 1 2000 103 E 12 R3 2 3 11500 RLOAD 3 4 100 4 tal 1 El 20 TI 2 3 1 MODEL 101M OUTPUTS VR2 VR3 COMPLEX PLOT RUN CONTROLS RUN INITIAL CONDITIONS PRINT EIGENVALUES PRINT EIGENVECTORS RUN AC INITIAL FREQUENCY 1E5 FINAL FREQUENCY 1E6 NUMBER FREQUENCY STEPS 20 TYPE FREQUENCY RUN LINEAR The automatic DC operating point set up procedure results in the Init
112. ed time as accumulated on the system clock and not CPU utilization time Another type of limit is available that operates on the number of passes made by the integration routine In the absence of any instruction from the user the program imposes a limit of 20 000 passes The user may change this limit by entering INTEGRATION PASSES number Start Time Most transient problems start at time equal to zero and this entry may be omitted Otherwise the appropriate entry is START TIME number Integration Routine Four integration routines are available for use with S 360 SCEPTRE Three are explicit XPO TRAP and RUK and one is implicit Implicit is not available on 7090 94 The default option is XPO and therefore this method is used unless one of the others is specifically requested When one of the others is desired the format is INTEGRATION ROUTINE TRAP 26 Quantity Default Information STOP TIME COMPUTER TIME LIMIT MAXIMUM INTEGRATION PASSES START TIME INTEGRATION ROUTINE MINIMUM STEP SIZE MAXIMUM STEP SIZE STARTING STEP SIZE MINIMUM ABSOLUTE ERROR MAXIMUM ABSOLUTE ERROR MINIMUM RELATIVE ERROR MAXIMUM RELATIVE ERROR Mode of Analysis NEWTON RAPHSON PASS LIMIT RELATIVE CONVERGENCE ABSOLUTE CONVERGENCE MAXIMUM PRINT POINTS COMPUTER SAVE INTERVAL VECTOR EQUATIONS XPLOT DIMENSION YPLOT DIMENSION TYPE FREQUENCY RUN NUMBER FREQUENCY STEPS COMPRESSION COUNT RUN MONTE CARLO j IN
113. ed with the collector junction Diffusion capacitance associated with the collector junction Junction capacitance associated with the emitter junction Diffusion capacitance associated with the emitter junction Base emitter saturation current with base collector open circuited Base collector saturation current with base emitter open circuited Base emitter saturation current with base collector short circuited Base collector saturation current with base emitter short circuited 72 17 fig E Figure 3 6 Alternate Ebers Moll Representation O Slope of In Ipe versus Vic Coe Constant of base emitter junction capacitance equation Coc Constant of base collector junction capacitance equation Ne Exponent of base emitter junction capacitance equation Ne Exponent of base collector junction capacitance equation Te Minority carrier transit time Ts Storage time constant Voe Built in potential in base emitter junction Voc Built in potential in base collector junction An alternative form of the Ebers Moll equivalent may be used as in figure 3 6 The effects of bulk resistors RB and RC have been incorporated into the representations for J1 the base emitter junction and J2 the base collector junction respectively The current generators themselves are represented by tabular data obtained by laboratory measurement Both versions of the basic equivalent circuit contain approximations of one form or another and others may b
114. ee transfer function of interest The process is simple and need be done only once An example of the storage procedure for a general second order transfer function will be given This model will then be called for use as a specific second order function Consider permanent storage of the following with m 2 n 2 F2 s on ans T Q15 T 00 7 bos icine bis T bo The required cards are ODEL DESCRIPTION MODEL 2ORDER PERM A B C D ELE ENTS JI A B 0 E0 D C X1 PA2 DP2 PA1 P2 PAO P1 DEFINED PARAMETERS DP2 X2 VJI PB1 P2 PBO P1 PB2 DP1 X3 P2 PAO 0 PAL 0 PA2 0 PBO 0 PB1 0 PB2 0 P1 0 P2 0 TA higher order model could be stored and degenerated to one of the desired order by proper manipulation of Defined Parameters The method suggested here uses less computer solution time fewer Defined Parameters and is less complicated 107 Here the Defined Parameters are named as PAO PBO to correspond with coefficients ap bp Pl and P2 serve as the dependent variables of the two differential equations The model is general in that any of the coefficients can be changed when the model is called from the originally assigned zero values It should be noted that even though this model is stored with provision for the case m n this will not be the case actually used unless parameter PA2 is made non zero in the model ca
115. egarding the collector capacitance is not substantially different as 3 4 becomes Co e GC pes O Voe Voc O Ts Ire Ics 3 6 In SCEPTRE language the total emitter capacitance may be entered as CE B X EQUATION 1 K1 K2 VCE K3 K4 JE K5 and EQUATION 1 A B C D ti F G A B C D E F G where the constants have been chosen as Kl Co K2 V e K3 ne K4 0 Te K5 los If JE is in a tabular form that insures JE gt 0 only or if the user is confident that his application cannot cause a negative capacitance a reasonable simplification permits the entry CE B X EQUATION 2 Kl K2 VCE K3 K4 J Gl and EQUATION 2 A B C D ira F A B C D E F A popularly used approximation is to consider that the junction component of capacitance is constant at some value K6 Then EQUATION 2 simplifies to CE B X EQUATION 3 K6 K4 J Gl EQUATION 3 A B C A B C Another approximation that is often made is to enter RBB as a constant resistor when it really is a nonlinear function of emitter current If the user desires a greater degree of sophistication in his model any of the above constants K1 K6 may be entered as a variable quantity in equation or tabular form The situation for the total collector capacitance is entirely analogous The following examples illustrate suggested NPN and PNP tr
116. ements 90 4 12 Convolution Representation Using Parallel Admittance Elements 91 4 13 Convolution Sample Problem Reference Schematic o o e 92 4 14 Convolution Reference Example Output e 93 4 15 Convolution Example Impedance Model Schematic o o e 93 4 16 Convolution Sample Problem Output 0000000 94 4 17 Monte Carlo Example Outputs 0 000000 0000000000005 96 4 18 Sensitivity Example Output 2 2 ee ee 98 4 19 Worst Case Example Outputs ee 100 4 20 Optimization Example Outputs ee 102 4 21 Schematic AC Example Equivalent Circuit o e e 103 4 22 A Transfer Function Block and the Equivalent SCEPTRE Representation 107 Az Voltage Source Loop lo o o a a la Pde ee 109 A 2 Current Source Cut Sets toi SG ee ER a de a 110 A 3 Voltage Source Inductor Loop 2 2 0 00000 bee ee 110 A 4 Current Source Capacitor Cut Sets e 111 A 5 Composite Plot Example 116 A 6 Circuit to Illustrate a Nodal Listing ee 117 A 7 Nodal Listing requested by LIST NODE MAP e 118 A 8 Network to Illustrate Differential Equation Identification oo 119 A 9 Separation of Linear and Non Linear Sub Networks 2 o o e e 121 A LOsImpedance Model tay ia s ee hes Be a A e ia E
117. en these functions are referenced by an EQUATION all variables that appear as the arguments of operational functions must be given in terms of dummy variables Mathematical definitions are not limited to 72 characters one card and may be continued on subsequent cards using as many as necessary Double precision entry names for FORTRAN subprogram functions must be used Thus the first character for each entry name of any FORTRAN library subprogram must be D as DLOG or DSIN Consult IBM System 360 FOR TRAN IV Library Subprograms FORM C28 6596 for available functions User written FORTRAN subprogram functions must be typed double precision For AC calculations complex defined parameters see subsection 2 2 3 may be entered using equations if desired In this event the argument list may contain both real and complex valued terms The complex entries are indicated 23 Function Real Arguments Complex Arguments Square root DSQRT ZSQRT Sine DSIN ZSIN Cosine DCOS ZCOS Exponential DEXP ZEXP Arctangent DATAN Absolute value DABS DZABS Natural logarithm DLOG ZLOG Common logarithm DLOG10 Each symbol is followed by an argument in parenthesis Trigonometric functions require the argument in radians Table 2 3 Functions of Real and Complex Arguments by the prefix E J V or I only No argument of any equation may use the prefix W Therefore in order to correctly distinguish between real and complex ar
118. endent upon resistor currents or current sources dependent upon resistor voltages are desired the user must make the appropriate conversion first A low frequency H parameter equivalent circuit is shown in figure 3 7 and its SCEPTRE representation and sample listing follow in figure 3 8 ELEMENTS RI B X 0 5 EA E X 0 0005 VR2 JB C E 50 IR1 R2 C E 1000 This discussion has emphasized diode and transistor equivalent circuits because they are by far the most common active elements that occur in practical circuit analysis today The experienced user should have no trouble using the flexibility of SCEPTRE to develop and use practical equivalent circuits for other devices However it is the user s responsibility to choose the proper equivalent circuit and the correct parameter values no matter what device is used 74 primary photo current AA 20 fig 50 TIME ns Figure 3 9 Voltage Dependent Primary Photo current 3 4 Insertion of basic radiation effects Probably the most basic radiation effect that must be simulated is the flow of charge across semiconductor junctions primary photo current that occurs in certain gamma rate environments The simplest way to do this is to insert a time dependent current generator in parallel with the equivalent circuit of the junction In the case of the diode equivalent circuit of figure 3 2 this current generator would normally be directed from
119. erconnecting lines The intent is to represent the large linear sub networks across this set of interconnecting lines Only a small number of interconnecting lines is permitted because the number of combinations C necessary to characterize the interaction between N lines referenced to but excluding the datum line is given by C N N 1 2 Thus for example a 12 line interface would need 12 x 13 156 elements at two elements per combination for the interface leaving approximately one half for the remaining non linear circuitry assuming a maximum of 300 elements Large Network 2 4 4 SCEPTRE time 10 10 elements frequency domain analysis domain analysis moderate size non large linear linear network 300 O network 2 04 elements including O 10 10 interface elements O elements 2 12 lines 6 156 elements interface F 1 fig Figure A 9 Separation of Linear and Non Linear Sub Networks A 8 4 Integration routine In general the convolution integral for continuous functions is given by t R t fae T F r dr where F T 0 forr lt 0 A 3 0 For a given t and a given subdivision of the 7 axis defined by To 0 lt T lt Ty 1 lt Ty t A 4 121 the integral in equation A 3 becomes N 1 Tipi Rt X Si where S i H t T F r dr A 5 i 0 T We assume the H and F functions are given in tabular form and that the data points are correct at
120. ers as possible to represent individual elements in stored models because the program must combine the element name with the circuit designation given under ELEMENTS but not with the model name If the above stored model is used in a network designated T11 the program must refer to the base emitter capacitance as CET11 In this case the maximum number of five alphanumeric characters has been used for a given element If either the circuit designation or the element name contained more characters the run would be aborted This consideration is independent of the model name Temporary Storage Each model intended for temporary storage must be described element by element under MODEL DESCRIPTION in the run in which it is to be used The words INITIAL and PRINT are never used on the MODEL DESCRIPTION card for temporary storage The rest of the entry format is the same as for permanent storage except the word TEMP MODEL name TEMP node node node or MODEL name node node node If neither TEMP or PERM is used the program will automatically assume temporary storage After the model is stored the circuit designation format in the main program for temporary models differs slightly from the format used for permanent models Where a permanently stored model is designated as T1 7 8 9 MODEL X476900 PERM a temporarily stored model could be designated as T1 7 8 9 MODEL X476900 TEMP or T1 7 8 9 MODEL X
121. f converting the general polynomial function of the complex variables given in equation 4 1 into a form that is compatible with the mathematical formulation of SCEPTRE see 2 If from equation 4 1 we define a apei E s E s Y bjs 4 2 i s bjsi 5 0 j 0 and a 3 aif E s E s 2 ajs 4 3 then the inverse transforms of equations 4 2 and 4 3 yield respectively eilt bne t bniet 07D bilt boelt 4 4 and o t ame t amiet MD ar t agelt 4 5 where the notation e t is used to represent the nth derivative of e t the general voltage variable 2This case may sometimes lead to computational delay 3Provided that the initial values of e t and all its derivatives are zero 105 The next step must be to properly simulate the operations given in Equations 4 4 and 4 5 within the framework of the SCEPTRE input language Simulation of equation 4 5 implies an output voltage source which is equal to a combination oTf derivatives The highest of these derivatives are obtained by a transposition of equation 4 4 which yields e t es t do _ Dr t boe t 4 6 Once the highest derivative is known all others may be obtained by successive integration Conversion of the mathematical operations inherent in equations 4 5 and 4 6 to SCEPTRE language requires recourse to the Defined Parameter feature of the program If the nodes of the four
122. fined parameter in a stored model can be changed to a constant table or equation see subsection 2 3 3 Multiple Changes When several different types of changes are desired the change statements described in 2 3 3 through 2 3 3 are separated by commas The overall change statement is enclosed in one set of parentheses For example Tl 7 8 12 MODEL 2N1741B PERM CHANGE CC 50 CE 30 SUPPRESS ALL PRINT 48 2 3 4 Initial conditions for a stored model Users should not store initial conditions with stored models since that would make the model circuit dependent To supply a set of initial conditions for a stored model the user need only supply entries of the form VC2T6 number for a circuit designation of T6 for the stored model These entries would be made under the INITIAL CONDI TIONS subheading of the main circuit 2 3 5 Model deletion An entire model may be removed from the user s permanent model library tape This can be done with an entry under MODEL DESCRIPTION of the following form MODEL 2N367A DELETE 2 4 RERUN feature The rerun feature will permit the user to run multiple versions of a master run which differ from the master in one or more ways The user need supply only the quantities that have been changed from the master run An unlimited number of reruns may be made from a single master run but each rerun will require approximately as much computer solution ti
123. ge described herein is used to convey all the necessary information to the SCEPTRE program The user is not required to write the network equations or to possess a knowledge of computer programming This Section describes the preparation of circuits and the circuit description language recognized by SCEPTRE 2 1 Circuit preparation The first step taken in using the SCEPTRE program is to prepare an equivalent circuit drawing of the circuit to be analyzed The equivalent circuit may consist of resistors capacitors inductors mutual inductance voltage sources and current sources and or stored models containing these elements All of these elements may be linear and or nonlinear Furthermore most equivalent circuits composed of these elements can be accommodated This allows the use of either standard or complex experimental equivalent circuits The value or behavior of any equivalent circuit element may be defined by a numerical constant tabular list or mathematical expression After the equivalent circuit has been drawn each node is given an arbitrary alphanumeric designation consisting of six characters or less A node is defined as the point of common potential voltage at the junction created by the connection of two or more network elements Next each component or element in the circuit is given a unique name consisting of not more than five alphanu meric characters The first character of each element name must be R C L E or J corre
124. gth of the table containing the Impulse Response Time Waveform Integer using format 110 This is the number of point pairs used to define the function 5 The Impulse Response Time Waveform Table in negative time format 2G20 8 The following describes this requirement in more detail The impulse response function f t for 0 lt t lt TMAX must be representable by a number N of point pairs designated LENGTH as in item 4 above but this is not the form in which it is to appear on the disk Consider the information as being initially in the form T 1 0 F 1 0 HZERO If we now define this casual function for negative time as f t f t then the desired information to be stored on Disk 12 pair wise is the negative time and its associated function value f t i e the original function after a symmetrical rotation about the t 0 axis This data is to be stored beginning with the MOST NEGATIVE time TAU 1 TMAX and increasing until TAU N 0 Thus Disk 9 would contain TAU 1 TMAX lst entry H 1 TMAX 2nd entry TAU N 0 H N 0 HZERO last entry The second step required is the insertion of a card into SCEPTRE S 360 PROGRAM CONTROL DECK see figure referencing the newly created Impulse Response Data Set The appropriate card entry is GO FT12F001 DD DSNAME name DISP OLD KEEP where name is up to eight alphanumeric characters The correct place for insertion is between
125. guments internally the letter Z has been reserved as the prefix to indicate all complex valued dummy arguments For example Under DEFINED PARAMETERS W 01 3 VR2 P3 Tl 113 and VR2 and the IL3 would denote complex valued arguments Then under FUNCTIONS Q1 A Z1 B C 22 mathematical expression where the dummy arguments Z1 and Z2 are used in place of VR2 and IL3 respectively Tabular Definition Sequence Every TABLE name that has been referenced under ELEMENTS or DEFINED PARAMETERS must be explicitly defined under the FUNCTIONS subheading The general format is TABLE name number number number or DIODE TABLE name number number number Acceptable variations of this format are shown in the examples following figure 2 5 Note that the designations TABLE 1 and DIODE TABLE 1 refer to the same table therefore these may not be used to name two different tables in any run The tabular data itself is represented by a series of numbers in pairs separated by commas in which the number representing the independent variable point comes first with the dependent variable point following Note that as figure 2 5 suggests any number of point pairs can be supplied per card The data pair points must be supplied such that the independent variable is in increasing algebraic order No specific limit to the number of point 24 ABLE ERIN value 4 ol i TIME 2
126. he control RUN WORST CAS Gl is used the nominal values are restored to the tables at the conclusion of the Worst Case calculation The Optimization process will be run if the Run Control OPTIMIZATION integer appears and if the appropriate entries are made under the OPTIMIZATION subheading see subsection 2 2 8 The integer which appears after the equal sign indicates the maximum number of optimization iterations which will be allowed for any objective function If the number is omitted thirty iterations will be allowed Since Optimization can be a time consuming process and may in fact fail if the network has pathological behavior additional Run Controls have been provided to assist the user If the card LIST OPTIMIZATION DETAILS is used auxiliary intermediate results will be provided to the user If he supplies the Run Control PUNCH OPTIMIZATION RESULTS the most recently updated values of the approximate inverse Hessian matrix see 2 subsection 2 4 5 of the gradient vector and of other parameters will be punched out Thus if the user wishes to limit the number of Optimization iterations until he examines the progress of the process he can save the intermediate results for use in reinitializing at a later run To be utilized these punched values must be provided as data cards in the SCEPTRE deck see Section and the card format INITIAL H MATRIX FACTOR 0 must be included among the Run Control
127. he prompt component while delayed components are included under the summation The prompt component and one or two delayed components are sufficient for most applications as illustrated in the following example Figure 3 10 and the following SCEPTRE entries can be used to determine the effects of the prompt component of a high intensity pulse of nuclear radiation on a tantalum oxide capacitor SCEPTRE entries under ELEMENTS l1 gt Transient Radiation Effects on Electronics Handbook DASA 14209 July 1966 Battelle Memorial Institute Columbus Ohio 76 5 C1 pF JP mA VC1 V C1 JP KP 5x10 R D t R s TABLE 1 D t vs TIME 6 TIME ns 21 fig Figure 3 10 Capacitor Radiation Equivalent Circuit JP 5 6 EQUATION 1 C1 VC1 5 E 7 TABLE 1 TIME lt under FUNCTIONS EQUATION 1 A B C D A B C D 1 E 9 TABLE 1 The point pairs describing the gamma exposure rate R sec versus time The factor 1 E 9 converts TABLE 1 D R sec to D R nsec to obtain a consistent set of units A second current generator JP1 for the first delayed component could be added in parallel with JP Using F1 t as the solution to the integral portion of equation 3 7 for the first delayed component F1 t may be obtained by solving the following differential equation F1 t F1 t rd D t with F1 0 0 3 8 using DEFINED PARAMETERS Fi t PF1 Fi t DPF1 td 09 10 ns Ka 4 107 Rms Ad
128. he user is uncertain as to how long the transient forcing functions should be delayed Another difficulty was imposed by the fact that sometimes small network time constants that had absolutely nothing to do with the final value of the initial conditions could cause an increase in integration steps and hence computer solution time The new procedure completely obviates these disadvantages To implement an effective method designed for this type of computation the following considerations had to be resolved The Solution Medium Implicit integration will automatically be selected regardless of the type of integration that will be used for the true transient problem that may remain after the DC steady state is obtained This will eliminate the time constant problem that often occurs in many practical problems Pseudo TIME will be used as the running variable for the integration routine but it will have no relation to any aspect of the associated transient run Maximum Minimum and Starting Step Size These controls must be preprogrammed since they will not in general have a connection with any STOP TIME that the user may supply The preprogrammed quantities are MINIMUM STEP SIZE 0 MAXIMUM STEP SIZE 1E74 STARTING STEP SIZE 1E 8 Transient Forcing Function All forcing functions will be automatically checked and held constant at their start time values 111 Termination Since i
129. hic characters are used to represent each quantity Use of this feature requires that all of the quantities which are to be plotted together may be requested on the same card or sequence of cards under OUTPUTS followed by a specific plot name For example OUTPUTS VC1 VC2 P13 PLOT VR11 VCET1 JET6 IE4 PLOT 1 In this case quantities VC1 VC2 and P13 would be plotted singly as usual Quantities VR11 VCET1 JET6 and IE4 would be plotted together since they have been requested together with a plot that has been named simply as 1 Any plot name may include up to six alphanumeric characters and more than one name may be used to plot different combinations of quantities The composite plot feature also requires a PLOT INTERVAL entry under RUN CONTROLS While this is a RUN CONTROL entry it is discussed here because it relates only to composite plots and its omission will cause the requested plots to appear in their usual separate formats The physical length of any composite plot may be controlled The number of pages encompassed by the abscissa independent variable is determined by the problem duration STOP TIME and a user supplied entry called PLOT INTERVAL The former divided by the latter will determine the number of lines required which will in turn determine the number of pages required For the system S 360 66 lines will fill one page Therefore a problem duration of 1000 and a PLOT INTERVAL of 5 will require 1000
130. ial Condition program SIMIC being written and executed This is followed by one pass through the transient program SIMTR in order to deterinine the values of any elements or outputs that may be dependent on the initial conditions Then the AC analysis proceeds using fixed resistor values representing the DC operating points instead of the original CLASS J9 diode sources The user will receive a listing of these various DC results as follows OUTPUTS BEFORE AC RUN vcecTl 1 3023927E 01 VCET1 3 6223429E 01 CETT 2 3449600E 12 CET1 1 1243506E 09 JAT1 1 8027600E 07 JBT1 6 5009336E 02 J1T1 6 5932389E 02 J2T1 5 4300000E 07 VR2 4 0836859E 01 VR3 1 2977793E 01 J9 SOURCE J1T1 IS REPLACED BY RESISTOR 0 3949750 J9 SOURCE J2T1 IS REPLACED BY RESISTOR 0 2400000E 13 LSNEW COMPLEX EIGENVALUES E REAL IMAGINARY MAGNITUDE 1 0 65292E 10 0 00000E 00 0 65292E 10 2 0 33353E 08 0 00000E 00 0 33353E 08 ATRACE 0 6562516388467601E 10 EIGENVALUE SUM 0 6562516388467599E 10 0 0000000000000000E 00 WHEN COMPARING A S WITH S LAMBDA THE WORST ERROR OBTAINED WAS 0 19073E 05 0 00000E 00 WHEN MULTIPLYING MODAL MATRIX BY INVERSE MODAL MATRIX WORST ERROR IN DIAGONAL TERM WAS 0 00000E 00 0 00000E 00 WORST ERROR IN OFF DIAGONAL TERM WAS 0 00000E 00 0 00000E 00 SINEW MODAL MATRIX S 1 2 1 1 0000E 00 0 0000E 00 9 9999E 01 0 0000E 00 2 2 0843E 03 0 0000E 00 3 9932E 03 0 0000E 00 SINEW INVERSE MODAL MATRIX SI 1 2
131. imum values of the indepen dent variables must be specified In all cases the element information is provided by bounds added in parentheses after the element values Except as noted at the end of this paragraph bounds are provided by statements under ELEMENTS of the form element name none nod number number number or element name node nod number number The first form gives two numbers in parentheses SCEPTRE reads the smaller number as the lower bound and the larger as the upper bound The second form has one number in parentheses In this form SCEPTRE reads the number as the percentage variation allowed in the nominal value of the elements Examples might be R2 NZ N5 12 11 13 and R1 N1 NB 6 10 13 The first example specifies the nominal value of R2 as 12 with lower and upper bounds of 11 and 13 respectively The second example specifies that the value of R1 is 6 10 For Worst Case and Optimization the lower and upper bounds are taken to be the limiting values for the element For these calculations the nominal value must lie within these limits For Monte Carlo calculations the element distribution mean and standard deviation are computed from the lower and upper bounds as upper bound lower bound mean 5 upper bound lower bound standard deviation 6 The exception mentioned above to the use of numbers exclusively in specifying elements with bounds is as follows Examples w
132. in terms of the symbols defined previously are subsequently detailed 2 2 2 Elements This subsection covers the formats required for entering element data into SCEPTRE The general discussion pertaining to all elements is followed by four subsections discussing special conditions which pertain to certain element entries These subsections cover mutual inductance subsection 2 2 2 source derivatives subsection 2 2 2 elements with bounds subsection 2 2 2 and AC complex sources subsection 2 2 2 All elements resistances capacitances inductances including mutual voltage and current sources source deriva tives and model circuit designations that are to be component parts of the network under analysis must be in troduced under this subheading Entries allowed under the elements subheading are summarized in table 2 2 Although any combination of alphanumeric characters maximum 4 can be used for model circuit designations names unique from other element names are recommended Alphanumeric character lengths are listed in table 2 10 subsection 2 2 9 The general form for entries under the ELEMENTS subheading is element name node nod valu Each network element is defined by stating the element name the nodes between which the branch is connected and the component value The connection nodes are specified in a from to order corresponding to the assumed direction of current flow The actual tabular values or analytical expressions
133. inal model storage ee 46 2 3 3 Changes to a stored model 0 20 0000 00 0000000 47 2 3 4 Initial conditions for a stored model o o a 49 DID Model deletion cmo a e ee RN ee AA 49 2 4 RERUN feature ron e ice dh hoe ES A tele E o ES eee A 49 ZAT General usage lt 2 cause ie de eb ae pee SRA eR Ae ba a et a 49 2 4 2 Limitations of the rerun feature 2 0 2 e 51 2 37 CONTINUE features is te ia ii bee a baw le bles E 54 25 1 General Usage oo A Pe A ee e A ba ee So aes 54 2 5 2 Limitations on the CONTINUE feature e 55 26 RE OUTPUT feature soci a A a See wea A ees 55 2 7 Subprogram capability ee a 56 2 7 1 Subprogram insertion 2 2 ee e 58 2 7 2 Subprogram With models 00 0 eee ee ee 58 2 8 Additional output andcontrol 2 2 a 58 2 8 1 SIMUL8 program data e a ge ee do ae ww eh ae Be ee ee bee 59 2 8 2 Noclementsort tcs Bad bak ab dike BE AE he eR ee R 59 2 8 3 Matrix printouts ipod Secu gee Bonet Pee See Bue Bee ge Bee 59 23 4 Nodal sins 22 3 2 4 sae ee ak Ea a bY A eS ei cee A 59 2 85 AC Matrix outputs 2 05 2244 we Se ep Ae bee e Se 8 60 2 8 6 Program Debug Output 60 2 9 Error dlapnosucs dar is aa ee SR A ce aod She a te eam da ai a 60 Equivalent circuits and associated notation 66 SL DiddeS cae s eg are A Ee Sha ee ee Pee bee SE Apes 66 3 2 Transistors large signal equivalent 2 2
134. ird step would be output No attempt is made to space the print increments if it happens that many steps are taken in the first half of a run and comparatively few in the last half the printed output will be spaced accordingly In most cases this is desirable and the basic format was chosen for that reason In some situations a different format can be attractive and has been made available The objective of the optional Specified Print Interval feature is to enable the user to precisely control the number of printed output points and to allow them to be more selectively chosen The user may supply the time interval at which print points are desired and only those solution points that fall on or immediately after integer multiples of the specified interval will be printed Assume for example that a transient problem is run to a STOP TIME 800 and that the first few solution points are at the following times 0 2 4 6 8 10 14 18 22 Assume also that 114 the user has specified a print interval of 10 In that case printed output would appear at times 0 10 22 and the number of print points would equal STOP TIME divided by PRINT INTERVAL 80 in addition to the one at time 0 The only situation in which the number of output print points would differ from the above relation is the rather uncommon situation in which the specified print interval is smaller than the step sizes actually taken This feature is optional and is activa
135. ire circuit without a detailed printout of any stored models The proper language for a detailed printout of any stored model is T1 7 8 12 2N1734B PERM PRINT Changes in FUNCTIONS This subsection describes the manner in which data listed under FUNCTIONS i e tables and equations in a stored model may be changed A table in a stored model may be changed by the entry Tl 7 8 12 MODEL 2N1741B PERM CHANGE TABLE 1 TABLE 7 which replaces TABLE 1 of the stored model with TABLE 7 TABLE 7 must be supplied under FUNCTIONS of the main circuit No correlation is required between the number of point pairs contained in the original table and the point pairs in the new table It is never possible to directly change DIODE TABLE X DIODE TABLE Y The same effect can be achieved by changing the element as in subsection 2 3 3 An equation in a stored model may be changed by the entry T1 7 8 12 MODEL 2N1741B PERM CHANGE Q1 Q2 which replaces the original EQUATION 1 of the stored model with EQUATION 2 EQUATION 2 must be supplied under FUNCTIONS of the main circuit The only special stipulation is that the same independent variables that held for the original equation must also apply to the new equation It is never possible to directly change an equation in a stored model to a table or a table in a stored model to an equation CHANGE EQUATION 1 TABLE 1 not allowed However an element or a de
136. is valid only if the junction is reverse biased To avoid this problem use instead two capacitors in parallel Cj which models the first term in the equation can be given either as a constant or as a table which will be a better representation of the semiconductor physics The second capacitor Cp K Ip Is should be given by an equivalent equation to avoid unnecessary computation Cp K Is e9 Y 1 Is KIge A 9 15 Rerun Under RERUN DESCRIPTION it is not possible to change a constant to a table or equation This can be done however by specifying the constant as a table or equation in the master run which can be changed to a different table or equation in reruns 131 Bibliography 1 D Becker Extended SCEPTRE Vol 1 User s Manual AFWL TR 73 75 NTIS ADA 009594 2 D Becker Extended SCEPTRE Vol 2 Mathematical Formulation AFWL TR 73 75 NTIS ADA 009595 3 J C Bowers S R Sedore SCEPTRE A Computer Program for Circuit and System Analysis Englewood Cliffs N J Prentice Hall Inc 1971 4 R W Jensen M D Lieberman IBM Electronic Circuit Analysis Program Techniques and Applications Englewood Cliffs N J Prentice Hall Inc 1968 5 Advanced Statistical Analysis Program ASTAP General Information Manual IBM GH20 1271 0 6 R W Jensen L P McNamee Handbook of Circuit Analysis Languages and Techniques Englewood Cliffs N J Prentice Hall Inc 1976 7 James C Bowers
137. ist of up to five al phanumeric characters The argument list may consist of any VARIABLE CONSTANT and TABLE and 1ts independent variable For example EQUATION 39 VCX J2 TIME TABLE 2 VC7 EXPRESSION Name Math Definition This form is an alternative to EQUATION entry that may be used to describe a variable quantity It is somewhat more complex than the EQUATION form but it has the virtue of needing no further description under FUNCTIONS The expression must be given a name prefixed by EXPRESSION or simply X and followed by the mathematical definition The EXPRESSION name may consist of up to five alphanumeric characters It is suggested that numerical designation be used to avoid any possible confusion with some internal parameters For example X14 10 SIN 628 TIME Any equation for table must be defined more completely under FUNCTIONS More detail is given in subsections 2 2 2 and 2 2 6 The input data deck describing a network is formed simply by punching the heading card and the associated data sequence for each of the defined data groups Remarks such as title user name and date may be supplied for output identification purposes by punching the desired remarks on cards following the CIRCUIT DESCRIPTION card and preceding the first subheading card The number of comment cards must not exceed 11 and the entire remark will appear as the title of the output listing and plots The sequence for each of the subheadings
138. ith bounds may be specified as values or diode equations if the values or diode equations are expressed in terms of defined parameters with bounds under DEFINED PARAMETERS Subsection 2 2 3 describes the allowable format for defined parameters with bounds An example of an entry under ELEMENTS is R3 N12 N10 X3 P3 P4 AC Sources Source voltages and currents for AC calculations are complex numbers and therefore require both real and imag inary parts or magnitude and phase for their definition The format for entering an AC source is Ename node node entry entry type for a voltage source and Jname node node entry entry type for a current source The word entered for type identifies the meaning of the two entries in the parentheses Type may be either DEGREES RADIANS or COMPLEX If DEGREES or RADIANS is entered the first entry in parentheses is the magnitude in the polar coordinate expression of the voltage or current and the second entry is phase angle If type is specified as COMPLEX the first entry in the parentheses is the real portion of the complex expression in cartesian coordinates and the second entry is the imaginary portion Type need not be specified If it is not the default value is DEGREES An entry as described above may be any of the following constant the problem frequency denoted by FREQ a TABLE name where the independent variables must be stated because the default va
139. late the run and define the storage required and two are associated with the optional CMPAC routine which provides in process smoothing of the calculated results with attendant saving of storage space The first two Run Controls allocate internal core storage for the two functions associated with the Convolution process These Run Controls are IMPULSE RESPONSE BUFFER number and 2Use of Convolution requires that the RUK integration routine be specified RUK is not the default integration mode See subsection 2 2 7 36 INPUT FUNCTION BUFFER number where number in the first instance is the average number of storage points required per impulse response function and in the second is the number of points required to store each corresponding kernel s input function The input functions are SCEPTRE generated and an equal number of storage spaces must be set aside for each If the allocated storage space is exceeded the run will terminate The other two Convolution Run Controls are optional They call and control the internal compression routine Without CMPAC the user must anticipate the number of steps the program might take and then allocate enough storage space via the INPUT FUNCTION BUFFER mechanism This approach obviously makes increasing de mands on storage as either the number of convolution kernels or the number of desired integration steps increases The CMPAC routine reduces the total core sto
140. ll Now that the model has been stored in general second order form the desired coefficients needed to represent a specific second order transfer function can be supplied when the model is called out for use under CIRCUIT DESCRIPTION If it desired to simulate E s 10s 4 Ej s s24 78 5 G2 1 2 7 8 MODEL 20RDER PERM CHANGE PAO PA1 10 PBO 5 PB1 0 7 4 PB2 1 The same model could be called repeatedly to represent many second order transfer functions with arbitrary coeffi cients The procedure is even simpler to simulate ideal amplifiers summing junctions and limit functions see 3 The ability of SCEPTRE to perform these operations now qualify it as a tool for systems analysis When one con bines this with its unmatched capability for nonlinear circuit analysis its potential for the solution of large systems that can be broken down into non linear circuitry and linear subsystems becomes clear 108 A Appendices A 1 Topological restrictions on SCEPTRE The purpose of this section is to illustrate circuit topologies that cannot be accommodated by SCEPTRE Most of these Situation are not generally encountered and those that are may readily be remedied by the user In general the transient portion of the program is more versatile than the default Newton Raphson method of computing initial condition solutions In other words there are some circuit configurations th
141. lue of the independent variable is TIME and the AC calculation takes time as zero or a real defined Parameter The maximum allowed number of independent AC sources is fifty The maximum number allowed for linearly dependent AC sources plus secondary dependent AC current sources is also fifty The following are examples of AC source definitions El N1 M3 12 4 COMPLEX means that voltage source El between nodes N1 and M3 is expressed in complex form as 12 4j volts J7 N4 N7 T1 FREQ P6 RADIANS means that current J7 between nodes N4 and N7 is expressed in polar coordinates where the magnitude is a function of frequency to be obtained from Table 1 and the phase angle in radians is as specified by P6 under DEFINED PARAMETERS 14 2 2 3 Defined parameters Any variable that can be described in terms of any network variable and or any Number may be defined and this quantity may be used as an ELEMENT value an argument in an equation or table or an output at each time step of the problem in the same manner as any conventional output Examples of the use of this feature are given in Section 4 More than one defined parameter may be entered on a card if they are separated by commas Real Valued Defined Parameters The input format for real valued defined parameters requires that the first letter be P followed by no more than five alphanumeric characters The general form for entries under DEFINED PARAMETER IS
142. ly compute a starting step equal to 1 x 1073 for explicit 1 x 1078 for implicit times the problem duration STOP TIME If a specific starting step size independent of the problem duration is desired the format is STARTING STEP SIZE number Error Criteria Unless otherwise specified any of the three explicit integration routines will operate with preset relative error criteria If it is desired to modify these criteria the proper formats would be MINIMUM ABSOLUTE ERROR number MAXIMUM ABSOLUTE ERROR number MINIMUM RELATIVE ERROR number MAXIMUM RELATIVE ERROR number The only error criterion that pertains to implicit integration is MINIMUM ABSOLUTE ERROR The SCEPTRE integration routines are described in detail in 2 Mode of Analysis SCEPTRE can compute DC AC or transient solutions only or certain combinations of these The combinations are DC with AC and DC with transient Runs combining AC with transient cannot be made The default mode of analysis is the transient run that is unless otherwise specified by the user only the transient solution will be computed The transient solution can be run with or without convolution see Appendix A 8 SCEPTRE offers five DC solution modes Initial Conditions Sensitivity Monte Carlo Worst Case and Opti mization Any of the five may be used alone or as a source of initial conditions data for a Transient or AC run Alternatively
143. me DJ value see subsection 2 2 2 Model Calls see subsection 2 3 name see note 7 nodel node2 MODEL name Elements with Bounds see subsection 2 2 2 G H W numberl number2 number3 ic pede node numberl number2 AC sources see subsection 2 2 2 entry entry t E name nodel node2 font any DEGREES J entry entry RADIANS entry entry COMPLEX Concolution Model Calls see note 10 K name nodel node2 gt FCONVE constant see note 11 FCONVJ constant f Jname is a primary dependent current source t entry constant defined parameter TABLI E name FREQ Table 2 2 Entries under ELEMENTS All C R L and M entries will be treated as REAL 8 constants in the AC calculations Before making the AC calculations SCEPTRE will evaluate any entries which are given as functions For example a capacitor may be a function of voltage and a resistor may be a function of time SCEPTRE will evaluate these functions at TIME 0 using supplied or calculated initial conditions The appropriate values so obtained will be used in the AC calculations Elements as a function of frequency are not permitted in AC calculations All voltage and current sources which are given as constants DC sources or as functions of TIME Transient sources will be given a value of zero in AC calculations a
144. me as did the master Each individual rerun will utilize all information from the master run except that which is specifically modified for that particular rerun Any intermediate reruns that may have been made will have no effect on a subsequent rerun Also see Appendix A 3 subsections A 3 2 and A 3 3 for special uses of the rerun feature 2 4 1 General usage As indicated in the general sequence the RERUN DESCRIPTION section follows the RUN CONTROLS sec tion of the main circuit description The RERUN DESCRIPTION card is followed by any of the five possible subheadings that are listed The format of the card is RERUN DESCRIPTION N where N is the number of reruns desired The N designation may be omitted if just one rerun is desired The user may not describe the values of more than one variable on the same card anywhere in the RERUN DESCRIPTION section ELEMENTS under Rerun The subheading ELEMENTS is used if any constant valued element is to be changed for any of the reruns If two reruns are desired in which resistor R1 is to assume constant values 9 3 and 9 5 then under ELEMENTS Rl 9 3 9 5 regardless of the constant value R1 had in the master run 49 DEFINED PARAMETERS Under Rerun This subheading is used if any constant defined parameter is to be changed for any of the reruns If a defined parameter PX was used as constant in the master run a legal entry for rerun under DEFINED PARAMETERS would be Bo
145. me nodes 14 21 and 23 of the main circuit Internal nodes 7 and 12 become 7 T1 and 12 T1 in the main circuit because all internal nodes of stored models have appended to them the circuit designation of that model Since no node name may contain more than six alphanumeric characters the user should use as few characters as possible for the circuit designation names and internal nodes of any stored model 2 3 1 Transistor model insertion Transistors deserve special mention because of the frequency with which they occur in contemporary networks The remainder of this section given the rules by which the user may store models of his choice Permanent Storage Any three terminal transistor may be permanently stored on tape using the following format after the MODEL DESCRIPTION card MODEL name PERM B E C 8 fig a b Figure 2 6 Example of the Stored Model Feature of SCEPTRE The name may contain up to 18 alphanumeric characters and the B E C combination is used to correspond to the specific nodes connected to the base emitter and collector terminals of the transistor Following the MODEL name would be subheadings ELEMENTS DEFINED PARAMETERS OUTPUTS INITIAL CONDITIONS and FUNCTIONS as specified earlier in this report The subheading RUN CONTROLS will never appear in a stored model For the special case of the first model permanently stored on any individual tape the first card must be MODEL DESCRIPTION INITIAL The
146. n 1 Introduction 1 1 SCEPTRE capabilities SCEPTRE is a unified system of digital computer programs by which the electrical engineer can communicate with the computer to determine the DC transient or AC response of electronic circuits SCEPTRE has been programmed to include many significant and useful features Briefly these include Stored models Any active element or interconnected group of elements that can be described as a combination of sources passive elements and mutual inductance may be stored on tape by the user and called into use at any point in a network Automatic Initial Conditions The user has the option of using the DC portion of the program to determine the initial conditions of a network The DC portion allows the user to optimize the initial conditions against user established criteria to compute worst case DC solutions or solutions with randomly chosen values of variables He may then use the transient section or the AC section in the same run or just accept the output of the initial condition section for inspection The DC mode can also compute the sensitivity of a network to changes in user selected variables Any run may use the initial conditions mode only the transient mode only the AC mode only or may automatically combine initial conditions with transient or with AC Time Domain Convolution A capability has been added to help solve problems involving interfaces between black boxes presented as impuls
147. n as functions of time Therefore in order to calculate present values it was necessary that the convolution routine be written so that in the impedance mode admittance mode it uses past history of the current voltage to estimate the present value of current voltage which in turn will yield the required terminal to terminal voltage current It then updates the current and voltage tables and repeats the procedures for the next time step 120 A 8 3 Network situations for which the convolution analysis may apply The following properties characterize the networks which are good candidates for solution using the convolution mode e The number of circuit elements exceeds the maximum allowed by SCEPTRE e The circuit possesses a moderate number of non linearities something in the order of 10 to 20 devices e The circuit contains a moderate number of independent forcing functions in the order of 10 to 20 devices e The network will allow one to consider the majority of elements as a large linear sub network where the following two conditions exist see figure A 9 The remaining elements form another sub network of moderate size Moderate size means something less than the maximum allowed by SCEPTRE We assume that all of the non linearities are placed in this sub network We also assume that all of the forcing functions are placed in this sub network The two partitioned sub networks are linked together with a small number of int
148. n example of Optimization input data is OPTIMIZATION IR1 P1 R1 P2 E1 VC1 J1 R2 In this example 3For Monte Carlo Worst Case and Optimization calculations the independent variables named here must be specified with bounds under the ELEMENTS sub headings of CIRCUIT DESCRIPTION see subsection 2 2 2 39 Name Description see Table 2 2 VC IE VJ IL IR VR Voltage across a capacitor Current through an independent voltage source Value of a primary dependent current source Voltage across an independent current source Current through an inductor Current through a resistor Voltage across a resistor Defined Parameter t f For a Sensitivity Optimization or Worst Case dependent variable Pname the differential GPname must also be supplied see subsection 2 2 3 Table 2 7 Dependent variables in DC calculations Name Description see Table 2 2 UEmp Resistor Independent Voltage Source Independent Current Source Defined Parameter f t A defined Parameter independent variable can only be the factor in a secondary dependent current source definition e g JO Pname J9 See subsection 2 2 3 for the format of defined parameters with bounds Table 2 8 Independent variables in DC calculations e IR is optimized with respect to R1 P2 El e Pl is optimized with respect to R1 P2 El e VCI is optimized with respect to J1 R2 An example input for Worst Case
149. n labeled and constructed form The required entry is BTFORM 1 to obtain the matrix for the transient program The corresponding matrix for the DC program is called by BTFORM 2 A card indicating the desired option must be placed immediately after the DATA card that normally precedes MODEL DESCRIPTION or CIRCUIT DESCRIPTION S 360 only The network B matrix which gives the topological relation between all network link and tree branches is available in labeled and constructed form To obtain the matrix for the transient program and or DC program the entry PRINT B MATRIX must be placed in the RUN CONTROLS section of the SCEPTRE input data 2 8 4 Nodal listing A printed listing of each network node and the elemente incident at the node can be generated with any run See Appendix A 6 This listing is requested by LIST NODE MAP 59 2 8 5 AC matrix outputs Three Run Controls are provided to enable the interested user to obtain additional outputs relative to an AC analysis The appropriate card formats as an indication of the outputted information are as follows PRINT A MATRIX This output depends on the particular case involved See 2 subsection 2 5 for an explanation of the four cases encountered For case 1 independent sources only the output will be the system Matrices A and G For case 2 independent sources and dependent sources the output will be the system Matrices A G and H For case 3 independent source
150. nction is reverse biased Furthermore component research indicates that some transistor junctions exhibit primary photo currents that are significantly voltage de pendent even under reverse bias conditions Consider the hypothetical situation in which measurements indicate the primary photo currents of a transistor or diode in a given environment are as shown in figure 3 9 The photo current is clearly a function of the voltage across the junction as well as time One manner in which this double dependency may be represented in SCEPTRE is to define the current generator under ELEMENTS as an equation This equation multiplies two tables the first table simply represents the 20 volt curve as a function of time and the second table effectively applies a scaling factor that appropriately reduces the photo current as a function of the junction voltage The entries could be T JX 4 3 EQUATION 2 TABLE 2 TIME TABLE 3 VCC 75 FUNCTIONS TABLE 2 0 0 50 5 100 3 300 1 600 0 700 O TABLE 3 90 72 0 20 107 0 Ly y UD lp Lp 62 EQUATION 2 A B A B The second table dependence is on the capacitor voltage assuming that capacitor CC shunts the transistor junction of interest The effects of neutron environments on transistor gain may be represented in several different ways If the analyst is interested only in the steady state result of beta degradation it is only necessary to operat
151. nd a WARNING message will be printed out whenever the argument TIME is used In order to obtain an AC analysis around a circuit s DC operating points the user must either supply Initial Conditions see paragraph 2 2 5 or must enter RUN INITIAL CONDITIONS under the RUN CONTROLS subheading of CIRCUIT DESCRIPTION If initial condition are supplied then SCEPTRE determines all element values dependent on these DC voltages and currents Primary and secondary dependent current source specifications may be used to represent certain semicon ductor junctions when requesting Initial Conditions solutions By Definition this class of current source can appear only if the appropriate diode source has previously been included The secondary source must be specified only as a value times the primary source Although this entry is permitted in AC calculations a time source and hence its derivatives are not mean ingful The source will be treated as in Note 2 above and the derivatives ignored Model circuit designation names can be any combination of no more than four alphanumeric characters Names unique from other element names are recommended If the topology of the circuit dictates that a time derivative is required for a transient analysis e g capacitor and independent voltage source loop or inductor and independent current source cut set then the same is true for an AC analysis However for AC no card entry is required
152. nd execution stops This is not the case if the user has specified RUN IC VIA IMPLICIT SCEPTRE will attempt to solve the problem resulting in a long and useless run It is therefore advisable to check the circuit before using IC VIA IMPLICIT 128 A 9 6 Element sort The state variables chosen by SCEPTRE are partially dependent on the ordering of the input under ELEMENTS It is sometimes helpful in cases where SCEPTRE chooses an inconveniently small step size for a transient run to resubmit the run with a different ordering of elements This will result in a new choice of state variables which may have larger time constants To get the effect of this reordering the card NO ELEMENT SORT should be included under RUN CONTROLS Since this technique requires some experimentation it is wise to limit the duration of the run COMPUTER TIME LIMIT and try several different element orderings The best one can then be used for the complete run A 9 7 Output reduction SCEPTRE produces printed output of each variable which it plots This often results in unnecessarily large volumes of output and high charges for printing If the user requires only plotted output he should specify MAXIMUM PRINT POINTS 1 in the RUN CONTROLS section To allow a subsequent list of the out variables the run should be set up to permit a RE OUTPUT run A 9 8 Some frequent errors The user should note that output controls must be under the RU
153. ne type of plot are given as functions of frequency The Nyquist plot gives the imaginary part of a complex function vs the real part The standard forms of requests under OUTPUTS variable variable variable and or variable variable variable will produce a tabular printout of magnitude vs frequency and phase in degrees vs frequency for each variable This is the default entry The word DEGREES is optional If the output is desired in radians the proper entry is variable variable RADIANS The entry variable COMPLEX produces a printout of the real part of each variable vs frequency and the imaginary part vs frequency If the word PLOT is added to the entry Variable COMPLEX PLOT a plot of the same data is also obtained as described in subsection 2 2 4 The Nyquist plot shows the imaginary part vs the real part for each variable The proper entry for the Nyquist plot is variable variable NYQUIST PLOT In this entry only the word PLOT is optional Both the plot and the printout will appear if the word NYQUIST appears in the entry 2 2 5 Initial Conditions The complete solution of the general transient analysis problem requires that all independent initial conditions be supplied The set of all capacitor voltages and inductor currents that exist at the start of the problem are sufficient for this purpose These may be supplied by the user or computed by the program 20 L5 C11 6 fig Figu
154. node 2 toward node 1 to reflect the fact that primary photo current usually flows across a reversed biased semiconductor junction The magnitude of the current generator is often explicitly described in tabular form under FUNCTIONS The situation with regard to Transistors is analogous to diodes Both junctions of the transistor are subject to primary photo currents when exposed to appropriate gamma rate environments As a practical matter however the larger dimensions of the collector base junction with respect to the base emitter junction often permit the analyst to make the approximation of omitting the current generator across the latter junction The basic procedure is illustrated in example 4 1 where current generator JX is placed across the collector base junction of a transistor to represent primary photo current This generator is indicated as a tabular form under ELEMENTS and then explicitly described as a function of time under FUNCTIONS The procedure given in the preceding paragraph is usually quite sufficient for most purposes However it does suffer the deficiency of assuming that the primary photo current is strictly time dependent and completely indepen dent of any circuit conditions This assumption can lead to significant error if the transistor junction in question becomes forward biased during the course of the run The primary photo current that flows under these condi tions is markedly different from that which flows when the ju
155. not exceeding six characters could as well have been used to designate the plot name Any of the dependent variables could have been renamed according to the format given in Manual subsec tion 2 2 4 and the number of composite plots is restricted only by the program limit of 100 output quantities The only independent variable allowed for these plots however is TIME Use of this feature does not affect the printed output format in any way Provision has also been made to allow the user to control the physical length of any composite plot The number of pages over which the length of any of these plots are spread depends upon the problem duration STOP TIME and a user supplied quantity called PLOT INTERVAL The number of lines covered by the plot will equal the STOP TIME divided by the PLOT INTERVAL For the System 360 59 lines will fill one page Therefore a STOP TIME of 1000 and a PLOT INTERVAL of 5 will require 200 lines and lead to a plot of about four pages in length The PLOT INTERVAL entry is supplied under RUN CONTROLS and only one such entry will be recognized regardless of the number of composite plots requested The user is free to control the length of any single plotted entry by simply supplying a plot name and a PLOT INTERVAL entry 115 PX PY PZ XSTPSZ 0 000E 00 1 000E 00 2 000E 00 3 000E 00 4 000E 00 5 000E 00 6 000E 00 7 000E 00 8 000E 00 9 000E 00 1 000E 01 1 100E 01 1 200E 01 1 300E 01 1 400E 01 1 500E 01 1
156. ns will be made The Newton Raphson process will iterate to the final DC solution for the master run then do the same for each of the reruns in turn Figure 4 6 shows the results of the master run and the three reruns in tabular form There is little change between the results of the master run and the reruns because of the inherent stability of the circuit The power supplied from the input source EIN increases successively in the reruns because the reduced alpha of the first stage permits more input current 85 4 4 Example 4 USE OF SMALL SIGNAL EQUIVALENT CIRCUIT A04 Figure 4 7 Schematic of Example 4 Low Frequency h Parameter Equivalent Circuit This example is intended to illustrate the proper use of one of a class of small signal equivalent circuits with SCEP TRE Figure 4 7 shows the schematic of a two stage linear RC coupled amplifier Let it be desired to determine the response of this circuit to a low amplitude 100 kHz sinusoidal input The low frequency small signal h parameter equivalent circuit shown in figure 4 7 will be temporarily stored As is customary in the use of this type of equivalent circuit all d c power supplies will be grounded since only the a c excursion around each of the individual operating points is of interest The automatic termination feature is invoked to halt the run if the voltage across the load resistor of the second stage reaches 20 volts A valid input sequence for Example 4 would b
157. nt in AC calculations Only sources recognizable as AC sources or one of the four dependent sources described here are used in AC calculations All others are considered DC sources and set to Zero A 9 2 Proper use of dependent sources in many cases it is to the user s advantage to force his dependent sources into one of the four types recognized by SCEPTRE see A 9 1 Thus a circuit containing a source dependent on capacitor voltage specified in a straightforward manner as El N1 N2 X 3 VC1 C1 NA NB could be rewritten with a large resistor in parallel with C1 allowing the source to become a resistor dependent source 127 El N1 N2 3 VR1 CL NA NB R1 NA NB large number This technique may not be helpful if it requires a significant increase in the number of circuit elements Similarly a voltage source depending on the current through a fixed resistor El N1 N2 X1 3 IR1 R1 NA NB 2 should be specified in the following electrically equivalent form which will be recognized by SCEPTRE as a type 1 source El N1 N2 1 5 VR1 Rl NA NB 2 A 9 3 Avoiding computational delay A computational delay occurs when the specification of an element depends on a circuit variable which SCEPTRE has not yet computed at this time step The value at the previous step is used This may force a smaller step size than would otherwise be required There are two techniques for avoiding this in certain
158. nt the user from representing the diode as a current generator without the shunt capacitance in fact some low frequency applications would tempt the user to do just this The difficulty with this practice is that the current generator is voltage dependent and the voltage in question must be across some element If the current generator is dependent on a capacitor voltage the current source will be updated at the start of each solution step based on known internal state variables If however the equivalent capacitor is removed and dependence is placed on the voltage across the current source itself or some shunt resistor the current source may be updated based on the information from the previous solution increment A computational delay will have been created and significant errors can result For this reason the user is cautioned against removing the shunt capacity associated with diodes for all transient applications This consideration does not hold for the initial conditions program When the diode model figure 3 2 or 3 3 is used the user will find it more convenient to assume the reference direction for the capacitor in the same direction as the current source The reason for this is that a positive capacitor voltage will correspond to a forward bias on the diode Post run solution interpretation usually is simpler in this case This convention is not mandatory 3 2 Transistors large signal equivalent See Definition of Terms
159. of cards would be SIBJOB ALTIO NOFLOW SIBFTC FGEN FULIST DECK FUNCTION FGEN VO V1 TO TR TD TF TP Z0 TIME This feature may be used more efficiently by inserting the subprogram in compiled form The compiled deck is simply inserted behind the second IBJOB card PGMC1970 as illustrated in figure S 360 only When S 360 subprogram cards are generated they are inserted in the second half of the SCEPTRE Program Control Deck behind the card identified as PGMCO310 in figure If instead an object deck is available it is simply inserted behind the card identified as PGMC0360 This example was intended to build a General wave for input purposes The imaginative user will find other applications in the course of practical analysis which cannot be implemented through conventional input 2 7 2 Subprogram with models There is no difficulty in combining the subprogram feature with stored models The models may be stored either permanently or temporarily with appropriate reference to the user s subprograms To illustrate ODEL DESCRIPTION MODEL name PERM 1 6 4 A ELEMENTS L2 1 2 FCOR IL1 IL2 IL3 25 100 Here the user would ensure that the model includes elements L1 L2 and L3 because the currents through these elements have been used as arguments in the subprogram The subprogram itself should be supplied in either source or object form as in subsection 2 7
160. olving convolution is described in Section A 8 2 The type of non linear network which is amenable to this approach is described in section A 8 3 The theory associated with the convolution mode within SCEPTRE is given in section A 8 4 A 8 5 and A 8 6 The required impulse response functions are assumed to reside on a disk file Instructions and formats required for preparing such a file are given in section A 8 7 The circuit description preparation required for the convolution mode is also described in Table 2 2 of section 2 2 2 and in example 4 6 A 8 2 Mixed domain approach The convolution feature is an integral portion of a more general technique designed primarily to permit a transient analysis of a certain class of large non linear networks The major steps in the approach are 1 Partition the network into two parts see section A 8 3 2 Use a frequency domain program capable of solving a large linear network to determine the driving point and transfer immittance functions H w at the interface terminals 3 Find the equivalent impulse response functions h t in the time domain by using Fourier inversion 4 Model these impulse response functions as either impedances or admittances The impedance admittance model assumes that a removed portion of an existing circuit is characterized at the interface by a Thevenin voltage source Norton current source and a driving point impedance admittance 5 Describe these time domain
161. ome previous time Only three quantities are requested for plotting VR6 VL1 VL2 under the main program but in addition to these the user will get six more from the stored models VCE VCC J1 for each transistor Four instructions are included under RUN CONTROLS The first is the problem duration which must be supplied whenever the transient program is used The second is a five minute limit on the amount of computer solution time that can be expended and the third entry requests that the initial conditions be computed and then used for the start of the transient run The fourth is an increase in the maximum print points to assure that every solution point is printed out Note that a change has been made in the stored model to use a lower current gain for the second transistor The input voltage caused a conduction pulse in both transistors The conduction of the second stage caused a voltage pulse in the primary of the transformer which was reflected into the secondary as a 1 6 volt swing The transient in the secondary had almost abated by the problem duration time of 500 nanoseconds even though significant current levels remained in the two transistors The plots of the transformer primary and secondary voltages are given in figure 4 4 ODEL DESCRIPTION ODEL 2N9999AA PERM B E C ELEMENTS 81 Figure 4 3 Schematic of the transformer coupled amplifier transistor model CE B E CC
162. or more of the other program data limits Also any change which affects the total amount of data storage will necessitate a change to the program storage and therefore the program S 360 only The main storage capacity on the IBM System 360 Data Processing System is facility dependent It is recom mended that the user consult with a system programmer concerning the main storage available for problem pro grams The disseminated version of the System 360 SCEPTRE is set up for OS MVT operation and requires a 224k byte region The program data limits remain unchanged Table 2 9 gives the program data limits which have been established in the program as it is distributed These limits are considered adequate for most normal circuit analysis work Approximate limits are also given for the number of TABLE and EQUATION functions If only one half of an input card is used to write the equation specification 160 equation functions could be used Conversely if each equation specification took two full data cards only 40 equations would be allowed Defining table functions involves a similar process which considers the number of x y coordinates and the number of tables Forty tables each containing 20 point pairs or eight tables each containing 100 point pairs would be allowed The limits shown in table 2 9 are checked by SCEPTRE as the data is read into storage If any limits are exceeded a message stating the limit is produced and the computer run
163. parentheses Decimal points must always be given with all constants used in an EXPRESSION This same entry is given in equation form in subsection 2 2 6 11 2 Mutual sign 1 L2 Inductance L1 e M12 g 13 M13 L3 M23 4 fig Figure 2 2 Mutual Inductance Polarities Mutual Inductance Mutual inductance is entered according to the general format Mname Lname Lname valu If coupling exists between inductors L1 and L2 the appropriate entry must include these elements in place of the node identification as MX L1 L2 TABLE 1 IL1 or MX L1 L2 32 4 In addition a physical limitation of the principle of mutual inductance must be observed in order to have a physi cally realizable circuit That is since coefficient of coupling k is always less than unity and by definition M k lt l yv LiLo the user should be certain that M lt y L L Stated in words the mutual inductance between any two inductors must be less than the square root of the product of the self inductances of the components between which the mutual inductance exists The sign of M is positive if in a given winding the induced voltage of mutual inductance acts in the same direction as the induced voltage of self inductance If the induced voltage of mutual inductance opposes the induced voltage of self inductance in a given winding M is negative The proper sign for M for the assumed current directions is illustrated in figure 2
164. pecified Minimum Step Size Any transient run will automatically terminate whenever a time step size is required that is smaller than the min imum step size If this quantity is not supplied the program will automatically compute a minimum limit For explicit integration this minimum limit is equal to 1 x 10 times the problem duration STOP TIME For im plicit integration the multiplying factor is 1 x 10714 If a specific minimum step size independent of the problem duration is desired the format is MINIMUM STEP SIZE number For example if in a run using explicit integration STOP TIME 5000 is specified the minimum size would automatically be 0 05 To change this to 0 01 use MINIMUM STEP SIZE 0 01 Maximum Step Size This quantity sets an upper limit to the time solution increment that can be used to prevent a complete transient solution composed of few solution points If this quantity is not supplied the program will automatically compute a maximum limit equal to 2 x 107 times the problem duration STOP TIME If a specific maximum step size independent of the problem duration is desired the format is MAXIMUM STEP SIZE number 28 Starting Step Size This quantity will be the size of the first time solution increment that is taken Subsequent increments are automat ically chosen by the integration routine If this quantity is not supplied the program will automatical
165. pendent variable If a different independent variable is desired for the plotted form the following format must be used IC14 PLOT VC14 In this case the current through capacitor C14 would be plotted as a function of the voltage across it The printed output would be IC14 as a function of time Additional flexibility is available to permit the user to attach a different label to any output quantity except TIME Consider that elements C1 and R7 exist in a given network and that the voltage across both VC1 and VR7 are of interest If the user decides to rename them as VIN and VOUT the outputs may be requested as VC1 VIN VR7 VOUT PLOT All renames must be limited to six alphanumeric characters and the first character may be any alphanumeric character The plot rename and choice of independent variable options can be presented in terms of the general format as yqty ylabel PLOT xqty xlabel If no rename is desired the general format reduces to YAEY aise ways PLOT xqty If in addition only time is desired as the independent variable this can be further reduced to YAEY rs oe ag j PLOT And if no plotted information is desired the simplest form arises as yaty 18 Composite Plots A specialized plot format is available in which up to nine dependent variables may be plotted against a common abscissa The ordinate for each dependent variable runs across the page and is separately scaled and unique grap
166. rage required by Convolution by compressing the SCEPTRE generated data tables that are convolved internally with the impulse response functions The first of the Run Controls which invoke and regulate this compression routine is COMPRESSION COUNT integer where integer which must be no greater than that set in by INPUT FUNCTION BUFFER is used to indicate the number of successful integration steps taken between successive calls to CMPAC The second entry is used in the internal decision making process to determine if intermediate points need to be retained This CMPAC control is COMPRESSION CRITERION constant where constant 100 indicates the maximum percentage area which may be lost due to omitting the middle point of any three consecutive data points For one pass through the algorithm this is also the maximum total percentage area lost due to leaving out all possible middle points However the routine is repeatedly cycled through until no more points can be removed For each additional pass this COMPRESSION CRITERION is automatically tightened by a factor of four Because of this tightening and repetition process the maximum possible percentage loss over a series of com pressions can exceed the value set in by the COMPRESSION CRITERION entry For normal criteria up to 05 however the maximum total loss on all passes could not exceed the criterion by more that 25 percent or from 05 to 0625 for example Run Controls
167. rdless of how many were plotted in the original run appropriate entries would be RE OUTPUT New output requests without the OUTPUTS subheading END Re output generally does not permit the printed output to exceed that which appeared in the original run The RE OUTPUT heading cannot be used in the same run with any other heading or subheading except END S 360 only The RE OUTPUT feature requires the subheading OUTPUTS which is followed by a list of the desired outputs as described in subsection 2 2 4 This list may contain any or all of the output requests from the original run Any quantity output originally may be obtained in either printed and or plotted form using this feature For example 55 E OUTPUT UTPUTS R1 VR2 C10 PLOT ND mds On RE OUTPUT also permits the subheading RUN CONTROLS MAXIMUM PRINT POINTS may be used under Run Controls For example E OUTPUT UTPUTS R1 VR2 C10 PLOT UN CONTROLS AXIMUM PRINT POINTS 2000 lt lt 0w we 5 Z iw On AC runs it is also possible to obtain a plot via the RE OUTPUT feature if it was not requested on the original run As is the case for other runs a plot cannot be obtained of an output which was not printed on the original run In the AC case this restriction extends to type of plot If the original run requested a print of magnitude and phase in degrees vs frequency a plot vs radians cannot be obtained A Nyquist plot can be ob
168. re 2 4 Voltage Polarity and Current Direction Manual Initial Conditions This section is usually superfluous if the run is being made in either the initial conditions only or the automatic initial conditions mode since the initial conditions will be computed by the program in these situations When initial conditions are supplied by the user the format it VC number Tela ties ee number Initial capacitor voltages and inductor currents may be supplied by simply listing the desired values Any initial conditions not specified will be taken as zero If all initial conditions are zero neither the heading card nor the data are required Care must be taken to establish the proper polarities for initial conditions Initial inductor currents are positive if they flow in the same direction as the assumed current direction for the inductor Also the initial capacitor voltages are positive when they are consistent with the assumed voltage polarity for the capacitor The assumed current direction through inductor L5 of figure 2 4 is from node 7 to node 8 If the initial inductor current is in this direction it is entered under the INITIAL CONDITIONS subheading as a positive quantity If however the current flows in the other direction it is preceded by a negative sign The same convention applies to the capacitor where the assumed positive sense of the voltage is associated with the tail of the reference arrow node 4 in figure 2 4 If the actu
169. re A 8 Network to Illustrate Differential Equation Identification A 8 Convolution analysis A 8 1 Introduction The SIMUL 3 program has been modified to permit multiple convolutions in conjunction with the RUK integration routine In order to apply this analysis technique it is first necessary to understand the larger context in which it is used Convolution analysis requires that a set of functions be supplied in addition to the prescribed CIRCUIT DESCRIPTION inputs These supplied functions are a set of impulse responses which replace a portion of the network at a known set of interface nodes between what is removed and the rest of the network to be solved by SCEPTRE Once these impulse functions have been readied and supplied to SCEPTRE the convolution feature may be used to provide a transient analysis of large networks linear or non linear which would otherwise exceed SCEPTRE s present limitations of 300 elements The convolution routine also offers an alternate means of handling networks which are within the size capability of SCEPTRE but whose elements are not all specified in the same manner Where some of the elements or groups 119 of elements are already described by their responses in the time domain or are described by their responses in the frequency domain and conversion to time domain is possible then the convolution approach might save manual calculation in preparing the network for analysis The larger context inv
170. s If this Run Control is used with a non zero number no attempt will be made to read previously punched values Instead the number will be used to scale the initial approximation to the inverse Hessian Careful use of any pre knowledge about the scale of the inverse matrix can improve optimization performance If this Run Control is not entered the initial approximation is the unit matrix The tolerance within which the value of objective function should be located is provided by the Run Control 35 OPTIMIZATION CRITERION number T If this card does not appear the iteration will stop whenever the estimated improvement will be less than 1077 Note that in the presence of a broad shallow minimum the objective function will be relatively insensitive to the values of the independent variables In this case even a small objective function tolerance will permit the program a wide latitude in its choice of final values of the independent variables Under some conditions particularly with a shallow minimum as described above the algorithm may not locate a true minimum because the error criterion permits it to stop at a neighboring point in the space of the independent variables To protect against this possibility two additional Run Controls have been implemented If the Run Control OPTIMIZATION RANDOM STEPS integer appears displacements in random directions from the assumed minimum will be made the indicated number of times
171. s a model for one run only plus whatever reruns may be made during that run This type of storage will probably prove most useful for experimental models or for models that are seldom used All stored models are transferred from storage to the main circuit where they are used by reference to their ex ternal nodes or terminals The user must ensure that corresponding nodes in both the main circuit and the stored model match in sequence Internal nodes of any stored model are of no particular significance and will be briefly mentioned later The stored model feature is best illustrated by an example Assume that the stored transistor model in figure 2 6b is to be inserted into the main circuit in figure 2 6a The stored model contains terminal nodes 1 2 and 3 which correspond to the base emitter and collector nodes of the transistor and internal nodes 7 and 12 The main circuit may also contain nodes 1 2 3 7 or 12 without danger of ambiguity Assuming that the model was originally stored with the node sequence 1 2 and 3 the user could enter the following under ELEMENTS of the main program T1 14 21 23 MODEL X476900 PERM This will match nodes 14 21 and 23 of the main circuit with nodes 1 2 and 3 of the stored model The circuit designation of the stored model is T1 and the name of this particular stored model is X476900 The stored model is transferred from the tape into the main circuit and nodes 1 2 and 3 of the model beco
172. s requiring time derivatives the output will be the system Matrices A G and Q For case 4 independent sources requiring time derivatives and dependent sources the output will be the system Matrices A G H and Q PRINT EIGENVALUES This entry will result in a listing of the N complex valued eigenvalues obtained in the analysis As a check on the correctness of the similarity transformation it will also cause a print out of the results of the calculation AS SA where S is the complex valued modal matrix and A is the diagonal matrix composed of the complex system eigenvalues If the transformation is correct the calculation gives the zero matrix PRINT EIGENVECTORS This entry will result in a listing of the S matrix and the inverse of this matrix S As a check on the correctiness of the inversion it will also provide the results of the calculation S S7 1 If the matrix inversion is correctly obtained this calculation gives the zero matrix 2 8 6 Program Debug Output A program debug outputting facility which is provided principally as a program debugging aid is available to the interested user With this feature data normally generated used and of concern only internal to the program can be printed out In normal application of the program this type of information is not desired and hence the facility is not normally activated To activate the debug printout feature request WRITE DEBUG
173. s this model becomes that shown in figure A 11 A J J1 J2 1 G B Figure A 11 Admittance Model A 8 7 Storing impulse response functions The impulse response functions used in the transient program to calculate voltages and currents associated with the various convolution kernels must be supplied by the user A preassigned disk number 12 has been set aside for the purpose of storing these functions Two positive actions are required by the user The first is the creation of the necessary permanent data set on disk 12 The following information is required for each impulse response function in the order listed and using the format given below 1 An Identifier Number Integer using format I10 as defined in American National Standard FORTRAN X3 9 1966 This number must agree with the argument of the Convolution kernel which uses this particular function This identification number is used by SCEPTRE to relate the Convolution kernel to the appropriate response function from disk 9 Therefore the order in which the various response function blocks appear on the disk is immaterial 125 2 The value of the Impulse Response Time Waveform at Time 0 format G20 8 Since all impulse response functions are casual their value at T 0 is given by HZERO 1 2 H 0 H 0 However the value required by the program is HZERO H 0 3 The value of the Impulse Response Frequency Waveform at FREQ 0 format G20 8 4 The len
174. second with four dependent and three independent variables 95 I C TRANSIENT VALUES AT TIME EQUALS ZERO OVCET1 3 5123970E 01 OVCCT1 8 9126370E 00 OVCET2 4 3874672E 01 OVCCT2 8 9197511E 00 INPUTS TO MONTE CARLO NAME NOMINAL PETI 9 6000000E 01 P1T2 9 6000000E 01 INITIAL RANDOM NUMBER DISTRIBUTION IS GAUSSIAN NORMAL MONTE CARLO TERMINATION AFTER FINAL RANDOM NUMBER OBSERVED STATIST INDEPENDENT VARIABLE P1T1 9 PITZ Os DEPENDENT VARIABLE VCET1 VCCT1 J1T1 VCET2 VCCT2 J1T2 PEC PEIN VR3 VR4 FOO KR OBN OW LBOUND 9 0000000E 01 9 0000000E 01 127263527 1007121511 ICS NOMINAL MINIMUM VALUE VALUE 6000000E 01 9 3082453E 01 6000000E 01 9 1926269E 01 NOMINAL MINIMUM VALUE VALUE 5123970E 0 3 5109792E 0 9126370E 00 8 9210128E 00 1824751E 02 2 1716713E 02 3874672E 0 4 3440367E 0 9197511E 00 9 0300613E 00 6675032E 0 4 0093037E 0 6903307E 00 4 0210736E 00 7254006E 04 6 3257750E 04 3104773E 0 6 0275509E 0 8670015E 0 1 6037217E 0 RESULTS OF INITIAL CONDITION COMPUTATIONS VCET1 VCCT1 J1T1 VCET2 VCCT2 J1T2 PEC PEIN VR3 VR4 POR ms RO BW OW 6510355E 0 8596399E 00 5455596E 02 3445810E 0 0300613E 00 0169492E 0 0323994E 00 4793579E 03 0486548E 0 6067799E 0 UBOUND FORA ds 0045 wow 9 8000000E 01 9 8000000E 01 10 ITERATIONS MAXIMUM VALUE MAXIMUM VALUE 6510355 8596399E 00 5455596E 02 3795162E 0 9392260 539405
175. situation can lead to erroneous results See 2 subsection 2 4 1 2 2 6 Functions In this data group each of the tables and equations referred to under ELEMENTS and DEFINED PARAM ETERS subsections 2 2 2 and 2 2 3 respectively must be defined in detail If no such references have been made neither the FUNCTIONS heading card nor data need be supplied The equation definition sequence will be discussed first Equation Definition Sequence Each unique equation used to define the variation of an element or defined parameter is defined by giving the equation name a dummy variable list and the mathematical definition The general format is EQUATION name Dummy Variable List Mathematical Definition or Q name Dummy Variable List Mathematical Definition The dummy variable list must contain the same number of entries as does the argument list in the original equation reference Each dummy variable may contain up to six alphanumeric characters the first of which must not be a number or the letters I through N inclusive For example if an equation has been referenced under ELEMENTS as LX3 9 3 EQUATION 15X ILX3 TIME VC1 then this equation could be explicitly defined under FUNCTIONS as EQUATION 15X A B C Mathematical Definition or Q 15X A B C Mathematical Definition The dummy variables in this case are A B C which replace ILX3 TIME and VC1 respectively The mathemati
176. sponding to the element type 1 e resistor capacitor inductor voltage source or current source respectively The letter M is used to des ignate mutual inductance in the same way The two exceptions to this are the circuit designation for a stored model see subsection 2 3 1 which has no specific rule for its first character but should be limited to a total of three alphanumeric characters and the Convolution model Appendix A 8 the first character of which is a K It is normally very helpful to record on the equivalent circuit diagram the names and nodes chosen Current flow directions and source polarities should also be indicated The circuit parameter values should be specified in a consistent set of parameter units Although any consistent set is acceptable the system given in table 2 1 is useful for high speed transistorized circuits If another system is desired the most effective choice is units of voltage current and time that correspond to the magnitude of those that are expected in the problems then determine units of R L and C from the fundamental current voltage relationships This choice is always possible in a practical circuit since the analyst should have some approximate idea of the range of variables In summary the circuit preparation steps are Draw an equivalent circuit comprising only resistors capacitors inductors and voltage and current sources e Assign a name or number to all nodes in the circuit e Give
177. st Case The defined parameter must be a function of one or more dependent variables and zero or more independent variables Valid dependent variables and independent variables for these calculations may be found in table 2 7 and table 2 8 The user should enter differentials of defined parameters under the DEFINED PARAMETERS subheading of CIRCUIT DESCRIPTION For a defined parameter Pname the total differential is given by GPname list List is a sum of products of the form PX DY where PX is a defined parameter representing the partial derivative of the dependent variable with respect to an independent variable and DY is the differential of the independent variable Example 1 DEFINED PARAMETERS PABC X1 IRL 2 ILA 2 GPABC P2 DIRL P3 DILA P2 X2 2 IRL P3 X3 2 ILA Example 2 DEFINED PARAMETERS PEX XA VC1 2 IR1 R1 2 GPEX PA DVC1 P3 DIR1 P4 DR1 PA X2 2 VC1 P32 X3 2 ITRT RLAY 2 P4 X4 2 R1 IR1 2 Complex Valued Defined Parameters Complex valued defined parameters are used to enable complex outputs from the AC analysis portion of the program Complex valued defined parameters are analogous in principle to the real valued defined parameters designated with a P The appropriate prefix for the complex valued defined parameter is W followed by no more than five alphanumeric characters Unlike the real valued defined parameter P
178. sufficient to cause SCEPTRE to insert internally the corresponding two elements associated with the model The suffix E in the subroutine name FCONVE is a reminder that the impedance model contains a voltage source The internally created node name will be given the kernel s four character identifier and the names for the resistor and voltage source are created by prefixing an R and E respectively to the kernel s identifier Thus the user can always know the correct name for each new element and can thereby obtain these and or their voltage or current under OUTPUTS if he so desires 4 6 3 Convolution admittance mode The three functions KHAB KHBC and KHAC given in figure 4 10 represent admittance functions They are identified respectively with the following arbitrarily preassigned integers 1101 1102 and 1103 see figure 4 12 KHAB A B FCONVJ 1101 KHBC B C FCONVJ 1102 90 VRKHAB VRKHAC VRKHBC gt U gt gt 45 fig C Figure 4 12 Convolution Representation Using Parallel Admittance Elements KHAC A C FCONVJ 1103 The suffix J in the subroutine name FCONVJ is a reminder that the admittance model contains the current source The names for the resistor and surrent source are automatically created by prefixing an R and J respectively to the kernel identifier 4 6 4 Sample problem This paragraph illustrates a way the Convolution mode may be used and gives the appropriate CIR
179. sults of any particular DC computation as initial conditions for the transient or AC solution to follow he must not request any of the DC options which appear after it in the above mentioned order For instance if the user wishes to use the results of a Monte Carlo solution as initial conditions for a transient or AC solution he must not enter a RUN WORST CASE or RUN OPTIMIZATION card or these DC solutions will remove the Monte Carlo data from the voltages currents and defined parameter tables If the entry RUN INITIAL CONDITIONS ONLY is omitted a transient solution will follow the DC solutions If the user desires an AC analysis with or without a DC analysis the entry is RUN AC plus entries for any DC analysis desired Under normal computational circumstances the initial conditions for any rerun are either inserted by the user or computed by the DC portion of the program see subsections 2 4 1 and 2 4 2 There may be situations however in which it is desirable to have the results of master runs either AC DC or transient used as the starting values for one or more associated reruns If it is intended that all associated reruns use the final values of the master run as initial conditions the appropriate entry under RUN CONTROLS is IC FOR RERUNS MASTER RESULTS If it is intended that each rerun use the final result of the preceding rerun in the sequence the entry is IC FOR RERUNS PRECEDING RESUL
180. t is unreasonable to expect the user to supply valid termination criteria for this type of computation it must be automated It is felt that the best way to accomplish this is to monitor the vector of the state variable derivatives Y and to terminate the solution when the relation MEU A 1 1s satisfied for all state variables Y Tests have been performed to determine appropriate values for the relative constant X1 and the absolute constant X2 in equation A 1 Acceptable results have been produced with X1 1E 8 X2 1E 6 and these values are programmed into this feature Language The necessary language required to call out this feature for use was chosen to fit all the computational combinations that exist Under RUN CONTROLS e For DC computation only with or without reruns RUN INITIAL CONDITIONS ONLY RUN IC VIA IMPLICIT e For DC and transient computation RUN IC VIA IMPLICIT STOP TIME X e For DC and transient computation rerun transient only UN IC VIA IMPLICIT TOP TIME X ERUN DESCRIPTION An J e ipo or DC and transient computation rerun both DC and Transient UN IC VIA IMPLICIT TOP TIME X ERUN DESCRIPTION UN CONTROLS UN 1C VIA IMPLICIT J V VUJ This feature was tested on Manual Example A03 This particular problem is a two stage transistor Darlington network that uses the stored model feature Only DC computation is requested and three reruns are called
181. tained only if a complex printout with or without a Nyquist plot had been requested on the initial run 2 7 Subprogram capability This feature is intended for the user with some experience in FORTRAN programming and with an occasional need for special computation that is not directly provided by SCEPTRE Any subprogram may be written according to the rules of FORTRAN IV Function Subprograms and retained on tape or cards until it is needed As an example of a practical use of this feature consider the problem of creating a periodic train of pulses as shown in figure 2 7 A voltage source e g El may generate a wave of this type An appropriate procedure would include under ELEMENTS El none node Fnam iran X TIME where the X quantities refer to constants or network variables and Fname refers to the chosen subprogram name The subprogram name must be unique and begin with the letter F It may not exceed six alphanumeric characters With specific reference to figure 2 7 the user could enter under ELEMENTS which references the following subprogram 7090 94 only FUNCTION FGEN VO V1 TO TR TD TF TP Z0 TIME DATA Z 1 A IF Z Z0 3 3 4 56 VO initial voltage V1 peak voltage TO pulse delay TR total rise time TD peak duration time TF total fall time TP period ZO number of complete TP pulses 10 fig To g Figure 2 7 Pulse Train
182. ted by the entry PRINT INTERVAL number under the RUN CONTROLS section This printed series will appear in addition to the normal output If only this printed series is desired the normal printed output format may be suppressed by the entry MAXIMUM PRINT POINTS 0 A 5 Composite plots The standard plot format with SCEPTRE has always been one dependent variable plotted against an independent variable with automatic scaling supplied for both the abscissa and ordinate The plots were output in machine plot format with all abscissas having physical lengths of 10 inches and ordinates of 8 1 2 inches A summary of all quantities that may be plotted is given in Manual subsection 2 2 4 A specialized plot format has been added in which up to nine quantities may be plotted against a common abscissa The ordinate values for each variable are separately scaled in order to preserve resolution and unique characters are used to represent each quantity Use of this feature requires that all of the quantities that are to be plotted together be requested on the same card under OUTPUTS followed by a specific plot name The plots illustrated in figure A 5 were obtained with the following entries OUTPUTS PX PY PZ XSTPSZ PLOT GREEN RUN CONTROLS PLOT INTERVAL 1 STOP TIME 80 Here the four quantities PX PY PZ and XSTPSZ are requested together with a specific plot name of GREEN Any alphanumeric combination
183. terminal system of figure 4 22a are as shown the user must define one current source and voltage source under ELEMENTS as implied in figure 4 22b The former is simply set equal to zero its function is to serve as an infinite input impedance across which will appear the system input voltage e t The voltage source given earlier by equation 4 5 may be equivalently written as EO amPm 1 Gm 1Pm a1 P2 aoP1 4 7 where the ao m coefficients are as defined from equation 4 1 and the defined Parameters P1 Pm 1 represent the appropriate derivatives from equation 4 5 In addition the user must define two types of expres sions under DEFINED PARAMETERS The first will simulate the highest order derivative of the system which was given by equation 4 6 and is here written equivalently as DP VJI by_1 Py b1 P2 bo P1 bn 4 8 where the bo 5 coefficients are as defined in the denominator of equation 4 1 Finally a series of n 1 expressions must also be entered in the general form DPn 1 Pr 4 9 DP2 P3 DP1 P2 Note that n differential equations must be supplied just what one would expect in order to simulate a nth order system Now that the format has been described a specific example will be considered to see what is actually involved Let it be desired to simulate the transfer function s 7s 10 F 5 472341082 205 1000 with the same node designation use
184. terminated The alphanumeric character limits are listed in table 2 10 The circuit designation used for models is always appended to any names used in a model description and the combined total characters must not exceed the circuit description limits For example element CB in a model designated as T15 in the circuit description becomes CBTIS 2 2 10 Vectorized notation When large networks are encountered SCEPTRE automatically reverts to an internal renaming feature VECTOR IZED NOTATION which effectively enlarges the capacity of the FORTRAN Compiler Large networks in this case refer to those containing 70 or more elements if a DC solution is requested or 100 or more elements if only a transient solution is to be made This feature will not affect the user operationally as long as the input formats given in this manual are followed It will however cause SIMULS8 to be written in terms of the renamed quantities A complete listing of all circuit Elements and Defined Parameters along with their corresponding internal names will be provided for every run in which renaming occurs 2 2 11 Internal Parameters A number of parameters are carried internally in the program The user has permitted access to these parameters for use as Equation arguments independent variables for tables and automatic termination quantities and outputs The nomenclature and definitions of these parameters are given in Table 2 11 41 Description of d
185. th objective functions and independent variables Only those defined parameters used to relate primary and secondaty current sources may be used as independent variables The defined parameters used for objective functions must have their total differentials provided see paragraph 2 2 3 Thus PEC EC IEC and its total differential is EC d IEC IEC d EC Since EC isD constant and not one of the independent variables it is not necessary to include its differential contribution to the total differential GPEC 101 INITIAL VALUES OF OPTIMIZATION PARAMETERS OBJECTIVE FUNCTION VR3 NUMBER OF INDEPENDENT VARIABLES 3 NUMBER OF RANDOM STEPS 0 INITIAL H MATRIX FACTOR 1 00000000E 00 CONVERGENCE CRITERION 1 00000000E 07 RANDOM STEP SIZE CONTROL 2 00000000E 01 MINIMUM FUNCTION ESTIMATE 0 00000000E 00 H MATRIX DETERMINAN 1 00000000E 00 INITIAL VALUES OF INDEPENDENT VARIABLES NOMINAL LOWER UPPER VARIABLE VALUE BOUND BOUND PITI 9 60000000E 01 9 00000000E 01 9 80000000E 01 P1T2 9 60000000E 01 9 00000000E 01 9 80000000E 01 EC 1 00000000E 01 9 50000000E 00 1 05000000E 01 INITIAL APPROXIMATION TO H MATRIX 1 0000000
186. the problem duration differs for each rerun an appropriate sequence would be RUN CONTROLS STOP TIME 500 600 700 The problem durations of the three reruns would be 500 600 and 700 units of time regardless of the duration of the master run 2 4 2 Limitations of the rerun feature There are certain features of the master run which cannot be changed in any of the corresponding reruns These are in the areas of output element form and operational mode Output There can be no difference between the quantities that are output in the master run and those that are outputs in any of the reruns Therefore no OUTPUTS subheading is allowed under RERUN Element Form No change in element form is allowed between the master run and the reruns If an element originally appears as a constant its rerun version must also be a constant An element originally appearing as a table must also be a table in the rerun version The new table would be defined under FUNCTIONS An element originally appearing as an equation must also be an equation in the rerun The only parts of an equation that may be changed are those that are defined under DEFINED PARAMETERS To illustrate consider that the master run had an element 51 JE 1 8 DIODE EQUATION PX1 PX2 where PX1 and PX2 are defined under DEFINED PARAMETERS A legal rerun would be RERUN DESCRIPTION DEFINED PARAMETERS PX1 number PX2 number
187. thence successful continuation of either the error scan or execution of the analysis phase Most input data errors fall into level 2 as illustrated by the following example of an initial condition specification which should contain an I prefix designating the initial current through inductor L3 INITIAL CONDITIONS vcl 100 L3 0 01 Gl n Error Message 1 level 2 simulation deleted ERROR SCAN CONTINUI INITIAL CONDITION LACKS A V OR I PREFIX Error messages Messages numbered 2 and 3 are not issued in the System 360 version Instead the run will be aborted after message 1 is issued and the system condition code set to terminate processing 1 INITIAL CONDITION LACKS A V OR I PREFIX 2 EQUAL SIGN MISSING 3 VARIABLE NAME EXCEED CHARACTER LIMIT 4 REDUNDANT VOLTAGE OR CURRENT SPECIFICATION 5 NO VALUE SPECIFICATION FOLLOWS EQUALS 6 INCORRECT VALUE SPECIFICATION 7 ORE THAN 100 INITIAL CONDITIONS HAVE BEEN SPECIFIED
188. this case the model will be inserted into the main circuit as it was originally stored If a change is desired in one or more internal elements or defined parameters of the stored model the proper entry could be T1 7 8 12 MODEL 2N1734B CHANGE CC 50 In this case CC of the original model has been changed to 50 units of capacitance regardless of its original form or size All other elements in the stored model would remain as originally stored Another practical situation could be reflected by the entry T1 7 8 12 MODEL 2N1734B CHANGE CC TABLE 7 VCCT1 JA 2 J2T1 JE DIODE TABLE 4 In this case CC of the original stored model has been changed to a tabular function which must be represented TABLE 7 under the FUNCTIONS subheading of the main circuit Also JA has been changed to a different math ematical definition and JE has been changed to another tabular function which must appear under FUNCTIONS The other elements of the stored model will remain in their original forms As a final example assume that it is desired to change CC in a stored model to a different equation Then T1 7 8 12 MODEL 2N1734B CHANGE CC EQUATION 5 VCCT1 VCX In this case CC of the stored model has been changed to a closed form function which must be represented by EQUATION 5 under FUNCTIONS of the main circuit description All elements or element voltages or currents within a model that ar
189. to determine the effect of perturbations in the first stage current gain on selected network voltages A comparison of the DC steady state transistor junction voltages is given in table A 1 for all four runs There is no significant difference between the result achieved by the DC algorithm and that obtained by transient analysis All results in table A 1 have been rounded to the fourth decimal place A 3 2 Reruns with the DC algorithm The DC portion of the program is based on a Newton Raphson iteration procedure that is designed to solve simul taneous nonlinear algebraic equations The key operation is given by equation 72 in 2 which can be written in simplified form as Vat FUVa 7 F2 V A 2 Repeated iterations of equation A 2 are carried out until the process converges to the final solution for each indi vidual run All individual DC runs whether they are part of a rerun series or not normally begin the first iteration 112 Rerun Variable via DC analysis via TR analysis Master VCETI 0 3382 0 3382 Run VCCTI1 8 9377 8 9377 VCET2 0 4422 0 4422 VCCT2 8 8227 8 8226 First VCETI 0 3377 0 3377 Rerun VCCT1 8 9456 8 9458 VCET2 0 4416 0 4416 VCCT2 8 8381 8 8383 Second VCETI 0 3370 0 3369 Rerun VCCTI1 8 9570 8 9572 VCET2 0 4408 0 4408 VCCT2 8 8603 8 8605 Third VCETI 0 3363 0 3362 Rerun VCCT1 8 9680 8 9680 VCET2 0 4399 0 4399 VCCT2 8 8813 8 8814 Table A 1 Comparison
190. tral representation The impedance representation was used see figure 4 15 and the spectra were evaluated The inverse Fourier transforms were then taken supplying an h t impedance kernel for each of the removed blocks for analysis by SCEPTRE in the Convolution mode Disk 12 was prepared in accordance with Appendix A 8 7 A SCEPTRE CIRCUIT DESCRIPTION was prepared in accordance with the guidelines in TABLE 2 2 in paragraph 2 2 7 and in the text preceeding this sample problem CIRCUIT DESCRIPTION A06B CONVOLUTION IMPEDANCE MODEL ELEMENTS El 0 1 Ql TIME R1 1 2 5000 92 0 0 5 1 1 5 2 2 5 3 3 5 4 4 5 5 TIME Figure 4 14 Convolution Reference Example Output convolution replacement models unD RB G k RKCV3 49 fig O Figure 4 15 Convolution Example Impedance Model Schematic 93 Plot not available Figure 4 16 Convolution Sample Problem Output Ely 2534S 25 C1 1 4 001 R2 3 4 3000 R3 3 5 2000 R4 4 0 8500 C2 4 6 004 R5 5 6 11000 L2 6 0 175 C3 5 7 0025 R6 6 8 1000 KCV1 7 8 FCONVE 1001 KCV2 8 0 FCONVE 1002 KCV3 7 0 FCONVE 1003 FUNCTIONS Q1 T 10 T DEXP 5 T Q2 A B A B DEFINED PARAMETERS PVOLT1 Q2 VRKCV1 EKCV1 PVOLT2 Q2 VRKCV2 EKCV2 PVOLT3 Q
191. trary spacing or location from columns to 72 During a single run the user cannot use all six major headings although all ten subheadings under CIRCUIT DESCRIPTION could well be used Unique sequences of symbols and punctuation are used to convey information in each of the subheadings A definition of each of the symbols in the subheadings follows Element Name Denotes the name given to each component including model circuit designations of a circuit e g RA LLX E17 No more than five alphanumeric characters may be used to name an element Model circuit designations are limited to no more than four alphanumeric characters Node Denotes the designation assigned to each node of a circuit No more than six alphanumeric characters may be used to name a node Number A numerical constant that may be written as a signed quantity in either integer or decimal form and with or without an exponent Up to 13 characters may be used to represent a number For example numbers may be written in the following forms 10 10 10 0 1 0 1 1 4 6 4E9 74 3E 7 7E 11 176 6667ES5 Constant Same as Number except a decimal point must be included in the specification of the numerical constant Value Will be used to denote any of the following Number Defined parameter TABLE EQUATION EX PRESSION or External Function Special Value Will be used to denote any of the following Value Constant Resistor Current Constant Resistor Voltag
192. uired before and after an operator A typical entry would be H ERMINATE IF VCC GT 0 which would automatically terminate that particular run whenever the voltage across capacitor CC became positive The termination feature may be extended to cover AND OR logical situations by using the logical operators AND and OR A legal entry could be H ERMINATE IF VCC GT 0 OR IL17 GE 7 This would terminate the run if the voltage across capacitor CC became positive or the current through inductor L17 exceeded 7 units of current The other logical possibility would be simply H ERMINATE IF VCC GT 0 AND IL17 GE 7 All automatic Termination conditions must apply to all reruns that are associated with a given master run see Section 2 4 1 One variation is available If it is desired that all remaining reruns be canceled if a termination condition is met the word STOP is used instead of TERMINATE Then a typical entry would be STOP IF VCC GT 0 Computer Save Interval Particularly long computer runs should be protected against complete loss arising from improper termination caused by electrical malfunction operator error etc This is done by periodically recording the status of the run on tape such that it can always be continued from the last saved point if improper termination does occur A 15 minute save interval is preset in the program which ensures that no more than
193. unds on Elements and Defined Parameters in Reruns Any elements or defined parameters which are unchanged under a RERUN DESCRIPTION heading will retain any bounds previously given subsections 2 2 2 and 2 2 3 However if the user specified an element or defined parameter value he may at the same time change delete or add bounds to the element value whether or not bounds had been previously specified For example under ELEMENTS for a RERUN DESCRIPTION with two reruns the user might include R3 4 6 9 8 0 10 5 Here the first rerun value of R3 is 4 6 with no bounds given regardless of whether its preceding value had bounds However in the second rerun bounds of 8 0 and 10 5 will be placed on the nominal value of 9 The user is cautioned however that the removal of bounds required for the DC options subsection 2 2 8 will result in an error INITIAL CONDITIONS Under Rerun This subheading is used to rerun any number of transient runs that start at different operating points For two reruns a sample form under INITIAL CONDITIONS would be vel 1 5 3 VC2 7 2 5 IL4 0 1 5 FUNCTIONS Under Rerun This subheading is used to change any part of a table that describes an element or defined parameter of the original run Changes in equations are discussed in subsection 2 4 2 If TABLE 7 was used to describe an element or group of elements in the master run it may be modified under FUNCTIONS in the rerun section as TABLE 7
194. user may define both generators under ELEMENTS as 2 TABLE 8 TABLE Tig LE ve 1 J2 1 Under FUNCTIONS the user would define TABLE 1 only once 25 2 2 7 Run controls This subsection contains all the auxiliary information needed to control the run The information does not directly affect the network Most of these quantities have automatic default entries that hold unless specific entries are supplied by the user The default entries are given in table 2 4 All possible entries under the RUN CONTROLS subheading are given in the following subsections These entries may be made in any order and as many may be placed on a card as will fit if they are separated by commas Run Limits All transient runs must have a problem duration in the time units consistent with those used to describe the circuit The form is simply STOP TIME number Since the user will never know in advance the computer time required for the solution of a given run it may sometimes be desirable to enter a limit that will automatically terminate the run if that limit is exceeded The limit in minutes may be entered as COMPUTER TIME LIMIT number The preset value for COMPUTER TIME LIMIT is set to 600 minutes This statement is active on IBM System 360 computers where a system clock is installed and applies to total elapsed time It should be noted that for operation under OS MVT the time used for the above statements is elaps
195. wed XMXISS Maximum step size allowed XMNAIE Minimum absolute error XMXAIE Maximum absolute error XRERNO Rerun number XMXPAS Maximum pass limit XMNRIE Minimum relative error XMXRIE Maximum relative error XMXICP Newton Raphson pass limit XICRER Newton Raphson relative convergence XICAER Newton Raphson absolute convergence XMXOTP Maximum number of print points XICPAS Newton Raphson pass number XNOPRQ Number of output requests XNDFEQ Number of differential equations XERT Elapsed computer time XSTPNO Transient solution step number XPASNO Transient solution pass number XRUNNO Run number including reruns XSTPSZ Transient solution step size XSAVE Save interval XTMON Elapsed computer time at start of transient solution FREQ Frequency TIME Time XPLTI Plot Interval XPRTI Print Interval XINFRQ Initial Frequency XFNFRQ Final Frequency XTYPFQ Type Frequency Run XNFRQS Number of Frequency Steps XNMCPS Number of Monte Carlo Samples XNOPPS Maximum number of Optimization Passes per Step XWCLHN Type of Worst Case Results to be left as Initial Values for Transient Run XDISTR Type of Monte Carlo Distribution XACRE Use Fixed AC Matrix in Reruns XNCONV Number of Convolution kernels entered XHAVE Impulse Response Buffer Storage Allocation XIAVE Input Function Buffer Storage Allocation XCMPCR Compression Criterion XCMPCT Compression Count XOPCR Optimization Criterion XNOPRS Number of Optimization R

Extended SCEPTRE Volume 1 User`s Manual

Contents

Download Pdf Manuals

Related Search

Related Contents