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1. by the antenna tuner for the 66 foot inverted V dipole is 1223 j 1183 Q At 14 1 MHz roughly the second harmonic the impedance is 148 j 734 Q The amount of harmonic attenu ation for a particular network will vary dramatically with the impedances presented at the different frequencies Harmonics and Multiband Antennas There are some antennas for which the impedance at the second harmonic is essentially the same as that for the fundamental This often involves trap antenna systems or wideband log periodic designs For example a system used by many amateurs is a triband Yagi that works on 20 15 and 10 meters The second harmonic of a 20 meter transmit ter feeding such a tribander can be objectionably strong for nearby amateurs operating on 10 meters such as at a Field Day or other multi position special event or contest station even with the approximately 60 dB of attenuation of the sec ond harmonic provided by the low pass filters at the output of modern solid state transceivers The third harmonic of a 144 2 MHz fundamental can cause interference on the 432 MHz band as well A linear amplifier can exacerbate the problem since its second harmonic may be suppressed only about 46 dB by the typical pi network output circuit used in many older amplifiers Most amateur antenna tuners will not attenuate the 10 meter harmonic much at all especially if the tuner uses a high pass T network This is the most common network used commer
2. Screen print of TLA program a DOS prede cessor of TLW for a T network antenna tuner with short at output terminals The tuner has been loaded up into itself dissipating all input power internally 22 4 of the power delivered to the input of the network For the legal limit of 1500 W the loss in the network is 335 W Of this 280 W ends up in the inductor which will probably melt Even if the inductor doesn t burn up the output capaci tor C2 might well arc over since it has more than 3800 V peak across it at 1500 W into the network Due to the losses in the components in a T network it is quite possible to load it up into itself causing real damage inside For example see Figure 24 4 where a T network is loaded up into a short circuit at 1 8 MHz The component values look quite reasonable but unfortunately all the power is dissipated in the network itself The current through the output capacitor C2 at 1500 W input to the antenna tuner would be 35 A creating a peak voltage of more than 8700 V across C2 Either C1 also at more than 8700 V peak or C2 will probably arc over before the power loss is sufficient to destroy the coil However the loud arcing might frighten the operator pretty badly The point you should remember is that the T network is indeed very flexible in terms of matching to a wide variety of loads However it must be used judiciously lest it burn itself up Even if it doesn t fry itself it c
3. Transmission Line Coupling and Impedance Matching J Hallas The ARRL Guide to Antenna Tuners Newington ARRL 2010 D J Healey An Examination of the Gamma Match QST Apr 1969 pp 11 15 57 J D Kraus and S S Sturgeon The T Matched Antenna QST Sep 1940 pp 24 25 R W Lewallen Baluns What They Do and How They Do It The ARRL Antenna Compendium Vol 1 Newington ARRL 1985 pp 157 164 R Lindquist OST Compares Four High Power Antenna Tuners Product Review QST Mar 1997 pp 73 77 M W Maxwell Some Aspects of the Balun Problem QST Mar 1983 pp 38 40 M W Maxwell Reflections IIT New York CQ Communications 2010 R A Nelson Basic Gamma Matching Ham Radio Jan 1985 pp 29 31 33 B Pattison A Graphical Look at the L Network QST Mar 1979 pp 24 25 F A Regier Series Section Transmission line Impedance matching QST Jul 1978 pp 14 16 R Rhea Yin Yang of Matching Parts 1 and 2 High Frequency Electronics Mar and Apr 2006 Also avail able from Agilent Technologies www agilent com as application notes 5989 9012EN and 5989 9015EN W Sabin Understanding the T tuner C L C Transmatch QEX Dec 1997 pp 13 21 24 53 J Sevick Understanding Building and Using Baluns and Ununs New York CQ Communications 2003 J Sevick Transmission Line Transformers 4th edition Noble Publishing 2001 J Sevick Simple Broad
4. S Eq 16 where S center to center spacing between conductors d diameter of conductors same units as S Zo characteristic impedance Q For cases where S lt 3d see the Transmission Lines chapter For example for a tapered line to match a 300 Q source to an 800 Q load the spacing for the selected conductor di ameter would be adjusted for a 300 Q characteristic imped ance at one end of the line and for an 800 Q characteristic impedance at the other end of the line The disadvantage of using open wire tapered lines is that characteristic imped ances of 100 Q and less are impractical 24 4 5 MULTIPLE QUARTER WAVE SECTIONS An alternate to the smooth impedance transformation of 24 24 Chapter 24 E N4 a N4 ANT0889 Z Z 2 0 1 So Figure 24 24 Multiple quarter wave matching sections ap proximate the broadband matching transformation provided by a tapered line Two sections are shown here but more may be used The more sections in the line the broader is the matching bandwidth Zo is the characteristic impedance of the main feed line while Z4 and Z are the intermediate imped ances of the matching sections See text for design equations the tapered line is provided by using two or more A 4 trans former sections in series as shown in Figure 24 24 Each section has a different characteristic impedance selected to transform the impedance at its input to that at its output Thus the overall imped
5. j100 250 j250 250 j250 Frequency Z Q 3 5 MHz 5 500 25 j100 25 j100 250 j250 250 j250 Frequency Z Q 30 MHz 5 500 25 j100 25 j100 250 j250 250 j250 Capacitor Input pF 5254 n a n a 1760 n a n a Capacitor Input pF 2700 n a n a 926 n a n a Capacitor Input pF 315 n a n a 140 n a n a Output pF n a 536 1408 n a 713 359 Output pF n a 275 720 n a 367 184 Output pF n a Capacitor Input pF Output pF 5256 500 2602 1000 966 1500 3410 500 1931 1000 1284 500 Capacitor Input pF Output pF 2706 500 1287 500 643 800 1886 300 934 500 859 300 Capacitor Input pF Output pF 321 200 118 50 103 100 205 30 71 50 77 30 Inductor uH 1 34 13 5 Inductor uH 0 08 0 79 0 72 0 58 0 79 0 79 Inductor uH 1 4 9 6 12 5 7 5 11 3 12 9 Inductor uH Transmission Line Coupling and Impedance Matching Capacitor Voltage Vp 100 W 1500 W 100 390 310 1210 290 1120 100 390 310 1210 310 1210 Capacitor Voltage Vp 100 W 1500 W 100 400 310 1200 290 1120 100 390 310 1210 310 1210 Capacitor Voltage Vp 100 W 1500 W 100 390 310 1210 290 1120 100 390 310 1210 310 1210 100 W 1500 W 100 390 310 1200 280 1110 280 1100 310 1210 310 1210 Capacitor Voltage Vp 100 W 1500 W 100 390 310 1200 280 1110 280 1430 310 1200 310 1200 Capacitor Voltage Vp 100 W 1500 W 100 390 310
6. 25 pF of the capacitors in Figure 24 7 allows for a wider range of matching imped ance compared with the circuit of Figure 24 6 where the minimum capacitance is 42 pF This circuit can t match loads with resistances greater than 200 Q Note that AAT also allows the operator to specify a switchable fixed value capacitor across the output capaci tor C2 to aid in matching low resistance loads on the lower frequency bands In Figure 24 7 a 400 pF fixed capacitor C4 was assumed to be switched across C2 for the 1 8 and 3 5 MHz bands Figure 24 8 shows the schematic for such a T network antenna tuner The power loss in Figure 24 7 on 3 5 MHz at a load of 6 25 j 3 125 Q is 7 2 while in Figure 24 6 the loss is 19 7 On the other hand the voltage rating of one or both capacitors is exceeded for a load with a 3200 resistance By the way it isn t exceeded by very much the computed voltage is 3003 V at 1500 W input just barely exceeding the 3000 V rating for the capacitor This is after all a strictly lit eral computer program Turning down the power just a small amount would stop any arcing Transmission Line Coupling and Impedance Matching C1A C3B 15 196 pF 15 196 pF 28 uH ANT0878 Figure 24 8 Schematic for the T network antenna tuner whose tuning range is shown in Figure 24 7 AAT produces similar tables for pi network and L network configurations mapping the matching capabilities for the component combin
7. Choke Baluns 24 7 3 Using Ferrite Beads in Choke Baluns 24 7 4 Measuring Choke Balun Impedance 24 8 Transmission Line Baluns 24 8 1 Detuning Sleeves 24 8 2 Quarter Three Quarter Wave Balun 24 8 3 Combined Balun and Matching Stub 24 8 4 Impedance Step Up Step Down Balun 24 9 Voltage Baluns 24 10 Bibliography Chapter 24 Transmission Line Coupling and Impedance Matching The Transmission Lines chapter presented the funda mentals of transmission line operation and characteristics This chapter covers methods of getting energy into and out of the transmission line at the transmitter and at the antenna This requires coupling the transfer of energy between two systems from a transmitter to the feed line or from the feed line to the antenna For coupling to be the most efficient both systems should have the same ratio of voltage to current im pedance wherever the two systems meet so that no energy is reflected at that interface This often requires impedance matching to convert energy at one ratio of voltage to current to another ratio all as efficiently as possible This can be done with LC circuits special structures and even transmis sion lines themselves The initial portions of this chapter discuss methods used at the transmitter to effectively transfer power into the antenna system feed line using LC impedance matching circuits and antenna tuners The subject then turns to choosing a transmis sion line
8. For the 1 core choke R 15 6 KO L 25 nH C 1 4 pF Q 3 7 For the 2 core choke R 101 K L 47 uH C 1 9 pF Q 20 RG 6 RG 8X RG 58 RG 59 Turns 7 8 7 8 5 Cores 5 toroids Big clamp on 4 toroids Big clamp on Big clamp on 4 toroids Big clamp on 2 toroids Big clamp on 5 toroids Big clamp on 5 toroids Big clamp on Use two chokes in series 1 6 turns on a big clamp on 2 5 turns on a big clamp on 4 turns on 6 toroids or 5 turns on a big clamp on Notes Chokes for 1 8 3 5 and 7 MHz should have closely spaced turns Chokes for 14 28 MHz should have widely spaced turns Turn diameter is not critical but 6 inches is good Transmission Line Coupling and Impedance Matching 24 45 10000 9000 HBK0446 8000 7000 6000 7 Turns 5 cores 6 Turns 6 cores 7 Turns 4 cores 6 Turns 5 cores 5 Turns 6 cores 4 6 Turns 4 cores Impedance Q 5 Turns 5 cores 5 Turns 4 cores 4 Turns 6 cores 4 Turns 5 cores 10000 9000 4 5 6 78910 20 30 40 506070 90 Frequency MHz HBK0447 8000 7000 6000 7 Turns 6 cores 7 Turns 5 cores 12 diam turns Y 6 Turns 5 cores 4 5 Turns 7 cores Impedance Q 4 Turns 7 cores 7 5 Turns 5 cores ae of 7 a E 3 Turns 9 cores we 4 4 Turns 5 cores 7
9. capacitance and the minimum series reactance between the source and load minimum inductance or maximum capaci tance The configuration that produces the minimum SWR with maximum reactance to ground and minimum series re actance will generally have the highest efficiency and broad est tuning bandwidth 24 2 4 THE TLW TRANSMISSION LINE FOR WINDOWS PROGRAM AND ANTENNA TUNERS The ARRL program TLW Transmission Line for Windows on the CD ROM included with this book does calculations for transmission lines and antenna tuners TLW evaluates four different networks a low pass L network a high pass L network a low pass pi network and a high pass T network Figure 24 5 shows the TLW output screen for an L network design example 24 7 Low Pass L Network 450 Ohrn Window Ladder Line Length 70 000 feet Frequency 7 15 MHz At load 88 j 37 ohms 88 ohms at 2 degrees Load SWR 4 6 Eff 2 3 1 6 1 SWR BW 1257 3 kHz 17 6 2 1 SWR BW Large Estimated power lost in tuner for 100 W input 2 VV 0 07 dB 1 5 lost Transmission line loss 0 12 dB Total loss 0 19 dB Power into load 95 7 W At 100 WW L1 C2 Unloaded Q 200 1000 Reactance 114 747 84 107 Peak Voltage 229 V 250 V RMS Current 14A 21A Est Pwr Diss 1W ow RMS Vin 70 71 V at 66 70 deg RMS Vout 176 69 V at 0 00 deg 2 55 uH Print Li TE 50 0 Ohms Main bo 103 25 j 148 66 Ohn Screen 264 7 pF Figure 24 5 Antenna tuner output screen of T
10. it is that resonance be established before an attempt is made to match the line This is particularly true of close spaced parasitic arrays With simple dipole antennas the tuning is not so critical and it is usually sufficient to cut the antenna to the length given by the appropriate equation The frequency should be selected to be at the center of the range of frequen cies which may be the entire width of an amateur band over which the antenna is to be used 24 25 24 5 2 CONNECTING DIRECTLY TO THE ANTENNA As discussed previously the impedance at the center of a resonant A 2 antenna at heights of the order of A 4 and more is resistive and is in the neighborhood of 50 to 70 Q The dipole may be fed through 75 Q coaxial cable such as RG 11 as shown in Figure 24 26 Cable having a characteristic im pedance of 50 Q such as RG 8 may also be used RG 8 may actually be preferable because at the heights many amateurs install their antennas the feed point impedance is closer to 50 than it is to 75 Q With a parallel wire feed line the system would be sym metrical but with coaxial line it is inherently unbalanced Stated broadly the unbalance with coaxial line is caused by the fact that the outside surface of the outer braid is not coupled to the antenna in the same way as the inner conductor and the inner surface of the outer braid The overall result is that common mode current will flow on the outside of the outer conductor in th
11. obtain values for the volt age across the load resistor V and the generator in frequency increments of about 5 over the range of interest recording the data in a spreadsheet If multiple chokes are being mea sured use the same frequencies for all chokes so that data can be plotted and compared Using the spreadsheet solve the voltage divider equation backwards to find the unknown impedance IZx Rroan Voen Vioapl Plot the data as a graph of impedance on the vertical axis vs frequency on the horizontal axis Scale both axes to display logarithmically Obtaining R L and C Values This method yields the magnitude of the impedance Zx but no phase information Accuracy is greatest for large values of unknown impedance worst case 1 for 5000 10 for 500 Q Accuracy can be further improved by cor recting for variations in the loading of the generator by the test circuit Alternatively voltage at the generator output can be measured with the unknown connected and used as Vcgn The voltmeter must be un terminated for this measurement In a second spreadsheet worksheet create a new table that computes the magnitude of the impedance of a parallel resonant circuit for the same range of frequencies as your choke measurements The required equations can be found in the section Parallel Circuits of Moderate to High Q of the Electrical Fundamentals chapter in the ARRL Handbook Set up the spreadsheet to compute resonant fr
12. special transmission line impedances are not required only sections of line with the same impedances that are to be matched This configuration is referred to as a twelfth wave transformer because when the ratio of the impedances to be matched is 1 5 1 as is the case with 50 and 75 Q cables the electrical length of the two matching sections between the lines to be matched is 0 0815 29 3 quite close to A 12 0 0833 or 30 Figure 24 20 shows that the SWR band width of the twelfth wave transformer is quite broad You can use this technique to make good use of surplus low loss 75 Q CATV hardline between 50 Q antennas and radios 24 4 3 SERIES SECTION TRANSFORMERS The series section transformer has advantages over either stub tuning or the 4 4 transformer Illustrated in Fig ure 24 21 the series section transformer bears considerable resemblance to the 4 4 and 4 12 transformers described ear lier Actually these are special cases of the series section transformer The important differences are 1 that the matching section need not be located exactly at the load 2 the matching section may be less than a quarter wavelength long and 3 there is great freedom in the choice of the char acteristic impedance of the matching section 24 22 Chapter 24 QS0910 HORO3 OE SL 4021 22 3 0 100 150 Percent of Nominal Frequency Figure 24 20 The bandwidth of the 1 12 transformer is
13. 1200 290 1100 285 1100 310 1200 310 1200 Efficiency Efficiency 24 17 24 3 TRANSMISSION LINE SYSTEM DESIGN The previous sections of this chapter looked at system design from the point of view of the transmitter examining what could be done to ensure that the transmitter load is its design load of 50 In this section we will look at antenna system design from the point of view of the transmission line We will examine what should be done to ensure that the transmission line operates at best efficiency once a particular antenna is chosen to do a particular job 24 3 1 TRANSMISSION LINE SELECTION Until you get into the microwave region where waveguides become practical there are only two practical choices for transmission lines coaxial cable and parallel conductor lines such as open wire or ladder line window line and twinlead The shielding of coaxial cable offers advantages in in cidental radiation and routing flexibility Coax can be tied or taped to the legs of a metal tower without problem for example Some varieties of coax can even be buried under ground Coaxial cable can perform acceptably even with significant SWR Refer to information in the Transmission Lines chapter A drawback of coaxial line is its loss par ticularly at moderate to high SWR For example a 100 foot length of RG 8 coax has 1 1 dB matched line loss at 30 MHz If this line were used with a load of 250 j 0 Q an SWR of 5 1 the
14. 14 100 MHz 0 dB 13 06 dBi Reference Yagi Elevation Ele Yagi w Slanted Coax Feed 14 100 MHz OdB 13 43 dBi B Figure 24 50 At A azimuthal response for two five ele ment 20 meter Yagis placed 0 71 over average ground The solid line represents an antenna fed with no feed line The dashed line represents a dipole fed with a 1 length of un balanced coax line slanted at 45 to ground through a transmitter at ground level The distortion in the rearward pattern is even more evident than in Figure 24 49 This Yagi loses a bit more forward gain 0 4 dB compared to the ref erence antenna At B elevation response comparison The slant of the feed line causes more common mode current due to asymmetry In this case placing a common mode choke of j 1000 Q at the feed point was not sufficient to eliminate the pattern distortion substantially Another choke was required 1 4 farther down the transmission line to elimi nate common mode currents of all varieties it did for the simple dipole Clearly the pattern of what is supposed to be a highly directional antenna can be seriously degraded by the pres ence of common mode currents on the coax feed line As in the case of the simple dipole multiples of 4 2 long resonant feed line to ground represents the worst case feed system even when the feed line is dressed symmetrically at right angles below the antenna And as found with the dipole the pattern deterior
15. 24 49 Air Space 1 2 to 1 Lower End Closed by Disc Soldered to Outer Conductor ANTO914 A Figure 24 61 Fixed balun methods for balancing the ter mination when a coaxial cable is connected to a balanced antenna These baluns work at a single frequency The balun at B is known as a sleeve balun and is often used at VHF The diameter of the coaxial detuning sleeve in Figure 24 61B should be fairly large compared with the diameter of the cable it surrounds A diameter of two inches or so is satisfactory with half inch cable The sleeve should be sym metrically placed with respect to the center of the antenna so that it will be equally coupled to both sides Otherwise a current will be induced from the antenna to the outside of the sleeve This is particularly important at VHF and UHF In both the balancing methods shown in Figure 24 61 the A 4 section should be cut to be resonant at exactly the same frequency as the antenna itself These sections tend to have a beneficial effect on the impedance frequency characteristic of the system because their reactance varies in the opposite direction to that of the antenna For instance if the operating frequency is slightly below resonance the antenna has capaci tive reactance but the shorted 4 4 sections or stubs have in ductive reactance Thus the reactances tend to cancel which prevents the impedance from changing rapidly and helps ma
16. 9 28 4 3089 j 774 0 6 8 1 arise Transmission lines with solid dielectric have voltage and current limitations At lower frequencies with electrically short antennas this can be a more compelling limitation than the amount of power loss The ability of a line to handle RF power is inversely proportional to the SWR For example a line rated for 1 5 kW when matched should be operated at only 150 W when the SWR is 10 1 At the mismatch on 1 83 MHz illustrated for the 66 foot inverted V dipole in Table 24 7 the line may well arc over burning the insulation due to the extremely high level of SWR at 1627 7 1 A feed line of 450 Q window type ladder line using two 16 AWG conductors should be safe up to the 1500 W level for frequencies where the antenna is nearly a half wavelength long For the 100 foot dipole this would be above 3 8 MHz and for the 66 foot long dipole this would be above 7 MHz For the very short antennas illustrated above however even 450 Q window line may not be able to take full amateur legal power Check the line s maximum rated voltage in the table in the Transmission Lines chapter and compare with that expected at your maximum power and expected maximum SWR 24 3 2 ANTENNA TUNER LOCATION To meet the goal of presenting a 50 Q load to the trans mitter in many antenna systems it is necessary to place an 24 19 100 Antenna eS 200 RG 213 100 Antenna il Dij
17. Stanley K4ERO see Bibliography also discusses tuned link coupling from the standpoint of the matching network providing both filter ing and impedance matching A fully balanced tuner has a symmetrical internal cir cuit with a tuner circuit for each side of the feed line and the balun at the input to the tuner where the impedance is close to 50 Several examples are shown in Figure 24 10 that can be recognized as being formed from the unbalanced 24 11 HBK05_21 010 networks described earlier with a mirror image of the net work being inserted in the ground side of the circuit A balun is inserted on the 50 Q side of the circuit to al low connection to unbalanced coaxial feed lines Some tuners are designed to use a 1 1 balun for this purpose while others transform the load impedance to 200 and use a 4 1 balun This allows the balun to operate at its design impedances regardless of load impedance A balun at the output of an unbalanced tuner must operate at whatever load impedance is presented which can lead to significant losses or arcing in the balun 50 Q A Balanced Tuned Variable Transformer D Balanced 7t network n E Balanced High pass T network L network for Z gt Z F Balanced Low pass T network B L network for Z lt Z ARRL0645 Figure 24 10 Configurations of balanced antenna tuners 24 12 Chapter 24 Figure 24 9 Simple an tenna tuners for coupling a transmitt
18. a high efficiency design with minimal losses including losses in the balun This led to the third objective Include a balun op erating within its design impedances For that reason this unit was designed with the balun at the input of the tuner This antenna tuner is designed to handle full legal power from 160 to 10 meters matching a wide range of either balanced or unbalanced impedances The network configuration is a high pass T network with two series vari able capacitors and a variable shunt inductor See Figure 24 12 for the schematic of the tuner Note that the schematic is drawn in a somewhat unusual fashion This is done to emphasize that the common connection of the series input and output capacitors and the shunt inductor is actually the subchassis used to mount these components away from the tuner s cabinet The subchassis is insulated from the main cabinet using four heavy duty 2 inch steatite ceramic stand off insulators O Bypass am c1B C2A While a T network type of tuner can be very lossy if care isn t taken it is very flexible in the range of impedances it can match Special attention has been paid to minimize power loss in this tuner particularly for low impedance loads on the lower frequency amateur bands Preventing arc ing or excessive power dissipation for low impedance loads on 160 meters represents the most challenging conditions for an antenna tuner designer To see the computed range
19. about 1000 for a typical air variable capacitor with wiper contacts An expensive vacuum variable capacitor can have an unloaded Qy as high as 5000 The power loss in coils is generally larger than in vari able capacitors used in practical antenna tuners The circulat ing RF current in both coils and capacitors can also cause severe heating The ARRL Laboratory has seen coils forms made of plastic melt when pushing antenna tuners to their extreme limits during product testing The RF voltages devel oped across the capacitors can be pretty spectacular at times leading to severe arcing Note that L networks cannot match all impedances to 50 Q The load and source impedances must have the proper relationship for the equations to solve to obtainable compo nent values The reactance at the load must also be cancella ble by the reactance of the L network If the load impedance is such that it cannot be matched by an L network try a reversing the network or b adding 4 8 to A 4 of transmis sion line between the load and network This does not change the SWR but it does transform the load impedance to a new combination of resistance and reactance that the L network may be able to match 24 2 2 THE PI NETWORK The impedances at the feed point of an antenna used on multiple HF bands varies over a very wide range particu larly if thin wire is used This was described in detail in the Dipoles and Monopoles chapter The transmission line feed
20. an antenna If that current is flowing close to electronic equipment such as a telephone or entertainment system RFI can result A choke balun is used on coaxial feed lines to reduce these currents as described in the section on baluns later in this chapter A third and perhaps even more prevalent myth is that you can t get out if the SWR on your transmission line is higher than 1 5 1 or 2 1 or some other such arbitrary fig ure On the HF bands if you use reasonable lengths of good coaxial cable or even better yet open wire line the truth is that you need not be overly concerned if the SWR at the load is kept below about 6 1 This sounds pretty radical to some amateurs who have heard horror story after horror story about SWR The fact is that if you can load up your transmitter without any arcing inside or if you use a tuner to make sure your transmitter is operating into its rated load resistance you can enjoy a very effective station using antennas with feed lines having high values of SWR on them For example a 450 Q open wire line connected to the multiband dipole shown in Table 24 1 would have a 19 1 SWR on it at 3 8 MHz Yet time and again this antenna has proven to be a great performer at many installations m A fourth myth is that changing the length of a feed line changes the SWR Changing a feed line s length does not change the SWR except for losses inside the line When someone tells you that adding or subtra
21. approximately to the entire width of the 7 MHz band if the antenna is resonant at the center of the band A wire antenna is assumed Antennas having a greater ratio of diameter to length will have a lower change in SWR with frequency Direct Feed Yagis Direct feed Yagis are designed to have a feed point im pedance of 50 or 75 Q so that a coaxial feed line can be con nected directly to the antenna without additional impedance matching These have become more common in recent years as antenna modeling has produced designs without the gain and pattern tradeoffs previously required for the higher feed point impedances required for direct feed There is some question as to whether a choke balun is required for direct feed antennas The same questions of symmetry and radiation from common mode current apply to direct feed Yagis as to dipoles and other types of anten nas If re radiation is an issue a choke balun should be used For commercial antennas if the manufacturer specifies that a balun be used or makes no recommendation use a choke balun at the feed point If the manufacturer specifies that no balun be used that is an indication that the feed line affects antenna performance in some way and the manufacturer s instructions for feed line placement and attachment should be followed exactly 24 5 3 THE DELTA MATCH Among the properties of a coil and capacitor resonant circuit is that of transforming impedances If a resistive im pe
22. cabinet In the prototype antenna tuner the balun was wound using 12 turns of 10 AWG Formvar insulated wire wound side by side in bifilar fashion on a 2 4 inch OD core of type 43 material After 60 seconds of key down operation at 1500 W on 29 7 MHz the wire becomes warm to the touch although the core itself remains cool We estimated that 25 W was being dissipated in the balun Alternatively if you don t intend to use the tuner for balanced lines you can delete the balun altogether In our unit a piece of RG 213 coax is used to connect the output coaxial socket in parallel with the hot insulated feedthrough insulator to SID common This adds approxi mately 15 pF fixed capacitance to ground An equal length of RG 213 is used at the cold feedthrough insulator so that the circuit remains balanced to ground when used with balanced transmission lines When the cold terminal is jumpered to ground for unbalanced loads that is using the coax connec tor the extra length of RG 213 is shorted out and is thus out of the circuit 24 14 Chapter 24 Construction The prototype antenna tuner was mounted in a Hammond model 14151 heavy duty painted steel cabinet This is an exceptionally well constructed cabinet that does not flex or jump around on the operating table when the roller inductor shaft is rotated vigorously The electrical components inside were spaced well away from the steel cabinet to keep losses down especially i
23. common mode current aris ing from radiation from a balanced antenna back onto its transmission line due to a lack of symmetry occurs for both coaxial or balanced transmission lines For a coax the inner surface of the shield and the inner conductor are shielded from such radiation by the outer braid However the outer surface of the braid carries common mode current radi ated from the antenna and then subsequently reradiated by the line For a balanced line common mode currents are induced onto both conductors of the balanced line again resulting in reradiation from the balanced line If the antenna or its environment are not perfectly sym metrical in all respects there will also be some degree of common mode current generated on the transmission line either coax or balanced Perfect symmetry means that the ground would have to be perfectly flat everywhere under the antenna and that the physical length of each leg of the antenna would have to be exactly the same It also means that the height of the dipole must be exactly symmetrical all along its length and it even means that nearby conductors such as power lines must be completely symmetrical with respect to the antenna In the real world where the ground isn t always perfectly flat under the whole length of a dipole and where wire legs aren t cut with micrometer precision a balanced line feeding Transmission Line Coupling and Impedance Matching a supposedly balanced an
24. equal delay trans mission line transformers Double Quarter Wave Transformer The double 2 4 transformer is a special case of the lt 4 gt lt 4 gt Zin i T i ZLOAD ZLoaD Z2 Z1 Zin ANT1122 multisection A 4 transformer If two 4 4 sections of feed line one with impedance Zp followed by another with an imped ance of 2Z as the input impedance as in Figure 24 25 the input to the transformer will be the load impedance divided by 4 The transformer can be turned around to step up the load impedance In general the transformation ratio is the square of the impedance ratio of the two A 4 sections and it is independent of the impedances of the input and output The Figure 24 25 The impedance transformation ratio of the double quarter wave transformer is the square of the differ ence between the characteristic impedances of the two 1 4 sections larger the difference in Zgo between the sections the smaller the bandwidth of the impedance transformation You are not restricted to the Z of single cables Paralleled cables with characteristic impedances of Z act as a combined cable with a characteristic impedance of Z 2 So for example a 4 4 section of two 50 Q cables in parallel Zo 25 Q connected to a A 4 section of 50 Q line has an impedance ratio of 2 1 and an impedance transformation ra tio of 4 1 This design could match 75 Q line to a 300 Q load using 50 Q cable If
25. fact that the SWR at the feed point is a very high 793 1 a direct result of the fact that the antenna is extremely short in terms of wavelength Table 24 7 summarizes the same information as in Table 24 6 but this time for a 66 foot long inverted V dipole whose apex is 50 feet over typical earth and whose included angle between its two legs is 120 The situation at 1 83 MHz is even worse as might be expected because this antenna is even shorter electrically than its 100 foot flattop cousin The line loss has risen to 15 1 dB Under such severe mismatches another problem can Transmission Line Coupling and Impedance Matching Table 24 6 Impedance of Center Fed 100 Foot Flattop Dipole 50 Feet High Over Average Ground Frequency Antenna Feed point Loss for 100 ft SWR MHz Impedance Q 450 Q Line dB 1 83 4 5 j 1673 8 9 792 9 3 8 39 j 362 0 5 18 3 7 1 481 j 964 0 2 6 7 10 1 2584 j 3292 0 6 16 8 14 1 85 j 123 0 3 5 2 18 1 2097 j 1552 0 4 8 1 21 1 345 j 1073 0 6 10 1 24 9 202 j 367 0 3 3 9 28 4 2493 j 1375 0 6 8 1 Table 24 7 Impedance of Center Fed 66 Foot Inv V Dipole 50 Foot High Apex Over Average Ground Frequency Antenna Feed point Loss for 100 ft SWR MHz Impedance Q 450 Q Line dB 1 83 1 6 j 2257 15 1 1627 7 3 8 10 879 3 9 195 7 7 1 65 j 41 0 2 6 3 10 1 22 648 1 9 68 3 14 1 5287 j 1310 0 6 13 9 18 1 198 j 820 0 6 10 8 21 1 103 181 0 3 4 8 24 9 269 570 0 3 4
26. ground in a symmetrical manner The feed point impedance in this symmetrical configuration changes only a small amount compared to the reference antenna 24 37 using a A 2 long coaxial feed line dropped vertically to the ground below the feed point Now the azimuthal response of the second dipole is no longer perfectly symmetrical It is shifted to the left a few dB in the area of the side nulls and the peak response is down about 0 1 dB compared to the reference dipole Many would argue that this sort of response isn t all that bad However do keep in mind that this is for a feed line placed in a symmetrical manner at a right angle below the dipole Asymmetry in dressing the coax feed line will result in more pattern distortion SWR Change with Common Mode Current If an SWR meter is placed at the bottom end of the coax feeding the second dipole it would show an SWR of 1 38 1 for a 50 Q coax such as RG 213 since the antenna s feed point impedance is 69 20 j 0 69 Q The SWR for the refer ence dipole would be 1 39 1 since its feed point impedance is 69 47 j 0 35 Q As could be expected the common mode impedance in parallel with the dipole s natural feed point impedance has lowered the net impedance seen at the feed point although the degree of impedance change is miniscule in this particular case with a symmetrical feed line dressed away from the antenna In theory at least we have a situation where a change in the lengt
27. into low impedances such as 3 to 4 Q the 24 35 Figure 24 44 A 4 winding wideband transformer with front cover removed with connections made for matching ratios of 4 1 6 1 9 1 and 16 1 The 6 1 ratio is the top coaxial connector and from left to right 16 1 9 1 and 4 1 are the others There are 10 quadrifilar turns of 14 AWG enameled wire on a Q1 2 5 inch OD ferrite core see text for numbers current in the bottom winding can be as high as 15 amperes This value is based on the high side of the transformer be ing fed with 50 Q cable handling a kilowatt of power If one needs a 16 1 match like this at high power then cas cading two 4 1 transformers is recommended In this case the transformer at the lowest impedance side requires each winding to handle only 7 5 A Thus even 14 AWG wire would suffice in this application of turns on different core materials The popular cores used in these applications are 2 5 inch OD ferrites of Q1 and Q2 material and powdered iron cores of 2 inches OD The permeabilities of these cores u are nominally 125 40 and 10 respectively Powdered iron cores of permeabilities 8 and 25 are also available In all cases these cores can be made to operate over the 1 8 to 28 MHz bands with full power capability and very low loss The main difference in their design is that lower per meability cores require more turns at the lower frequen cies For example Q1 material requires 10 turns to c
28. is rarely a need for power or SWR metering on automatic antenna tuners Automatic models are available that are activated manually or that sense the RF frequency and tune immediately or that tune based on a computer control input or control link to the host transceiver Remote antenna tuners are essentially auto matic antenna tuners in enclosures designed to be mounted outside or out of sight of the operator and have no operating controls or displays As an example of the impedance matching task column one of Tables 24 1 and 24 2 list the computed impedance at the center of two common dipoles mounted over average ground with a conductivity of 5 mS m and a dielectric con stant of 13 The dipole in Table 24 1 is 100 feet long and is mounted as a flattop 50 feet high The dipole in Table 24 2 is 66 feet long overall mounted as an inverted V whose apex is 50 feet high and whose legs have an included angle of 120 The second column in Tables 24 1 and 24 2 shows the computed impedance at the transmitter end of a 100 foot long transmission line using 450 Q window open wire line Please 24 2 Chapter 24 Table 24 1 Impedance of Center Fed 100 Foot Flattop Dipole 50 Feet High Over Average Ground Frequency Antenna Feed point Impedance at Input of MHz Impedance Q 100 ft 450 Q Line Q 1 83 4 5 j 1673 2 0 j20 3 8 39 j 362 888 j 2265 7 1 481 j 964 64 j 24 10 1 2584 j 3292 62 j 447 14 1 85 j 123 84 j65 18
29. loss with SWR However the decrease would be slight because the loss in open wire balanced transmission line is small even with relatively high SWR on the line See the Transmission Lines chapter for a thorough discussion on additional line loss due to SWR Size of Coax At HF the diameter of the coax feeding a 2 dipole 24 38 Chapter 24 is only a tiny fraction of the length of the dipole itself In the case of Figure 24 45 above the model of the coax used assumed an exaggerated 9 inch diameter just to simulate a worst case effect of coax spacing at HF However on the higher UHF and microwave frequen cies the assumption that the coax spacing is not a signifi cant portion of a wavelength is no longer true The plane bisecting the feed point of the dipole in Figure 24 45 down through the space below the feed point and in between the center conductor and shield of the coax is the center of the system If the coax diameter is a significant percentage of the wavelength the center is no longer symmetrical with reference to the dipole itself and significant imbalance will result Measurements done at microwave frequencies show ing extreme pattern distortion for balunless dipoles may well have suffered from this problem 24 6 2 ASYMMETRICAL ROUTING OF THE FEED LINE Figure 24 45 shows a symmetrically located coax feed line one that drops vertically at a 90 angle directly below the feed point of the symmetrical dipole W
30. or balanced The antenna tuner in such a system may only consist of the LC network necessary to transform impedance This is typical of custom LC networks constructed to match an antenna used on a single band that may be located away from the transmitter An antenna tuner used on multiple bands and located in the shack usually includes some type of SWR bridge or meter See the Transmission Line and Antenna Measurements chapter Other features common in commercial antenna tuners include directional wattmeters switches for the use of mul tiple feed lines and for bypassing the tuner and balanced and single wire outputs An overview of antenna tuner functions and features is provided in The ARRL Guide to Antenna Tuners by Joel Hallas W1ZR See Bibliography 24 1 2 HARMONIC ATTENUATION This is a good place to bring up the topic of harmonic attenuation as it is related to antenna tuners One potentially desirable characteristic of an antenna tuner is the degree of extra harmonic attenuation it can provide by acting as a tuned circuit While this is desirable in theory it is not always achieved in practice For example if an antenna tuner is used with a single fixed length antenna on multiple bands the im pedances presented to the tuner at the fundamental frequency and at the harmonics will often be radically different as shown in Table 24 2 For example at 7 1 MHz the impedance seen Transmission Line Coupling and Impedance Matching
31. pF of stray capacitance associated with each section Both sections are wired in parallel for the output capacitor while they are switched in or out using switch S1B for the input capacitor This strategy allows the minimum capacitance of the input capacitor to be smaller to match high impedance loads at the higher frequencies The roller inductor is a high quality Cardwell 229 203 1 unit with a steatite body to enable it to dissipate heat with out damage The roller inductor is augmented with a series 0 3 uH coil made of four turns of inch copper tubing formed on a 1 inch OD form which is then removed This fixed coil can dissipate more heat when low values of induc tance are needed for low impedance loads at high frequen cies Both variable capacitors and the roller inductor use ceramic insulated shaft couplers since all components are hot electrically Each shaft goes through a grounded bushing at the front panel to make sure none of the knobs is hot for the operator The balun allowing operation with balanced loads is placed at the input of this antenna coupler rather than at the output where it is commonly placed in other designs Putting the balun at the input stresses the balun less since it is operating into its design resistance of 50 once the network is tuned For unbalanced coax operation the com mon point at the bottom of the roller inductor is grounded using a jumper at the feedthrough insulator at the rear of the
32. piece of sheet aluminum that is 0 030 inch thick The tuner s 10 x 8 inch subchassis forms the other plate of this homebrew capacitor For mechanical rigidity the subchassis uses two o inch thick aluminum plates The c inch thick glass is epoxied to the bottom of the subchassis The 4 x 6 inch aluminum sheet forming the second plate of the 400 pF fixed capacitor is in turn epoxied to the glass to make a stable high voltage high current fixed capacitor Two strips of wood are screwed down over the as sembly underneath the subchassis to make sure the capacitor stays in place The estimated breakdown voltage is 12 000 V See Figure 24 16 for a bottom view of the subchassis DE A RT bids er E E Figure 24 16 Bottom view of subchassis showing the two strips of wood ensuring mechanical stability of the C3 capacitor assembly Transmission Line Coupling and Impedance Matching Note The dielectric constant of the glass in a cheap 2 at Wal Mart picture frame can vary The final dimen sions of the aluminum sheet secured with one hour epoxy to the glass was varied by sliding it in and out until 400 pF was reached while the epoxy was still wet using an Autek RF 1 antenna analyzer as a capacitance meter Don t let epoxy slop over the edges this can arc and burn permanently S1 is bolted directly to the front of the cabinet S1 is a spe cial high voltage RF switch from Radio Switch Corporation with fo
33. procedure is tedious es pecially if several iterations are needed to find a practical set of dimensions The procedure has been adapted for computer calculations by R A Nelson WB IKN who wrote his pro gram in Applesoft BASIC see Bibliography A similar pro gram for Windows compatible computers called GAMMA in BASIC source code with modifications suggested by Dave Leeson W6NL may be downloaded from www arrl org antenna book The program can be used for calculating a gamma match for a dipole or driven element of an array or for a vertical monopole such as a shunt fed tower The inputs to GAMMA are as shown in Figure 24 31 Z the complex impedance of the unmatched antenna Z R j X normally measured with dipole halves split S center to center spacing of the circular antenna element to the circular gamma rod D or d2 diameter of the circular antenna element d or dl diameter of the circular gamma rod L length of the gamma rod C the added series capacitance used to null any resulting inductive reactance Note that S is a center to center dimension not a surface to surface value As an example of computer calculations assume a 14 3 MHz Yagi beam is to be matched to 50 Q line The driven element is 1 4 inches in diameter and the gamma rod is a length of 4 inch tubing spaced 6 inches from the element center to center The driven element has been shortened by 3 from its resonant length Assum
34. the common mode voltage the only effect of high SWR on power handling of wound coax chokes is the peaks of differential current and voltage along the line established by the mismatch Experience shows that 5000 Q is also a good design goal to prevent RFI noise coupling and pattern distortion While 500 1000 has long been accepted as sufficient to prevent 24 44 Chapter 24 pattern distortion Chuck Counselman W1HIS has correctly observed that radiation and noise coupling from the feed line should be viewed as a form of pattern distortion that fills in the nulls of a directional antenna reducing its ability to reject noise and interference Chokes used to break up a feed line into segments too short to interact with another antenna should have a choking impedance on the order of 1000 to prevent interaction with simple antennas A value closer to 5000 Q may be needed if the effects of common mode current on the feed line are filling the null of directional antenna Building Wound Coax Ferrite Chokes Coaxial chokes should be wound with a bend radius suf ficiently large that the coax is not deformed When a line is deformed the spacing between the center conductor and the shield varies so voltage breakdown and heating are more likely to occur Deformation also causes a discontinuity in the impedance the resulting reflections may cause some wave form distortion and increased loss at VHF and UHF Chokes wound with any large diamet
35. the variable inductor enough so that you wouldn t want to keep your hand on it for long None of the other components became hot in this test At higher frequencies and into a 50 Q load at 1 8 MHz the roller inductor was only warm to the touch at 1500 W key down for 30 seconds The 10 AWG balun wire as ARRLO599 50 Input Output to 10 1 SWR 50 Input Output to 10 1 SWR mentioned previously was the warmest component in the antenna tuner for frequencies above 14 MHz although it was far from catastrophic 24 2 8 GENERAL PURPOSE TUNER DESIGNS Several antenna tuner designs were created by Joel Hallas W1ZR for the book The ARRL Guide to Antenna Tuners The TLW program was used to determine component values for a set of common load impedances and three popu lar antenna tuner circuits shown in Figure 24 17 Tables 24 3 to 24 5 show the required component values to match those load impedances at 1 8 3 5 and 30 MHz the extremes of HF operation for antenna tuners Cin Cour 50 Q Input Output to 10 1 SWR C Figure 24 17 Schematic diagrams of a high pass T network A pi network B and a low pass L network C Tables 24 3 to 24 5 give component values at 1 8 3 5 and 30 MHz to match different values of load impedances to 50 Capacitor Voltage Vp Efficiency 100 W 1500 W 180 710 96 323 1250 98 790 3070 92 1040 4030 86 380 1470 98 525 2030 96 Capacitor Voltage Vp Efficiency 100 W 1500
36. wires wound on 2 4 inch toroidal cores with p 850 will cover the whole range from 1 8 to 30 MHz The 4 1 current balun at the right is wound on two cores which are physically separated from B each other 24 10 BIBLIOGRAPHY Source material and more extended discussion of topics covered in this chapter can be found in the references given below and in the textbooks listed at the end of the Antenna Fundamentals chapter G Barrere Magnetic Coupling in Transmission Lines and Transformers QEX Sep Oct 2006 pp 28 36 D K Belcher RF Matching Techniques Design and Example QST Oct 1972 pp 24 30 W Bruene Introducing the Series Parallel Network QST Jun 1986 pp 21 23 W Caron Antenna Impedance Matching Newington ARRL 1989 out of print G Cutsogeorge Managing Interstation Interference 2nd edition International Radio 2009 T Dorbuck Matching Network Design QST Mar 1979 pp 26 30 B A Eggers An Analysis of the Balun QST Apr 1980 pp 19 21 D Emerson Try a Twelfth Wave Transformer QST Jun 1997 pp 43 44 D Geiser Resistive Impedance matching with Quarter Wave Lines QST Feb 1963 pp 63 67 J D Gooch O E Gardner and G L Roberts The Hairpin Match QST Apr 1962 pp 11 14 146 156 G Grammer Simplified Design of Impedance Matching Networks QST Part 1 Mar 1957 pp 38 42 Part 2 Apr 1957 pp 32 35 Part 3 May 1957 pp 29 34
37. 0 pF making the actual range from 42 to 251 pF with an unloaded Q of 1000 This value of Q is typi cal for an air variable capacitor with wiping contacts Next you choose a variable inductor with a maximum inductance of let s say 28 uH and an unloaded Q of 200 again typical values for a practical inductor Set a power loss limit of 20 equivalent to a power loss of about 1 dB Then let AAT do its computations AAT tests matching capability over a very wide range 24 8 Chapter 24 of load impedances in octave steps of both resistance and reactance For example it starts out with 3 125 j 3200 Q and checks whether a match is possible It then proceeds to 3 125 j 1600 Q 3 125 j 800 Q etc down to 3 125 j 0 Q Then AAT checks matching with positive reactances 3 125 j 3 125 3 125 j 6 25 3 125 j 12 5 etc on up to 3 125 j 3200 Q Then it repeats the same process over the same range of negative and positive reactances for a series resistance of 6 25 Q It continues this process in octave steps of resistance all the way up to 3200 resistive A total of 253 impedances are thus checked for each frequency giving a total of 2277 combinations for nine amateur bands from 1 8 to 29 7 MHz If the program determines that the chosen network can match a particular impedance value while staying within the limits of voltage component values and power loss imposed by the operator it stores the lost power percent age i
38. 1 2097 j 1552 2666 j 884 21 1 345 j 1073 156 614 24 9 202 j 367 149 j 231 28 4 2493 j 1375 68 174 Table 24 2 Impedance of Center Fed 66 Foot Inv V Dipole 50 Feet at Apex 120 Included Angle Over Average Ground Frequency Antenna Feed point Impedance at Input of MHz Impedance Q 100 ft 450 Q Line Q 1 83 1 6 j 2257 1 6 j44 3 8 10 j 879 2275 j 8980 7 1 65 j41 1223 j 1183 10 1 22 648 157 j 1579 14 1 5287 j 1310 148 j 734 18 1 198 j 820 138 j595 21 1 103 181 896 j 857 24 9 269 570 99 j 140 28 4 3089 j 774 74 j 223 recognize that there is nothing special or magic about these antennas they are merely representative of typical anten nas used by real world amateurs The intent of the tables is to show that the impedance at the input of the transmission line varies over an extremely wide range when antennas like these are used over the entire range of amateur bands from 160 to 10 meters The imped ance at the input of the line that is at the antenna tuner s output terminals will be different if the length of the line or the frequency of operation is changed It should be obvious that an antenna tuner used with such a system must be very flexible to match the wide range of impedances encountered under ordinary circumstances and it must do so without arcing from high voltage or overheating from high current 24 1 1 THE IMPEDANCE MATCHI
39. 3 Turns 7 cores 1000 3 Turns 5 cores Close spacing 24 46 Chapter 24 4 5 6 7 8910 40 506070 90 Frequency MHz Figure 24 55 Typical transmitting wound coax common mode chokes suitable for use on the HF bands Figure 24 56 Impedance versus frequency for HF wound coax trans mitting chokes using 2 4 inch toroid cores of 31 material with RG 8X coax Figure 24 57 Impedance versus frequency for HF wound coax transmitting chokes using toroid cores of 31 material with RG 8 coax Turns are 5 inch diameter and wide spaced unless noted Figure 24 58 Impedance versus fre quency for HF wound coax transmit ting chokes wound on big clamp on HBK0448 cores of 31 material with RG 8X or RG 8 coax Turns are 6 inch diameter wide spaced except as noted 8 turns RG8X 7 7 turns ye RG8X GS co O G ao ko 2 6 turns RG8X 7 Stums RG8X 42 3 Clamps a 6C 3 turns RG8 ose 3 Close turns spaced RG8 74 turns RG8X 5 6 7 8910 20 Frequency MHz 2 Clamps 3 turns RG8 1 2 3 4 1000 transmitting chokes of various sizes Fourteen close spaced 3 inch diameter turns of RG 58 size cable on a 31 toroid is a very effective 300 W choke for the 160 and 80 meter bands Table 24 11 summarizes designs that meet the 5000 Q criteria for the 160 through 6 meter ham b
40. 4 feed lines and the 1 2 delay of the longer line to cause equal and opposite currents to flow in the antenna terminals 24 50 Chapter 24 part of the matching system This requires that the radiation resistance be fairly low as compared with the line Zp so that a match can be brought about by first shortening the antenna to make it have a capacitive reactance and then using a shunt inductor across the antenna terminals to resonate the antenna and simultaneously raise the impedance to a value equal to the line Zp This is the same principle used for hairpin matches The balun is then made the proper length to exhibit the desired value of inductive reactance The basic matching method is shown in Figure 24 63A for parallel wire line and the balun adaptation to coaxial feed is shown in Figure 24 63B The matching stub in Figure 24 63B is a parallel line section one conductor of which is the outside of the coax between point X and the antenna the other stub conductor is an equal length of wire A piece of coax may be used instead as in the balun in Figure 24 61A The spacing between the stub conductors can be 2 to 3 inches The stub of Figure 24 63 is ordinarily much shorter than 1 4 and the impedance match can be adjusted by altering the stub length along with the antenna length With simple coax feed even with a 1 4 balun as in Figure 24 61 the match depends entirely on the actual antenna impedance and the Zp of the cable no adjustment i
41. 5 in 12 T 4 25 in 4 T 6 625 in 1 Layer 1 Layer 1 Layer Freq Z Phase Z Phase Z Phase MHz Q or Q 1 26 88 1 65 89 2 26 88 3 2 51 88 7 131 89 3 52 88 8 3 77 88 9 200 89 4 79 89 1 4 103 89 1 273 89 5 106 89 3 5 131 89 1 356 89 4 136 89 2 6 160 89 3 451 89 5 167 89 3 7 190 89 4 561 89 5 201 89 4 8 222 89 4 696 89 6 239 89 4 9 258 89 4 869 89 5 283 89 4 10 298 89 3 1103 89 3 333 89 2 11 340 89 3 1440 89 1 393 89 2 12 390 89 3 1983 88 7 467 88 9 13 447189 2 3010 87 7 556 88 3 14 514 89 3 5850 85 6 675 88 3 15 594 88 9 42000 44 0 834 87 5 16 694 88 8 7210 81 5 1098 86 9 17 830 88 1 3250 82 0 1651 81 8 18 955 86 0 2720 76 1 1796 70 3 19 1203 85 4 1860 80 1 3260 44 6 20 1419 85 2 1738 83 8 3710 59 0 21 1955 85 7 1368 87 2 12940 31 3 22 3010 83 9 1133 87 7 3620 77 5 23 6380 76 8 955 88 0 2050 83 0 24 15980 29 6 807 86 3 1440 84 6 25 5230 56 7 754 82 2 1099 84 1 26 3210 78 9 682 86 4 967 83 4 27 2000 84 4 578 87 3 809 86 5 28 1426 85 6 483 86 5 685 87 1 29 1074 85 1 383 84 1 590 87 3 30 840 83 2 287 75 0 508 87 0 31 661 81 7 188 52 3 442 85 7 32 484 78 2 258 20 4 385 83 6 33 335 41 4 1162 13 5 326 78 2 34 607 32 2 839 45 9 316 63 4 35 705 58 2 564 56 3 379 69 5 24 42 Chapter 24 8T 6 625 in 8T 6 625 in 1 Layer Bunched Z Phase Z Phase ag ay 74 89 2 94 89 3 150 89 3 202 89 2 232 89 3 355 88 9 324 89 4 620 88 3 436 89 3 1300 86 2 576 89 1 8530 59 9 759 89 1 2120 81 9 1033 88
42. 600 3200 L L L DNDCODEP ARERR ra SII NUDDGDGHDIIMOOHNrS WDMDONMNON UF WwW J vVuddnFH SHEE HHH HUDOS WIDD HAA HBWHALHWOD Sic BsewwwwwwwwwhnwoG BNDUOYEHDWUBWO TO SII PwwwnnwwnNnnnNnNnNWUSS NMNNMNOWWODOANWOAHDUM SASRPMUNNNNNNNNNNNNNWA FPOAUWHEUDWWWEBWHWUO SMP NOFPRPEPHENNRPRP RP RRP RPRN OSS WUIODHWDMDOWDODDWWUWDDAUO SNR RRP RP EP RP RP RP RP RR RRR ROW DANUNAHD TDWI IIANIDWONOW SAAINMNNMNNNMNNNNNNNNMNNNWG YAWWWWWWWW WWW bP BSAWOW SHRWWWWWWWWWWWWWwWwWwwwnw pd H Aa Www www ww w w w w www ds bao Ce A o a E o e E o o E e E E a Loss percentage for Tee network series cap shunt inductor series cap Freq 29 7 MHz Z0 50 1500W Vmax 3000 V Qu 200 Qc 1000 Var Cap 25 to 402 pF with switched 160 80 m output cap 400 pF 3312562251255 25 50 100 400 800 1600 3200 Ra C C C C C C G C C C C CcC C cC cC c C C Cz C C cC C c C C C C Cs c C C Cs c C C C C GS C C C G C C C C C C C C C C c C C Gs C C C C C C Ca C C Cs C C C Q anaa et Pea YTOUULSABDHAALUDOBUD Q I Q oe a ae OL ik ues 8 NOWrFWOWWOFWOWW e eo 8 6 Pd4fIuUPBwwwnw buon EREN MAAT A NOAA BH OUEF amp OWNNENFRFNN EAD WHR RR RRP RP RPRNWO ae ie et cr et ie her ey eae oouULSUA A BRWU PL PRR RPrRPOrRPOOCORN Ss ANOrPOTW DODD WWFrE COrPODDDDDOCCORPNSA FPODOCOCOCCOOOCOOCOCOCOOrFRFRNOD ey ta eet ae E a a ae e
43. 8 1019 85 7 1514 87 3 681 86 5 2300 83 1 518 86 9 4700 73 1 418 87 1 15840 5 2 350 87 2 4470 62 6 300 86 9 2830 71 6 262 86 9 1910 79 9 231 87 0 1375 84 1 203 87 2 991 82 4 180 86 9 986 67 2 164 84 9 742 71 0 145 85 1 1123 67 7 138 84 5 859 84 3 122 86 1 708 86 1 107 85 9 613 86 9 94 85 5 535 86 3 82 85 0 466 84 1 70 84 3 467 81 6 60 82 7 419 85 5 49 81 7 364 86 2 38 79 6 308 85 6 28 75 2 244 82 1 18 66 3 174 69 9 9 34 3 155 18 0 11 37 2 569 0 3 21 63 6 716 57 6 32 71 4 513 72 5 46 76 0 Table 24 10 Coiled Coax Choke Baluns Wind the indicated length of coaxial feed line into a coil like a coil of rope and secure with electrical tape The balun is most effective when the coil is near the antenna Lengths are not critical Single Band Very Effective Freq RG 213 RG 8 RG 58 MHz 3 5 22 ft 8 turns 20 ft 6 8 turns 7 22 ft 10 turns 15 ft 6 turns 10 12 ft 10 turns 10 ft 7 turns 14 10 ft 4 turns 8 ft 8 turns 21 8 ft 6 8 turns 6 ft 8 turns 28 6 ft 6 8 turns 4 ft 6 8 turns Multiple Band Freq RG 8 58 59 8X 213 MHz 3 5 30 10 ft 7 turns 3 5 10 18 ft 9 10 turns 1 8 3 5 14 30 40 ft 20 turns 8 ft 6 7 turns impedance at the indicated frequencies as measured with an impedance meter This construction technique is not effective with open wire or twinlead line because of coupling between adjacent turns The inductor formed by the coaxial cable sh
44. F IFW QAP RRP RRP RPRPRPEPRP te 6 ee eS SCC COCOCCOCOFPF WADADAAADAHROFRA ONDE BRPAPROPR SCCOCCCCCOOCOOCOOOFFRFD a ae ee ee ee ee ee ee er er ee er YUNNAN NNNSN PREP RPP RPP PRP PPP PODORPRPERPRPEPEPRPNWOA Figure 24 6 Sample printout from the AAT program showing 3 5 and 29 7 MHz simulations for a T network antenna tuner using 42 251 pF variable tuning capacitors including 10 pF of stray with voltage rating of 4500 V and 28 uH roller inductor The load varies from 3 125 j 3200 Q to 3200 j 3200 Q in geometric steps Symbol L indicates that a match is impossible because more inductance is needed C indicates that the minimum capacitance is too large V indicates that the voltage rating of a capacitor has been exceeded P indicates that the power rating limit set by the operator to 20 has been ex ceeded A blank indicates that matching is not possible at all probably for a variety of simultaneous reasons Transmission Line Coupling and Impedance Matching 24 9 Loss percentage for Tee network series cap shunt inductor series cap Freq 3 5 MHz ZO 50 1500W Vmax 3000 V Qu 200 Qc 1000 Var 25 to 402 pF with switched 160 80 m output cap 400 pF 3125 6 25632 5 25 50 100 200 400 800 1600 3200 Ra L Et L L L L L L V L L L L L C L L L L L C L C t9 16 14 13 12 12 i lep Be 6 25 11 12 5 10 25 50 100 200 400 800 1
45. LW soft ware Note the tuner schematic with parts values shown The data above the schematic provide additional impor tant information Not only does TLW compute the exact values for net work components but also the full effects of voltage cur rent and power dissipation for each component Depending on the load impedance presented to the antenna tuner the internal losses in an antenna tuner can be disastrous See the documentation file TLW PDF for further details on the use of TLW which some call the Swiss Army Knife of transmis sion line software 24 2 5 THE AAT ANALYZE ANTENNA TUNER PROGRAM As you might expect the limitations imposed by prac tical components used in actual antenna tuners depends on the individual component ratings as well as on the range of impedances presented to the tuner for matching ARRL has developed a program called AAT standing for Analyze Antenna Tuner to map the range over which a particular design can achieve a match without exceeding certain opera tor selected limits AAT may be downloaded from www arrl org antenna book Let s assume that you want to evaluate a T network on the ham bands between 1 8 to 29 7 MHz First you select suitable variable capacitors for C1 and C2 You decide to try the Johnson 154 16 1 a commonly available surplus or used component rated for a minimum to maximum range from 32 to 241 pF at 4500 V peak Stray capacitance in the circuit is estimated at 1
46. NG SYSTEM Over the years radio amateurs have derived a number of circuits for use as antenna tuners At one time when parallel wire transmission line was more widely used link coupled tuned circuits were in vogue With the increasing popularity of coaxial cable used as feed lines other circuits have become more prevalent The most common form of antenna tuner in recent years is some variation of a T network configuration ANT0870 Antenna Transmission Antenna Line Tuner Any Type Figure 24 1 Essentials of an impedance matching sys tem between transmitter and transmission line The SWR meter indicates the quality of the match provided by the antenna tuner and may be part of the antenna tuner or the transmitter Transmitter The basic system of a transmitter impedance matching network transmission line and antenna is shown in Fig ure 24 1 As usual we assume that the transmitter is designed to deliver its rated power into a load of 50 Q The problem is one of designing a matching circuit that will transform the actual line impedance at the input of the transmission line into a resistive impedance of 50 jO This impedance will be unbalanced that is one side will be grounded since modern transmitters universally ground one side of the output connector to the chassis The line to the antenna however may be unbalanced coaxial cable or balanced parallel wire line depending on whether the antenna itself is unbalanced
47. Such a line operates as a broadband impedance transformer Because tapered lines are used almost 24 23 Tapered Line Section a Zo ANT0888 Figure 24 23 A tapered line provides a broadband frequen cy transformation if it is one wavelength long or more From a practical construction standpoint the taper may be linear exclusively for matching applications they are discussed in this chapter The characteristic impedance of an open wire line can be tapered by varying the spacing between the conductors as shown in Figure 24 23 Coaxial lines can be tapered by varying the diameter of either the inner conductor or the outer conductor or both The construction of coaxial tapered lines is beyond the means of most amateurs but open wire tapered lines can be made rather easily by using spacers of varied lengths In theory optimum broadband impedance transfor mation is obtained with lines having an exponential taper but in practice lines with a linear taper as shown in Figure 24 23 work very well A tapered line provides a match from high frequencies down to the frequency at which the line is approximately 1 long At lower frequencies especially when the tapered line length is 4 2 or less the line acts more as an impedance lump than a transformer Tapered lines are most useful at VHF and UHF because the length requirement becomes unwieldy at HF Air insulated open wire lines can be designed from the equation E dx1020 276 2
48. TABLE OF CONTENTS 24 1 Coupling the Transmitter and Line 24 1 1 The Impedance Matching System 24 1 2 Harmonic Attenuation 24 1 3 Myths About SWR 24 2 Impedance Matching Networks 24 2 1 The L Network 24 2 2 The Pi Network 24 2 3 The T Network 24 2 4 The TLW Transmission Line for Windows Program and Antenna Tuners 24 2 5 The AAT Analyze Antenna Tuner Program 24 2 6 Balanced Antenna Tuners 24 2 7 Project High Power ARRL Antenna Tuner 24 2 8 General Purpose Tuner Designs 24 3 Transmission Line System Design 24 3 1 Transmission Line Selection 24 3 2 Antenna Tuner Location 24 3 3 Using TLW to Determine SWR 24 4 Transmission Line Matching Devices 24 4 1 Quarter Wave Transformers 24 4 2 Twelfth Wave Transformers 24 4 3 Series Section Transformers 24 4 4 Tapered Lines 24 4 5 Multiple Quarter Wave Sections 24 5 Matching Impedance at the Antenna 24 5 1 Antenna Impedance Matching 24 5 2 Connecting Directly to the Antenna 24 5 3 The Delta Match 24 5 4 Folded Dipoles 24 5 5 The T and Gamma Matches 24 5 6 The Omega Match 24 5 7 The Hairpin and Beta Matches 24 5 8 Matching Stubs 24 5 9 Resonant Circuit Matching 24 5 10 Broadband Matching 24 6 Common Mode Transmission Line Currents 24 6 1 Unbalanced Coax Feeding a Balanced Antenna 24 6 2 Asymmetrical Routing of the Feed Line 24 6 3 Common Mode Current Effects on Directional Antennas 24 7 Choke Baluns 24 7 1 The Coaxial Choke Balun 24 7 2 Transmitting Ferrite Core
49. The value of A is 1 570 Calculating 1 yields 57 5 Adding 180 to obtain a positive result gives 1 122 5 or 0 340 To find the physical lengths 1 and 2 we first find the free space wavelength 984 f MHz Multiply this value by 0 79 the velocity factor for both types of line and we obtain the electrical wavelength in coax as 26 81 feet From this 41 0 340 x 26 81 9 12 feet and 2 0 065 x 26 81 1 74 feet This completes the calculations Construction consists of cutting the main coax at a point 9 12 feet from the antenna and inserting a 1 74 foot length of the 75 Q cable The antenna in the preceding example could also have been matched by a 4 4 transformer at the load Such a trans former would use a line with a characteristic impedance of 42 43 Q It is interesting to see what happens in the design of a series section transformer if this value is chosen as the characteristic impedance of the series section Following the same steps as before we find n 0 849 r 0 720 and x 0 From these values we find B 8 and 2 90 Further A 0 and 1 0 These results represent a A 4 section at the load and indicate that as stated earlier the A 4 transformer is indeed a special case of the series section transformer 33 93 feet 24 4 4 TAPERED LINES A tapered line is a specially constructed transmission line in which the impedance changes gradually from one end of the line to the other
50. W 190 720 96 343 1330 98 613 2373 95 880 3403 88 381 1475 98 670 2600 94 Capacitor Voltage Vp Efficiency 100 W 1500 W 160 640 96 370 1470 97 400 1560 98 440 1710 93 300 1150 98 360 1410 97 Table 24 3 Component Requirements for High Pass Shunt L T Network Antenna Tuners at 10 1 SWR Frequency Z Q Capacitor Inductor uH 1 8 MHz Input pF Output pF 5 1136 3000 2 1 500 548 500 13 9 25 j100 343 300 10 3 25 j100 170 300 20 250 j250 308 200 10 5 250 j250 337 300 16 9 Frequency Z Q Capacitor Inductor uH 3 5 MHz Input pF Output pF 5 563 1500 1 1 500 265 200 7 3 25 j100 275 200 3 5 25 j100 104 200 8 6 250 j250 333 100 5 6 250 j250 136 100 10 8 Frequency Z Q Capacitor Inductor uH 30 MHz Input pF Output pF 5 79 200 0 12 500 29 50 0 77 25 j100 91 30 0 24 25 j100 24 100 0 46 250 j250 36 100 0 9 250 j250 29 100 0 6 24 16 Chapter 24 Table 24 4 Component Requirements for Low Pass Series L L Network Antenna Tuners at 10 1 SWR Frequency Z Q 1 8 MHz 5 500 25 100 25 j100 250 j250 250 j250 Frequency Z Q 3 5 MHz 5 500 25 j100 25 j100 250 j250 250 j250 Frequency Z Q 30 MHz 5 500 25 j100 25 j100 250 j250 250 250 Table 24 5 Component Requirements for Low Pass Pi Network Antenna Tuners at 10 1 SWR Capacitor Voltage Vp Frequency Z Q 1 8 MHz 5 500 25 100 25
51. WWORNKHKDADHNW 200 V 400 V 800 P 1600 3200 L L L Loss percentage for Tee network series cap shunt inductor series cap Freq 29 7 MHz Z0 50 1500W Vmax 4500 V Qu 200 Qc 1000 Var Cap 42 to 251 pF with switched 160 80 m output cap 0 pF xa 3 125 6 425 12 5 25 50 100 200 400 800 1600 3200 Ra 3200 C cC C C C C C C C C C 1600 cC C C C C C C C C C C 800 c C C C C C C C C C C 400 C C C cC C C C C C C C 200 C cC C C C C C C C C 100 C C C 2 ee C C C C 50 C C C C cC C 25 C C C C C 12 5 c C C C 6 25 C C C C 3 125 C C 0 C C C C 32125 C C C cC 6 25 c C C C 12 5 C C C C 25 C C C C 50 C C C C 100 c C C C 200 C C C C 400 C C cC C 800 C C C C 1600 C C C C 3200 cC C cC C SSNAN ONNIN SSI SEHK HEHE KA KH RUDON SS FP GMWwWwWwhhWWWWWWwWwwwundd 6 6 OR at a ee ee oe a a E TO E O POW TDONWDITIDDODAOND NNWWWWWWWWWWWWWWwwwuocd e kna EO O68 a Oe ee ee ee eS UWADE ANWAR EHBUUUNRPWRUOF WNHWNHONNNNNNNNNNNNNHNWUW 6 8 ee bY bee aay eee ee ee er A Je DAWNDONDOWOTDITDNIMDDOWOINAY FWNYNNNNNNNNNNNNNNNNWHED ONDWWHEKBUUNNNUUMA DON Ww I OPWWWWWWWWWWWWWwwwwnwhud NOKPWWWWHEA HEHEHE HL APPR PMOYDNS UPA A A A HEHE HLL SF HE HH HEHEHE HUU AT WWD HDAATYIAIYIAIYIYYAYIYVANYNYIYODOOAN NO Q NAWRORPDOORANDN OURWWABRUD PWWHONYNNNWWU DCONUFPAUDANUOW MVNONNFPRPRPEFPENN MOOONIHNHS
52. a simple high Q paral lel resonance and they must be used below resonance They are simple inexpensive and unlikely to overheat Choking impedance is purely inductive and not very great reducing their effectiveness Effectiveness is further reduced when the inductance resonates with the line at frequencies where the line impedance is capacitive and there is almost no resistance to damp the resonance Adding ferrite cores to a coiled coax balun is a way 24 47 Table 24 12 Combination Ferrite and Coaxial Coil So Measured Impedance Freq 7 ft 4turns 1 Core 2 Cores MHz of RG 8X 1 8 520 Q 3 5 E 660 1 4 KQ 7 1 6 KQ 3 2 KQ 14 560 Q 1 1 KQ 1 4 KQ 21 42 KQ 500 Q 670 Q 28 4709 E to increase their effectiveness The resistive component of the ferrite impedance damps the resonance of the coil and increases its useful bandwidth The combinations of ferrite and coil baluns shown in Table 24 12 demonstrate this very effectively Eight feet of RG 8X in a 5 turn coil is a great balun for 21 MHz but it is not particularly effective on other bands If one type 43 core Fair Rite 2643167851 is inserted in the same coil of coax the balun can be used from 3 5 to 21 MHz If two of these cores are spaced a few inches apart on the coil as in Figure 24 60 the balun is more effective from 1 8 to 7 MHz and usable to 21 MHz If type 31 material was used the Fair Rite 2631101902 is a similar core low frequency performance would be ev
53. actor that limits the range of impedances that can be matched by this method is the range of values for Zp that is physically realizable The latter range is approximately 50 to 600 Practically any type of line can be used for the matching sec tion including both air insulated and solid dielectric lines The A 4 transformer may be adjusted to resonance before being connected to the antenna by following the procedures for determining line length in the chapter Transmission Line and Antenna Measurements Yagi Driven Elements Another application for the A 4 transformer is in matching the low antenna impedance encountered in close spaced monoband Yagi arrays to a 50 Q transmission line The impedances at the antenna feed point for typical Yagis range from about 8 to 30 Let s assume that the feed point impedance is 25 A matching section is needed Since there is no commercially available cable with a Zp of 35 4 Q a pair of 2 4 long 75 Q RG 11 coax cables connected in parallel will have a net Z of 75 2 37 5 Q close enough for practical purposes 24 4 2 TWELFTH WAVE TRANSFORMERS The Q section is really a special case of series section matching described below There s no restriction other than complexity that there be just one matching section In fact the two section variation shown in Figure 24 19B is quite handy for matching two different impedances of transmission line such as 50 Q coax and 75 Q hardline Best of all
54. al tape Because of the bulk and weight of the balun this type is seldom used with wire line antennas suspended by insulators at the antenna ends More commonly it is used with multiele ment Yagi antennas where its weight may be supported by the boom of the antenna system See the K1FO designs in the VHF and UHF Antenna Systems chapter where 200 Q T matches are used with such a balun 24 51 24 9 VOLTAGE BALUNS The voltage baluns shown in Figure 24 65A and Figure 24 65B cause equal and opposite voltages to appear at the two output terminals relative to the voltage at the cold side of the input They are flux linked impedance transformers similar to power transformers If the impedances of the two antenna halves are per fectly balanced with respect to ground the currents flowing from the output terminals will be equal and opposite and no common mode current will flow on the line This means if the line is coaxial there will be no current flowing on the outside of the shield if the line is balanced the currents in the two conductors will be equal and opposite These are the conditions for a nonradiating line Under this condition the 1 1 voltage balun of Fig 75 Q Coax Any Length ANT0917 ANT0916 Figure 24 64 A balun that pro vides an impedance step up ratio of 4 1 The electrical length of the U shaped section of line is 4 2 24 52 Chapter 24 1 1 Balanced to Unbalanced Voltage Balun ure 24 65A perform
55. alanced driven element s feed point without the need for an intervening feed line The dashed line represents the second Yagi which is modeled with a A 2 long unbal anced coaxial feed line going to ground directly under the balanced driven element s feed point Minor pattern skewing evident in the case of the dipole now becomes definite deterioration in the rearward pattern of the otherwise superb pattern of the reference Yagi The side nulls deteriorate from more than 40 dB to about 25 dB The rearward lobe at 180 goes from 26 dB to about 22 dB In short the pattern gets a bit ugly and the gain decreases as well Figure 24 50 shows a comparison at 0 71 A height be tween a reference Yagi with no feed line and a Yagi with a 1 A long feed line slanted 45 to ground Side nulls that were deep at more than 30 dB down for the reference Yagi have been reduced to less than 18 dB in the common mode afflicted antenna The rear lobe at 180 has deteriorated mildly from 28 dB to about 26 dB The forward gain of the antenna has fallen 0 4 dB from that of the reference antenna As expected the feed point impedance also changes from 22 3 j 25 2 Q for the reference Yagi to 18 5 j 29 8 Q for the antenna with the unbalanced feed The SWR will also change with line length on the balanced Yagi fed with unbalanced line just as 24 40 Chapter 24 5 Ele Yagi w Slanted Feed Line ANTO911 Reference 5 Ele Yagi 15 Elevation
56. alanced terminals such as at an antenna s feed point An impedance transformer may or may not perform the balun function Impedance transformation changing the ratio of voltage and current is not required of a balun nor is it prohibited There are balanced to balanced impedance transformers transformers with isolated primary and second ary windings for example just as there are unbalanced to unbalanced impedance transformers autotransformer and transmission line designs A transmission line transformer Transmission Line Coupling and Impedance Matching is a device that performs the function of power transfer with or without impedance transformation by utilizing the char acteristics of transmission lines Multiple devices are often combined in a single package called a balun For example a 4 1 balun can be a 1 1 cur rent balun in series with a 4 1 impedance transformer Other names for baluns are common such as line isolator for a choke balun Baluns are often referred to by their construc tion bead balun coiled coax balun sleeve balun etc What is important is to separate the function power transfer between balanced and unbalanced systems from the construction Schematic Representation of a Choke Balun The choke balun has the hybrid properties of a tightly coupled transmission line transformer with a 1 1 transfor mation ratio and a coil The transmission line transformer a
57. an be stated as follows 1 The input impedance increases as the distance A is made larger but not indefinitely In general there is a dis tance A that will give a maximum value of input impedance after which further increase in A will cause the impedance to decrease 2 The distance A at which the input impedance reaches a maximum is smaller as d2 d1 is made larger and becomes smaller as the spacing between the conductors is increased d1 is the diameter of the lower T conductor in Figure 24 29 and d2 is the diameter of the antenna 3 The maximum impedance values occur in the region where A is 40 to 60 of the antenna length in the average case 4 Higher values of input impedance can be realized when the antenna is shortened to cancel the inductive reac tance of the matching section The T match has become popular for transforming the balanced feed point impedance of a VHF or UHF Yagi up to 200 Q From that impedance a 4 1 balun is used to transform down to the unbalanced 50 Q level for the coax cable feeding the Yagi See the various K1FO designed Yagis in the VHF and UHF Antenna Systems chapter and the section later in this chapter concerning baluns The structure of the T match also affects the length of the driven element by increasing the element s electrical diam eter A typical T match is approximately 5 to 10 times greater in diameter than the element alone This results in the need to extend the length of the driven ele
58. an waste that precious RF power you d rather put into your antenna Additional discus sion of the T network as an antenna tuner is provided in the article by Sabin listed in the Bibliography Adjusting T Network Antenna Tuners The process of adjusting an antenna tuner can be sim plified greatly by using a process that not only results in minimum SWR to the transmitter but also minimizes power losses in the tuner circuitry If you have a commercial tuner and read the user s manual the manufacturer will likely provide a method of adjustment that you should follow in cluding initial settings If you do not have a user s manual first open the tuner and determine the circuit for the tuner To adjust a T network type of tuner 1 Set the series capacitors to maximum value This may Transmission Line Coupling and Impedance Matching not correspond to the highest number on the control scale verify that the capacitor s plates are fully meshed 2 Set the inductor to maximum value This corresponds to placing a switch tap or roller inductor contact so that it is electrically closest to circuit ground 3 If you have an SWR analyzer connect it to the TRANSMITTER connector of the tuner Otherwise connect the transceiver and tune it to the desired frequency but do not transmit 4 Adjust the inductor throughout its range watching the SWR analyzer for a dip in the SWR or listen for a peak in the received noise Return the induct
59. ance The driven element s feed point impedance must exhibit a specific amount of capacitive reactance as shown in the text 24 31 N g D Q Ex e 5 6 6 i f D c o 4 c 2 3 o ip D amp w 0 0 2 0 3 0 4 0 5 ANT0899 X Zo of Matching Section Figure 24 37 Inductive reactance normalized to Zo of matching section scale at bottom versus required hairpin matching section length scale at left To determine the length in wavelengths divide the number of electrical de grees by 360 For open wire line a velocity factor of 97 5 should be taken into account when determining the electri cal length terminating impedance as seen by the feed line Greater re sistances are obtained with longer hairpin sections mean ing a larger value of shunt inductor and smaller resistances with shorter sections The remaining reactance at the feed point terminals is tuned out by adjusting the length of the driven element as necessary If a fixed length hairpin section is in use a small range of adjustment may be made in the effective value of the inductance by spreading or squeezing together the con ductors of the hairpin Spreading the conductors apart will have the same effect as lengthening the hairpin while placing them closer together will effectively shorten it Instead of us
60. ance Matching A ug Figure 24 59 W2DU bead balun con sisting of 50 FB 73 2041 ferrite beads over a length of RG 303 coax See text for details 40 50 6070 90 impedance is often insufficient to limit current to a low enough value to prevent overheating Equally important the lower choking impedance is much less effective at rejecting noise and preventing the filling of nulls in a radiation pattern Newer bead balun designs use type 31 and 43 beads that are resonant around 150 MHz are inductive below reso nance and have only a few tens of ohms of strongly inductive impedance on the HF bands Even with 20 of the type 31 or 43 beads in the string the choke is still resonant around 150 MHz is much less effective than a wound coaxial ferrite choke and is still inductive on the HF bands so it will be ineffective at frequencies where it resonates with the line Be aware that the heat dissipating capability of small diameter ferrite beads can be exceeded where there is a seri ous imbalance that results in large common mode currents Beads nearest the feed point can become very warm and can even shatter under extreme conditions of imbalance Be careful not to skimp on using sufficient beads to choke off common mode currents in the first place Adding Ferrite Beads to Air Wound Coaxial Chokes Air wound coaxial chokes are less effective than bead baluns Their equivalent circuit is also
61. ance transformation from source to load takes place as a series of gradual transformations The frequency bandwidth with multiple sections is greater than for a single section This technique is useful at the upper end of the HF range and at VHF and UHF Here too the total line length that is required may become unwieldy at the lower frequencies A multiple section line may contain two or more 2 4 transformer sections the more sections in the line the broad er is the matching bandwidth Coaxial transmission lines may be used to make a multiple section line but standard coax lines are available in only a few characteristic impedances Open wire lines can be constructed rather easily for a specific impedance designed from Eq 16 above The following equations may be used to calculate the intermediate characteristic impedances for a two section line Z 4RZ Eq 17 Zo 3R Z Eq 18 where terms are as illustrated in Figure 24 24 For example assume we wish to match a 75 Q source Zp to an 800 Q load From Eq 17 calculate Z to be 135 5 Q Then from Eq 18 calculate Z to be 442 7 Q As a matter of interest for this example the virtual impedance at the junction of Z and Z is 244 9 Q This is the same impedance that would be required for a single section 4 4 matching section Multisection 4 4 transformers are discussed by Randy Rhea in High Frequency Electronics magazine See Bibli ography This technique is related to the
62. and deciding the best configuration of feed line and impedance matching devices Finally at the other end of the feed line several sections address methods of impedance matching at the antenna and minimizing unwanted interac tion between the feed line and antenna 24 1 COUPLING THE TRANSMITTER AND LINE A lot of effort is expended to ensure that the impedance presented to the transmitter by the antenna system feed line is close to 50 Q Is all that effort worthwhile Like most broadly phrased questions the answer begins It depends Vacuum tube transmitters with the wide adjustment range of the output amplifier s pi network could comfortably deliver rated output power into a wide variety of loads The draw back was that the output network needed to be readjusted whenever the operating frequency changed significantly The modern amateur transceiver does not require output tuning adjustment at all for its broadband untuned solid state final amplifiers that are designed to operate into 50 Such a transmitter is able to deliver its rated output power at the rated level of distortion only when it is operated into the load for which it was designed Generating full power from such a transmitter into loads far from 50 can result Transmission Line Coupling and Impedance Matching in distortion products causing interference to other stations Further modern radios often employ protection cir cuitry to reduce outp
63. and uses practical values for the components However as in almost everything in radio there is a price to be paid for this flex ibility The T network can be very lossy compared to other network types This is particularly true at the lower frequen cies whenever the load resistance is low Loss can be severe if the maximum capacitance of the output capacitor C2 in Figure 24 2C is low For example Figure 24 3 shows the computed values for the components at 1 8 MHz for four types of networks into a load of 5 j 0 Q In each case the unloaded Q of the inductor used is assumed to be 200 and the unloaded Q of the capacitor s used is 1000 The component values were computed using the program TLW described later in this chapter 24 6 Chapter 24 5254 1 pF Q 3 0 Loss 1 8 C2 O 5837 5 pF 1 5 uH QL 3 0 Loss 1 8 Loss 1 8 C2 180 3 pF 500 0 pF L 11 5 uH QL 34 2 Loss 22 4 ANT0877 Figure 24 3 Computed values for real components Qy 200 for coil Qy 1000 for capacitor to match 5 load resis tance to 50 Q line At A low pass L network with shunt input capacitor series inductor At B high pass L network with shunt input inductor series capacitor Note how large the ca pacitance is for these L networks At C low pass pi network and at D high pass T network The component values for the T network are practical although the loss is highest for this particular network at 22 4
64. ands and several practical transmitting choke designs that are tuned or opti mized for ranges of frequencies The table entries refer to the specific cores in the preceding paragraph If you construct the chokes using toroids remember to make the diameter of the turns large enough to avoid deformation of the coaxial cable Coaxial cable has a specified minimum bend radius Space turns evenly around the toroid to minimize inter turn capacitance 24 7 3 USING FERRITE BEADS IN CHOKE BALUNS The ferrite bead current baluns developed by Walt Maxwell W2DU formed simply by stringing multiple beads in series on a length of coax to obtain the desired choking impedance are really common mode chokes Maxwell s designs utilized 50 very small beads of type 73 material as shown in Figure 24 59 Product data sheets show that a single type 73 bead has a very low Q resonance around 20 MHz and has a predominantly resistive impedance of 10 20 on all HF ham bands Stringing 50 beads in series simply multiples the impedance of one bead by 50 so the W2DU balun has a choking impedance of 500 1000 and because it is strongly resistive any resonance with the feed line is minimal This is a fairly good design for moderate power levels but suitable beads are too small to fit most coax A specialty coaxial cable such as RG 303 must be used for high power applications Even with high power coax the choking Transmission Line Coupling and Imped
65. ar that as the reactance increases the power loss increases particularly for capacitive reactance This occurs because the series capacitive reactance of the load adds to the series reactance of C2 and losses rise accordingly For most loads a larger value for the output capacitor C2 decreases losses Typically there is a tradeoff between the range of minimum to maximum capacitance and the voltage rating for the variable capacitors that determines the effective impedance matching range See Figure 24 7 which assumes that capacitors C1 and C2 have a larger range between mini mum to maximum capacitance but with a lower peak voltage rating Each tuning capacitor is representative of a Johnson 154 507 1 dual section capacitor which has a range from 15 to 196 pF in each section at a peak voltage rating of 3000 V The two sections are placed in parallel for the lower frequen cies Again a stray capacitance of 10 pF is assumed for each variable capacitor The result at 3 5 MHz in Figure 24 7 is a shift of the matching map toward the left This means that lower values of series load resistance can be matched with lower power loss However it also means that the highest value of load resistance 3200 Q now runs into the limitation of the voltage rating of the output capacitor something that did not happen when the 4500 V capacitors were used in Figure 24 6 Now compare Figure 24 6 and Figure 24 7 at 29 7 MHz The smaller minimum capacitance
66. ation becomes even worse if the feed line is dressed at a slant under the antenna to ground although this sort of installation with a Yagi is not very common For least interaction the feed line still should be dressed so that it is symmetrical with respect to the antenna In the computer models used to create Figures 24 46 24 48 and 24 49 placing a common mode choke described in the next sections whose reactance is j 1000 Q at the antenna s feed point removed virtually all traces of the prob lem This was always true for the simple case where the feed line was dressed symmetrically directly down under the feed point Certain slanted feed line lengths required additional common mode chokes which should be placed at A 4 inter vals beginning 4 2 down the transmission line from the feed point Placing the first choke A 2 from the antenna feed point avoids creating a low impedance point on the outside of the coax shield at the feed point Remember that the free space wavelength is used on the outside of coax while the VF must be applied inside the coax 24 7 CHOKE BALUNS In the preceding sections the problems of directional pattern distortion and unpredictable SWR readings were traced to common mode currents on transmission lines Such common mode currents arise from several types of asym metry in the antenna feed line system either a mismatch between unbalanced feed line and a balanced antenna or lack of symmetry in placem
67. ations chosen All computations are of course only as accurate as the assumed values for un loaded Qy in the components The unloaded Qy of variable inductors can vary quite a bit over the full amateur MF and HF frequency range Computations produced by AAT have been compared to measured results on real antenna tuners and they correlate well when measured values for unloaded inductor Qy are plugged into AAT Individual antenna tuners may well vary depending on what sort of stray inductance or capacitance is introduced during construction 24 2 6 BALANCED ANTENNA TUNERS Modern antenna tuners often include a toroid wound balun at their output for use with balanced or parallel wire feed lines This allows a transmitter s unbalanced coaxial output to be connected to the balanced feed line Baluns are discussed later in this chapter Be aware that at very high or very low impedances the balun s power rating may be exceeded at high transmitted power levels The inductive or link coupling circuits seen in Figure 24 9 are sometimes used but have largely been replaced by the toroid wound balun A more detailed discussion on inductive coupling is available on this book s CD ROM as is a low power link coupled tuner project that uses the configuration shown in Figure 24 9D and instructions for building the 100 W Z Match antenna tuner designed by Phil Salas AD5X The article FilTuners a New Old Approach to Antenna Matching by John
68. band Matching Networks QST Jan 1976 pp 20 23 W Silver ed 20 1 ARRL Handbook 88th edition Newington ARRL 2011 J Stanley Hairpin Tuners for Matching Balanced Antenna Systems QST Apr 2009 pp 34 35 J Stanley FilTuners a New Old Approach to Antenna Matching The ARRL Antenna Compendium Vol 6 Newington ARRL 1999 pp 168 173 24 54 Chapter 24 R E Stephens Admittance Matching the Ground Plane Antenna to Coaxial Transmission Line Technical Correspondence QST Apr 1973 pp 55 57 H F Tolles How to Design Gamma Matching Networks Ham Radio May 1973 pp 46 55 E Wingfield New and Improved Formulas for the Design of Pi and Pi L Networks QST Aug 1983 pp 23 29 F Witt Baluns in the Real and Complex World The ARRL Antenna Compendium Vol 5 Newington ARRL 1997 pp 171 181 F Witt How to Evaluate Your Antenna Tuner QST Part 1 Apr 1995 pp 30 34 and May 1995 pp 33 37 B S Yarman Design of Ultra Wideband Antenna Matching Networks New York Springer 2008
69. be tapped at appro priate points to obtain other ratios such as 1 5 1 2 1 and 3 1 Terminal numbering corresponds to the ends of the wires of the windings Odd numbered wire ends 1 and 3 are at the same end of the winding ANTO905 E2 46E1 12 1 4 IT 13 3 4 1 Z2 16 Z1 Figure 24 43 Four winding broadband variable imped ance transformer Connections a b and c can be placed at appropriate points to yield various ratios from 1 5 1 to 16 1 See Figure 24 42 for an explanation of the wire numbering scheme 1000 W of power By tapping at points 4 2 and of the way along the top winding ratios of approximately 1 5 1 2 1 and 3 1 can also be obtained One of the wires should be covered with vinyl electrical tape in order to prevent voltage breakdown between the windings This is necessary when a step up ratio is used at high power to match antennas with impedances greater than 50 Q Figure 24 43 shows a transformer with four wind ings permitting wideband matching ratios as high as 16 1 Figure 24 44 shows a four winding transformer with taps at 4 1 6 1 9 1 and 16 1 In tracing the current flow in the windings when using the 16 1 tap one sees that the top three windings carry the same current The bottom winding in order to maintain the proper potentials sustains a current three times greater The bottom current cancels out the core flux caused by the other three windings If this transformer is used to match
70. cable This arrangement acts as an independent A 2 dipole on each band Interaction between the individual dipoles is discussed in the Multiband HF Antennas chapter Another type of multiband antenna is a log periodic dipole array LPDA which features moderate gain and pattern with a low SWR across a fairly wide band of frequencies See the Log Periodic Dipole Arrays chapter for more details Yet another popular multiband antenna is the trap trib and Yagi or a multiband interlaced quad On the amateur HF bands the triband Yagi is almost as popular as the simple 2 dipole See the HF Yagis and Quads chapter for more information on this antenna A multiband antenna doesn t present much of an antenna system design challenge you simply feed it with coax that has characteristic impedance close to the antenna s feed point impedance Usually 50 Q cable such as RG 8 is used Feeding a Multiband Nonresonant Antenna Let s say that you wish to use a single antenna such as a 100 foot long dipole on multiple amateur bands You know from the Antenna Fundamentals chapter that since the physical length of the antenna is fixed the feed point imped ance of the antenna will vary on each band In other words except by chance the antenna will not be resonant or even close to resonant on multiple bands This presents special challenges with regard to feed line selection For multiband nonresonant antenna systems the most appro
71. cially because of the wide range of impedances it will match Some T network designs have attempted to im prove the harmonic attenuation using parallel inductors and capacitors instead of a single inductor for the center part of the tee Unfortunately this often leads to more loss and more critical tuning at the fundamental while providing little if any additional harmonic suppression in actual installations The lesson here is to not depend on the antenna tuner for harmonic suppression use filters at the transmitter Harmonics and Pi Network Tuners If a low pass pi network is used for an antenna tuner there will be additional attenuation of harmonics perhaps as much as 30 dB for a loaded Q of 3 The exact degree of harmonic attenuation however is often limited due to the stray inductance and capacitance present in most tuners at harmonic frequencies Further the matching range for a pi network tuner is fairly limited because of the range of input and output capacitance needed for widely varying loads Harmonics and Stubs Far more reliable suppression of harmonics can be achieved using quarter wave and half wave transmission line stubs at the transmitter output For example a typi cal 20 meter 4 4 shorted stub which is an open circuit at 20 meters but a short circuit at 10 meters will provide about 25 dB of attenuation to the second harmonic It will handle full legal amateur power too The characteristics of such stubs ar
72. cting length chang es the SWR they are really telling you that their SWR meter reading was affected by the changing impedance in the line or that common mode currents were affecting the measurement Changing the feed line length can af fect the impedance of the line to common mode current and thus how much common mode current is flowing at a particular point 24 2 IMPEDANCE MATCHING NETWORKS This section reviews the operation of several common impedance matching networks that are used as antenna tun ers As a supplement to this chapter a review of impedance matching circuit designs and characteristics contributed by Robert Neece K KR is included on this book s CD ROM The material includes m Factors to be Considered in Creating or Assessing Matching Unit Designs for the MF HF Spectrum m Comparison Table of Matching Unit Designs Baluns in Matching Units Along with the discussion is an extensive collection of ref erences The student of impedance matching will find the material to supplement and complement the material here giving examples of commercial equipment and addressing the general advantages and disadvantages of each type 24 2 1 THE L NETWORK A comparatively simple but very useful matching circuit for unbalanced loads is the L network as shown in Fig ure 24 2A L network antenna tuners are normally used for only a single band of operation although multiband versions can be made with switched or variable co
73. ction forces the current at the output terminals to be equal and the coil portion chokes off common mode currents See Figure 24 51 for a schematic representation of such a balun This characterization is attributed to Frank Witt AILH Zy is the winding impedance that chokes off common mode currents The winding impedance is mainly inductive if a high frequency ferrite core is involved while it is mainly resistive if a low frequency ferrite core is used The ideal transformer in this characterization models what Unbalanced Balanced Port Port A ANT0912 Figure 25 51 Choke balun model also known as a 1 1 current balun The transformer is an ideal transformer Zw is the common mode winding impedance Sources of loss are the resistive part of the winding impedance and loss in the transmission line This model is by Frank Witt AI1H 24 41 happens either inside a coax or for a pair of perfectly coupled parallel wires in a two wire transmission line Although Zw is shown here as a single impedance it could be split into two equal parts with one placed on each side of the ideal transformer Note that you can compute the amount of power lost in a balun by transforming the polar representation imped ance magnitude and phase angle shown in Table 24 9 to the equivalent parallel form R resistance and X shunt reac tance The power lost in the balun is then the square of half the voltage across the load divided by the equival
74. d a capacitance in series as indicated schematically in Figure 24 35B The inductive portion of the resonant circuit at C is a hairpin of heavy wire or small tubing that is connected across the driven element center terminals The diagram of C is redrawn in D to show the circuit in conventional L network form R4 the resistive component of the feed point impedance must be a smaller value than Ry the impedance of the feed line usu ally 50 Q If the approximate value of R4 for the antenna system is known Figures 24 36 and 24 37 may be used to gain an idea of the hairpin dimensions necessary for the desired match The required value of X 4 the feed point impedance s capaci tive reactance component is Reflector A rs s Driven Element Rin Director ANT0897 Figure 24 35 For the Yagi antenna shown at A the driven element is shorter than its resonant length with a capacitive feed point impedance as represented at B By adding an inductor as shown at C the low value of R is made to ap pear as a higher impedance at terminals XY At D the dia gram of C is redrawn in the usual L network configuration Transmission Line Coupling and Impedance Matching Xa VJRa Rin Ra The curves of Figure 24 36 were obtained from design equations for L network matching presented earlier in this chapter Figure 24 37 is based on the equation X Zo j tan 0 which gives the inductive reactance as normalized to th
75. dance Z in Figure 24 27 is connected across the outer terminals AB of a resonant LC circuit the impedance Z as viewed looking into another pair of terminals such as BC will also be resistive but will have a different value depending on the mutual coupling between the parts of the coil associated with each pair of terminals Z will be less than Z in the circuit shown Of course this relationship will be reversed if Z is connected across terminals BC and Z is viewed from terminals AB As stated in the Antenna Fundamentals chapter a ANT0890 l o B Figure 24 27 Impedance transformation with a resonant circuit together with antenna analogy resonant antenna has properties similar to those of a tuned circuit The impedance presented between any two points symmetrically placed with respect to the center of a 4 2 an tenna will depend on the distance between the points The greater the separation the higher the value of impedance up to the limiting value that exists between the open ends of the antenna This is also suggested in Figure 24 27 in the lower drawing The impedance Z between terminals 1 and 2 is lower than the impedance Zp between terminals 3 and 4 Both impedances however are purely resistive if the antenna is resonant This principle is used in the delta matching system shown in Figure 24 28 The center impedance of a A 2 dipole is too low to be matched directly by any practical type of air insulated paral
76. determine 1 a negative electric length will result for 41 If this happens add 180 The resultant electrical length will be correct both physically and mathematically In calculating B if the quantity under the radical is nega tive an imaginary value for B results This would mean that Z the impedance of the matching section is too close to Zo and should be changed Limits on the characteristic impedance of Z may be calculated in terms of the SWR produced by the load on the main line without matching For matching to occur Z should either be greater than 7 o VSWR OF less than Z SWR An Example As an example suppose we want to feed a 29 MHz ground plane vertical antenna with RG 58 type foam dielec tric coax We ll assume the antenna impedance to be 36 Q Transmission Line Coupling and Impedance Matching Figure 24 22 Example of series section matching A 36 Q antenna is matched to 50 Q coax by means of a length of 75 Q cable ANT0887 pure resistance and use a length of RG 59 foam dielectric coax as the series section See Figure 24 22 Zo is 50 Q Z is 75 Q and both cables have a velocity factor of 0 79 Because the load is a pure resistance we may determine the SWR to be 50 36 1 389 From the above Z must have an impedance greater than 5041 389 From the ear lier equations n 75 50 1 50 r 36 50 0 720 and x 0 Further B 0 431 positive sign chosen and 2 23 3 or 0 065
77. e 100 Antenna FII 50 of 300 Q Line Transmitter 150 RG 213 TO a Tuner a 2 RGR HBK0143 Figure 24 18 Variations of an antenna system with different losses The examples are discussed in the text 24 20 Chapter 24 antenna tuner between the transmit ter and the transmission line going to the antenna This is particularly true for a single wire antenna used on multiple amateur bands The tuner is usually located near the transmitter in order to adjust it for different bands or an tennas If a tuner is in use for one particular band and does not need to be adjusted once set up for mini mum VSWR it can be placed in a weatherproof container near the antenna Some automatic tuners are designed to be installed at the antenna for example For some situations placing the tuner at the base of a tower can be particularly effective and eliminates having to climb the tower to perform mainte nance on the tuner It is useful to consider the per formance of the entire antenna sys tem when deciding where to install the antenna tuner and what types of feed line to use in order to minimize system losses Here is an example using the program TLW Let s as sume a flattop antenna 50 feet high and 100 feet long and not resonant on any amateur band As extreme examples we will use 3 8 and 28 4 MHz with 200 feet of transmis sion line There are many ways to configure this system but three ex ample
78. e On Arm 1 of the dipole Il is shown going directly into the center conductor of the feed coax However the situation is different for the other side of this dipole Once current I2 reaches the end of the coax it splits into two components One is I4 going directly into Arm 2 of the dipole The other is I3 and this flows down the outer surface of the coax shield Again because of skin effect I3 is separate and distinct from the current I2 on the inner surface The antenna current in Arm 2 is thus equal to the difference between I2 and I3 The magnitude of I3 is proportional to the relative im pedances in each current path beyond the split The feed point impedance of the dipole by itself is somewhere be tween 50 to 75 depending on the height above ground The impedance seen looking into one half of the dipole is half or 25 to 37 5 Q The impedance seen looking down the outside surface of the coax s outer shield to ground is called the common mode impedance and I3 is aptly called the common mode current The term common mode is more readily appreciated if parallel conductor line is substituted for the coaxial cable used in this illustration Current induced by radiation onto both conductors of a two wire line is a common mode current since it flows in the same direction on both conductors rather than in opposite directions as it does for transmission line current The outer braid for a co axial cable shields the inner conductor fr
79. e characteristic impedance Zp of the hairpin looking at it as a length of transmission line terminated in a short circuit For example if an antenna system impedance of 20 Q is to be matched to 50 Q line Figure 24 36 shows that the inductive reactance required for the hairpin is 41 Q If the hairpin is constructed of 4 inch tubing spaced 1 inches its characteristic impedance is 300 from equations in the Transmission Lines chapter Normalizing the required 41 Q reactance to this impedance 41 300 0 137 By entering the graph of Figure 24 37 with this value 0 137 on the scale at the bottom you can see that the hair pin length should be 7 8 electrical degrees or 7 8 360 A For purposes of these calculations taking a 97 5 velocity factor into account the wavelength in inches is 11 508 f MHz If the antenna is to be used on 14 MHz the required hairpin length is 7 8 360 x 11 508 14 0 17 8 inches The length of the hairpin affects primarily the resistive component of the Eq 19 D N i pa Oo E o a x A nol g oO oO x a x lt for 20 30 40 50 Resistive Component Rg of the ANTO898 Antenna Feed Point Impedance Figure 24 36 Reactance required for a hairpin to match various antenna resistances to common line or balun im ped
80. e covered in the sections of this chapter on im pedance matching at the antenna The use of stubs as filters 24 3 is covered in the ARRL Handbook and the excellent book Managing Interstation Interference by George Cutsogeorge W2VIJN See Bibliography 24 1 3 MYTHS ABOUT SWR There are some enduring and quite misleading myths in Amateur Radio concerning SWR Despite some claims to the contrary a high SWR does not by itself cause RF interference or TVI or telephone in terference While it is true that an antenna located close to such devices can cause overload and interference the SWR on the feed line to that antenna has nothing to do with it providing of course that the tuner feed line or con nectors are not arcing The antenna is merely doing its job which is to radiate The transmission line is doing its job which is to convey power from the transmitter to the radiator m A second myth often stated in the same breath as the first one above is that a high SWR will cause excessive radia tion from a transmission line SWR has nothing to do with excessive radiation from a line Common mode currents on feed lines cause radiation but they are not directly related to SWR An asymmetric arrangement of a transmission line and antenna can result in common mode currents be ing induced on the outside of the shield of coax or as an imbalance of currents in an open wire line Common mode current will radiate just as if it were on
81. e eal See Rr oe Seat en VOUUKDAHITNIVOOH IW DerFWOOO0 CORP RP RP RFF ND W UID PRR RP RP RP RRP RP RP RRP RRR dtm DUNNUAARAAAGAAAHAHAAHAAA Ost NO NM NOM NM NN NH NM NM NH NH NHN KN Po w N w w w w w w w Ww Ww Ww UW Ww bu Figure 24 7 Another sample AAT program printout using a dual section variable capacitor whose overall tuning range when in parallel varies from 25 to 402 pF but with a 3000 V rating The same 28 uH roller is used but an auxiliary 400 pF fixed capacitor can now be manually switched across the output variable capacitor Note that the overall matching range has in effect been shifted over to the left from that in Figure 24 6 for the lower frequency because the maximum output capacitance is higher The range has been extended on the highest frequency because the minimum capacitance is smaller 24 10 Chapter 24 has been exceeded It may be possible in such a circumstance to reduce the power to eliminate arcing Where P is shown the power limit has been exceeded meaning that the loss would be excessive Where a blank occurs no combination of matching components resulted in a match It should be clear that with this particular set of capaci tors the T network suffers large losses when the load resis tance is less than about 12 5 Q at 3 5 MHz For example for a load impedance of 12 5 j 100 Q the loss is 16 7 At 1500 W into the tuner 250 W would be burned up inside mainly in the coil It should also be cle
82. e is called for Reactances formed from sections of transmission line are called match ing stubs and are designated as open or closed depending on whether the free end is open or short circuited The two types of matching stubs are shown in the sketches in Figure 24 38 The distance from the load to the stub dimension A in Figure 24 38 and the length of the stub B depend on the characteristic impedances of the line and stub and on the ratio of Zp to Zo Since the ratio of Zp to Zp is also the standing wave ratio in the absence of matching and with a resonant antenna the dimensions are a function of the SWR If the line and stub have the same Zp dimensions A and B are dependent on the SWR only Consequently if the SWR can be measured before the stub is installed the stub can be properly located and its length determined even though the actual value of load impedance is not known Typical applications of matching stubs are shown in Figure 24 39 where open wire line is being used From in spection of these drawings it will be recognized that when an antenna is fed at a current loop as in Figure 24 39A Zp is less than Zp in the average case and therefore an open stub is called for installed within the first 1 4 of line measured from the antenna Voltage feed as at B corresponds to Zp greater Transmission Line Coupling and Impedance Matching than Zo and therefore requires a closed stub A Smith Chart may be used to determine
83. e orienta tion of the ground wiring from the transmitter chassis to the rest of the station s grounding system Pattern Distortion for a Dipole with Symmetrical Coax Feed Figure 24 46 compares the azimuthal radiation pattern for two A 2 long 14 MHz dipoles mounted horizontally A 2 above average ground Both patterns were computed for a 28 elevation angle the peak response for a A 2 high dipole The model for the first antenna the reference dipole shown as a solid line has no feed line associated with it it is as though the transmitter were somehow remotely located right at the center of the dipole This antenna displays a classical figure 8 pattern Both side nulls dip symmetrically about 10 dB below the peak response typical for a 20 meter dipole 33 feet above ground or an 80 meter dipole placed 137 feet above ground The second dipole shown as a dashed line is modeled ANTO907 Reference Dipole 28 Elevation OdB 7 31 dBi 14 100 MHz Figure 24 46 Comparison of azimuthal patterns of two i 2 long 14 MHz dipoles mounted 1 2 over average ground The reference dipole without effect of feed line distortion modeled as though the transmitter were located right at the feed point is the solid line The dashed line shows the pattern for the dipole affected by common mode current on its feed line due to the use of unbalanced coax to feed a balanced antenna The feed line is dropped directly from the feed point to
84. e simple arrangement shown in Figure 24 26 The unbalance is small if the line diameter is very small compared with the length of the antenna a condition that is met fairly well at the lower amateur frequencies It is not negligible in the VHF and UHF range however nor should it be ignored at 28 MHz If the feed line is oriented asymmetrically with respect to the antenna so that it is closer to one side of the antenna than the other higher common mode currents will flow on the outside of the feed line The system can be detuned for currents on the outside of the line by using a choke balun later in this chapter for more details about balanced loads used with unbalanced transmis sion lines This system is designed for single band operation although it can be operated at odd multiples of the funda mental For example an antenna that is resonant near the low frequency end of the 7 MHz band will operate with a relatively low SWR across the 21 MHz band At the fundamental frequency the SWR should not exceed about 2 1 within a frequency range 2 from the frequency of exact resonance Such a variation corresponds 468 Length in Feet f MHz cM pe Inner Conductor ANT0885 Figure 24 26 A antenna fed with 75 Q coaxial cable The outside of the shield of the line acts as a third wire connected to the dipole s left leg A choke balun can be used to reduce current flowing on this conductor 24 26 Chapter 24
85. e the antenna has a radia tion resistance of 25 Q and a capacitive reactance component of 25 Q about the reactance that would result from the 3 shortening The overall impedance of the driven element is therefore 25 j 25 At the program prompts enter the fre quency the feed point resistance and reactance don t forget the minus sign the line characteristic impedance 50 Q and Figure 24 32 Typical gamma match construction for HF and VHF Yagis Gamma Rod ANT1125 24 29 the element and rod diameters and center to center spacing GAMMA computes that the gamma rod is 38 9 inches long and the gamma capacitor is 96 1 pF at 14 3 MHz As another example say we wish to shunt feed a tower at 3 5 MHz with 50 Q line The driven element tower is 12 inches in diameter and 12 AWG wire diameter 0 0808 inch with a spacing of 12 inches from the tower is to be used for the gamma rod The tower is 50 feet tall with a 5 foot mast and beam antenna at the top The total height 55 feet is approximately 0 19 We assume its electrical length is 0 2 or 72 Modeling shows that the approximate base feed point impedance is 20 j 100 Q GAMMA says that the gamma rod should be 57 1 feet long with a gamma capacitor of 32 1 pF Immediately we see this set of gamma dimensions is im practical the rod length is greater than the tower height So we make another set of calculations this time using a spacing of 18 inch
86. ear their resonance However the resonance is quite difficult to measure and it is so narrow that it typically covers only one or two ham bands Away from resonance the choke becomes far less effective as choking impedance falls rapidly and its reactive component resonates with the line Figure 24 55 shows typical wound coax chokes suit able for use on the HF ham bands Figures 24 56 24 57 and 24 58 are graphs of the magnitude of the impedance for HF 100000 70000 50000 30000 20000 10000 7000 5000 3000 2000 Q Q O C Oo mo oO Qa 1000 700 500 300 200 100 HBK0449 5 6 7 8910 20 30 Frequency MHz Table 24 11 Transmitting Choke Designs Freq Band s Mix MHz 1 8 3 8 31 3 5 7 10 1 31 or 43 7 14 14 21 28 7 28 31 or 43 10 1 28 or 14 28 14 28 50 RG 8 RG 11 Turns Cores 7 5 toroids 6 5 toroids 5 5 toroids 5 5 toroids 5 4 toroids 4 6 toroids 4 5 toroids 4 6 toroids 4 5 toroids Use two chokes in series 1 4 turns on 5 toroids 2 3 turns on 5 toroids Two 4 turn chokes each w one big clamp on Two 3 turn chokes each w one big clamp on 40 506070 90 Figure 24 54 Impedance versus fre quency for HF wound coax transmitting chokes wound with RG 142 coax on toroid cores of 61 material
87. edance where a match is indeed possible Where a C appears AAT is saying that a match can t be made because the minimum capacitance of one or the other variable capacitors is too large This often happens on the higher frequency bands but can occur on the lower bands when the power loss is greater than the specified limit and AAT continues to try to find a condition where the power loss is lower It does this until it runs into the mini mum capacitance limit of the input capacitor C1 Similarly where a C appears a match can t be made because the maximum capacitance of one or the other vari able capacitors is too small Where an L is placed in the grid the match fails because more inductance is needed Where a V is shown the voltage limit for some component Loss percentage for Tee network series cap shunt inductor series cap Freq 3 5 MHz Z0 50 1500W Vmax 4500 V Qu 200 Qc 1000 Var Cap 42 to 251 pF with switched 160 80 m output cap 0 pF Xa 3 125 6 25 12 5 25 50 100 200 400 800 1600 3200 Ra 3200 L L L L L L L L V 1600 L L L L L 800 L L C C 400 C C C V 200 C C P 13 100 C C 16 7 10 50 C C 14 25 C C 13 12 5 C C 12 6 25 C C 12 3 125 c 19 8 11 0 C 19 611 r E da C 19 3 11 6 25 C 19 111 12 63 C 18 6 11 25 C 17 6 10 50 C 15 100 P 11 V P P DODnanre wono WwW OLUN BUANNBUNN NUNO WARP PRE DDAUWOErFP BH WW OUFRPNAD
88. en better The 20 turn multiple band 1 8 3 5 MHz coiled coax balun in Table 24 11 weighs 1 pound 7 ounces The single ferrite core com bination balun weighs 6 5 ounces and the two core version weighs 9 5 ounces Figure 24 60 Choke balun that includes both a coiled cable and ferrite beads at each end of the cable 24 48 Chapter 24 24 7 4 MEASURING CHOKE BALUN IMPEDANCE A ferrite RF choke creates a parallel resonant circuit from inductance and resistance coupled from the core and stray capacitance resulting from interaction of the conduc tor that forms the choke with the permittivity of the core If the choke is made by winding turns on a core as opposed to single turn bead chokes the inter turn capacitance also becomes part of the choke s circuit These chokes are very difficult to measure for two funda mental reasons First the stray capacitance forming the paral lel resonance is quite small typically 0 4 5 pF which is often less than the stray capacitance of the test equipment used to measure it Second most RF impedance instrumentation measures the reflection coefficient see the Transmission Lines chapter in a 50 Q circuit As a result reflection based measurements have increas ingly poor accuracy when the unknown impedance is more than about three times the characteristic impedance of the analyzer because the value of the unknown is computed by differencing analyzer data When the differences are small as
89. ent of the feed line A device called a balun can be used to eliminate these common mode currents The word balun is a contraction of the words balanced to unbalanced Its primary function is to prevent common mode currents while making the transition from an unbalanced transmission line to a balanced load such as an antenna Baluns come in a variety of forms which we will explore in this section The term balun applies to any device that transfers differential mode signals between a balanced system and an unbalanced system while maintaining symmetrical energy distribution at the terminals of the balanced system The term only applies to the function of energy transfer not to how the device is constructed It doesn t matter whether the balanced unbalanced transition is made through symmetrical transmis sion line structures flux coupled transformers or simply by blocking unbalanced current flow A common mode choke balun described below for example performs the balun func tion by putting impedance in the path of common mode cur rents and is therefore a balun A current balun forces symmetrical current at the bal anced terminals regardless of voltage This is of particular importance in feeding antennas since antenna currents deter mine the antenna s radiation pattern A voltage balun forces symmetrical voltages at the balanced terminals regardless of current Voltage baluns are less effective in causing equal currents at their b
90. ent parallel resistance E 2 R For example in Table 24 9 the balun made with 8 turns of RG 213 on a 6 inch diameter coil form at 14 MHz has an impedance of 262 2 86 9 Converting polar to rectangular this is equal to 14 17 j 261 62 Q and converting series to parallel we have 4844 j 262 38 For an RF voltage of 273 9 V RMS the power lost in the balun is 273 9 2 7 4844 8 3 9 W while for a 50 Q load the power is 273 92 50 1500 W The amount of power lost in the balun is very small compared to the power delivered to the load 24 7 1 THE COAXIAL CHOKE BALUN The following sections were updated by Jim Brown K9YC originally for the 20 0 ARRL Handbook The sim plest construction method for a choke balun is simply to wind a portion of the coaxial cable feed line into a coil see Figure 24 52 creating an inductor from the shield s outer surface This type of choke balun is simple cheap and effec tive Currents on the outside of the shield encounter the coil s impedance while currents on the inside are unaffected A scramble wound flat coil like a coil of rope shows a broad resonance that easily covers three octaves making it reasonably effective over the entire HF range If particu lar problems are encountered on a single band a coil that is resonant on that band may be added The choke baluns described in Table 24 10 were constructed to have a high Table 24 9 K2SQ Measurements on Coiled Coax Baluns 6T 4 2
91. equency and Q from manually entered values for R L and C The spread sheet should also compute and plot impedance of the same range of frequencies as the measurements and with the same plotted scale as the measurements 1 Enter a value for R equal to the resonant peak of the measured impedance 2 Pick a point on the resonance curve below the reso nant frequency with approximately one third of the imped ance at resonance and compute L for that value of inductive reactance 3 Enter a value for C that produces the same resonant frequency of the measurement 4 If necessary adjust the values of L and C until the computed curve most closely matches the measured curve The resulting values for R L and C form the equivalent circuit for the choke The values can then be used in circuit modeling software VEC SPICE to predict the behavior of circuits using ferrite chokes Accuracy This setup can be constructed so that its stray capacitance is small but it won t be zero A first approximation of the stray capacitance can be obtained by substituting for the un known a noninductive resistor whose resistance is in the same general range as the chokes being measured then varying the frequency of the generator to find the 3 dB point where Xc R This test for the author s setup yielded a stray capaci tance value of 0 4 pF A thin film surface mount or chip resis tor will have the lowest stray reactances If a surface mount resistor
92. er cable have more stray capacitance than those wound with small diameter wire There are two sources of stray capacitance in a ferrite choke the capacitance from end to end and from turn to turn via the core and the capacitance from turn to turn via the air dielectric Both sources of capacitance are increased by in creased conductor size so stray capacitance will be greater with larger coax Turn to turn capacitance is also increased by larger diameter turns At low frequencies most of the inductance in a ferrite choke results from coupling to the core but some is the re sult of flux outside the core At higher frequencies the core has less permeability and the flux outside the core makes a greater contribution The most useful cores for wound coax chokes are the 2 4 inch OD 1 4 inch ID toroid of type 31 or 43 material and the 1 inch ID x 1 125 inch long clamp on of type 31 material Seven turns of RG 8 or RG 11 size cable easily fit through these toroids with no connector attached and four turns fit with a PL 259 attached Four turns of most RG 8 or RG 11 size cable fit within the 1 inch ID clamp on The toroids will accept at least 14 turns of most RG 6 RG 8X or RG 59 size cables Practical Chokes Joe Reisert W1JR introduced the first coaxial chokes wound on ferrite toroids He used low loss cores typically type 61 or 67 material Figure 24 54 shows that these high Q chokes are quite effective in the narrow frequency range n
93. er equations give design data for matching sections A being the distance from the antenna to the point at which the line is connected and A B being the total length of the matching section The equations apply only in the case where the characteristic impedance of the matching section and transmission line are the same Equations are available for the case where the matching section has a different Zp than the line but are somewhat complicated A graphic solu tion for different line impedances may be obtained with the Smith Chart see the supplement on this book s CD ROM Adjustment In the experimental adjustment of any type of matched line it is necessary to measure the SWR with fair accuracy in order to tell when the adjustments are being made in the proper direction In the case of matching stubs experience has shown that experimental adjustment is unnecessary from a practical standpoint if the SWR is first measured with the stub not connected to the transmission line and the stub is then installed according to the design data ANTO903 Figure 24 41 Application of matching sections to com mon antenna types 24 5 9 RESONANT CIRCUIT MATCHING Antennas with a high feed point impedance such as end fed wires close to 4 2 in length and voltage fed antennas such as the Bobtail Curtain often use a parallel tuned circuit at the feed point to effect an impedance match The circuit is adjusted to resonance and then the
94. er to a balanced line presenting a load dif ferent from the transmit ter s design load imped ance usually 50 A and B respectively are series and parallel tuned circuits using variable inductive coupling between coils C and D are similar but use fixed inductive coupling and a variable series ca pacitor C1 A series tuned circuit works well with a low impedance load the parallel circuit is better with high impedance loads sev eral hundred ohms or more A disadvantage of balanced tuners is the higher cost from the additional components and the more complex mechanical arrangements to adjust more than one component at the same time with a single control The hairpin tuner configuration in Figure 24 11 is a bal anced tuner for use at VHF and UHF where solenoid wound ANT1121 Figure 24 11 Balanced tuner configurations At A con ventional tapped coil based tuner at B the hairpin equiva lent C shows a hairpin tuner for 144 MHz The technique can be used from 10 meters through 70 cm coils may have too much inductance The tuner is described in the April 2009 QST article Hairpin Tuners for Matching Balanced Antenna Systems by John Stanley K4ERO that is included on this book s CD ROM 24 2 7 Project HIGH POWER ARRL ANTENNA TUNER Dean Straw N6BV designed this antenna tuner with three objectives in mind First it would operate over a wide range of loads at full legal power Second it would be
95. es between the rod and tower The results this time are that the gamma rod is 49 3 feet long with a capacitor of 43 8 pF This gives us a practical set of starting dimensions for the shunt feed arrangement The preferred method of building a gamma match is illustrated in Figure 24 32 The feed line is connected directly to the center element This is usually done using a clamp or strap from an RF connector but depends on the physical size of the antenna The gamma capacitor is created from an insulated wire inside the tube that forms the gamma rod For 2 inch OD aluminum tube and the center conduc tor and insulation from RG 8 or RG 213 the capacitance is approximately 25 pF ft of wire inserted into the tube Do not use the center conductor and insulation from foam di electric coax as it will absorb water Seal the end of the wire inserted into the tube to reduce the tendency to arc when wet or if insects or debris are present After a satisfactory match has been obtained by adjusting the gamma capacitor as described below the variable capacitor may be replaced with an equivalent length of wire in the gamma rod Adjustment After installation of the antenna the proper constants for the T and gamma generally must be determined experimen tally The use of the variable series capacitors as shown in ANT0895 Figure 24 33 The omega match 24 30 Chapter 24 Figure 24 30 is recommended for ease of adjustment With a trial position
96. ethod using the Smith Chart and the other is algebraic You can take your choice Of course the algebraic method may be adapted to obtaining a computer solution The Smith Chart graphic method is described in an article included on this book s CD ROM Algebraic Design Method The two lengths 1 and 2 are to be determined from the characteristic impedances of the main line and the matching section Zo and Z respectively and the load impedance Z R j X The first step is to determine the normalized impedances 21 Eq 11 n Zo Eq 11 RL r Z q 12 Xi sAn Eq 13 x Zo Eq 13 Next 42 and 1 are determined from 42 arctan B where 2 2 Bat r 1 x Eq 14 1 2 r a 2 r 1 x n 1 arctan A where n B x ASSA M Eq 15 r xnB 1 Lengths 2 and 1 as thus determined are electrical lengths in degrees or radians The electrical lengths in wave lengths are obtained by dividing by 360 or by 27 radians The physical lengths main line or matching section as the case may be are then determined from multiplying by the free space wavelength and by the velocity factor of the line The sign of B may be chosen either positive or negative but the positive sign is preferred because it results in a shorter matching section The sign of A may not be chosen but can turn out to be either positive or negative If a negative sign occurs and a computer or electronic calculator is then used to
97. explained by the fact that the two conductors in parallel form a single conductor of greater effective diameter A folded dipole will not accept power at twice the funda mental frequency However the current distribution is correct for harmonic operation on odd multiples of the fundamental Because the feed point resistance is not greatly different for a 3A 2 antenna and one that is 4 2 a folded dipole can be operated on its third harmonic with a low SWR in a 300 0 line A 7 MHz folded dipole consequently can be used for the 21 MHz band as well Folded dipoles are sometimes used as the driven element of Yagi antennas at VHF and UHF The low feed point im pedance of a Yagi often less than 20 when multiplied by four presents a good match to 75 Q coaxial cable 24 5 5 THE T AND GAMMA MATCHES The T Match The current flowing at the input terminals of the T match consists of the normal antenna current divided between the radiator and the T conductors in a way that depends on their relative diameters and the spacing between them with a superimposed transmission line current flowing in each half of the T and its associated section of the antenna See Fig ure 24 29 Each such T conductor and the associated antenna conductor can be looked upon as a section of transmission line shorted at the end Because it is shorter than A 4 it has inductive reactance As a consequence if the antenna itself is exactly resonant at the operating frequenc
98. fairly broad as shown in this family of curves for different impedance transformation ratios For 75 and 50 imped ances a ratio of 1 5 1 the points at which an SWR of 1 2 1 are reached are approximately 75 and 125 of the design frequency Se ANTO0886 Figure 24 21 Series section transformer Z for matching transmission line Zo to load Z In fact the matching section can have any characteris tic impedance that is not too close to that of the main line Because of this freedom it is almost always possible to find a length of commercially available line that will be suitable as a matching section As an example consider a 75 Q line a 300 Q matching section and a pure resistance load It can be shown that a series section transformer of 300 Q line may be used to match any resistance between 5 Q and 1200 Q to the main line Frank Regier ODSCG described series section trans formers in July 1978 QST See Bibliography This informa tion is based on that article The design of a series section transformer consists of determining the length 42 of the series or matching section and the distance 1 from the load to the point where the section should be inserted into the main line Three quantities must be known These are the characteristic impedances of the main line and of the matching section both assumed purely resistive and the complex load impedance Either of two design methods may be used One is a graphic m
99. fed with a balanced line a balun may be used with a coax feeder as shown in Figure 24 34 see the section later in this chapter about baluns and the driven element must be split at the center and insu lated from the boom This latter requirement complicates the mechanical mounting arrangement for the element by ruling out plumber s delight construction As indicated in Figure 24 34 the center point of the hairpin is electrically neutral As such it may be grounded or connected to the remainder of the antenna structure re storing de ground to the feed line and driven element The hairpin itself is usually secured by attaching this neutral point Electricall a Neutral Point Coaxial Cable ANTO0896 Figure 24 34 The hairpin match to the boom of the antenna array The Hy Gain beta match is electrically identical to the hairpin match the difference being in the mechanical construction of the matching section With the beta match the conductors of the matching section straddle the Yagi s boom one conductor being located on either side and the electrically neutral point consists of a sliding or adjustable shorting clamp placed around the boom and the two matching section conductors The capacitive portion of the L network circuit is produced by slightly shortening the antenna driven ele ment shown in Figure 24 35A For a given frequency the impedance of a shortened 4 2 element appears as the antenna resistance an
100. feed line attached to a tap on the inductor that is moved until an SWR minimum is obtained The circuit may need a slight retuning following by a final position adjustment of the feed line See the chapters Multiband HF Antennas and Broadside and End Fire Arrays for more information on these antennas and typical feed systems The matching bandwidth of this technique is quite nar row requiring frequent retuning or operation over a narrow bandwidth In addition the voltages at the hot or unground ed end of the tank circuit can be very high Caution must be used in construction to prevent contact with the high voltages and adequately rated components must be used 24 5 10 BROADBAND MATCHING Material from previous editions in the chapter Broadband Antenna Matching by Frank Witt AI1H is in cluded for reference on this book s CD ROM It presents and analyzes various techniques used to increase the bandwidth of antenna feed point impedance Broadband Matching Transformers Broadband transformers have been used widely because of their inherent bandwidth ratios as high as 20 000 1 from a few tens of kilohertz to over a thousand megahertz This is possible because of the transmission line nature of the windings The interwinding capacitance is a component of the characteristic impedance and therefore unlike a conven tional transformer forms no resonances that seriously limit the bandwidth At low frequencies where interw
101. ge in imped ance when the frequency is changed greatly For this reason it is usually possible to match the line impedance only on one frequency A matched antenna system is consequently a one band affair in most cases It can however usually be Transmission Line Coupling and Impedance Matching operated over a fair frequency range within a given band The frequency range over which the SWR is low is determined by how rapidly the impedance changes as the frequency is changed If the change in impedance is small for a given change in frequency the SWR will be low over a fairly wide band of frequencies However if the imped ance change is rapid implying a sharply resonant or high Q antenna the SWR will also rise rapidly as the operating frequency is shifted away from antenna resonance where the line is matched See the discussion of Q in the Dipoles and Monopoles chapter in the section dealing with changes of impedance with frequency Antenna Resonance In general achieving a good match to a transmission line means that the antenna is resonant Some types of long wire antennas such as rhombics are exceptions Their input impedances are resistive over a wide band of frequencies making such systems essentially nonresonant Antennas that are not resonant may also be matched to transmission lines of course but the additional cancellation of reactance complicates the task The higher the Q of an antenna system the more essential
102. gure 24 48 Azimuthal response for two dipoles placed as shown in Figure 24 47 The solid line represents a refer ence dipole with no feed line modeled as though the trans mitter were located directly at the feed point The dashed line shows the response of the antenna with feed line slant ed 45 down to ground Current induced on the outer braid of the 1 long coax by its asymmetry with respect to the antenna causes the pattern distortion The feed point im pedance also changes causing a different SWR from that for the unaffected reference dipole 24 39 Reference 5 Ele ANTO0910 Yagi 5 Ele Yagi w Coax Feed Line 14 100 MHz 15 Elevation 0 dB 11 07 dBi Figure 24 49 Azimuthal response for two five element 20 meter Yagis placed 1 2 over average ground The solid line represents an antenna fed with no feed line as though the transmitter were located right at the feed point The dashed line represents a dipole fed with a 1 2 length of un balanced coax line directly going to ground through a transmitter at ground level The distortion in the rearward pattern is evident and the Yagi loses a small amount of for ward gain 0 3 dB compared to the reference antenna In this case placing a common mode choke of j 1000 at the feed point eliminated the pattern distortion above average ground The solid line represents the reference antenna where it is assumed that the transmitter is located right at the b
103. h of the unbalanced coaxial cable feeding a balanced dipole will cause the SWR on the line to change also This is due to the changing common mode impedance to ground at the feed point The SWR may even change if the operator touches the SWR meter since the path to RF ground is subtly altered when this happens Even changing the length of an antenna to prune it for resonance may also yield unexpected and confusing results on the SWR meter because of the common mode impedance When the overall effective length of the coaxial feed line to ground is not a multiple of a A 2 resonant length but is an odd multiple of 4 4 the common mode impedance trans formed to the feed point is high in comparison to the dipole s natural feed point impedance This will cause I3 to be small in comparison to I2 meaning that radiation by I3 itself and the imbalance between I1 and I4 will be minimal Modeling this case produces no difference in response between the di pole with unbalanced feed line and the reference dipole with no feed line Thus a multiple of a half wave length for coax and ground wiring represents the worst case for this kind of imbalance when the system is otherwise symmetrical If the coax in Figure 24 45 were replaced with balanced transmission line the SWR would remain constant along the line no matter what the length To put a fine point on it the SWR would actually decrease slightly toward the transmit ter end This is because of line
104. hat happens if the feed line is not dressed away from the antenna in a com pletely symmetrical fashion that is not at a right angle to the dipole Figure 24 47 illustrates a situation where the feed line goes to the transmitter and ground at a 45 angle from the dipole Now one side of the dipole can radiate more strongly onto the feed line than the other half can Thus the currents radiated onto the feed line from each half of the symmetrical dipole won t cancel each other In other words the antenna itself radiates a common mode current onto the transmission line This is a different form of common mode current from what was discussed above in connection with an unbalanced Symmetrical A 2 Dipo Transmitter Z ANT0908 Figure 24 47 Drawing of 1 2 dipole placed 0 71 above average ground with a 1 A long coax feed line connected at far end to ground through a transmitter Worst case feed line radiation due to common mode current induced on the outer shield braid occurs for lengths that are multiples of 1 2 coax feeding a balanced dipole but it has similar effects Figure 24 48 shows the azimuthal response of a 0 71 A high reference dipole with no feed line as though the transmitter were located right at the feed point compared to a 0 71 A high dipole that uses a 1 A long coax feed line slanted 45 from the feed point down to ground through the transmitter The 0 71 A height was used so that the slanted coax co
105. he delta match is somewhat awkward to adjust when the proper dimensions are unknown because both the length and width of the delta must be varied An additional disadvantage is that there is always some radiation from the delta This is because the conductor spacing does not meet the requirement for negligible radiation The spacing should be very small in comparison with the wavelength 24 5 4 FOLDED DIPOLES Basic information on the folded dipole antenna appears in chapter Dipoles and Monopoles The input impedance of a two wire folded dipole is so close to 300 Q that it can be fed directly with 300 Q twinlead or with open wire line without any other matching arrangement and the line will operate with a low SWR The antenna itself can be built like an open wire line that is the two conductors can be held apart by regular feeder spreaders TV ladder line is quite suitable It is also possible to use 300 line for the antenna in addition to using it for the transmission line Since the antenna section does not operate as a transmis sion line but simply as two wires in parallel the velocity factor of twinlead can be ignored in computing the antenna length The reactance of the folded dipole antenna varies less rapidly with frequency changes away from resonance than a single wire antenna Therefore it is possible to operate over a wider range of frequencies while maintaining a low SWR on the line than with a simple dipole This is partly
106. he low frequency slope and high frequency slope When using these values in a circuit model use the values that most closely match the behavior of the choke in the frequency range of interest 24 8 TRANSMISSION LINE BALUNS The properties of transmission lines explored in the Transmission Lines chapter can be put to work isolating loads and transforming impedances Here are a few useful designs for use with your antenna projects 24 8 1 DETUNING SLEEVES The detuning sleeve shown in Figure 24 61B is essen tially an air insulated 4 4 line but of the coaxial type with the sleeve constituting the outer conductor and the outside of the coax line being the inner conductor Because the imped ance at the open end is very high the unbalanced voltage Transmission Line Coupling and Impedance Matching on the coax line cannot cause much current to flow on the outside of the sleeve Thus the sleeve acts just like a choke to isolate the remainder of the line from the antenna The same viewpoint can be used in explaining the action of the A 4 arrangement shown at Figure 24 61A but is less easy to understand in the case of baluns less than 1 4 long A sleeve of this type may be resonated by cutting a small longitudinal slot near the bottom just large enough to take a single turn loop which is in turn link coupled to a dip meter If the sleeve is a little long to start with a bit at a time can be cut off the top until the stub is resonant
107. he transmission line and stub would be a T connector A special case is the use of a coaxial matching stub in which the stub is associated with the transmission line in such a way as to form a balun This is described in detail later on in this chapter The antenna is shortened to introduce just enough reactance at its feed point to permit the matching stub to be connected there rather than at some other point along the transmission line as in the general cases discussed here To use this method the antenna resistance must be lower than the Z of the main transmission line since the resistance is transformed to a higher value In beam antennas such as Yagis this will nearly always be the case Matching Sections If the two antenna systems in Figure 24 39 are redrawn in somewhat different fashion as shown in Figure 24 41 a system results that differs in no consequential way from the matching stubs described previously but in which the stub formed by A and B together is called a quarter wave match ing section The justification for this is that a 1 4 section of line is similar to a resonant circuit as described earlier in No Connection Between Conductors C Dis Closing End of Conductors ANT0902 Figure 24 40 Open and closed stubs on coaxial lines 24 34 Chapter 24 this chapter It is therefore possible to use the 4 4 section to transform impedances by tapping at the appropriate point along the line Earli
108. heck the frequency Its length may then be adjusted so that the overall system is again resonant at the desired frequency Construction In constructing a balun of the type shown in Figure 24 61A the additional conductor and the line should be maintained parallel by suitable spacers It is convenient to use a piece of coax for the second conductor the inner con ductor can simply be soldered to the outer conductor at both ends since it does not enter into the operation of the device The two cables should be separated sufficiently so that the vinyl covering represents only a small proportion of the di electric between them Since the principal dielectric is air the length of the 1 4 section is based on a velocity factor of 0 95 approximately 24 8 4 IMPEDANCE STEP UP STEP DOWN BALUN A coax line balun may also be constructed to give an impedance step up ratio of 4 1 This form of balun is shown in Figure 24 64 If 75 Q line is used as indicated the balun will provide a match for a 300 Q terminating impedance If 50 line is used the balun will provide a match for a 200 0 terminating impedance The U shaped section of line must be an electrical length of 4 2 long taking the velocity factor of the line into account In most installations using this type of balun it is customary to roll up the length of line represented by the U shaped section into a coil of several inches in di ameter The coil turns may be bound together with electric
109. icular antenna Let s start with some simple cases Feeding a Single Band Antenna If the antenna system is only required to operate on a single band and if the feed point impedance of the antenna 24 18 Chapter 24 doesn t vary too radically across the band then the choice of transmission line is easy Most amateurs would opt for con venience they would use coaxial cable to feed the antenna usually without an antenna tuner An example of such an installation is a half wave 80 meter dipole fed with 50 Q coax The matched line loss for 100 feet of 50 CQ RG 8 coax at 3 5 MHz is only 0 33 dB At each end of the 80 meter band this dipole will exhibit an SWR of about 6 1 The additional loss caused by this level of SWR at this frequency is less than 0 6 dB for a total line loss of 0 9 dB Since 1 dB represents an almost undetectable change in signal strength at the receiving end it does not matter whether the line is flat low SWR or not for this 80 meter system This is true provided that the transmitter can operate properly into the load presented to it by the impedance at the input of the transmission line Even if the feed line loss is low an antenna tuner is sometimes required to ensure that the transmitter operates into its design load impedance On the other amateur bands where the percentage bandwidth is smaller than that on 75 80 meters a simple dipole fed with coax will provide an acceptable SWR for most transmitte
110. ield is self resonant due to the distributed capacitance between the turns of the coil The self resonant frequency can be found by us ing a dip meter Leave the ends of the choke open couple the coil to the dip meter and tune for a dip This is the parallel resonant frequency and the impedance will be very high Ed Gilbert K2SQ measured a series of coaxial coil bal uns with a Hewlett Packard 4193A vector impedance meter He constructed the coiled coax baluns using either 4 inch or 6 inch plastic pipe Table 24 9 lists the results The distributed capacitance of a flat coil choke balun can be reduced or at least controlled by winding the cable as a single layer solenoid around a section of plastic pipe an empty bottle or other suitable cylinder Figure 24 53 The coil form is then removed if desired The cable is secured with electrical tape as shown in Figure 24 52 A coil diameter of about 5 inches is reasonable for RG 8X or RG 58 59 cable Use a diameter of 8 inches or more for larger cable This type of construction reduces the stray capacitance between the ends of the coil For both types of coiled coaxial chokes use cable with solid insulation not foamed to minimize migration of the center conductor through the insulation toward the shield The diameter of the coil should be at least ten times the cable diameter to avoid mechanically stressing the cable 24 7 2 TRANSMITTING FERRITE CORE CHOKE BALUNS A ferrite choke is simp
111. if provi sion is made for canceling or tuning out this reactive part of the input impedance only the resistance will remain Since this resistance is equal to the Zp of the transmission line the section from the reactance cancellation point back to the gen erator will be properly matched Tuning out the reactance in the equivalent series circuit requires that a reactance of the same value as Xg but of op posite kind be inserted in series with the line Tuning out the reactance in the equivalent parallel circuit requires that a reactance of the same value as Xp but of opposite kind be connected across the line In practice it is more convenient to use the parallel equivalent circuit The transmission line is simply connected to the load which of course is usually a resonant antenna and then a reactance of the proper value is connected across the line at the proper distance from the load From this point back to the transmitter there are no standing waves on the line A convenient type of reactance to use is a section of Zr Less Than Zo Zp Greater Than Zo ANTO900 Figure 24 38 Use of open or closed stubs for canceling the parallel reactive component of input impedance ANTO901 Figure 24 39 Application of matching stubs to com mon types of antennas transmission line less than 4 4 long terminated with either an open circuit or a short circuit depending on whether capaci tive reactance or inductive reactanc
112. il taps To determine 24 4 Chapter 24 the range of circuit values for a matched condition the in put and load impedance values must be known or assumed Otherwise a match may be found by trial and error There are several versions of the L network In Figure 24 2A L is shown as the series reactance X and C1 as the shunt or parallel reactance Xp However a capacitor may be used for the series reactance and an inductor for the shunt reactance to satisfy mechanical or other considerations The version shown in Figure 24 2A is the most popular with amateurs because of its low pass characteristics that reduce harmonics reasonable component values and convenient construction from available component styles A complete discussion of L networks is available in the ARRL Handbook The ratio of the series reactance to the series resistance Xs Rs is defined as the network Q The four variables Rg Rp Xs and Xp for lossless components are related as given in the equations below When any two values are known the other two may be calculated Xs _ Rp Rs Rs Xp Eq 1 ANT0876 Figure 24 2 At A the L matching network consisting of L and C1 to match Z1 and Z2 The lower of the two imped ances to be matched Z1 must always be connected to the series arm side of the network and the higher impedance Z2 to the shunt arm side The positions of the inductor and capacitor may be interchanged in the network At B the Pi netw
113. inding capacitances can be neglected these transformers are similar in operation to a conventional transformer The main difference and a very important one from a power standpoint is that the windings tend to cancel out the induced flux in the core Thus high per meability ferrite cores which are not only highly nonlinear but also suffer serious damage even at flux levels as low as 200 to 500 gauss can be used This greatly extends the low frequency range of performance Since higher permeability also permits fewer turns at the lower frequencies HF perfor mance is also improved since the upper cutoff is determined mainly from transmission line considerations At the high frequency cutoff the effect of the core is negligible Bifilar matching transformers lend themselves to unbal anced operation That is both input and output terminals can have a common ground connection This eliminates the third magnetizing winding required in balanced to unbalanced voltage balun operation By adding third and fourth wind ings as well as by tapping windings at appropriate points various combinations of broadband matching can be ob tained Figure 24 42 shows a 4 1 unbalanced to unbalanced configuration using 14 AWG wire It will easily handle Transmission Line Coupling and Impedance Matching ANT0904 E2 2E1 1 1 2 11 Z2 2 4Z1 Figure 24 42 Broadband bifilar transformer with a 4 1 im pedance ratio The upper winding can
114. ing a hairpin of stiff wire or tubing this same matching technique may be used with a lumped constant inductor connected across the antenna terminals Such a method of matching has been dubbed tongue firmly in cheek as the helical hairpin The inductor of course must exhibit the same reactance at the operating frequency as the hairpin it replaces A cursory examination with computer calculations indicates that a helical hairpin may offer a very slightly improved SWR bandwidth over a true hairpin 24 32 Chapter 24 24 5 8 MATCHING STUBS As explained in the Transmission Lines chapter a mismatch terminated transmission line less than A 4 long has an input impedance that is both resistive and reactive The equivalent circuit of the line input impedance at any one frequency can be formed either of resistance and reactance in series or resistance and reactance in parallel Depending on the line length the series resistance component Rg can have any value between the terminating resistance Zp when the line has zero length and Z 2 Zp when the line is exactly A 4 long The same thing is true of Rp the parallel resistance component Rg and Rp do not have the same values at the same line length however other than at zero and 1 4 With either equiv alent there is some line length that will give a value of Rg or Rp equal to the characteristic impedance of the line However there will be reactance along with the resistance But
115. ing the antenna transforms the wide range of impedances at the antenna s feed point to another wide range of impedances at the transmission line s input This often mandates the use of a more flexible antenna tuner than an L network The pi network shown in Figure 24 2B offers more flexibility than the L network since there are three variables instead of two The only limitation on the circuit values that may be used is that the reactance of the series arm the induc tor L in the figure must not be greater than the square root of the product of the two values of resistive impedance to be matched The following equations are for lossless compo nents in a pi network For R1 gt R2 R Xc o Eq 6 R1 R2 Xo Eq 7 ad Q 1 RI R2 Transmission Line Coupling and Impedance Matching 24 5 QxRp X c2 Q 1 Eq 8 The pi network may be used to match a low impedance to a rather high one such as 50 to several thousand ohms Conversely it may be used to match 50 Q to a quite low value such as 1 Q or less For antenna tuner applications C1 and C2 may be independently variable L may be a roller inductor or a coil with switchable taps Alternatively a lead fitted with a suitable clip may be used to short out turns of a fixed inductor In this way a match may be obtained through trial It will be possible to match two values of impedances with several different settings of L C1 and C2 This results because the Q
116. intain a low SWR on the line over a band of frequencies 24 8 2 QUARTER THREE QUARTER WAVE BALUN The coaxial balun in Figure 24 62 is a 1 1 decoupling balun made from two pieces of coaxial cable One leg is 1 4 long and the other 34 4 long The two coaxes and the feed line are joined together with a T connector At the antenna the shields of the cables are connected together and the center conductors connected to the terminals of the antenna feed point The balun has very little loss and is reported to have a bandwidth of more than 10 The balun works because of the current forcing func tion of a transmission line an odd number of A 4 long The current at the output of such a transmission line is Viy Zo regardless of the load impedance similarly to the behavior of a current source Because both lines are fed with the same voltage being connected in parallel the output currents will also be equal The current out of the 3 4 line is delayed by 4 2 from the current out of the A 4 line and so is out of phase The result is that equal and opposite currents are forced into the terminal of the load 24 8 3 COMBINED BALUN AND MATCHING STUB In certain antenna systems the balun length can be considerably shorter than 4 4 the balun is in fact used as Length A 4 500 Unbalanced 50 QO Balanced Length 3 4 ANT1126 Connect Shields Together Figure 24 62 The 1 4 3 4 balun uses the current forcing function of odd
117. is not available use a 4 W carbon composition leaded resistor with leads trimmed to the minimum amount necessary to make the connections Since the measured curve includes stray capacitance the actual capacitance of the choke will be slightly less than the computed value If you have determined the value of stray capacitance for your test setup subtract it from the computed value to get the actual capacitance You can also use this corrected value in the theoretical circuit to see how the choke will actually behave in a circuit that is without the stray capacitance of your test setup You won t see the change in your measured data only in the theoretical RLC equivalent Dual Resonances In NiZn ferrite materials 61 43 there is only circuit resonance but MnZn materials 77 78 31 have both circuit resonance and dimensional resonance See the RF Techniques chapter of the ARRL Handbook for a discussion of ferrite resonances The dimensional resonance of 77 and 78 material is rather high Q and clearly defined so R L and C values can often be computed for both reso nances This is not practical with chokes wound on 31 cores because the dimensional resonance occurs below 5 MHz is very low Q is poorly defined and blends with the circuit resonance to broaden the impedance curve The result is a dual sloped resonance curve that is curve fit ting will produce somewhat different values of R L and C when matching t
118. k only transforms the impedance presented to its output terminals into a different impedance at its input terminals Many mod ern transceivers feature an internal antenna tuner that can compensate for SWR up to 3 1 sometimes more In many publications such an impedance matching network is often called a transmatch meaning a transmit ter matching network Another common name is matchbox after the E F Johnson product line A network operated au tomatically by a microprocessor is often called an auto tuner Regardless of the name the function of an antenna tuner is to transform the impedance at the input end of the transmis sion line whatever it may be to the 50 needed for the transmitter to operate properly An antenna tuner does not alter the SWR between its output terminals and the load such as on the transmission line going to the antenna It only ensures that the transmitter sees the 50 Q load for which it was designed Antenna tuners come in three basic styles manual ad justed by the operator automatic adjusted under the con trol of a microprocessor and remote an automatic version designed to be mounted away from the operating position Manual tuners are the most common and often include an SWR or power meter to aid the operator in adjusting the tuner Automatic tuners may be internal to the transmitter or external standalone equipment Since the controlling micro processor measures SWR on its own there
119. lel conductor line However it is possible to find between two points a value of impedance that can be matched to such a line when a fanned section or delta is used to couple the line and antenna The antenna length is that required for resonance The ends of the delta or Y should be attached at points equidistant from the center of the antenna When so connected the terminating impedance for the line will be resistive Obviously this technique is useful only when the Z of the chosen transmission line is higher than the feed point impedance of the antenna Based on experimental data for the case of a typical A 2 antenna coupled to a 600 Q line the total distance A between the ends of the delta should be 0 120 for fre quencies below 30 MHz and 0 115 for frequencies above 30 MHz The length of the delta distance B should be 0 150 These values are based on a wavelength in air and on the assumption that the center impedance of the antenna is approximately 70 The dimensions will require modifi cations if the actual impedance is very much different The delta match can be used for matching the driven element of a directive array to a transmission line but if the impedance of the element is low as is frequently the case the proper dimensions for A and B must be found by experimentation ANT0891 Figure 24 28 The delta matching system Transmission Line Coupling and Impedance Matching T
120. ly a very low Q parallel resonant Transmission Line Coupling and Impedance Matching a Figure 24 52 n RF choke balun formed by coil ing the feed line at the point of connection to the antenna The inductance of the choke isolates the antenna from the outer surface of the feed line 2 HBK0622 Tiewrap Coax Tiewrap PVC Pipe Figure 24 53 Winding a coaxial choke balun as a single layer solenoid may increase impedance and self resonant frequency compared to a flat coil choke circuit tuned to the frequency where the choke should be ef fective Passing a conductor through most ferrite cores that is one turn produces a resonance around 150 MHz By choosing a suitable core material size and shape and by add ing multiple turns and varying their spacing the choke can be tuned optimized for the required frequency range A table of ferrite and powdered iron core toroid data is provided on this book s CD ROM Transmitting chokes differ from other common mode chokes because they must be designed to work well when the line they are choking carries high power They must also be physically larger so that the bend radius of the coax is large enough that the line is not deformed Excellent common mode chokes having very high power handling capability can be formed simply by winding multiple turns of coax through a sufficiently large ferrite core or multiple cores Chokes made by winding c
121. ment by 2 3 to return it to resonance The Gamma Match The gamma match arrangement shown in Figure 24 30B is an unbalanced version of the T suitable for use directly with coaxial lines Except for the matching section being connected between the center and one side of the antenna the remarks above about the behavior of the T apply equally well The inherent reactance of the matching section can be canceled either by shortening the antenna appropriately or by using the resonant length and installing a capacitor C as shown in Figure 24 30B For a number of years the gamma match has been widely used for matching coaxial cable to all metal parasitic beams Because it is well suited to plumber s delight construction where all the metal parts are electrically and mechanically connected it has become quite popular for amateur arrays Because of the many variable factors driven element length gamma rod length rod diameter spacing between rod and driven element and value of series capacitors a number of combinations will provide the desired match The task of finding a proper combination can be a tedious one as the settings are interrelated A few rules of thumb have evolved that provide a starting point for the various factors For matching a multielement array made of aluminum tubing to 50 Q line the length of the rod should be 0 04 to 0 05 its diameter to 4 that of the driven element and its spacing center to center fr
122. n memory and proceeds to the next impedance If AAT determines that a match is possible but some parameter is violated for example the voltage limit is exceeded it stores the out of specification problem to memory and tries the next impedance For the pi network and the T network which have three variable components the program varies the output capacitor in discrete steps of capacitance It is possible for AAT to miss very critical matching combinations because of the size of the steps necessary to hold execution time down You can some times find such critical matching points manually using the TLW program which uses the same algorithms to determine matching conditions Once all impedance points have been tried AAT writes the results to two disk files one is asummary file TEENET SUM in this example and the other is a detailed log TEENET LOG of successful matches and matche that came close ex cept for exceeding a voltage rating Fig ure 24 6 is a sample printout of part of the summary AAT output for the 3 5 MHz band and one for the 29 7 MHz band The printouts for 1 8 MHz and the bands from 7 1 to 24 9 MHz are not shown here This is for a T network whose variable capacitors C1 and C2 including 10 pF stray range from 42 to 251 pF each with a voltage rating of 4500 V The coil is assumed to go up to 28 uH and has an unloaded Q of 200 The numbers in the matching map grid represent the power loss percentage for each imp
123. n the variable inductor There is also lots of clearance between components and the chassis itself to prevent arcing and stray capacitance to ground See Fig ures 24 13 and 24 14 showing the layout inside the cabinet of Figure 24 13 Interior view of the ARRL Antenna Tuner The balun is mounted near the input coaxial connector The two feedthrough insulators for balanced line operation are located near the output coaxial unbalanced connector The Radioswitch Corporation high voltage switch is mounted to the front panel Ceramic insulated shaft couplers through ground inch panel bushings couple the variable compo nents to the knobs Figure 24 14 Bottom view of the subchassis showing the four white insulators used to isolate the subchassis from the cabinet The homemade 400 pF fixed capacitor C3 is epoxied to the bottom of the subchassis sandwiching a piece of plate glass as the dielectric between the subchas sis and a flat piece of aluminum E d Figure 24 15 Front panel view of the ARRL Antenna Tuner The high quality turns counter dial is from Surplus Sales of Nebraska the prototype tuner Figure 24 15 shows a view of the front panel The turns counter dial for the roller inductor was pur chased from Surplus Sales of Nebraska The 400 pF fixed capacitor is constructed using low cost plate glass from a 5 x 7 inch picture frame together with an approximately 4 x 6 inch flat
124. nd the balun s additional weight and expense are also avoided The coax back to the transmit ter can be buried or laid on the ground and it is perfectly matched Burial of the cable will also prevent any additional common mode currents from being induced on the coax shield The tuner is then adjusted for minimum SWR on the cable as measured in the shack at the transmitter 24 3 3 USING TLW TO DETERMINE SWR The program TLW can be used in two important ways to determine SWR and impedance on the other end of trans mission lines The first case occurs when you are given a certain load impedance such as that of an antenna feed point and wish to know what the SWR and impedance will be at the input of the feed line This type of information is used to design impedance matching networks and antenna tuners for use in the shack From the program s main screen select the feed line type and length Enter frequency and the load resistance and reactance specifying LOAD for the location of the impedance The SWR and impedance at the input of the feed line will be displayed at the bottom of the window The additional loss due to SWR is also calculated The second case works in reverse It occurs when you know the SWR or impedance at the input to the feed line and want to know the SWR or impedance at the load an tenna end of the feed line Enter the cable type and length frequency and a value for RESISTANCE equal to SWR x Zp If you k
125. now the input impedance enter it instead Specify INPUT for the location where SWR is specified The SWR and impedance will be displayed at the bottom of the win dow along with the additional line loss due to SWR 24 4 TRANSMISSION LINE MATCHING DEVICES 24 4 1 QUARTER WAVE TRANSFORMERS The impedance transforming properties of a 4 4 trans mission line synchronous transformer or Q section shown in Figure 24 19A can be used to good advantage for matching the feed point impedance of an antenna to the characteristic impedance of the line As described in the Transmission Lines chapter the input impedance of a 1 4 line terminated in a resistive impedance Zp is Zo Eq 9 ZF Eq 9 where Z the impedance at the input end of the line Zo the characteristic impedance of the line Z the impedance at the load end of the line Rearranging this equation gives Zo Zia q 10 Transmission Line Coupling and Impedance Matching Any Length N4 Transformer LQ A 4 Length 12 Transformer Length L1 N 12 QS0910 HORO1 B Figure 24 19 The wave A Q section and 42 wave B synchronous transformers 24 21 This means that any value of load impedance Z can be transformed into any desired value of impedance Z at the input terminals of a 4 4 line provided the line can be con structed to have a characteristic impedance Zo equal to the square root of the product of the other two impedances The f
126. oaxial cable on ferrite cores will be re ferred to as wound coax chokes to distinguish them from the coiled coax chokes of the preceding section Because 24 43 of the isolation between the inside and outside conducting surfaces of coaxial cable all of the magnetic flux associated with differential mode current is confined to the dielectric the insulating material between the center conductor and the shield The external ferrite core carries only flux associated with common mode current If the line is made up of parallel wires a bifilar winding a significant fraction of the flux associated with differential current will leak outside the line to the ferrite core Leakage flux can exceed 30 of the total flux for even the most tight ly spaced bifilar winding In addition to this leakage flux the core will also carry the flux associated with common mode current When a transformer as opposed to a choke is wound on a magnetic core all of the field associated with current in the windings is carried by the core Similarly all forms of voltage baluns require all of the transmitted power to couple to the ferrite core Depending on the characteristics of the core this can result in considerable heating and power loss Only a few ferrite core materials have loss characteristics suitable for use as the cores of high power RF transform ers Type 61 material has reasonably low dissipation below about 10 MHz but its loss tangent rises
127. of impedances it can handle look over the tables in the ASCII file called TUNER SUM on this book s CD ROM The tables were created using the program AAT described previously in this chapter For example assume that the load at 1 8 MHz is 12 5 j 0 For this example the output capacitor C3 is set by the program to 750 pF This dictates the values for the other two components At 1 8 MHz for typical values of component unloaded Q 200 for the coil 7 9 of the power delivered to the input of the network is lost as heat For 1500 W at the input the loss in the network is thus 119 W Of this 98 W ends up in the inductor which must be able to handle this without melting or detuning The T network must be used judiciously lest it burn itself up or arc over internally One of the techniques used to minimize power lost in this tuner is the use of a relatively large output capacitor The output variable capacitor has a maximum capacitance of approximately 400 pF including an estimated 20 pF of stray capacitance An additional 400 pF of fixed capacitance F aa T Bypass Bypass a j amp O 400 pF J2 C2B Output ry CLIT LVL Common Subchassis L2 L1 oe 0 3 uH Bypass Tuner All capacitors are 15 196pF ANTO880 Figure 24 12 Schematic diagram of the ARRL Antenna Tuner C1 C2 15 196 pF transmitting variable with voltage rat ing of 3000 V peak such as the Cardwell Johnson 154 507 1 www cardwellcondense
128. of the input power Figure 24 3A is a low pass L network Figure 24 3B is a high pass L network and Figure 24 3C is a pi network At more than 5200 pF the capacitance values are pretty unwieldy for the first three networks The loaded Q for all three is only 3 0 indicating that the network loss is small In fact the loss is only 1 8 for all three because the loaded Q is much smaller than the unloaded Qy of the components used The T network in Figure 24 3D uses more practical realizable component values Note that the output capacitor C2 has been set to 500 pF and that dictates the values for the other two components The drawback is that the loaded Q in this configuration has risen to 34 2 with an attendant loss of TLA Ver 4 00AE Copyright 1993 1997 ARRL by N6BU Frequency 1 830 MHz Transmission line 450 Ohm Window Ladder Line Length At Antenna Tuner output 0 00 j 0 00 2 0 00 R at 0 69 Highest network effective Q 999 9 Est power lost in tuner for 1500 W 1500 W 50 81 dB 100 00 lost 0 00 dB Total loss 50 81 dB Into load 0 0 u 0 60 ft Xasn line loss At 1500 u Cin L Cout Unloaded Q 1660 200 1000 Reactance 1119 115 Q 150 2 173 0 2 Peak Voltage 8669 U v 8677 U BMS Current SSA 7A 35 3 A Pover Diss nu 1 216 u 77 7 f 500 0 pF gt gt 4 0 00 2 13 1 pH j 9 00 az gt Z 2 Cs C Freq F Defaults D Network N 1 4 Main M Exit X J Figure 24 4
129. of the network is being changed If a match is maintained with other adjustments the Q of the circuit rises with increased capacitance at C1 Of course the load usually has a reactive component along with resistance You can compensate for the effect of these reactive components by changing one of the reactive elements in the matching network For example if some reactance were shunted across R2 the setting of C2 could be changed to compensate for inductive or capacitive shunt reactance As with the L network the effects of real world unload ed Q for each component must be taken into account in the pi network to evaluate real world losses Pi networks are used in vacuum tube amplifiers to match the high tube output impedance to the 50 Q imped ance of most feed lines and antenna systems See the ARRL Handbook chapter RF Power Amplifiers for more informa tion on and design software for the pi network 24 2 3 THE T NETWORK Both the pi network and the L network often require un wieldy values of capacitance that is large capacitances are often required at the lower frequencies to make the desired transformation to 50 Often the range of capacitance from minimum to maximum must be quite wide when the imped ance at the output of the network varies radically with fre quency as is common for multiband single wire antennas The high pass T network shown in Figure 24 2C is ca pable of matching a wide range of load impedances
130. of the tap or taps on the antenna measure the SWR on the transmission line and adjust C both capacitors simultaneously in the case of the T for minimum SWR If it is not close to 1 1 try another tap position and repeat It may be necessary to try another size of conductor for the match ing section if satisfactory results cannot be brought about Changing the spacing will show which direction to go in this respect 24 5 6 THE OMEGA MATCH The omega match is a slightly modified form of the gamma match In addition to the series capacitor a shunt capacitor is used to aid in canceling a portion of the inductive reactance introduced by the gamma section This is shown in Figure 24 33 C1 is the usual series capacitor The addition of C2 makes it possible to use a shorter gamma rod or makes it easier to obtain the desired match when the driven element is resonant During adjustment C2 will serve primarily to determine the resistive component of the load as seen by the coax line and C1 serves to cancel any reactance 24 5 7 THE HAIRPIN AND BETA MATCHES The usual form of the hairpin match is shown in Fig ure 24 34 Basically the hairpin is a form of an L matching network in which the feed point s capacitive reactance forms the shunt capacitor Because it is somewhat easier to adjust for the desired terminating impedance than the gamma match it is preferred by many amateurs Its disadvantages compared with the gamma are that it must be
131. om such an induced current but the unwanted current on the outside braid is still called common mode current The common mode impedance will vary with the length of the coaxial feed line its diameter and the path length from the transmitter chassis to whatever is actually RF ground Note that the path from the transmitter chassis to ground may go through the station s grounding bus the transmitter power cord the house wiring and even the power line service ground In other words the overall length of the coaxial outer surface and the other components making up ground can ac tually be quite a bit different from what you might expect by casual inspection The worst case common mode impedance occurs when the overall effective path length to ground is a multiple of A 2 making this path half wave resonant In effect the line and ground wire system acts like a sort of transmission line transforming the short circuit to ground at its end to a low Transmission Line Coupling and Impedance Matching impedance at the dipole s feed point This causes I3 to be a significant part of I2 I3 not only causes an imbalance in the amount of current flowing in each arm of the otherwise symmetrical dipole but it also radiates by itself The radiation in Figure 24 45 due to I3 would be mainly vertically polarized since the coax is drawn as being mainly vertical However the polarization is a mixture of horizontal and vertical depending on th
132. om the driven element approximately 0 007 The capacitance value should be approximately 7 pF per meter of wavelength This translates to about 140 pF for 20 meter operation The exact gamma dimensions and value for the capacitor will depend on the radiation resis tance of the driven element and whether or not it is resonant These starting point dimensions are for an array having a feed point impedance of about 25 Q with the driven element shortened approximately 3 from resonance Calculating Gamma Dimensions A Starting point for the gamma dimensions and capaci tance value may be determined by calculation H F Tolles W 7ITB has developed a method for determining a set of pa rameters that will be quite close to providing the desired im pedance transformation See Bibliography The impedance of the antenna must be measured or computed for Tolles s procedure If the antenna impedance is not accurately known ANT1123 Figure 24 31 The gamma match as used with tubing ele ments Parameters are those used for the GAMMA dimen sion calculation software Note that S is a center to center value not surface to surface The transmission line may be either 50 Q or 75 Q coax Length Spacing i Capacitance Coax to Transmitter Transmission Line Coupling and Impedance Matching modeling calculations provide a very good starting point for initial settings of the gamma match The math involved in Tolles s
133. or to the setting for lowest SWR or highest received noise a Ifno SWR minimum or noise peak is detected reduce the value of the capacitor closest to the transmitter in steps of about 20 and repeat b If still no SWR minimum or noise peak is detected return the input capacitor to maximum value and reduce the output capacitor value in steps of about 20 c If still no SWR minimum or noise peak is detected return the output capacitor to maximum value and reduce both input and output capacitors in 20 steps 5 Once a combination of settings is found with a definite SWR minimum or noise peak a If you are using an SWR analyzer make small ad justments to find the combination of settings that produce minimum SWR with the maximum value of input and output capacitance b If you do not have an SWR analyzer set the trans mitter output power to about 10 W ensure that you won t cause interference identify with your call sign and transmit a steady carrier by making the same adjustments as in step Sa c For certain impedances the tuner may not be able to reduce the SWR to an acceptable value In this case try add ing feed line at the output of the tuner from 4 to 2 A electri cal wavelength long This will not change the feed line SWR but it may transform the impedance to a value more suitable for the tuner components In general for any type of tuner begin with the maxi mum reactance to ground maximum inductance or minimum
134. ork tuner matching R1 to R2 The Pi provides more flexibility than the L as an antenna tuner circuit See equa tions in the text for calculating component values At C the T network tuner This has more flexibility in that compo nents with practical values can match a wide variety of loads The drawback is that this network can be inefficient particularly when the output capacitor is small i _ QRp Xs QRs 140 Eq 2 Rp RpRs Re eke er gas uae a Ris See Eq 4 Q 41 Rp 2 Rg Xs Ea 5 Rp Rg 1 Q QXp S Eq 5 Rs The reactance of loads that are not purely resistive may be taken into account and absorbed or compensated for in the reactances of the matching network Inductive and capacitive reactance values may be converted to inductor and capacitor values for the operating frequency with standard reactance equations It is important to recognize that Eq 1 through 5 are for lossless components When real components with real unloaded Qs are used the transformation changes and you must compensate for the losses Real coils are represented by a perfect inductor in series with a loss resistance and real capacitors by a perfect capacitor in parallel with a loss resistance At HF a physical coil will have an unloaded Qy between 100 and 400 with an average value of about 200 for a high quality airwound coil mounted in a spacious metal enclosure A variable capacitor used in an antenna tuner will have an unloaded Qy of
135. over the 1 8 MHz band Q2 requires 12 turns and powdered iron 10 requires 14 turns Since the more common powdered iron core is generally smaller in diameter and requires more turns because of lower permeability higher ratios are some times difficult to obtain because of physical limitations When you are working with low impedance levels unwanted para sitic inductances come into play particularly on 14 MHz and above In this case lead lengths should be kept to a minimum 24 6 COMMON MODE TRANSMISSION LINE CURRENTS In discussions so far about transmission line operation it was always assumed that the two conductors carry equal and opposite currents throughout their length This is an ideal condition that may or may not be realized in practice In the average case the chances are rather good that the currents will not be balanced unless special precautions are taken The degree of imbalance and whether that imbalance is actually important is what we will examine in the rest of this chapter along with measures that can be taken to restore balance in the system There are two common conditions that will cause an imbalance of transmission line currents Both are related to the symmetry of the system The first condition involves the lack of symmetry when an inherently unbalanced coaxial line feeds a balanced antenna such as a dipole or a Yagi driven element directly The second condition involves asymmetrical routing of a tran
136. priate transmission line is often a parallel wire line be cause of the inherently low matched line loss characteristic of these types of lines Such a system is called an unmatched system because no attempt is made to match the impedance at the antenna s feed point to the Z of the transmission line Commercial 450 Q window ladder line has become popular for this kind of application It is almost as good as traditional open wire or ladder line for most amateur systems The transmission line will be mismatched most of the time and on some frequencies it will be severely mismatched Because of the mismatch the SWR on the line will vary widely with frequency As shown in the Transmission Lines chapter such a variation in load impedance has an impact on the loss suffered in the feed line Let s look at the losses suffered in a typical multiband nonresonant system Table 24 6 summarizes the feed point information over the HF amateur bands for a 100 foot long dipole mounted as a flattop 50 feet high over typical earth In addition the table shows the total line loss for 100 feet of 450 Q ladder line and the SWR at the antenna feed point As usual there is nothing particularly significant about the choice of a 100 foot long antenna or a 100 foot long transmission line Both are practical lengths that could very well be encountered in a real world situation At 1 8 MHz the loss in the transmission line is large 8 9 dB This is due to the
137. r com C3 Home made 400 pF capacitor more than 10 kV volt age breakdown Made from plate glass from a 5 x 7 inch picture frame sandwiched in between a 4 x 6 inch 0 030 inch thick aluminum plate and the electrically floating subchassis that also forms the common connection be tween C1 C2 and L1 Transmission Line Coupling and Impedance Matching Equal Lengths for Balance Jumper for A D Unbalanced Operation en L1 Fixed inductor approximately 0 3 uH 4 turns of inch copper tubing formed on 1 inch OD tubing L2 Rotary inductor 28 uH inductance Cardwell 229 203 1 with steatite coil form www cardwellcondenser com B1 Balun 12 turns bifilar wound 10 AWG Formvar wire side by side on 2 4 inch OD Type 43 core Amidon FT240 43 24 13 can be switched across the output variable capacitor on 80 or 160 meters At 750 pF output capacitance at 1 8 MHz and a 12 5 Q load enough heat is generated at 1500 W input to make the inductor uncomfortably warm to the touch after 30 seconds of full power key down operation but not enough to destroy the roller inductor For a variable capacitor used in a T network tuner there is a trade off between the range of minimum to maximum capacitance and the voltage rating This tuner uses two iden tical Cardwell Johnson dual section 154 507 1 air variable capacitors rated at 3000 V Each section of the capacitor ranges from 15 to 196 pF with an estimated 10
138. rapidly above that frequency The loss tangent of type 67 material makes it useful in high power transformers to around 30 MHz Leakage flux corresponding to 30 40 of the transmit ter power causes heating in the ferrite core and attenuates the transmitted signal by a dB or so At high power levels tem perature rise in the core also changes its magnetic properties and in the extreme case can result in the core temporarily losing its magnetic properties A flux level high enough to make the core hot is also likely to saturate the core producing distortion harmonics splatter clicks Flux produced by common mode current can also heat the core if there is enough common mode current Dissipated power is equal to I R so it can be made very small by making the common mode impedance so large that the common mode current is very small Design Criteria It can be shown mathematically and experience con firms that wound coax chokes having a resistive impedance at the transmit frequency of at least 5000 Q and wound with RG 8 or RG 11 size cable on five toroids are conservatively rated for 1500 W under high duty cycle conditions such in contesting or digital mode operation While chokes wound with smaller coax RG 6 RG 8X RG 59 RG 58 size are conservatively rated for dissipation in the ferrite core the voltage and current ratings of those smaller cables suggests a somewhat lower limit on their power handling Since the chokes see only
139. rs without an antenna tuner If you want a better match at the antenna feed point of a single band antenna to coax you can provide some sort of matching network at the antenna We ll look further into schemes for achieving matched antenna systems later in this chapter when we ll examine single band methods of match ing feed point and feed line impedances Feeding a Multiband Antenna A multiband antenna is one where special measures are used to make a single antenna present a consistent feed point impedance on each of several amateur bands Often trap circuits are employed Information on traps is given in the Multiband HF Antennas chapter For example a trap dipole presents a feed point impedance similar to that of a A 2 dipole on each of the bands for which it is designed Note that resonance only means that the self imped ance of the antenna is completely resistive no reactance and does not imply that the value of the impedance is low For example the 135 foot dipole may be resonant on 3 5 MHz and all harmonics but its feed point impedance will vary from low values at the fundamental and odd harmonics 10 5 17 5 24 5 MHz to very high impedances at even harmonics 7 0 14 0 21 0 28 0 MHz Yet it may be resonant at all of those frequencies Another common multiband antenna is constructed from several dipoles cut for different frequencies and connected in parallel at a common feed point and fed with a single coaxial
140. s are shown in Figure 24 18 Example 1 in Figure 24 18A shows a 200 foot run of RG 213 go ing to a 1 1 balun that feeds the an tenna A tuner in the shack reduces the VSWR for proper matching in the transmitter Example 2 Figure 24 18B shows a similar arrangement using 300 Q transmitting twin lead Example 3 Figure 24 18C shows a 50 foot run of 300 line dropping straight down to a remote tune near the ground and 150 feet of RG 213 going to the shack Table 24 8 sum marizes the losses and the L network component values required Some interesting conclusions can be drawn First direct feeding this antenna with coax through a balun is very lossy a poor solu tion If the flattop were A 2 long a resonant half wave dipole direct Table 24 8 Tuner Settings and Performance Total Example Frequency Tuner L C Loss Fig 24 18 MHz Type uH pF dB 1 3 8 Rev L 1 46 2308 8 53 28 4 Rev L 0 13 180 9 12 3 2 3 8 L 14 7 46 2 74 28 4 L 0 36 15 6 3 52 3 3 8 L 11 37 332 1 81 28 4 L 0 54 94 0 2 95 coax feed would be a good method In the second example direct feed with 300 Q low loss line does not always give the lowest loss The combination method in Example 3 provides the best solution Example 3 has some additional advantages It feeds the antenna in a symmetrical arrangement which is best to reduce common mode current pickup on the shield of the feed line The shorter feed line will not weigh down the antenna as much a
141. s exactly the same function as the current balun of Figure 24 66A as there is no current in winding b If the antenna isn t perfectly balanced however unequal currents will appear at the balun output causing antenna current to flow on the line an undesirable condi tion Voltage baluns can be used as impedance transformers in this application if a 1 1 current or choke balun is added at the unbalanced input to prevent the common mode current flow Another potential shortcoming of the 1 1 voltage balun is that winding b appears across the line If this winding has insufficient impedance a common problem particularly near the lower frequency end of its range the impedance transfor mation ratio will be degraded 4Z Balanced Unbalanced Z Unbalanced 4 1 Ratio Z Unbalanced Toroidal Core Unbalanced 4 1 Balanced to Unbalanced Voltage Balun A B Figure 24 65 Voltage type baluns These have largely been supplanted by the current choke type of balun Balanced Balanced Z Unbalanced Z l Toroidal Unbalanced Balanced 1 1 Balanced to Unbalanced Current Balun ANT0913 A 4 1 Balanced to Balanced Transformer 4Z Balanced Figure 24 66 Ferrite core bal uns Each uses transmission line techniques to achieve wide fre quency coverage The transmis sion line can consist of coaxial cable or tightly coupled side by side bifilar enameled wires Typically 12 turns of 10 AWG
142. s possible Antenna Less Than A 2 Matching Stub Parallel Wire Line to Xmtr Antenna Matching Stub ANT0915 to Xmtr Figure 24 63 Combined matching stub and balun The ba sic arrangement is shown at A At B the balun arrangement is achieved by using a section of the outside of the coax feed line as one conductor of a matching stub Transmission Line Coupling and Impedance Matching Adjustment When a A 4 balun is used it is advisable to resonate it be fore connecting the antenna This can be done without much difficulty if a dip meter or impedance analyzer is available In the system shown in Figure 24 61A the section formed by the two parallel pieces of line should first be made slightly longer than the length given by the equation The shorting connection at the bottom may be installed permanently With the dip meter coupled to the shorted end check the frequency and cut off small lengths of the shield braid cutting both lines equally at the open ends until the stub is resonant at the desired frequency In each case leave just enough inner con ductor remaining to make a short connection to the antenna After resonance has been established solder the inner and outer conductors of the second piece of coax together and complete the connections indicated in Figure 24 61A Another method is to first adjust the antenna length to the desired frequency with the line and stub disconnected then connect the balun and rec
143. smission line near the antenna it is feeding 24 6 1 UNBALANCED COAX FEEDING A BALANCED ANTENNA Figure 24 45 shows a coaxial cable feeding a hypo thetical balanced dipole fed in the center The coax has been drawn highly enlarged to show all currents involved In this 24 36 Chapter 24 Dipole Arm 2 Dipole Feed Line NP Junction Coaxial N Feed Line ANTO906 Figure 24 45 Drawing showing various current paths at feed point of a balanced dipole fed with unbalanced coaxial cable The diameter of the coax is exaggerated to show cur rents clearly drawing the feed line drops at right angles down from the feed point and the antenna is assumed to be perfectly sym metrical Because of this symmetry one side of the antenna induces current on the feed line that is completely canceled by the current induced from the other side of the antenna Currents I1 and I2 from the transmitter flow on the inside of the coax I1 flows on the outer surface of the coax s inner conductor and I2 flows on the inner surface of the shield Skin effect keeps I1 and I2 inside the transmission line con fined to where they are within the line The field outside the coax is zero since Il and I2 have equal amplitudes but are 180 out of phase with respect to each other The currents flowing on the antenna itself are labeled I1 and I4 and both flow in the same direction at any instant in time for a resonant half wave dipol
144. t has the proper value of reactance Correct lengths can be determined using TLW or the Smith Chart for dissimilar types of line In using matching stubs it should be noted that the length and location of the stub should be based on the SWR at the load If the line is long and has fairly high losses measuring the SWR at the input end will not give the true value at the load This point is discussed in the section on attenuation in the Transmission Lines chapter Reactive Loads In this discussion of matching stubs it has been assumed that the load is a pure resistance This is the most desirable condition since the antenna that represents the load prefer ably should be tuned to resonance before any attempt is made to match the line Nevertheless matching stubs can be used even when the load is considerably reactive A reactive load simply means that the loops and nodes of the standing waves of voltage and current along the line do not occur at integral 24 33 multiples of 1 4 from the load If the reactance at the load is known the Smith Chart or TLW may be used to determine the correct dimensions for a stub match Stubs on Coaxial Lines The principles outlined in the preceding section apply also to coaxial lines The coaxial cases corresponding to the open wire cases shown in Figure 24 39 are given in Figure 24 40 The equations given earlier may be used to determine dimensions A and B In a practical installation the junction of t
145. tenna is no guarantee that common mode transmission line currents will not occur However dressing the feed line so that it is symmetrical to the antenna will lead to fewer problems in all cases 24 6 3 COMMON MODE CURRENT EFFECTS ON DIRECTIONAL ANTENNAS For a simple dipole many amateurs would look at Figure 24 46 or Figure 24 48 and say that the worst case pattern asymmetry doesn t look very important and they would be right Any minor unexpected change in SWR due to com mon mode current would be shrugged off as inconsequential if indeed it is even noticed All around the world there are many thousands of coax fed dipoles in use where no special effort has been made to smooth the transition from unbal anced coax to balanced dipole For antennas that are specifically designed to be highly directional however pattern deterioration resulting from common mode currents is a very different matter Much care is usually taken during design of a directional antenna like a Yagi or a quad to tune each element in the system for the best compromise between directional pattern gain and SWR bandwidth What happens if we feed such a carefully tailored antenna in a fashion that creates common mode feed line currents Figure 24 49 compares the azimuthal response of two five element 20 meter Yagis each located horizontally 4 2 Reference Dipole ANTO909 Dipole w Slanted Coax Feed 20 Elevation 0 dB 7 71 dBi 14 100 MHz Fi
146. the input section were composed of three cables in parallel the impedance ratio would be 3 1 and the transformation ratio 9 1 this could match 50 Q at the input to 450 at the output 24 5 MATCHING IMPEDANCE AT THE ANTENNA Since operating a transmission line at a low SWR re quires that the line be terminated in a load matching the line s characteristic impedance the problem can be approached from two standpoints 1 selecting a transmission line having a characteristic impedance that matches the antenna impedance at the point of connection or 2 transforming the antenna resistance to a value that matches the Zo of the line selected The first approach is simple and direct but its application is obviously limited the antenna impedance and the line impedance are alike only in a few special cases Commercial transmission lines come in a limited variety of characteristic impedances while antenna feed point impedances vary over a wide range The second approach provides a good deal of freedom in that the antenna and line can be selected independently The disadvantage of the second approach is that it is more complicated in terms of actually constructing the matching system at the antenna Further this approach sometimes calls for a tedious routine of measurement and adjustment before the desired match is achieved 24 5 1 ANTENNA IMPEDANCE MATCHING Impedance Change with Frequency Most antenna systems show a marked chan
147. the length of the stub and its distance from the load as described on the supplement on this book s CD ROM or the ARRL program TLW also included on the CD ROM may be used If the load is a pure resistance and the characteristic impedances of the line and stub are identical the lengths may be determined by equations For the closed stub when Zp is greater than Zp they are A arctanvSWR Eq 20 B arctan owe Eq 21 SWR 1 For the open stub when Zp is less than Zo A arctan l Eq 22 SWR B arctan SWRI Eq 23 In these equations the lengths A and B are the distance from the stub to the load and the length of the stub respec tively as shown in Figure 24 39 These lengths are expressed in electrical degrees equal to 360 times the lengths in wavelengths In using the above equations it must be remembered that the wavelength along the line is not the same as in free space If an open wire line is used the velocity factor of 0 975 will apply When solid dielectric line is used the free space wavelength as determined above must be multiplied by the appropriate velocity factor to obtain the actual lengths of A and B see the Transmission Lines chapter Although the equations above do not apply when the characteristic impedances of the line and stub are not the same this does not mean that the line cannot be matched under such conditions The stub can have any desired char acteristic impedance if its length is chosen so that i
148. they are for high impedances measured this way even very small errors in the raw data cause very large errors in the computed result While the software used with reflection based systems use calibration and computation methods to remove systemic errors such as fixture capacitance from the measurement these methods have generally poor accuracy when the impedance being measured is in the range of typical ferrite chokes The key to accurate measurement of high impedance fer rite chokes is to set up the choke as the series element Zy of a voltage divider Impedance is then measured using a well calibrated voltmeter to read the voltage across a well cali brated resistor that acts as the voltage divider s load resistor Ryoap The fundamental assumption of this measurement method is that the unknown impedance is much higher than the impedance of both the generator and the load resistor The RF generator driving the high impedance of the volt age divider must be terminated by its calibration impedance because the generator s output voltage Vogn is calibrated only when working into its calibration impedance An RF spectrum analyzer with its own internal termination resistor can serve as both the voltmeter and the load Alternatively a simple RF voltmeter or scope can be used with the calibrated load impedance being provided by a termination resistor of known value in the frequency range of the measurement With the ferrite choke in place
149. total line loss would be 2 2 dB This represents about a half S unit on most receivers On the other hand open wire line has the advantage of both lower loss and lower cost compared to coax At 30 MHz 600 Q open wire line has a matched loss of only 0 1 dB If you use such open wire line with the same 5 1 SWR the total loss would about 0 3 dB In fact even if the SWR rose to 20 1 the total loss would be less than 1 dB Typical open wire line sells for about 4 the cost of good quality coax cable Despite their inherently low loss characteristics open wire lines are not often employed above about 100 MHz This is because the physical spacing between the two wires begins to become an appreciable fraction of a wavelength leading to undesirable radiation by the line itself Some form of coaxial cable is almost universally used in the VHF and UHF amateur bands Open wire line is enjoying a renaissance of sorts with amateurs wishing to cover multiple HF bands with a single wire antenna This is particularly true since the bands at 30 17 and 12 meters became available in the early 1980s The 102 foot long dipole fed with open wire line into an antenna tuner has become popular as a simple all band antenna The simple 135 foot long flattop dipole fed with 450 Q window line is also very popular as an all band antenna So apart from concerns about convenience and the mat ter of cost how do you go about choosing a transmission line for a part
150. touch up the tuner s controls if necessary When tuning keep your transmissions brief and identify your station For operation above 10 MHz again initially use S1 set to position 2 and if SWR cannot be lowered properly try S1 set to position 3 This will probably be necessary for 24 or 28 MHz operation In general you want to set C2 for as much capacitance as possible especially on the lower fre quencies This will result in the least amount of loss through the antenna tuner The first position of S1 permits switched through operation direct to the antenna when the antenna tuner is not needed Comments Surplus coils and capacitors are suitable for use in this circuit L2 should have at least 25 WH of inductance and be constructed with a steatite body There are roller inductors on the market made with Delrin plastic bodies but these are very prone to melting under stress and should be avoided The tun ing capacitors need to have 200 pF or more of capacitance per section at a breakdown voltage of at least 3000 V You could 24 15 save some money by using a single section variable capacitor for the output capacitor rather than the dual section unit we used It should have a maximum capacitance of 400 pF and a voltage rating of 3000 V Measured insertion loss for this antenna tuner is low The worst case load tested was four 50 Q dummy loads in parallel to make a 12 5 Q load at 1 8 MHz Running 1500 W key down for 30 seconds heated
151. uld be exactly 1 A long directly grounded at its end through the transmitter and so that the low elevation angle response could be emphasized to show pattern distortion The feed line was made 1 A long in this case because when the feed line length is only 0 5 and is slanted 45 to ground the height of the dipole is only 0 35 A This low height masks changes in the nulls in the azimuthal response due to feed line common mode currents Worst case pattern distortion occurs for lengths that are multiplies of 2 2 as before The degree of pattern distortion is now slightly worse than that for the symmetrically placed coax but once again the overall effect is not really severe Interestingly enough the slanted feed line dipole actually has about 0 2 dB more gain than the reference dipole This is because the left hand side null is deeper for the slanted feed line antenna adding power to the frontal lobes at 0 and 180 The feed point impedance for this dipole with slanted feed line is 62 48 j 1 28 for an SWR of 1 25 1 compared to the reference dipole s feed point impedance of 72 00 j 16 76 Q for an SWR of 1 59 1 Here the reactive part of the net feed point impedance is smaller than that for the reference dipole indicating that detuning has occurred due to mutual coupling to its own feed line This change of SWR is slightly larger than for the previous case and could be seen on a typi cal SWR meter You should recognize that
152. ur poles and three positions It is not inexpensive but we wanted to have no weak points in the prototype unit A more frugal ham might want to substitute two more common surplus DPDT switches for S1 One switch would bypass the tuner when the operator desires to do that The other would switch the additional 400 pF fixed capacitor across variable C3 and also parallel both sections of C1 together for the lower frequencies Both switches would have to be capable of han dling high RF voltages of course Operation The ARRL Antenna Tuner is designed to handle the output from transmitters that operate up to 1 5 kW An ex ternal SWR indicator is used between the transmitter and the antenna tuner to show when a matched condition is attained Most often the SWR meter built into the transceiver is used to tune the tuner and then the amplifier is switched on The builder may want to integrate an SWR meter in the tuner cir cuit between J1 and the arm of SIA Never hot switch an antenna tuner as this can damage both transmitter and tuner For initial setting below 10 MHz set S1 to position 2 and C1 at midrange C2 at full mesh With a few watts of RF adjust the roller inductor for a decrease in reflected power Then adjust C1 and L2 alternately for the lowest possible SWR also adjusting C2 if necessary If a sat isfactory SWR cannot be achieved try S1 at position 3 and repeat the steps above Finally increase the transmitter power to maximum and
153. ut power automatically if the SWR rises above 2 1 Protective circuits are needed because the higher voltages or currents encountered at such loads can quickly destroy solid state amplifier transistors Modern solid state transceivers often include built in antenna tuners to match impedances when the SWR isn t 1 1 The impedance at the input of a transmission line is determined by the frequency the characteristic impedance Zo of the line the physical length velocity factor and the matched line loss of the line as well as the impedance of the load the antenna at the output end of the line If the imped ance at the input of the transmission line connected to the transmitter differs appreciably from the load resistance into which the transmitter output circuit is designed to operate 24 1 an impedance matching circuit must be inserted between the transmitter and the line input terminals These circuits called networks in professional literature have one of several configurations with the L pi and T being the most common The name of the network reflects the letter L II or T that the usual shape of the circuit schematic most closely resembles The use of impedance matching networks in a stand alone piece of equipment is usually referred to as an antenna tuner or just tuner This is somewhat of a misnomer since the network does not tune the antenna at all even if located directly at the terminals of the antenna The networ
154. y the input im pedance of the T will show inductive reactance as well as 24 27 resistance The reactance must be tuned out if a good match to the transmission line is to be obtained This can be done either by shortening the antenna to obtain a value of capaci tive reactance that will reflect through the matching system to cancel the inductive reactance at the input terminals or by inserting a capacitance of the proper value in series at the input terminals as shown in Figure 24 30A Theoretical analyses have shown that the part of the _ _468 o Length in Feet MHZ I gt ANT0892 Figure 24 29 The T matching system applied to a an tenna and 600 line Transmission Line Transmission Line ANT0893 Figure 24 30 Series capacitors for tuning out residual re actance with the T and gamma matching systems A maxi mum capacitance of 150 pF in each capacitor should pro vide sufficient adjustment range in the average case for 14 MHz operation Proportionately smaller capacitance val ues can be used on higher frequency bands Receiving type plate spacing will be satisfactory for power levels up to a few hundred watts 24 28 Chapter 24 impedance step up arising from the spacing and ratio of conductor diameters is approximately the same as given for a folded dipole The actual impedance ratio is however con siderably modified by the length A of the matching section Figure 24 29 The trends c

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