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1. gt and lt for both conductors and layers Finally it includes the definition of the form form shape containing the four different shapes strip rectangle circle and polygon The file cust dialog c contains the definition of all the complex dialog windows except the help dialog which is included in help_dialog c Once the name of the callback is defined it 1s sufficient to look at the resource file graphtool h see Appendix A which contains all the functions of XRLGC ordered by file 60 All the arrays and variables used in XRLGC are summarized in graphtool h as well The C file containing the callback function is hence easily found For example we shall consider the button Erase located towards the bottom of the layer column This button is part of the form form button2 defined in the file graphtool c more precisely in the function create form button2 The definition of the button Erase is given in Fig 5 11 According to this definition the callback of the button Erase is the function Erase layer However this function does not ask any specific input NULL Nevertheless if this button was selected with the help of the context sensitive help the function helpCB would be called with the input Erase button4 l XtVaCreateManagedWidget Erase xmPushButtonWidgetClass form button2 XmNtopAttachment XmATTACH WIDGET XmNtopWidget button3 1 XmNbo
2. New Layer In order to get layers lying on top of each other the x y coordinates of the dielectric layer are automatically completed for each new layer created Consequently this first layer has coordinates 0 0 Second the characteristics of the bottom layer 2 5 mm Fr4 should be completed on the form located towards the bottom of the layer column Fig 4 5 The user should select the option Fr4 among the various material located at the top of the layer column The permittivity and conductivity of Fr4 4 3 o o 0 will be automatically completed by the program on the form located at the bottom of the layer column The user should then 29 Fig 4 5 30 manually complete the dielectric height value in this same form The button Plot allows the user to see the new layer displayed on the drawing area The conductor column Fig 4 5 will be used next in order to design the strip itself This part of the interface is located on the left of the drawing area and towards the center of the interface First the shape of the conductor is chosen among the four possibilities strip rectangle circle polygon at the top of the conductor column In our case a microstrip line is a strip conductor placed on top of the dielectric therefore we choose the shape Strip Once this is done the new strip may be created by selecting New Conductor In order to draw a strip some information about this conductor is needed its
3. and data lines may be of very long length up to 1 2 cm The resulting delay cannot be neglected since the line length is comparable to the signal wavelength 1 8 to 2 5 cm Moreover the fast switching speed and high density 1 create increased signal distortion coupling between transmission lines and electromagnetic interference EMI The use of computer aided tools 4 for predicting those losses in signal integrity linked to interconnects has become essential to understand the behavior of high speed digital circuits The simple model of capacitive load 3 may not be sufficient anymore for a transmission line of long length and high resistance The entire distributed RLGC model resistance inductance conductance and capacitance needs to be considered involving the full electromagnetic properties of transmission lines The terminal voltages and currents can be deduced accurately from this model Moreover transmission lines may present discontinuities like open end terminations bends junctions and vias 5 6 especially in MCMs where the interconnects are often very closely packed The prototyping 2 of package interconnections involves the network extraction followed by electromagnetic modeling determination of the circuit parameters and lastly the definition of adequate simulation algorithms The circuit can then be simulated with a software like SPICE or MDS The modeling methods that can be used to characterize an intercon
4. 2 7 Closed Form Green s Function The program XRLGC uses the closed form Green s function 18 instead of the traditional Green s function in order to avoid the numerical integration of a nested infinite sum involved in using an integral equation with the classical Green s function 22 25 An additional simplification is performed by considering real instead of complex exponential functions 26 in order to approximate the real Green s function in the spectral domain If the Green s function is replaced by its closed form version in Equation 8 in Section 2 3 we get the closed form integration formula used in XRLGC for the construction of the moment matrix The closed form Green s function for a multilayered dielectric medium is obtained by approximating the spectral domain Green s function with real exponential functions and by inverting it analytically to the space domain Because MoM is already an approximate way of solving an integral equation it is not necessary to have perfect precision for the Green s 12 function G and a moderate number of exponential functions 5 to 7 was generally sufficient to solve most problems The method used by K S Oh 18 to get the expression of the closed form Green s function is summarized below As shown in Fig 2 1 the coordinates xo yo Zo indicate the position of the source in the mth layer and the coordinates x y z indicate the point of computation of the Green s function in the nth
5. 53 The resource file RLGC h declaring the functions included in RLGC c V2D c appx c lu c and intg c is only used in RLGC and V2D The package RLGC including these three main programs was therefore rather difficult to use The user often needed to run them more than once before getting any satisfying results If the user wished to make even minor changes in the shape or size of the conductors and layers all three programs had to be run all over again wasting time The user also needed to generate the mesh for each conductor sometimes by running Mesh2D many times Moreover the use of RLGC implied manually changing the input file changing units adequately before filling in the geometry of the structure The slightest error in this manual input would automatically lead to wrong results at the output 5 2 XRLGC New Features 5 2 1 Overview The files included in the source of XRLGC are the following C source RLGCI c Mesh2D c V2D c appx c intg c lu c aux c frontend14 c graphtool6 c manageform c cond call c layer call c apply c cust dialog3 c help dialog c toolbar c H files RLGC h aux h ansi compat h apply h cond call h layer call h math h graphtool h manageform h mytool h The makefile see Fig 5 8 compiles one unique program XRLGC which will compute the RLGC parameters and the charge and voltage distributions according to the detailed description of the multilayered and multi
6. NS s layerI NS l int current type layer int type layer NS int current material cond current material strip current material rect current material circle int material cond NCl int ground new file char name file char input file 256 char output file 256 char Q2D file 256 Widget textel texte2 texte4 label4 label textex textey textex3 textey3 drawing Widget form form data rect form data strip form data circle Widget strip rectangle polygon circle Widget button1 l button2 l button3 l button4 1l form button2 graphics GC gc Display display XGCValues xgcv unsigned long gc mask Window window long int fill pixel fill layer stores current colour of fill black default Colormap cmap XtActionsRec actions int new char colours 256 9 graphics for the result Potential distribution 67 GC gc2 Display display2 XGCValues xgcv2 unsigned long gc mask2 Window window2 68 REFERENCES 1 A Ruehli H Heeb Circuit model for three dimensional geometries including dielectrics IEEE Trans Microwave Theory Tech vol 40 pp 1507 1516 July 1992 2 J E Schutt Aine Signal integrity and interconnects for high speed applications class notes for ECE 497 JS Department of Electrical and Computer Engineering University of Illinois at Urbana Champaign Fall 1997 3 A Deutsch et al Modeling and characterization of long on chip interconne
7. Papatheodorou R F Harrington and J R Mautz The equivalent circuit of a microstrip crossover in a dielectric substrate IEEE Trans Microwave Theory Tech vol MTT 38 pp 135 140 Feb 1990 26 M I Aksun and R Mittra Derivation of closed form Green s functions for a general microstrip geometry IEEE Trans Microwave Theory Tech vol MTT 40 pp 2055 2062 Nov 1992 27 J Schutt Aine Transmission Line Simulation Program nln c User guide Department of Electrical and Computer Engineering University of Illinois at Urbana Champaign Nov 1997 71
8. The new strip is then created by selecting New Conductor This push button calls the function New Cond callback in the file cond call c This function updates the conductor counter compteur and the total number of conductors nombre_conducteur while it completes the form located at the bottom of the conductor column with zeros The counter tells the interface at which index it should look inside the conductors arrays to find the right conductor see below The selection of the material Fe calls again the function toggleCB in frontend c and updates the variable current material cond to the value 3 Each material is recorded with a different value so that the interface can record which material has been chosen for that specific conductor Once the values x y and width are completed the user may select Plot to display the conductor This push button will then call the callback function store_data in frontend c which is very similar to store data layer except that it is dealing with conductors instead of layers and that there are three types of conductors to consider strip rectangular and circular The function store data updates the arrays Width Height x y resistivity and the indice accordingly at the index compteur The array indice indicates what kind of conductor is considered strip rectangular or circular The color of the display
9. ThreeRect V2D The resulting matrices may be displayed by selecting the option RLGC from the view menu The L G and C matrices will be of dimension 3H3 because there were three conductors considered in the structure If this structure was to be viewed or modified again in the future only the file ThreeRect which contains the geometry of the interconnect is required However the files ThreeRect out and ThreeRect V2D which contain the RLGC matrices and the potential distribution would be necessary in order to see the results of the last simulation 4 4 Four Conductors in a Layered Medium 4 4 1 Hypothesis and geometry considered We consider the structure shown in Fig 4 14 We assume that the four rectangular conductors are identical and that the number of basis functions per side is 50 for each conductor 40 Conductor Design three conductors three steps One step p Type of Conductor Type of Conductor Type of Conductor 3 Choose the material 1 Press Rectangle 2 Press New Conductor 4 Complete w h x y 5 Press Plot Fig 4 13 Conductor design 41 Free Space w 10 um Eo Substrate Si Substrate hy 10 uum Fr4 s 5 um Ground Plane Fig 4 14 Four rectangular conductors in a two layer structure The structure may again be described like Example 1 seen in Section 4 2 1 Geometry and material four identical conductors width w 10 m h
10. c Mesh2D c V2D c appx c intg c lu c aux c H files RLGC h aux h ansi_compat h The original makefile see Fig 5 1 compiles separately the three different programs Mesh2D RLGC and V2D These three programs are then used consecutively to get the RLGC parameters and the charge and voltage distributions Original makefile RLGC You need to change this path BIN DIR mnt users decwd ksoh bin default cc g o RLGC RLGC c lu c appx c intg c aux c lm mv RLGC BIN DIR cc o Mesh2D Mesh2D c aux o lm mv Mesh2D BIN DIR cc o V2D V2D c appx o aux o intg o lm mv V2D BIN DIR clean rm o Fig 5 1 Original makefile for the RLGC package 5 1 2 Constructing the mesh files and input file of RLGC In order to construct the mesh files the Mesh2D program is called once for each conductor of different shape and size A sample running of Mesh2D and the resulting mesh file are given in Figs 5 2 and 5 3 The program asks for the type of conductor desired the name of the file to create the dimensions of the conductor and the precision of the simulation measured by the number of basis functions In the example given here the conductor is rectangular of width 5 mm height 5 mm and only 5 basis functions on each side poor precision The mesh file of Fig 5 3 contains the coordinates of points evenly spaced on the four borders of the rectangular conductor The points are considered two by two starting from 0 0 0 1
11. capacitance matrix C According to 18 the solution of 2 D magnetostatic problems Equation 13 can often be found by considering the equivalent electrostatic problem with V 4 where Vj is the magnetic flux difference between the ith signal conductor and the reference conductor L y 13 If Qeq and Ceg are the charge and capacitance matrices found in 11 and 12 as a solution to the equivalent electrostatic problem defined above the inductance matrix L can easily be computed by solving I so I xii L Ca a 14 10 2 5 Conductance Matrix Because conductance matrix G models losses due to the dielectric it can be computed by applying N voltage excitations to the multilayered multiconductor system where N is the number of modes and by observing the resulting shunt current 18 If we consider N independent voltage excitations Vj and the corresponding matrix V the conductance matrix G can be computed by solving G I V L lq p c p d c o lp 3 15 where j is the shunt current created by Vj on the ith conductor The charge distribution q p of the lossy system can be approximated by the charge distribution of a lossless system defined in part 2 3 therefore no additional electrostatic problem needs to be solved The shunt current j may be deduced from the charge distribution and Equation 15 leads immediately to the conductance matrix G 2 6 Resistance Matrix For low frequencies the
12. diagonal resistance matrix is obtained simply by considering the inverse of the conductivity multiplied by the cross section of each conductor However both edge and proximity effect appear at high frequency resulting in a nonuniform current distribution on each conductor and in an increased complexity for the resistance matrix R 18 Nevertheless even for high frequency the resistance matrix is assumed to be diagonal 18 This diagonal matrix does not model power losses as accurately as the nondiagonal matrix but it is less sensitive to the current distribution considered and therefore more adapted to the calculation of the resistance matrix R Losses due to the ground planes as well as to the conductors are taken into account in this matrix If we consider the total power loss Pj due to the serie of conduction current vectors 11 ICi in the multiconductor structure the diagonal resitance matrix R is given by 3 R P 16 where Rs j is the surface resistivity of the jth conductor and the conduction vector and power loss are given by P 21 J a0 dp N P 3 IR K d dp j le Au e E 17 Once the power loss and the conduction current vector are known the diagonal resistance matrix R may then be deduced from Equation 16 Nevertheless according to 18 this last equation may still be simplified by noting that R is a diagonal matrix and that it may be replaced by a vector containing the diagonal element of R only
13. first column on the left called the layer column is used to design the dielectric layers of the structure considered The second column called the conductor column is used to add the conductors to this structure These two columns allow the user to specify diverse characteristics for both layers and conductors shape as well as material size and position They also allow the user to create new conductors and layers to display or plot them to erase them or to modify them The layer and conductor columns on the left of the interface have a very similar structure including analog options and design techniques Multiple buttons like Plot Erase lt or gt are included in both columns and they act the same in both columns except that the buttons on the layer column deal only with dielectric layers while the buttons on the conductor column deal only with the conductors There may be some slight differences between them which will be explained in detail in the paragraphs below We may now consider in more detail all the different options that will allow the user to design the final multilayered multiconductor structure 3 4 2 Design options The option New Conductor located on the conductor column allows the user to create a new conductor of the shape chosen beforehand strip rectangle or circle Strip is the default value Once the user has created this new conductor the right cha
14. layer The length dn corresponds to the distance between the top of the nth layer and the optional bottom ground plane and j corresponds to the permittivity of the nth layer We will first consider the simple case involving a multilayered structure with no ground or one bottom ground only In this case the exponential approximation may be directly applied to the spectral domain expression of the Green s function leading to e I py 24 X y 2 d_ d y G xylr 25 y Ki um n e o K 4ym n e o m 1 n m 1 p Aron X y y 2d V toz js y m n e Ki ym n e g m 18 for y gt yo The expression found for the case y lt yo is similar 13 Optional Ground Plane Nd Ho Nd e e n Ho gt e My p e e P lt m Ho Mo Xo Yyo Zo e e e 1 1 Optional Ground Plane Fig 2 1 Multilayered dielectric medium The four coefficient functions Kj j 1 to 4 m n 7 of the spectral domain Green s function can be approximated by the exponential form given in N D i E T M ss mn K annve C nil ge 19 where m and n correspond to the layer where the source is located and to the layer where G2D is being evaluated respectively and Nm n i is the number of exponential functions used in the approximation For more details concerning the evaluation of the coefficient functions refer to 18 Once Equation 18 of the spectral domain Green s function is analytical
15. leads to q c Ap p 6c D G xk q x dx 6d In Equation 6d the Green s function G x x and total potential are known while the charge distribution g x is unknown This is equivalent to Equation 1 where L is the Green s function G fis the charge distribution q and g is the potential 4 2 3 Capacitance Matrix For the sake of simplicity the MoM documented in Section 2 2 was only applied to 1 D electrostatic field problems the unknown charge distribution being only a function of x If the charge distribution considered was two or three dimensional the principle would stay the same For instance in the 2 D domain 18 the relationship between the potential Xr applied on a conductor and the charge g p accumulating on the surface of the conductor is given by prel G plo a p dr LG q a where is the contour of all the conductors ground excluded and G is the closed form Green s function Consequently the generic form of integrations involved in the construction of the moment matrix for the 2 D electrostatic problem is 2D IIT o G glp B o dp dp pp Hh 8 The functions T and B are the testing and basis functions which have been seen in the above 1 D MoM The segments and correspond to the source line and the testing line respectively The double integration is then reduced to a single integration using the method of collocation with pulse type basis functions and a test
16. the creation of nine files FourRect FourRect in FourRect out FourRect Q2D FourRect V2D and the mesh files Rectl mesh Rect2 mesh Rect3 mesh and Rect4 mesh The R L G and C matrices are obtained by selecting the option RLGC in the view menu The L G and C matrices will be of dimension 4H4 because there were four conductors considered in the structure If this structure was to be viewed or modified again in the future only the file FourRect containing the geometry of the interconnect and optionally the files FourRect out and FourRect V2D containing the results of the last simulation would be required 4 5 Conclusion Various structures have been discussed in this chapter involving different types of conductors and dielectrics The first example including one conductor and one layer only gave a quick insight on the basic use of XRLGC The second example extended the use of XRLGC to a more complex structure involving multiple layers and multiple conductors Finally the third example showed how an already existing structure may be modified to easily obtain another structure These three examples implied the use of strips and rectangular conductors but the use of circular conductors would be identical It is only essential to know that the shape of the conductor should be chosen before the new conductor in that particular shape is created Moreover the arrows may only be us
17. to look at the menubar located at the top of the GUI The menubar shown on Fig 3 2 includes the file edit view and help menus The help menu has already been seen in detail in the preceding section so we will concentrate here on the three first menus file edit and view File Edit View Help Context Sensitive Help Qualit Using Help Product Information Fig 3 2 XRLGC menubar 3 3 2 File menu The file menu allows the user to create open or save a file or to run a simulation on the data implied The option New in the file menu allows the user to create a new circuit For a circuit called Example five files may be created using options Save and Solve Example contains the structure of the circuit layers and transmission lines Example in contains the input file for RLGC and Example out Example Q2D and Example V2D contain the result of the solving process RLGC matrix Charge and Voltage distribution Moreover mesh files containing the mesh for each conductor inside of the structure may be created In order to simplify the notations this paper will always use the name Example for the circuit considered unless otherwise indicated The option Open in the file menu allows the user to open a circuit that was originally created with the program XRLGC Only the file Example is needed to open a circuit If this circuit has already been simulated the files E
18. x i ylil indicelil resistivity i FillColor i material cond i For each layer i Width layer il Height layerlil x layer i y layerlil e layer il s layer il FillLayer i Fig 5 10 Sample for the circuit file 5 2 4 Callback functions It would be too extensive to describe all the possibilities given by the interface Nevertheless the principle described above is always valid Each button pressed each menu option selected each action on the drawing area resize draw will call an adequate callback function This function will record some data open additional windows if necessary or update the structure on the drawing area In order to determine which callback function is linked to which widget the C developer may look at the definition of the corresponding widget Each object or widget is defined with certain characteristics including size parameters and callback function The definition of a widget may be found in any of the following files The main function of frontend c defines most of the widgets including all the menu options and all the toggle buttons The file graphtool c contains the definition of the three forms located at the bottom of the layer column and the conductor column form data layer form data strip form data rect and form data circle It also defines the main drawing area and the forms form button and form button2 including the four push buttons Plot Erase
19. 000e 00 00000e 00 00000e 00 Fig 5 3 Sample output file of Mesh2D rect mesh next program V2D to compute the potential distribution The program V2D is started by RLGC also determines the charge distribution included in the circuit Q2D file The charge distribution is given in the following format for each pair of points x1 y 1 X2 y2 defined in the mesh file the value of the charge q12 is determined This result is used by the typing V2D will ask for certain parameters as well size of the window considered number of points in each direction and index of the excited conductor A simple running of V2D is given in Fig 5 6 The resulting file circuit V2D contains the potential distribution according to the format given in Fig 5 7 V2D circuit in 51 Kyung S Oh 3 24 94 WI a Ss ek I eame ILEGALES ona ux IWIuE QAM xe ILL Qaa lue Convention Used O X y coordinates are used in the program o If there is ground plane at the bottom it is at y 0 o The conductor numbers used in the program are ordered as listed in this file o The dielectric number is assigned from bottom to top o Conductivity Unit S m o Resistivity Unit ohm mm O All parameters associated with length are in mm T Xp CMM c TEL M Acc ee al a es ey Number of conductors N mesh file namel Resistivity x y mesh file name2 Resistivity x y mesh file nameN Resistivity x y Note The mesh file
20. C matrix will be available in the file Example out but it may also be displayed using the command View RLGC on the menu The option Exit in the file menu allows the user to quit the program The user should save any modification in the circuit using the option File Save before using this command 20 Any modification of the circuit that has not been solved using File Save will be lost once the user exits the application 3 3 3 Edit menu The edit menu enables the user to modify some important parameters like the units used as reference the scale of the drawing area and the precision of the simulation The option Units in the edit menu allows the user to modify the units used as reference concerning length capacitance inductance and resistance The default length units are millimeters If the length unit is modified absolutely all the distances used in the circuit will be changed to those new units the distance defined for the structure before as well as after this modification Obviously the circuit displayed on the drawing area will not change because proportions are maintained The option Quality in the edit menu allows the user to modify the speed of the simulation and therefore its precision The user determines the number of basis functions used for the mesh construction This number is valid for all the conductors involved in the structure The minimum and maximum numbers that may be con
21. Mesh Construction 1 Strip 2 Rectangular 3 Polygon 4 Circle 5 quit Enter the Selection 2 Enter the mesh file name to be created rect mesh Enter width and height of line in mm 5 5 49 gt Enter of basis functions for width and height 5 5 Fig 5 2 Sample running of Mesh2D moving along each border and turning clockwise around the rectangular conductor There are five points per side according to the number of basis functions chosen The structure of mesh files for strips or circular conductors is similar This program needs to be called a few times to get all the mesh files for the structure considered Once the mesh files for each conductor are created the next step is to manually fill out the input file of the second program RLGC This input file contains the overall structure of the multiconductor multilayered transmission line The user carefully completes the number and dimensions of the conductors and layers according to certain standards defined at the beginning of the template file see Fig 5 4 The example given in Fig 5 4 considers one circular conductor of resistivity 1 73e 8 OHmm radius 0 5 mm located at x y 2 0 3 mm and included in a single layer of relative permittivity 4 and conductivity 2 67e 5 S m The structure has only one bottom ground 5 1 3 Running the simulation Once the input file circuit in is completed and all the mesh files are constructed the simulation is execut
22. RLGC I Directories lestrade XRLGC lestrade KRLGC ThreeRect in ThreeRect out ThreeRect Q2D ThreeRect V2D Selection homes I le les lestrade X RLGC ThreeRect Fig 4 15 Open file window 44 ThreeRect FourRect w 10 um w 10 um Free Space Free Space Eo AL lt gt Fo a lt gt h2 10 pm Substrate h1 210 um Fr4 Bottom Ground Plane Bottom Ground Plane Fig 4 16 Comparing the structures of ThreeRect and FourRect 45 The second conductor has the right width and height w 10 m h 3 my but the coordinates x y need to be changed from 15 10 to 30 10 Once those new coordinates are typed in and the button Plot located on the conductor column is pressed the modified second conductor will appear on the screen The right arrow may be used again to check the correctness of Conductor 3 The geometry of Conductor 3 w 210 m hz3 m x 30 m y 20 m being adequate the next step is to create the fourth conductor In order to design this last conductor the user selects New Conductor types in the four parameters w 10 _m h 3 m xz0 y 20 m and presses Plot 4 4 4 Saving and solving the circuit The four conductors are now displayed on the drawing area according to the structure shown in Fig 4 14 This structure may be saved by selecting the option Save from the file menu The mesh file construction and simulation are done quite similarly to Section 4 3 2 and they result in
23. XRLGC USER GUIDE A 2 D QUASISTATIC INTERCONNECT MODELING TOOL BY CLAIRE E LESTRADE French National Engineering Diploma Ecole Nationale Superieure des Telecommunications 1997 THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering in the Graduate College of the University of Illinois at Urbana Champaign 1998 Urbana Illinois Second page Certificate of committee approval TABLE OF CONTENTS CHAPTER 1 INTRODUCTION 1 1 Overview 1 2 The 2 D Quasistatic Modeling Tool XRLGC 1 3 Structure of the Thesis 5 BACKGROUND 2 1 Methods Implemented 6 2 2 Method of Moments 2 2 1 Basics 2 2 2 Application to a simple electrostatic field problem 2 3 Capacitance Matrix 2 4 Inductance Matrix 10 2 5 Conductance Matrix 2 6 Resistance Matrix 11 2 7 Closed form Green s Function 12 OVERVIEW OF XRLGC 3 1 Compiling and Running XRLGC 3 22 Using the Help Dialog 18 3 3 Using the Menu 3 3 Introduction 3 3 2 File menu 3 3 3 Edit menu PAGE oo 00 OQ wd 11 17 17 19 19 19 21 3 4 23 3 3 4 View menu Design of a Multilayered Multiconductor Structure 3 4 1 Introduction 3 4 2 Design options 3 4 3 Using the mouse EXAMPLES OF APPLICATIONS 4 1 4 2 4 3 44 4 5 Starting XRLGC A Single Microstrip Line 4 2 1 Hypothesis and geometry considered 4 2 2 Creating a new file 4 2 3 Drawing the struct
24. bstrate Si h2 10 um Substrate Fr4 hy 10 um Ground Plane Fig 4 10 Three rectangular conductors in a two layer structure The structure may be described as in Example 1 in Section 4 2 1 Geometry and material three identical conductors width w 10 m height h 3 m spacing s 5 m and material Cu x1 y1 0 10 m x2 y2 15 10 m x3 y3 30 20 m two dielectric layers first layer height h 10 m material Fr4 4 3 5 o 0 second layer height h2 10_m material Si 2 3 9 and o 0 0016 4 3 2 Starting The user may start as described in Section 4 2 However if XRLGC is already loaded and a different circuit is displayed on the drawing area three steps must be carried out First save this circuit by selecting File Save Then clear the drawing area by clicking on the clear button located towards the bottom of the interface Finally create a new circuit by selecting File New and naming the circuit for our purposes ThreeRect 4 3 3 Designing the circuit The first modification that needs to be done in this circuit is as follows The user 36 changes the default length units to microns instead of millimeters The user selects the option Edit Unit from the menu to open the corresponding dialog see Fig 4 11 Once the unit window is open the user selects Um for the length unit Um stands for microns and clicks OK A
25. conductor structure that has been collected by the interface d Makefile XRLGC SOURCES frontendl4 c mytool c graphtoole c manageform c cond call c layer call c RLGCl c lu c appx c intg c aux c apply c cust dialog3 c 54 help dialog c toolbar c V2D c OBJECTS frontend14 o mytool o graphtool6 o manageform o cond_call o layer call o RLGCl o lu o appx o intg o aux o apply o cust_dialog3 o help dialog o toolbar o V2D o CC gcc CFLAGS g I LFLAGS 1Xm 1Xt 1X11 1m PRODUCT XRLGC all result result OBJECTS CC S CFLAGS o PRODUCT OBJECTS LFLAGS clean rm o Fig 5 8 Makefile for XRLGC 5 2 2 Technical file description Sources of XRLGC include files that were part of the original RLGC package Those files have been slightly modified in order to communicate with the interface during the simulation and to give some warning to the user if some data are missing and the simulation could not be fulfilled Besides those small changes the files RLGC c V2D c Mesh2D c aux c appx c lu c and intg c are basically the same as in the original package The description of each C file and H file that is linked to the interface itself follows The variables and functions used in XRLGC are all defined in the file graphtool h The file frontend14 c contains the resources colors fonts label of all the C Motif widgets and the main function called by XRLGC The main function defines the interfac
26. ctions for high performance microprocessors BM J Res Develop vol 39 pp 547 567 Sept 1995 4 J E Schutt Aine Electromagnetic modeling of packages and interconnects Department of Electrical and Computer Engineering University of Illinois at Urbana Champaign Tech Rep June 1997 5 K S Oh J E Schutt Aine R Mittra and W Bu Computation of the equivalent capacitance of a via in a multilayered board using the closed form Green s function JEEE Trans Microwave Theory Tech vol MTT 44 pp 347 349 Feb 1996 6 J E Schutt Aine and K S Oh Modeling interconnections with nonlinear discontinuities in MCMs EEE Int Symp on Circuits and Syst vol 3 pp 2122 2124 1993 7 J E Schutt Aine Scattering parameters for the simulation of transmission line networks JEEE Int Symp on Circuits and Syst vol 4 pp 2693 2695 1990 8 W T Beyene and J E Schutt Aine Accurate frequency domain modeling and efficient circuit simulation of high speed packaging interconnects IEEE Trans Microwave Theory Tech vol 45 pp 1941 1947 Oct 1997 9 W T Beyene and J E Schutt Aine Efficient transient simulation of high speed interconnects characterized by sampled data in Proc IEEE 5th Topic Meeting on Electric Perform of Electronic Packag Oct 1996 pp 162 165 10 D B Kuznetsov and J E Schutt Aine The optimal transient simulation of transmission lines IEEE T
27. d O Top and bottom O Top and bottom 1 Press New Layer AUTE 3 Complete the height 4 Press Plot Fig 4 12 Layer design 39 The material Cu may then be chosen and the other parameters completed x y width height according to the calculation done above for the first conductor This conductor will then be displayed by clicking on Plot towards the bottom of the conductor column The user may repeat those steps for each rectangular conductor see Fig 4 13 In case an error is committed it is possible to use the arrows to go back to the corresponding conductor Once the error is corrected the user may press Plot again 4 3 4 Saving and solving the circuit The user may follow the guidelines given in Section 4 1 the file is saved using the option File Save from the menubar the quality of simulation is chosen from the Edit Quality menu 50 for every conductor and the mesh construction is started by selecting Mesh Construction from the file menu Once this is done four files have been created ThreeRect and the mesh files Rectl mesh Rect2 mesh and Rect3 mesh These files do not need to be saved for future use The user may then simulate the structure by selecting the option File Solve on the menubar and completing the potential simulation dialog Four additional files have been created in the process ThreeRectin ThreeRectout ThreeRect Q2D and
28. e and most of the widgets associated with it However graphtool6 c helps to unload the main function of frontend14 c by taking care of the creation of certain complex forms and their children widget for example the form containing the drawing area or the form displaying the four different shapes of conductors strip rectangular circular polygonal The functions included in manageform c manage the adequate form depending on the type of conductor chosen strip rectangular or circular This form asks for the dimensions width height radius and position x y of the conductor In the case of the strip the width and position x y are sufficient to model the conductor Similarly the rectangular conductor is characterized by its width height and coordinates x y while a circular conductor is characterized by its radius and coordinates x y The file cond_call c is only concerned with the conductors creating and erasing a conductor and going back and forth between conductors to modify them Similarly the file 55 layer_call c deals only with the layers creating and erasing a layer and going back and forth between the layers to modify them The functions included in apply c run all the different parts of the simulation mesh construction formerly Mesh2D computation of the R L G and C parameters formerly RLGC and estimation of the potential distribution formerly V2D This file constitu
29. ed by running RLGC and V2D successively First RLGC is started by typing gt RLGC circuit in The program RLGC computes the four parameters resistance inductance conductance and capacitance of the structure included in the input file Fig 5 4 Those parameters are given in the output file circuit out Fig 5 5 Rect mesh UnitFactor 1000 NumberOfBasisFns 20 MeshType Rectangular 5 00000e 00 5 00000e 00 0 00000e 00 0 00000e 00 0 00000e 00 1 00000e 00 0 00000e 00 1 00000e 00 0 00000e 00 2 00000e 00 0 00000e 00 2 00000e 00 0 00000e 00 3 00000e 00 0 00000e 00 3 00000e 00 0 00000e 00 4 00000e 00 0 00000e 00 4 00000e 00 0 00000e 00 5 00000e 00 0 00000e 00 5 00000e 00 1 00000e 00 5 00000e 00 1 00000e 00 5 00000e 00 2 00000e 00 5 00000e 00 2 00000e 00 5 00000e 00 3 00000e 00 5 00000e 00 3 00000e 00 5 00000e 00 4 00000e 00 5 00000e 00 4 00000e 00 5 00000e 00 5 00000e 00 5 00000e 00 50 ENW d Ul UI Ul UI Ul UW 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 COOOORNWHU 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 QO H N UU d UI UI Ul U1 UI 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 OOoOoooonNUu 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00000e 00 00
30. ed conductor is directly linked to the material and is stored in the array FillColor at the index compteur This function also updates the three counters compteur s compteur r and compteur_c for each kind of conductor These counters are essential when the user wants to go back and forth between conductors of the same shape The microstrip should be now displayed on the drawing area as well as the layer The completed structure may now be saved through the file menu The user will first select the option New in the file menu leading to the opening of a simple prompt dialog asking for the name of the new file The function NewFile in frontend c records the name of the new file circuit Second the selection of the option Save in the file menu will call the function Save_File in frontend c and thus create the file named circuit according to precise rules given in Fig 5 10 The full geometry of the structure will be saved in this file so that the structure may be opened again in the future by selecting the option Open in the file menu the user is calling the functions OpenFile and indirectly read file in frontend c This last function will read the file created above and display the corresponding structure It 59 will also update all the arrays for the conductors and the layers that have been defined earlier Ground options GND 0 1 or 2 For each conductor i Width i Height i
31. ed to go back and forth among 46 conductors of the same shape strip rectangle or circle If for example a conductor of circular shape needs to be modified the circular shape should be selected first Then the arrows may be used accordingly Similarly a layer may be modified by using the arrows located in the layer column Unfortunately if the user modifies the height of a layer the layer coordinates x y are no longer completed automatically in order to get layers lying on top of each other Consequently those coordinates have to be completed by the user 47 CHAPTER 5 STRUCTURE OF XRLGC This section will discuss the original program RLGC written by K S Oh before adding the interesting elements inherent to XRLGC and its GUI The RLGC package is made out of three main programs First Mesh2D creates a mesh file for one conductor given its geometry and the number of basis functions considered This program is called for each conductor of the structure and the output is a mesh file The second program RLGC computes the RLGC matrix and the charge distribution for the multiconductor multilayer structure described in an input file in Those results are stored in two separate files out and Q2D The input file is manually completed by the user The third program V2D computes the potential distribution given the same input file in and the charge distribution Q2D The program XRLGC presented
32. eight h 3 _m spacing s 20 m and material Cu x1 y1 0 h1 0 10 m x2 y2 w s h1 30 10 m x3 y3 w s h h2 30 20 _m x4 y4 0 h h2 0 20 m two dielectric layers first layer height h 10 _m material Fr4 4 3 0o o 0 second layer height h2 10 m material Si 2 3 9 o and o 0 0016 4 4 2 Starting It would be possible to design and simulate this third example in a way similar to the two preceding examples This would imply creating from scratch a new file and designing the two layers and the four conductors However a better solution will be exposed in this section The structure considered is similar to the three conductor example solved in Section 4 3 First the layered structure is absolutely identical Second two of the conductors are the same and the two others have the same dimensions but different coordinates Therefore this interconnect may be easily designed by slightly modifying the file ThreeRect created in Section 4 3 The design of the structure may therefore be started by opening the file 42 ThreeRect The window shown in Fig 4 15 will appear on the screen once the option Open in the file menu has been chosen The user may select the file ThreeRect and then close the window with OK The next step involves opening a new file under the name of FourRect The user may select the option New from the file men
33. he drawing area Step 1 of Fig 4 12 Resistance QQ O KQ O MO Inductance QH O nH O H Length Qum O mils Q mm O m Resistance pF O nF Q F 37 Fig 4 11 Units dialog The user follows similar directions to create the top layer Step 2 of Fig 4 12 with the parameters h2 10 Si The other parameters including position of the layer x y permittivity and conductivity are filled automatically once the material is chosen One layer is now positioned on top of the other Similarly the conductor column is used to add the three rectangular conductors to the circuit This process is easy and it only needs a short preliminary analysis of the structure considered the user should be able to give the origin lower left corner and dimensions of each conductor In this example the width and height of each rectangular conductor are 10 um and 3 m For the first conductor x 0 _m y h 10 m for the second conductor x w s 15_m y h 10_m for the third conductor x 2 w s 30 m y h1 h 20 m Once this is known it is very easy to design the structure in the following way The user chooses the rectangular shape represented by a rectangle on the top part of the conductor column and then clicks on New Conductor 38 Layer Generation two layers two steps One step Type of Dielectric Type of Dielectric 2 Choose the material D OPK Qs CA Or Qs oO No ground O No ground OD Bottom ground OD Bottom groun
34. he new layer on the drawing area The function store data layer updates the layer arrays Width layer Height layer x layer y layer e layer and s layer accordingly at the index compteur_layer In case the button New layer had not been called the layer located at this index simply would have been erased and replaced by this new layer with its new characteristics In order to display the new set of layers the full window is cleared and everything is drawn again In this example this set of actions led to the display of the layer in the drawing area Now the microstrip is added to the structure in the following way The selection of the strip shape calls the function manage strip in the file manageform c This function manages the correct form form data strip located at the bottom of the layer column so that it asks for the coordinate x y and width of the strip only The three forms form data strip form data rect and form data circle are already created when XRLGC is started and they are managed or unmanaged as needed This form asks for the dimensions width height radius and position x y of the conductor In case of the strip the width and position x y are sufficient to model the 58 conductor Similarly the rectangular conductor is characterized by its width height and coordinates x y while a circular conductor is characterized by its radius and coordinates x y
35. in this thesis links the three programs using a GUI The circuit is displayed on a drawing area and can be easily modified by the user The processing of the transmission line parameters is done in two steps mesh generation for each conductor menu File Mesh and solving menu File Solving Solving involves first automatic creation of the input file containing all the information about layers and conductors that have been collected by the interface and second computing the RLGC matrix charge distribution and potential distribution With the file menu the user can also create a new file open an already existing file and save the changes made to the circuit File New Open Save options The file contains the geometry of the multilayered multiconductor structure created With the edit menu the user can choose the different units distance inductance capacitance resistance determine the quality of simulation number of basis functions used and choose some parameters used for potential computation The RLGC matrix obtained through the simulation may also be displayed using the option View RLGC The potential and charge distributions are obtained in separate files that will be eventually displayed by the GUI With the help menu the user has an index and contextual help available 5 1 Structure of RLGC 48 5 1 1 Overview The files included in the source of RLGC are following C source RLGC
36. ine method yields to E t H t The transmission line simulation 2 implies consideration of the telegrapher s equations the eigen analysis E H Am and determination of propagation parameters Zm Zc Vm Three different methods can then be applied the transform approach the Green s function approach or the open loop numerical integration method Proficient transient simulation of transmission lines has been studied in the past 9 15 It has been seen that the optimal approach 10 may be found by considering closely the formulation the line characterization the line model and the transient simulation method used The resulting optimal method 10 applies the time only formulation with terminal voltages and currents only the open loop characterization the device model which can be directly incorporated into a circuit simulator as opposed to noncircuit models like scattering parameters and transient simulation based on indirect numerical integration This optimal simulation method has been applied to uniform 10 and nonuniform lines 16 17 This thesis focuses on the actual modeling of transmission lines through the R L G and C parameters The complex geometries involved in the VLSI system 18 can be modeled in two dimensions as long as the cross section of the conductors stays constant for a comparatively large distance The four parameters R L G C of quasi TEM lines may also be computed statically with go
37. ing point pc located at the center of the testing segment 1G p dp P 9 Now according to 18 if we apply MoM to the integral equation 7 by approximating each conductor with a polygon and by expanding the charge density in a set of basis functions we obtain p M M CM P P M M CM P j C p M NA M NO CM N N Py N 10a where P V p V dengthN i i 1 g d b d ength N M I G p lp lp ize N xN p 10b Here Nc is the number of conductors considered in the structure For a given conductor i Nj is its number of basis functions V is its voltage relative to the ground qij is the coefficient of gi according to the jth basis function Tig corresponds to the qth line segment and pije is the center point of the j basis function used in the point matching technique The charge distribution can then be deduced by solving Equation 10 Consequently the total charge Qj of the conductor i may be expressed as a function of the length and the charge density of each line segment N Q 3 liq gs 11 The capacitance matrix is then deduced immediately by solving V Q C C l C Vy Qv es where Vj is the voltage of the conductor i relative to the ground 2 4 Inductance Matrix The MoM applied to a 2 D electrostatic problem gave in Section 2 3 the charge distribution g p from which was deduced the total charge Qj for each conductor and therefore the
38. inter client data XtPointer call data void managematrix Widget widget XtPointer client data XtPointer call data void manageunity Widget widget XtPointer client data XtPointer call data void manageQuality Widget widget XtPointer client data XtPointer call data I void manageScale Widget widget XtPointer client data XtPointer call data void manageVoltage Widget widget XtPointer client data XtPointer call data void create graphic context result void void DrawShapes2 Display display Window window GC gc int width int height void drawCB2 Widget widget XtPointer client data XtPointer call data void Get Window Callback Widget widget XtPointer client data XtPointer call data functions included in help dialog c void manageIntro Widget widget XtPointer client data XtPointer call data Widget CreateIntroDlg Widget parent void manageHelp Widget widget XtPointer client data XtPointer call data Widget CreateIntroDlg Widget parent void HelpDlgShow void void HelpDlgCreate Widget parent XtCallbackProc topic callback XtPointer topic data XtCallbackProc help callback XtPointer help text data XtPointer help topic data void HelpDlgSetText char text void HelpDlgAddTopic char topic void HelpDlgDeleteAllTopics void void helpCB Widget widget XtPointer client data XtPointer call data void topicCB Widget widget XtPointer client data XtPointer call data Widget CreatePushbut
39. ion etc The help dialog will open and tell the user more about this particular element In Fig 3 1 one can see for example some instructions about the command Exit according to the help dialog the option Exit in the file menu allows the user to quit the program The help dialog also advises the user to save every modification in the circuit before using the command Such information is available on every option available through the menu or through any other element action buttons like Clear Plot New Conductor the drawing area itself and more When the user is done reading the corresponding instructions the dismiss button will close the help window Help Dialog Help on Exit Basic Information The option Exit in the File Menu allows the user to quit the program The user should save any modification in the circuit before using this command Dismiss Fig 3 1 Help dialog In order to use the index the Using Help option of the help menu should be selected The same window as for the Context Sensitive Help will appear on the screen The user just needs to choose the desired element in the left hand list The corresponding information should appear on the right hand side of the dialog 3 3 Using the Menu 3 3 1 Introduction After getting more familiar with the XRLGC program and the different options 18 through the help dialog described above the user may try
40. isticated modeling tool described above The design 19 of GUIs for electromagnetic simulation tools results not only in user friendliness but also involves a significant increase in user productivity First the input data files don t need to be typed by the user They are automatically extracted from the drafting tool which results in important time savings The simulation is also usefully documented by the precise drawing involved in the design of the multilayered multiconductor structure considered Finally the GUI allows the user to interactively run simulations and analyze the simulation results without concern for lower level computer processing XRLGC can therefore be used without any computer expertise 1 3 Structure of the Thesis The ease of learning a GUI based program makes it more accessible to new users However the accuracy of the results obtained through the interface is fixed by the simulation tool itself In other words the description of a GUI would be incomplete 19 without a detailed portrait of the electromagnetic tool involved including capacities limits and reliability Consequently before getting deeper into the use of the graphical user interface itself Chapter 2 will briefly present the methods implemented by K S Oh in his 2 D quasistatic modeling tool RLGC Among other important criteria 19 the GUI should be easy to use it should comply to industry standards like X Windows thus escaping any hardware o
41. l then begin Shortly thereafter the user will see a small window stating that the simulation is done The main results can be seen by choosing the option RLGC in the view menu A new window will then display the four matrices R L G and C see Fig 4 9 The potential distribution may be read in a separate file Microstrip V2D Refer to Section 5 1 3 for more information about the format of the V2D output files 33 Window used for the V2D Simulation Window Coordinates Bottom Left Top Right Number of Points Excited Conductor Number Fig 4 8 V2D simulation dialog 34 RLGC matrix Inductance Matrix nH m 5 20862e 02 Capacitance Matrix pF m 6 43547e 01 Conductance matrix S m 0 00000e 00 Resistance matrix ohm m 1e 09 0 00000e 00 Fig 4 9 RLGC custom dialog for the microstrip case 4 3 Three Conductors in a Layered Medium 4 3 1 Hypothesis and geometry considered Example 1 with one layer and one conductor showed the basic features of the GUI This example will study the design of multilayered and multiconductor structures We consider the structure shown in Fig 4 10 We assume that the three rectangular conductors are identical and the number of basis functions per side is chosen equal to 50 for each conductor The coordinates xj yj of the three conductors can easily be deduced from Fig 4 10 as will be seen in Section 4 3 3 35 Free Space w 1Q um Eo Su
42. label2 1label s buttonl button2 button3 labelx labely frame shape form shape label3 labelx2 labely2 textex2 textey2 texte3 labelx3 labely3 button4 label layer form_layer form_common Clear Exit menubar menus menus2 menus3 menus4 cascades cascades2 cascades3 cascades4 buttons 9 buttons1 3 buttons2 5 buttons3 5 dialogi dialog2 New frame cond frame layer radio box radio buttoni radio button2 radio button3 radio button4 frame radio box radio box2 radio button12 radio button22 radio button32 radio button42 frame radio box2 labele textee labels textes form es labell s textel s label2 s texte2 s textex s textey s labelx s labely s 66 labele s labels s textee s textes s form data rect s New layer radio box g radio buttonl g radio button2 g radio button3 g radio button4 g frame radio box g cust unity RLGC drawing result label matrixC label matrixL label matrixR label matrixCo label RLGC sep2 Intro label intro title warning working Quality label quality title quality scale quality Scale texte scale Voltage frame Voltage label Voltage title voltage texte2 V texte3 V texte5 V texte6 V texte2 V2 texte5 V2 texte2 V3 XtAppContext app int k n i screen screen2 int store layer store char buffer BUFFERSIZE double Width NC Height NC xI NC y NC X NC Y NC resistivity NC int indice NC long int FillColor NC FillLayer NS double Width layer NS Height layer NS x layer NS y layer NS e layer
43. ll document the installation of XRLGC The second section will then describe the use of the online help dialog The third section will go into more detail about the different options given by the menu including file managing in the file menu units quality and scale options in the edit menu and finally displaying the results through the view menu The design of a multilayered multiconductor structure with the help of the interface will also be studied in the last section 3 1 Compiling and Running XRLGC The program XRLGC may be compiled by following the subsequent instructions First in order to unzip the file the user needs to type gt gzip d XRLGC tar gz gt tar xvf XRLGC tar or gt tar zxvf XRLGC tar gz Second in order to compile the program on an HP workstation the user will type these additional commands gt make f Makefile_HP or gt cp Makefile_HP Makefile gt make Third in order to run the program the user may simply type gt XRLGC amp 3 2 Using the Help Dialog Once the program XRLGC is successfully compiled and running the next important 17 step is to look at the help menu which gives the option to use either an index or a context sensitive help dialog In order to use the latter the user may press the Context Sensitive Help option of the help menu The mouse arrow will take the shape of a question mark The user may then use the mouse to click on the desired element a pushbutton a menu opt
44. ll the dimensions appearing in the GUI will then be microns by default In this example the structure has only one bottom ground so the option bottom ground only should be chosen Next two layers will be created by using the layer column on the left hand side of the interface First the user should select New Layer to create the bottom layer The user may note that the x y coordinates of the dielectric layer are automatically completed for each new layer created in order to get layers to lie on top of each other Consequently the first layer has coordinates 0 0 the second layer has coordinates 0 57 and the nth layer 0 E hj where hj is the height of the ith layer XRLGC cannot compute the parameters of interconnects involving a more complex dielectric structure In order to have a successful simulation the user should therefore not change the coordinate values x y located at the bottom of the layer column Second the characteristics of the bottom layer hy 10 Fr4 should be completed accordingly The user should select the option Fr4 from the material located at the top of the layer column The permittivity and the conductivity of Fr4 4 345 o7 0 will be automatically completed by the program on the form located at the bottom of the layer column The user should then manually complete the dielectric height value in this same form The button Plot allows the user to see the new layer displayed on t
45. ly inverted into the space domain the final expression obtained for the closed form Green s function is given by Neu T G lo c 5 3 fi p m i l 20a where for i 1 m N mal 2D gt gt Tj P 2 2 j 28 fi olo amp 3 Cy in amp x y d a n E j 1 20b Similar expressions for the functions fj with i 2 3 and 4 may be found easily When there is both top and bottom ground the expression for the spectral domain Green s function will be similar except that the four coefficient functions Kj y m n have a pole at y 0 that must be extracted before the approximation through real exponential functions 18 The spectral domain Green s function may hence be written as the sum of two terms G yl e R G i ylr G y ylr 21a 15 where G corresponds to the case of no ground or only one bottom ground which has been seen previously and Gh corresponds to an homogeneous medium between the top and bottom grounds According to 18 G is given by 3E 2 po 2 gt solo gal 2 In of amp x 6 y 2 l dd Ju 3 4 i amp x y 2kh 21b The closed form Green s function has therefore been evaluated for all cases involving no ground only one bottom ground or both bottom and top grounds 16 CHAPTER 3 OVERVIEW OF XRLGC This overview will help the user to manipulate the program XRLGC easily and efficiently The first section wi
46. mm material Fr4 permittivity 2 4 3 o conductivity o 0 This is a very good way to summarize the main characteristics of a given interconnect The geometry and the material of each conductor and of each layer should be included when there is more than one conductor and more than one layer The coordinates x y of the lower left corner of each conductor should be included as well In the case of the strip the value given to x is arbitrary because it is the first conductor The value of y is deduced from the height of the first layer y h 5 mm Once this description is done the design of the structure itself with the program XRLGC should be extremely simple 4 2 2 Creating a new file The option New in the file menu allows the user to create a new file with the help of a custom dialog Fig 4 4 Once the dialog appears on the screen the user may type the name of the file to create for example Microstrip and then choose OK to close the window Another option would be to open an already existing file using the option Open in the file menu This will be seen in Section 4 5 Name of new File 28 Fig 4 4 New file window 4 2 3 Drawing the structure In this example the structure has only one bottom ground so the option bottom ground only on the layer column Fig 4 5 which is located on the left hand side of the interface should be chosen Next the unique layer will be created by selecting
47. names do not have to be distinct x y is the global coordinate of the local origin for each mesh file Nconductors 1 circle mesh 1 73611111e 8 0 0 3 0 Number of layers without ground planes Nlayers L Wen ees oo ee ses rimus edi a ba apa EA mma uc matu cam See a man e IARE Lm AMI Se eve OS LL aa EE cod m ee oS ey Ground plane options 0 for no ground plane 1 at the bottom layer only 2 for ground planes at top and bottom GND GND option Resistivities iff any ex GND 0 GND 1 Rvalue GND 2 Rvalue lower Rvalue upper GND LO Er 4 0 The conductivity of the layers Conductivity 2 67e 5 p a fea ERAT a MT PTT rre ee a oer me VE a IR ee a ty ds are the distances from the ground plane to dielectric interfaces The bottom ground plane is assumed to be at y 0 The value of the last entry is the location of the top ground plane If there is no top ground plane enter an arbitrary number ds mm 1e10 frequency fstart fstop fstep Frequency 0 1e9 0 1e9 0 1e9 Fig 5 4 Template for the input file of RLGC circuit in 52 circuit out Capacitance Matrix pF m 8 97505e 01 Inductance Matrix nH m 4 95211e 02 Conductance Matrix S m 6 76611e 05 Resistance Matrix ohm m 1e 08 8 44559e 04 Fig 5 5 Sample of an output file of RLGC circuit out gt V2D circuit in gt Enter X Y coord of the BOTTOM LEFT corner of window mm O O gt Enter X Y coord of the TOP RIGHT corner
48. nd basically updating the variable ground to the Value 1 The Value 0 means no 56 Fig 5 9 57 ground the Value 1 means a bottom ground and finally the Value 2 means both bottom and top ground This value is automatically recorded by the interface Then a new layer has been created by clicking on New Layer consequently calling the function New Layer callback in the file layer_call c This function updates the counter compteur layer and the total number of layers nombre_layer while it completes the form located at the bottom of the layer column in order to get layers located on top of eachother The counter is useful when the user decides to move from one layer to the other with the arrows and lt The counter tells the interface at which index it should look inside the layer arrays to find the right layer see below Thereafter the type of layer Fr4 may be selected at the top of the layer column The function toggleCB in frontend c is called again setting the variable current type layer to 3 and completing the form located at the bottom of the layer column to get a relative permittivity of 4 3 The user may then complete the height of the new layer h 2 5 m and click on Plot This push button will then call the callback function store data layer in frontend c This function is a rather complex procedure that involves updating many variables and the display of t
49. nect are the finite element method FEM the partial element equivalent circuit method PEEC the finite difference time domain method FDTD and the method of moments MoM The simulation methods can employ scattering parameters 7 8 model order reduction or a difference model Finally optimization can be obtained using neural networks genetic algorithms or simulated annealing The circuit modeling 2 may be static d dt 0 or dynamic d dt o 0 The static analysis of a physical model considering the integral form of Maxwell s equations implies the use of either Green s function in spectral domain or in closed form or the PEEC method in conjunction with solvers like MoM the conjugate gradient method CGM or the fast multipole method The charge distribution and the RLGC model can be deduced from there However if the static analysis considers the differential form of the Maxwell s equations then the method applied is the static FEM or the Method of Line MoL in conjunction with a matrix solver sparse or full matrix technique The potential distribution and the RLGC model are then deduced The dynamic analysis may be done in time domain or in frequency domain In frequency domain the full wave techniques yield E f H f which are the respective Fourier transforms of E t H t The dynamic circuit model RH Li CA G f can then be deduced This model can be found similarly in time domain once the FDTD or TLM transmission l
50. ng of interconnects and capacitive discontinuities in high speed digital circuits EMC Lab Technical Report no EMC 95 1 June 1995 19 O Nayac G Irwin and A Neufeld GUI enhances electromagnetic transients simulation tools IEEE Computer Applications in Power vol 8 pp 17 22 Jan 1995 20 K S Oh D B Kuznetsov and J E Schutt Aine Capacitance computation in a multilayered dielectric medium using closed form spatial Green s function IEEE Trans Microwave Theory Tech vol MTT 42 pp 1443 1453 Aug 1994 21 I Hajj Computational techniques for circuit analysis and design class notes for ECE 452 Department of Electrical and Computer Engineering University of Illinois at Urbana Champaign Spring 1997 22 W T Weeks Calculation of coefficients of capacitance of multiconductor transmission lines in the presence of a dielectric interface IEEE Trans Microwave Theory Tech vol MTT 18 pp 35 43 Jan 1970 70 23 C Wei R F Harrington J R Mautz and T K Sarkar Multiconductor transmission lines in a multilayered dielectric media JEEE Trans Microwave Theory Tech vol MTT 32 pp 439 450 April 1984 24 W Delbare and D D Zutter Space domain Green s function approach to the capacitance calculation of multiconductor lines in multilayered dielectrics with improved surface charge modeling EEE Trans Microwave Theory Tech vol MTT 37 pp 1562 1568 Oct 1989 25 S
51. od accuracy because the transverse distribution of the fields at any time t will be nearly identical to that computed by static analysis Consequently XRLGC models the transmission lines statically using the MoM method in conjunction with the closed form Green s function The 2 D quasistatic modeling tool XRLGC can therefore compute accurately the electrical parameters of multilayered multiconductor structures using those computationally efficient algorithms 1 2 The 2 D Quasistatic Modeling Tool XRLGC The XRLGC package models a 2 D multiconductor transmission line in a multilayered dielectric medium by computing the four transmission line parameters R resistance L inductance G conductance and C capacitance as well as the charge and the potential distributions in this structure The cross section of the conductors may be strip like rectangular or circular It is assumed that the length of the conductors is long compared to the constant cross section The microstrip case as well as the stripline case may be handled by using the ground options accordingly no ground bottom ground only or both top and bottom grounds The output of XRLGC can also be used as an input to another program deducing voltages and currents along the transmission line 2 The 2 D quasistatic tool XRLGC uses the MoM in conjunction with the closed form instead of the classical Green s function The long computation involved in determining the classical Green
52. of window mm 10 10 gt Enter number of point in x and y direction 10 10 gt Enter the excitated conductor number 1 Fig 5 6 Sample running of V2D O0 Nx Ny Dx Dy Xstart Ystart Xstop Ystop V x 1 v 1 V x 2 y 1 V x Nx y 1 V x 1 v 2 V x 2 y 2 V x Nx y 2 V x 1 y Ny V x 2 y Ny V x Nx y Ny Fig 5 7 Format of an output file of V2D circuit V2D 5 1 4 Technical file description Now that we have seen how the three programs work and how they interact to compute the final results it is interesting to look at the corresponding files one by one RLGC c Mesh2D c and V2D c are respectively the main routines for the three programs described above The four additional C files contain a set of tools useful to those main programs Appx c generates the closed form Green s function Intg c is a set of integration routines Lu c includes the LU factorization and forward and backward routines Aux c contains the utility functions to create the vectors and matrices The Mesh2D program basically uses Mesh2D c and aux c the V2D program uses V2D c aux c appx c and intg c and the RLGC program uses RLGC c and all four additional C files aux c appx c intg c and lu c The resource file aux h defining some structures and declaring the functions included in aux c is used in the three programs Mesh2D RLGC and V2D
53. og will open asking for the window coordinates used in the voltage simulation the number of points in each direction and the excited conductor number see Fig 4 8 31 Quality of the Simulation Specify the Quality of the Simulation The Simulation may run faster or be more precise according to the desire of the user Choose the number of basis functions used to create the Meshfiles Precision or Speed Low Number Quick and Unprecise High Number Slow and very precise 0 50 100 Quick Unprecise Slow Precise Fig 4 6 Quality of the simulation Working Dialog Mesh Created Fig 4 7 Mesh creation window 32 If the user does not want to consider this second simulation but would prefere to look at the RLGC simulation results right away it is possible to skip this part by pressing Cancel instead of OK in the voltage window In the example given in Fig 4 8 the bottom left corner of the simulation window is 0 0 and the top right corner is 10 10 The number of points in each direction is equal to 10 Furthermore the microstrip is chosen to be the excited conductor The conductor number corresponds to the order in which it has been created and displayed on the drawing area The microstrip has been created first and it is the only conductor present in the structure so the conductor number of the microstrip is simply 1 Once the necessary data is filled the user shall click OK The simulation wil
54. olved in the structure For example if the structure includes two rectangular conductors and one circular conductor the files created will be rectl mesh rect2 mesh and circle3 mesh The option Solve in the file menu allows the user to run the simulation on the circuit It will use as an input the circuit displayed in the drawing area and the mesh files created by the option Mesh Consequently the mesh creation should be done before running the simulation with Solve Once the option Solve has been chosen the program XRLGC will start to compute the R L G and C parameters of the structure considered As soon as the RLGC simulation is done a new custom dialog will appear on the screen This dialog allows the user to specify the window used for the potential simulation The user will also decide which conductor should be excited and the number of points that should be used in the x and y directions Having typed in the corresponding information the user may click on the button OK of the potential simulation dialog This allows the program XRLGC to complete the full simulation However if instead the button Cancel is chosen then the potential distribution will not be computed Once the simulation is done an information window will warn the user that the circuit has been solved Charge and potential distribution will then be available in the files Example Q2D and Example V2D The RLG
55. piling XRLGC may be started by typing in the command line gt XRLGC amp A small window should appear on the screen describing succinctly the program see Fig 4 1 Once the information is displayed click OK to get to the main program The main window will then appear on the screen see Fig 4 2 Note the presence of a drawing area on the right hand side where the simple structure will be drawn The left part of the interface is divided into the layer column and the conductor column as shown in Chapter 3 Those two columns are essential to the design of the multilayered multiconductor structure 4 2 A Single Microstrip Line 4 2 1 Hypothesis and geometry considered We consider the structure shown in Fig 4 3 It is assumed that the line is infinitely thin and the number of basis function is 50 25 Introduction About RLGC Introduction to RLGC Program This Program has been written by Claire Lestrade K S Oh Jose Schutt Aine Last Modification July 97 Fig 4 1 Introduction window 26 Edit View Q No ground Bottom ground DRAWING AREA Top and bottom Fig 4 2 Main window w 3mm Free Space Eo lt gt Substrate h 5mm Fr4 Ground Plane Fig 4 3 A single microstrip line The following description should be done for every structure considered Geometry and material one conductor strip width w 3 mm material Fe xy 15 5 one dielectric layer height h 5
56. position x y its dimensions width and the material used In Example 1 the width of the conductor is w 2 3 mm the position x y 15 mm 5 mm and the material is iron Once this information is given the user may click on Plot to see the strip appear on the drawing area Now that the structure is completely drawn on the screen one can go to the next step saving and starting the simulation 4 2 4 Saving changes and creating the mesh files First of all the option Save in the file menu should be selected in order to save the new file Microstrip Then before starting the simulation the user should select Quality from the edit menu and indicate 50 basis functions Fig 4 6 The mesh file for the strip will then be created according to the number of basis functions chosen by selecting the option Mesh Creation in the file menu Shortly thereafter the user will see a small window stating that the mesh has been created Fig 4 7 This working window may be closed by simply pressing OK Two new files have been created Microstrip and stripl mesh 4 2 5 Starting the simulation and looking at the results The user may now choose the option Solve from the file menu to simulate our single microstrip structure Both RLGC parameters and potential distribution will be determined through this simulation Once the RLGC simulation is finished the potential simulation will begin A new custom dial
57. r software needs and or compatibility problems and it should involve online help on useful topics The interface presented here possesses all these features Nevertheless without a good user manual the user may occasionally be unsure of various technical details Chapter 3 gives a quick overview of the essential topics including the installation of XRLGC the online help the various menu options and directions for the design of any interconnect structure These guidelines may then be applied using the examples given in Chapter 4 Because integrated circuit technology develops and changes rapidly computer aided design CAD tools need to be capable of adapting quickly and efficiently to the future needs of the user The comments and notes embedded in the source code might not always be sufficient to explain the whole program structure so that it can be proficiently improved Consequently Chapter 5 documents in detail the structure of the program XRLGC so that a C developer can modify the source code adequately CHAPTER 2 BACKGROUND 2 1 Methods Implemented The interconnects considered by XRLGC have a complex 2 D structure involving up to 20 layers and up to 20 conductors of small cross section compared to their length The cross section shapes available for the conductor in XRLGC are the strip the rectangle and the circle The limits given to the number of layers and conductors implied in the structure may be easily changed in the resou
58. racteristics can be inserted in the proper places width height and origin x y The conductor can then be displayed using the pushbutton Plot The user can also draw with the mouse directly on the drawing area Similarly the option New Layer located on the layer column allows the user to create a new layer Afterwards the user should insert the corresponding characteristics in the layer column width height origin x y relative permittivity and resistivity The dielectric will be displayed on the drawing area using the Pushbutton Plot The user can also draw with the mouse directly on the drawing area However the different dielectrics will always lie on top of each other 22 Once the conductor or the layer is displayed on the screen it is always possible to modify it again by correcting the corresponding data on the interface dimensions shape origin or other characteristics and pressing Plot again However if other conductors or layers have been created using New Conductor or New Layer it is possible to go back to this first conductor or layer by using the arrows and then correct the desired data as described above The corrected conductor or layer will be displayed by pressing Plot once again In other words the user has permanent access to the whole structure The left arrow on the conductor column will allow the user to go back to the conductors of the same shape s
59. rans Circuits Syst I vol CAS 43 pp 110 121 Feb 1996 11 T Dhaene L Martens and D De Zutter Transient simulation of arbitrary nonuniform interconnection structures characterized by scattering parameters EEE Trans Circuits Syst vol 39 pp 928 937 Nov 1992 69 12 D B Kuznetsov J E Schutt Aine and R Mittra The optimal transient simulation of distributed lines JEEE Multichip Module Conf pp 164 169 Feb 1995 13 J S Roychowdhury and D O Pederson Efficient transient simulation of lossy interconnects in Proc 28Th ACM IEEE Design Automation Conf June 1991 pp 740 745 14 N Orhanovic and V K Tripathi Nonlinear transient analysis of coupled RLGC lines by the method of characteristics Int J Microwave Millimiter Wave CAE vol 2 pp 109 115 1992 15 E Chiprout and M S Nakhla Transient waveform estimation of high speed MCM networks using complex frequency hoping in Proc Multichip Module Conf MCMC Santa Cruz CA March 1993 pp 134 139 16 D B Kuznetsov and J E Schutt Aine Efficient circuit simulation of nonuniform transmission lines submitted to IEEE Trans Microwave Theory Tech Jan 1997 17 F Y Chang Transient simulation of frequency dependent nonuniform coupled lossy transmission lines IEEE Trans Components Packaging and Manufacturing Tech vol 17 pp 3 14 Feb 1994 18 K S Oh and J E Schutt Aine Efficient modeli
60. rce file The XRLGC program may also be extended to any polygon shaped conductor cf Section 5 The RLGC parameters of an interconnect are computed accurately in the XRLGC program by using the following methods 18 20 Capacitance C is determined using the MoM associated with the closed form Green s function avoiding the use of numerical integration or nested infinite sum involved in the classical full Green s function Inductance L is deduced from the equivalent capacitance problem The charge distribution obtained during the computation of C and L is used to deduce resistance R and conductance G In other words no additional electrostatic problem is solved in the process The model of the diagonal resistance matrix has been chosen because it is not as sensitive to the choice of the current excitation as is the usual nondiagonal resistance matrix Both losses on conductors and ground planes are taken into account in the computation of R MoM will be briefly explained and its application to the capacitance computation presented The methods used for the computation of the three other matrices L G and R will then be introduced succinctly Finally the closed form version of the Green s function used in MoM will be defined in the last section 2 2 Method of Moments 2 2 1 Basics MoM 2 basically consists of solving Eq eg 1 where L is an integral or differential operation f is an unknown function and g is a known function We will see ho
61. rge LSD or very large VLSI The lossy coupled metal interconnects have width and height of about 4 and 3 um respectively At the package level interconnections link the chip to the board as well as chips to eachother for multichip modules MCM using tape automated bonding TAB pin grid array PGA ball grid array BGA or dual in line packaging DIP The low loss coupled metal lines are 1 10 mil wide and spaced at about 2 12 mil Packaging needs to follow adequate guidelines to get short delays high bandwith and a large I O count with a dense wiring and a compact size Consequently the high density creates signal integrity problems including cross talk attenuation distortion reflections dispersion and radiation The bandwidth limitations are also due to the skin effect the non TEM propagation and propagation of higher order modes and parasitics For example with current technology both the CPU and the whole cache system may be included on one single microprocessor chip working at a high clock rate up to 300 Mhz involving according to 3 from 4 to 9 million transistors and thus high density wiring Those transistors may be interconnected through a structure of between three and five layers The high density implies also that interconnects have very small width and spacing less than le 6 m and therefore high resistance 35 to 500 Q cm The interconnects between the processor and the cache including clock lines control lines
62. rip case Three rectangular conductors in a two layer structure Units dialog Layer design Conductor design Four rectangular conductors in a two layer structure Open file window Comparing the structures of ThreeRect and FourRect Original makefile for the RLGC package Sample running of Mesh2D Sample output file of Mesh2D rect mesh Template for the input file of RLGC circuit in Sample of an output file of RLGC circuit out vi 14 18 19 26 27 28 29 30 32 33 35 38 39 41 42 44 49 50 5 6 5 7 53 5 8 5 9 57 5 10 5 11 Sample running of V2D Format of an output file of V2D circuit V2D Makefile for XRLGC Simple microstrip case Sample for the circuit file Definition of a widget vii 33 55 60 61 viii CHAPTER 1 INTRODUCTION 1 1 Overview Constant progress in integrated technology has occurred in recent years involving extremely high numbers of transistors and interconnects and also improved performance 1 Signal rise time and cycle time have decreased consequently the delay due to interconnects can no longer be neglected Interconnections may be found at the chip package and board levels as well as at the assembly level implying large differences of their density and size 2 At the chip level transmission lines connect an increasing number of gates depending on the scale of integration small SSI medium MSI la
63. s function in the spatial domain 18 is thereby avoided Only one electrostatic problem is solved in order to compute the capacitance matrix The inductance matrix L is deduced from the equivalent capacitance problem In addition the charge distribution obtained during the computation of the capacitance matrix C and the inductance matrix L is used to deduce the resistance matrix R and conductance matrix G The original RLGC package written by K S Oh in 1995 applies the same methods to model a multilayered multiconductor transmission line However RLGC is made of three different programs Mesh2D V2D and RLGC Mesh2D creates the mesh file for a given conductor V2D computes the potential distibution and RLGC computes the R L G and C parameters and the charge distribution of the structure considered Consequently the design of any structure with the package RLGC implies the multiple use of these three different programs For example Mesh2D needs to be called for each conductor of the structure Similarly a complex input file needs to be completed for each structure considered containing the detailed geometry and characteristic of each element layer or conductor The use of the package RLGC is therefore difficult and time consuming However the program XRLGC presented in this thesis links the three programs together using a graphical user interface GUI This GUI has one main goal to provide the user a way to use easily the very soph
64. sidered are five and one hundred basis functions per side the default value being five basis functions per side This number defines the quality and speed of the simulation The higher the number the slower and more precise the simulation The lower the number the quicker and more imprecise the simulation Obviously this choice should be done before the mesh is created The option Scale in the edit menu allows the user to zoom in on the lower left part of the drawing area by choosing the size of the window The default value Xmax Ymax 100 default unit mm may be modified through the scale dialog 3 3 4 View menu The view menu enables the user to display the result of the simulation The option RLGC in the view menu opens a window that displays the RLGC matrix of the circuit This menu may be improved by adding two options charge and potential distribution For now those results are only available through the Example Q2D and Example V2D files 3 4 Design of a Multilayered Multiconductor Structure 21 3 4 1 Introduction Now that each option of the menu has been clearly identified it is time to see how to use XRLGC to actually design a multilayered multiconductor structure We will consider the different design options below then see actual examples in Section 4 The interface is divided into four main parts the menu on the top part the drawing area on the right and two adjacent columns on the left part The
65. t width int height void drawCB Widget widget XtPointer client data XtPointer call data void Exit mesh Widget w XtPointer client data XtPointer call data void store data Widget w XtPointer client data XtPointer call data void NewFile Widget w int client data XmSelectionBoxCallbackStruct call data void OpenFile Widget w int client data XmSelectionBoxCallbackStruct call data void store data layer Widget w XtPointer client data XtPointer call data void toggleCB Widget widget XtPointer client data XtPointer call data void read data char fname void colour call int n int p void cancelCB Widget w XtPointer client data XtPointer call data void okCB Widget w XtPointer client data XtPointer call data void AddStdCallbacks Widget widget char name 63 functions included in manageform c void manage strip Widget widget XtPointer client data XtPointer call data void manage rect Widget widget XtPointer client data XtPointer call data void manage circle Widget widget XtPointer client data XtPointer call data functions included in graphtool c void create drawing area void void create form strip void void create form circle void void create form rect void void create form button void void create form button2 void void create type frame void void create graphic context void void draw cbk Widget w XButtonEvent event String args int num args void Eq
66. tes the main link between the GUI and the original RLGC The file cust dialog3 c creates all the custom dialogs except the help dialog introduction dialog units dialog quality dialog RLGC dialog and voltage dialog These complex dialogs have been designed specifically for this program The more simple dialogs like the working dialogs or the prompt dialogs are already partially implemented by Motif The file help dialog c creates the help dialog and associated functions Finally toolbar c put adequate bitmaps on pushbuttons including the strip rectangle circle and polygon representing the possible cross sections for a conductor This file also inserts the arrows to go back and forth between conductors and layers A more detailed description of those different files and the functions included is given inside the sources themselves The goal of each function is given in the form of commentaries embedded inside the C files 5 2 3 File interaction In the preceding section each file has been described in detail In this section the interaction between those files will be clarified through a simple example The first example seen in Section 4 2 will be considered to explore how each widget included in the interface does its task Fig 5 9 includes all the action performed by the user In the layer column the option bottom ground only has first been selected calling the function toggleCB in the file frontend c a
67. tonWithHelp Widget parent char name XtCallbackProc callback XtPointer client data XtCallbackProc help callback XtPointer help data void contextCB Widget widget XtPointer client data XtPointer call data functions included in toolbar c Pixmap CreatePixmapFromBitmap Widget widget int weight 65 int height Pixmap bitmap Boolean LoadBitmapLabel Widget widget char filename Pixmap ReadBitmapFile Widget widget char filename int width int height void SetLabelPixmap Widget widget Pixmap pixmap BRK RR KR KKK KKK KKK KK KK k k k k k ke k k k k k kk k e e x Global variables and constants BRR RR kkk KKK KKK k k k KKK KR KR k k k k KKK KK KK DEFINE define PI 3 141592653589793238462643 define BUFFERSIZE 800 define OK 1 define CANCEL 2 define MAXIMAL NUMBER SEGMENTS 20 define NC 20 Maximal number of conductors define NS 10 Maximal number of layers define N E 5 number of edge circle define E 100 Scale echelle Global variables int type compteur s compteur r compteur c compteur nombre conducteur compteur local type local compteur local2 int nombre layer compteur layer int width total height total Arg al 10 args 10 Cardinal ac double size double ind unity capa unity res unity length unity int no exit singular matrix int E int Chosen NB N F N F w N E h Widget toplevel mainbox form cond form button frame labell
68. trip rectangular or circular that have already been displayed and to modify their main characteristics including their width height and location x y Similarly the pushbutton lt on the layer column allows the user to go back to already created layers and to modify their characteristics width height location x y resistivity and permittivity The right arrow gt allows the user to go forward again assuming that the pushbutton backward 1 lt has already been used For conductors the combination of these two functions in the conductor column gt and lt allows the user to go back and forth between the different conductors of the same shape strip rectangular or circular and to modify their characteristics width height and location x y Similarly the combination of these two functions on the layer column allows the user to go back and forth between the different layers displayed and to modify their characteristics width height location x y resistivity and permittivity The pushbutton Plot allows the user to display the conductors layers in the drawing area Once the characteristics of a conductor layer have been modified using the left and right arrows the user may push Plot to see those modifications on the screen The pushbutton Erase allows the user to erase one conductor or layer in the drawing area The user should use the left and right arro
69. ttomAttachment XmATTACH FORM XmNrightAttachment XmATTACH FORM XmNleftAttachment XmATTACH FORM NULL XtAddCallback button4 l1 XmNactivateCallback Erase layer NULL XtAddCallback button4_1 XmNhelpCallback XtCallbackProc helpCB XtPointer Erase Fig 5 11 Definition of a widget In this example the function Erase_layer may be found in the resource file graphtool h Appendix A It is labeled as a function included in the file layer call c This function may therefore be easily found Moreover each function is preceded by a short overview of the content of the function in the form of comments embedded in the source This method should be very useful for the C developer in order to understand better and then improve the behavior of any widget 5 3 Conclusion This thesis has presented the program XRLGC at every level First it includes the technical background and the methods adopted for the EM specialist Second its user guide is adapted for the beginner as well as for the computer expert Finally it includes an overview of the structure of XRLGC containing guidelines on how to approach and improve this complex program with relative ease Ideally this program should be preserved and adapted by 61 engineers who combine both the technical EM background and the ease of the good programmer Technical improvements to this program may involve the extension of the GUI to include another program that wo
70. u type in FourRect and select OK to close the window The drawing area still contains the structure of the file threerect with the two layers and the three conductors In order to save this structure under the name FourRect the user may then select the option Save from the file menu 4 4 3 Designing the Circuit For now the file FourRect contains the two layers and the three conductors that were involved in the structure of ThreeRect The goal of this section is to design the four conductors structure given in Fig 4 14 starting from this three conductors structure Obviously the default length units should be changed to microns instead of millimiters see Section 4 3 3 The geometry of the dielectric layers has not changed so no modification is needed However the geometry of the conductors is similar but not identical Conductors 1 and 3 are identical see Fig 4 16 but Conductor 2 has different coordinates 25 10 instead of 10 10 Moreover Conductor 4 needs to be completely designed The user will therefore check each conductor successively with the help of the arrows located at the bottom of the conductor column starting with Conductor 1 The geometry of Conductor 1 w 210 m h 3 m xz0 y 10 m is adequate the length unit being now set to microns Consequently the conductor 1 is not modified and the right arrow may be used to look at the second conductor 43 Filter homes I le les lestrade X
71. ual int i functions included in cond call c void Erase conductor Widget w XtPointer client data XtPointer call data void New conductor Widget w XtPointer client data XtPointer call data void go forward Widget w XtPointer client data XtPointer call data void go back Widget w XtPointer client data XtPointer call data functions included in layer call c void New Layer callback Widget w XtPointer client data XtPointer call data void go back layer Widget w XtPointer client data XtPointer call data void Erase layer Widget w XtPointer client data XtPointer call data void go forward layer Widget w XtPointer client data XtPointer call data functions included in RLGC c void RLGC main void functions included in V2D c void V2D main double xb double yb double xt double yt int Nx int Ny int Ne functions included in apply c void Solve Widget w XtPointer client data XtPointer call data void RunMesh Widget w XtPointer client data XtPointer call data void RunV2D void functions included in cust dialog c 64 Widget CreateCustomDialog Widget parent char name Widget CreateCustDlg Widget parent Widget CreateMatrixDlg Widget parent Widget CreateUnityDlg Widget parent Widget CreateQualityDlg Widget parent Widget CreateScaleDlg Widget parent void scaleCB Widget widget XtPointer client data XtPointer call data void manageCust Widget widget XtPo
72. uld perform the transient simulation of the multilayered multiconductor structure with the input parameters R L G and C An example of such a program and its user guide is given in 27 Another possibility would be the addition of an optimization program involving for example neural networks Moreover the XRLGC program is implemented in C Motif complying to the industry standard X Windows thus escaping any hardware or software needs as well as any compatibility problems However a better choice might be to use the modern programing language Java which is platform independent and may be called easily through the World Wide Web 62 APPENDIX A RESOURCE FILE OF XRLGC The following file is the main resource file of XRLGC It contains the definition of all the functions arrays and variables used for the GUI kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk OK graphtool h Headfile of XRLGC Declarations of functions and variables K kkkkxkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk ee Last Modified Claire Lestrade February 97 Sy ee RRR KKK KKK ke ke ke ke ke ke ke ke ee ee e e KK e ex Declaration of Functions RR KKK RRR ke ke ke ke ke ke ke ke ke e eee e eee e ex functions included in frontend c void Clear drawing Widget widget XtPointer client data XtPointer call data void DrawShapes Display display Window window GC gc in
73. ure 4 2 4 Saving changes and creating the mesh files 4 2 5 Starting the simulation and looking at the result Three Conductors in a Layered Medium 4 3 1 Hypothesis and geometry considered 4 3 2 Starting s 4 3 3 Designing the circuit 4 3 4 Saving and solving the circuit Four Conductors in a Layered Medium 4 4 1 Hypothesis and geometry considered 4 4 2 Starting 4 4 3 Designing the circuit 4 4 4 Saving and solving the circuit Conclusion STRUCTURE OF XRLGC 5 1 5 2 Structure of RLGC 5 1 1 Overview 5 1 2 Constructing the mesh files and input file of RLGC 5 1 3 Running the simulation 5 1 4 Technical file description XRLGC New Features 5 2 1 Overview 22 22 22 24 25 25 25 25 29 29 31 31 35 35 39 37 40 42 42 43 43 46 47 48 49 49 49 50 53 54 54 5 2 2 Technical file description 5 2 3 File interaction 56 5 2 4 Callback functions 5 3 Conclusion APPENDIX A RESOURCE FILE OF XRLGC REFERENCES 55 60 62 63 69 LIST OF FIGURES 2 1 3 1 3 2 4 1 4 2 4 3 4 4 4 5 4 6 4 7 4 8 34 4 9 4 10 36 4 1 4 12 4 13 4 14 4 15 4 16 45 5 1 5 2 5 3 51 5 4 52 5 5 53 Multilayered dielectric medium Help dialog XRLGC menubar Introduction window Main window A single microstrip line New file window Layer and conductor columns Quality of the simulation Mesh creation window V2D simulation dialog RLGC custom dialog for the microst
74. w this problem exactly fits the electrostatic field problem where L is the Green s function G fis the charge distribution p and g is the potential The first step in MoM involves expanding the function f in a set of basis functions Bn which leads to f 3a B VA La es 2b In addition the inner product of Equation 2b with a set of test functionsTm develops into 3 a T L B T gy 3 Equation 3 may also be understood as the matrix equation Pm In T 8m 4a where lmn and gmn are defined by Lim T wL B 4b g 7 T 8 4c The unknown parameters amp m may be obtained by inverting the known lmn matrix and taking its product with the known vector gm However the computationally expensive matrix inversion may be avoided by using alternate methods 21 Moreover both the matrix lmn and the vector gm depend of the sets of basis and test functions which in general are chosen to be equal Examples of commonly used functions are givenin B x 3 iis Allt Otherwise 5 a 1 xl x A lt x lt x A n n 0 Otherwise 5b where xj is an array of real number Once the sets of basis and test functions have been chosen the matrix Equation 4a may be solved and the unknown function f is easily deduced from Equation 2a 2 2 2 Application to a simple electrostatic field problem If we apply MoM to a 1 D electrostatic field problem 2 we get c AD q 6a which
75. ws to select the right conductor or layer 3 4 3 Using the mouse The Drawing area will display layers and conductors of different shapes strip rectangular or circular according to the wishes of the user Two methods may be used 1 The conductors and the layers may be drawn directly on the screen with the mouse press New Conductor or New Layer to go back and forth between both and choose the shape of 23 the conductor as desired 2 They can also be automatically drawn according to the parameters given by the user on the left of the drawing area After choosing width height and position of the element just press Plot 24 CHAPTER 4 EXAMPLES OF APPLICATION The third chapter presented a quick overview of XRLGC Those guidelines may now be successfully applied with a few hands on examples given in this chapter We assume in these examples that the program has already been compiled according to the instructions in Section 3 2 Note that this interface saves more time as the structure considered gets more complex In the first example we will consider a very simple structure a single layer with a single microstrip line In the second example we will consider a slightly more complex structure involving two layers and three identical rectangular conductors Finally the third example shows useful options including file management and modification of a given structure 4 1 Starting XRLGC Once the program is com
76. xample out Example Q2D and Example V2D will also be available to the program and the user may view the corresponding RLGC matrices through the menu View RLGC If desired the circuit can be simulated again with other options increasing for example the number of basis functions and therefore the quality of the simulation or simply by modifying the multilayered 19 multiconductor structure The option Save in the file menu allows one to save the circuit currently being worked on in the Example format This command can only be used after having either created a new file or opened an already existing file The user does not need to save the circuit displayed on the drawing area except to keep it for future use once the circuit is saved it may be opened and modified any time using the option Open in the file menu The option Mesh in the file menu enables the user to create the mesh files for all the conductors of the circuit However the number of basis functions per side has to be defined first in the menu Edit Quality cf Section 3 4 2 Once the quality of the simulation has been defined the user may start the mesh creation using the Mesh option in the file menu An information window will warn the user when the mesh creation is done There are three types of mesh files strip mesh rect mesh and circle mesh depending on the shape of the conductor One file will be created for each conductor inv

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