Research and Uevt•!opmt•iit Inich RtcIx)rt Il-

ECOM-?9•9

, o BROADBAND TRANSFORMER DESIGN

FOR RF TRANSISTOR POWER AMPLIFIERS

by

Octavius Pitzalls, Jr.Thomas P. Couse

1 July 1968 L

DI1TIS IBUTION iTATfMVNT III

feei . %,Ot Oon Qpledý i~ , unhim,

UNITED STATES ARMY ELECTRONICS COMMAND . FORT MONMOUTH, N.J.

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IN ITICESr

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The citaLion of trade namt's and names of manufaoturers inthin report is not to be oonatrusd as ofticil 0ovemimot|ifdorssisnt Of ppmvlrv| of ommlaercia| P"Vcb Of services

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1n.ports control Wm~ OOD-366

TEM. MI4CAL REPORT SCOM. 2989

DROADAN 1TAIW8ORX DESIGN OR

IpF TUMNI&MO pOVWT AM.WLWIFI

Octsvius pitt~alis, Jr.Thom$ P, Cois4

E!atoi components LaboratorY

JULy 1968

DA Task~ No. LH6-22O1-AO05 6 -13.

Us S. aRm ELECTRONICS CONMANDFORT moNmuT1{ NEW JERSEY

fWS~ytRIUyjiON STATEMENT (1)

.1..ang sale. its ditstobutiofl Is unillmIfted

ABSTRACT

Various forms of broadband transmiosicn linie transformers for use

through VHF and concepts basic to their opeLzAon are suanwarized and

described. Broadband power adding and power dividing iyt rids for push-pull

amplifiers and parallel additive uses are given rtAm±lAr attention. Me

design of broadband input and output matching elements for a single-ended

stage using a 2N5071 transistor for 30 W of output power from 30 to 80 1Mz Is

illustrated. Useful curves for guiding the design of 4:1 transforre vith

resistive loads are given. Curves showing typical input imedance veu

frequency of a pair of cascaded 4:1 transformers loaded by the large-sigal

R-L-C equivalent input circuit of the 2N5071 are included. The use of by-

brids to operate a pair of these treArsistors in push-pull operation is

described.

ii

CONTENTrS

INTRODUCTION I

SURVEY OF SOME POPULAR FROADPAND TRANSMISSION LINE COMP•rFNTS 1I

The 4:1 Impedance Tranuformer I

Upper Frequency Cutoff Factors ILow Frequency Cutot'f Factors 2

Higher Ratio Impedance Transformers 3

Broadband Power Adding and Power Dividing Networks 3

Zero Degree Hybrid 41800 Phase Hybrid 4

APPLICATION OF BROADBAND TRANSMISSION LINE STRUCTURES TO THE DESIGN OFUNMTUED BROADBAND RF TRANSISTOR AMPLIFIERS 5

- SINGLE-ENDED RF POWER STAGE DESIGN 5

Output Matching 5Measurements 7"Input Matching 8

PUSH-PULL DESIGN 10

Output Matching 10Input Matching 10

CONCLUSIONS 10

ACKNOWLEDGEMENTS ii

REFERENCES 11

FIGURES

1 1. 4: Transformer (a) Autotransformer analogue; (b) Equivalenttransmission line form; (c) Pictorial representation ofconstruction using twisted pair transmission line; (d) Actualunits of twisted pair, strip, and coaxial transmission line. 12

2. 9:1 impedance transformer; (b) 16:1 impedance transformer. 13

3. Broadband hybrid for power adding or splitting of In-pnasesignals. 14

iii

Page

4. Broadband hybrid for power adding or splitting signals1800 out of phasej (a) Normal balanced conditions forpower adding (PIN = PIN2); (b) Severe mismatch operationfor power adding (PINI m EI, PIN2 o 0). 15

5. Normalized input resistance RIN at the low impedance portof the 4:1 transformer with real load RL versus length oftransmission line in wavelengths for various values ofcharacteristic imrdanr• -, 16

6. Normalized input reactance XIN at the low impedance portof the 4:1 transformer with real load RL versus length oftransmission line in wavelengths for various values of

characteristic impedance ZOO 17

7. Phase of input impedance at the low impedance port of the4:1 transformer with real load RL versus length of trans-mission line in wavelengths for various values of charac-teristic impedance Zo. 18

8. Insertion loss of the 4:1 transformer with real load RLversus length of transmission line in wavelengths forvarious values of characteristic impedance Zoo 19

9. Curves comparing measured and calculated insertion lossfor a 4:1 transformer with real load RL versus length of"tranemission line in wavelengths for several values ofcharacteristic impedance Zo. 20

10. Calculated and measured curves of input resistance R(at the high impedance port of a 4:1 transformer with

transistor load) versus frequency for various lengthsof transmission line with Zo = 12A.. 21

11. Calculated and measured curves of input reactance XINI(at the high impedance port of a 4:1 transformer withtransistor loal) versus frequency for various lengthsof transmission line with ZO W 12A. 22

12. Input resistance RINI (at the high. impedance port of a4:1 transformer with transistor load) versus frequencyfor various values of characteristic impedance Zo.(Line length constant at 2.5 in) 23

13. Input reactance XIN1 (at the high impedance port of a4:1 transformer with transistor load) versus frequency forvarious values of characteristic impedance Zo. (Linelength constant at 2.5 in) 24

iv

Si i I I I [ . . . . . . .

PRge

14. Curves of input resistance RIN2 and phase of input

impedance ZIN2 (at the high impedance port of two •cascaded 4:1 transformers with transistor load)versus frequency. 25

15. Block diagram of the 30 W, 30-80 MHz power amplifier'with input and output matching transformers. 26

16. Basic schematic for a pair ot 2N5071 tru.-si.torsoperating in a broadband push-pull amplifier with1800 phase hybrids for power splitting and poweradding. 27

V Tj

INTRODUCTION

In the past few yenrs F power transistors have attained performancelevels which have made them attractive for implementing many solid-statetransmitters intended for military and commercial communications. Many ofthese applications are for selective frequency operation over one or morefrequency bands, a band being typically between 0.4 and 0.8 of an octave inbandwidth. With modern trends stressing minimized tuning operations, theuse of untuned bro-IT-d interstage and output matching networks has be-come popularly sought. The most suitable broadband impedance matching net-works in the realm of lumped components, applicable from LF into UHF, havebeen broadband transmission line transformers and baluns of the type ori i-nally proposed by GuanellaI and more recently expanded upon by Ruthroff.§

Short lengths of transmission line (parallel strip, coaxial or twisted pair)provide upper frequency capabiliLy free from normal transformer interwindingresonance limitations. High permeability materials, such as ferrites ex-tend the lower bandwidth capabilities. Though the concept of these broad-band transformers is not new, to date little analysis of their two-port.parameters as a function 6f frequency, or transmission line length andcharacteristic line impedance has been available.

SURMEY OF SOME POPULAR BROADBAND TRANSMISSION LINE COMPONETS

The 4:1 Impedance Transformer

The 4:1 transmission line transformer is a popular element for impedancematching a single-ended source to a single-ended load. A close analogueamong conventional transformers is the autotransformer with a 21 turnsratio as depicted in Fig. la, showing a load RL transformed to kL at the in-put. IT

The transmission line counterpart is shown schematically in Fig. lb.The transmission line provides excellent coupling of the magnetic andelectric fields. This ensures a minimum of leakage reactance over the use-ful frequency range of the line. With conventional windings, interwindingcapacitance limits the performance at high frequencies. Between transmissicline conductors, the uniformly distributed capacitance acts harmoniouslywith series distributed inductance to give reactance free operation overbroad frequency range.

Upper Frequency Cutoff Factors

The transmission line transformer has upper frequency limitations re-lated to the length of the transmission line in wavelengths and to the ratiobetween the characteristic impedance Zo of the line and the load Jmpedanc(.In most cases, the length of transmission line is chosen to be X/8 or lersat the uppermost frequency desired. The optimum match is Zo = , L for 't+,down of a purely resistive load and Z0 = 2 RL when the transformer is beingused to step up the load from RL to RE. As expected with transmisslon ri c

matching, the shorter the physical length of the line in wavelength.: theless important exact matching becomes. The interconnection of the trans-mission line is important in keeping with the two general matching princl-

pies for a flat line: 1) The voltage between conductors must be maintainedconstant as a wave propagates from the input until it reaches the load.This is illustrated in Fig. lb by the voltage E, between pcints . and 3 atthe driven end and also at the load end between points 2 and 4. Differ-ences in the signal path length to corresponding points along the line causephase differences increasing with frequency. Such phase differences in the4:1 connection (not typical of normal matched transmission line) deter-mine the final bandwidth capability of the transformer. 2) For a currentflowiag in one conductor (i.e., 1/2 flowing from 1 to 2), an equal currentin the opposite direction should exist in the other conductor (i.e., 1/2flowing from 4 to 3).

Low-Frequency Cutoff Factors

Transmission line transformers have a low-frequency cutoff determinedby the falloff of primary reactance as frequency is decreased. This re-actance is determined by the series inductance of the transmission line con-ductors. Therefore, the longer the length of line, the greater the seriesinductance, extending performance to lower frequency. This Is in directconflict with extending the upper frequency performance which, as previouslystated, is enhanced by shortening the physical length of the tranismissionline. Minimizing the overall length consistent with achieving the suitablereactance for low-frequency requirements can be accomplished with bAgh per-meability materials such as ferrites. Inductance of a conductor is dLrectliproportional to the relative permeability of the surrounding medium. A highpermeability material placed close to the transmission line conductors actson the external fringe field present and can magnify the inductance appre-ciably and thereby provide a lower cutoff frequency. There is no influenceupon internal magnetic fields nor upon the characteristic impedance of theline. The power transferred from input to output is not coupled throughthe ferrite material, but rather through the dielectric medium separatingthe transmission line conductors. This is an important concept for design.Relatively small cross-section ferrite material can perform iunaturated atimpressively high power levels. In contrast to this, conventional trans-formers couple power from primary to secondary entirely through a highpermeability core which must be chosen to suitably carry the total powerwithout saturating. Figure lc illustrates a popular construction for a4:1 transformer using twisted pair wound on a ferrite tcrcid. A basic ad-vantage of this construction is the ability to mirnimize the length of theinterconnection from point 1 to point 4. Figure id is a photograph ofseveral 4:1 transformers made in this manner. The larger In the upper rowhave windings from 3.5 to 4.5 in. long. The transformer at the upper leftuses a loosely twisted pair of number 20 formvar coated transfcrmcr wirehaving a Z. = 504J. The middle unit is twisted of two bifilar w.ndings ofnumber 26 formvar wire for a Zo = 204. The unit at the u•Ter right I,constructed of homemade strip transmission line. Flat formvar transformerwire about .10 in. wide paired together with contact bond cement, 171 vo-Zo = 10L. These transformers havc each carried 100 W t-f KRF •0•r w• cut

saturating the fen-its cores. With properly matched res1-ttv -ond thave less than 0.1 dB insertion loss at an upper frejueny zf .Yo M!7 -ni rlower frequency of 2.0 MHz. The lower two transformerns Pre __n-truc'i w÷tsmall toroids and have 2.5 in. lengths of tru.nsmissUoi li::1 wcu I . ,•,t tt1em.The transformer at the lower right uses RG-196 (504. c(vxial Uire) with the

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F-igu.r'e Inb shown the noxt logical extension ot the 91l, One additionallength of trunsmieeion line is employe to aHhieve a l6ae impettnae thnes.former, T moe geneoal winding asnproah may be obsried from Fig, ft aend band sxtens.4 to hbig r o e ration by induction.

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fU (4)____

flroixtiand Dcovr Addin ad 4 P r Di viclig Network

It i. troquently necessary to utu two or more transistors to attain someoutput power Iseyond that of any available single device, Broadband power.A.ding and dividing can be nicely accomplished with hybrids constrnutedsimply as transmission line structures. Hybrids permit swumming the pawerfrom two or more sources with insignificant interaction between the individ-Ual sources. The hybrid provides excellent isolation between the inputports when separate souroes of power' are to be added (or alternately isola-tion between two output ports acting as separate sources when power split-t.ing). The input Impetlnce (or outpuit Impedance in the alternate case) aton3~ port remains essentially invariant regardlessi of conditions of an opencircuit or a short circuit at the second port., Obviously, such character-istics will effectively eliminvite ohnin type rallures conmon in multipletransistor output stagee with trnnelstors directly paralleled at their out-puts.

A hyltritl on It* %toiot eot ' "Ai 06 otvreili pihann tyro forr it4tlnX In.put* w~itfih IPP %poimatoly W~ 10nso, Mlmtsiit14,1 It will dall o% stngWoInput Into two Identtlm Ii1.p0%pme Nmulr'psI

Ituthlror' ihpoorlt,,o Aor.o t t pslt~ro, p~hno hybriti., Floiro 11 Illus.

tlktta Adhohttloklly Itn 1•1t•niemlatlti Ul to%" on. O•ulh hyhbrla t',a,,th.r withvoltA.e, Our,,4nt uid Inmpeloeo relationilitra. The omcponent 1%, im phlaoR1resistor vhioh ilstipto, non-.ddabble Input power, •its wuste pover to ro..lattki to phipe t11A/or amplAtude dlfferennei betw.et% the uignsala ot ports Iand Fo er the extreme Oatt* where one port I# open situate, t or Short jir-uult4* on•e hal ato the total Inpi* pA wer 1'rima the other port. Im 4MtsuaitedIn hr Wnt half Is lelgverpi to th'o lo Ite.

The push-pull operttion of two power tranatlntore in ofton desirablo Inoutput st~qes. Push-pull usually reduce# the second harmonic output powerby about 8 0 ovir single-endod stages# thereby easing the demande for aso.ond hmarmoni r.jvttoton in the low peas* output filter*

The 1800 phase hybrid affords all the virtues of isolmtion between ad.Jacent ports, described previousap plus 1800 phase splitting (or an addingfor two signals 1800 out of phase).

Figure la Illustrates the interconneotions nnd noperaitng rlatiornshipsfor a 180 rhames hybrid being used for power adding. Figure 4b shown thevoltage and ourrent relations when one part ti either open or short•d. Ascan be noted# under this •O•d•itionp one-half of the Input at the worItingport to dissipated in lN. In general for this hybridiQ

P1 *

Pher,: Pout V- -l 21 con (

Pout a power into the load R1.

P3 W power into port 1

P2 - power into port 2

0 M phase angle between signals at ports I and 2.

When used for power splitting, tbis hybrid will contribute equal outof phase power to each transistor load. If one load is open circuited,short oircuited or in general diasimilar from the alternate load, the inputdrive to the alternate load will remain unchanged. This is controlled by ekchange in impetlance at the input port.

With Zo - RL, the length of the series output line section is unim-portant since it performs as a simple length of transmission line terminatedin its characteristic impedanice. With very low values el' load impedance itIs impractical to exactly match Zo to RL; the length of this section must bemaintained quite short relative to N/8 if reactive effects due to mismatchare to be avoided.

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ltensive charactv,1znt1•n or the h:2, trainformer will be deveribed ns

part of this design.

MNOL3-.MMED I• POWER STAGE DES3ION

Matohing for power transistor otnges consinto of (.) Converting some fix-ed real antenna load to the appropriate load line for the final power ntagesuah that some specified power output can be realized with good efficiencyat all operating froquenoiesj and (2) tnterstage matohligp which requirestransforming the reactive low input impedunce of a transistor into a suitableload line for the driving stage at all ope3ting frequencioe.

To demonstrate the design or broadband elements to accomplish matching,a tyVical power output stage vill be investigated. The transistor is a2N5071 operating from a 28 V d.c. supply. Operation is specified to be 30 Wof IR4B output power from 30 to 80 MIlz. The antenna load is 50D9..

output 1ate

T1h aftimum load line for produning 30 W of output power from thist-4i stor oen athin from 28 V d*c. ia l3IL to 15 A•. One 4:•1 transformer

step down the 50.4-antenna load to 12.5.0.. Equations for terminalimpedance of the 4:1 transformer can be derived from two Kirchoff loopequations for the circuit of Fig. lb solved simultaneously with the twogeneral defining ejuatione for voltage and current at Qe end of a loselesstransmission line. At the low impedance port (aj -M " i.ethe load isstepped down:

ZIN Zo 7; (6)

at the high impedance port (RIN W 4 RL) i.e.,,the load is stepped up:

1 I

(7L#

whore ZL is tho load impedano., 8 he. phase constant of the transmissionline in radians per unit length, and A. is the lotgth or the lines section.For the broad number of applications where the load impedanoe is purely re-sistive, normal11e deu•i~n curves can doearibe ZrN Re a funotion of fre.quenoy and length of line (in terms o7.L) and Rs a, funutlLon of Zoo

Figures 5, 6, and 7 display RI, XXN, and phase respectively, at the aovimpedance port (i.e,• transformer used for load atep down) ts a function oflength and, Z of the transmission line. The RIN and XIN value. can b6 un-normalized by multiplying by 1/4,. The various Z. values are simply relatedto RL as shom. The curves apply only to high-frequency cutoff effects anduse=*e nonexistence of low-frequency effo to. With Zo e*4ual to Zo optimum,ftN drops off gradually from a value of J, with increasing length of line

(i4e.,the equivalent of increasing frequency for a fixed length of line).An inductive XZX becomes apparent beyond 0.10 X. With ZO optimum the in-ductive character of the input impedance is accented, The behavior closelyapproaches a fixed R-L serie@ circuit when Z. is Zo optimum or greater.With Z values less than Zo optimum, the input impedance behaves as a paral-lel R-0 circuit.

Figure 8 shov curves of insertion lose as a function of line length forvarious values of Zo. Inuertinn loss is defined as the ratio of power intothe load to power available from a source E with internal resistance R9matched to the ideal RkN value of the translormer. It should be clearlyunderstood that the transformer is as internally lossless as the transmissionline comprising it. As typical of lossless filters, power transfer is de-termined by the variation of terminal impedance with frequency. There isinsignificant accuracy loss in assuming that real power into the transformerPIN equals real power into the load Pout* An expression for insertion losswith any generalized impedance ( A a gp 4j Xso ) represented at a partic-ular value of A is:

Pout R. RInsertion Loss w ot (8)

Pavailable ýL

where R-- the value of RN at o = gfoz load step down or

R w 4RL the value of R1 at j=o for load step up.

Note that in Fig. 8 pairs of Zo values, related by KZ, optimum andZQ optimum, where K can be any given constant, yield identical insertion

K

loss.For each of the curves described above the abscissa is given in wave-

lengths \ which allows relating units of length and frequency for any de-sign case. Knowing the highest operating frequency fu in MHz and nextjudging from the chart the largest fractional part of a wavelength n,which afford.z RIN and X X within acceptable limits, the physical length of

6

line is given by: L • 7A00 K I.nhea.

This expression holds for linea conatructod with conventional dielectrics ofrelative dielectric oonstants ranging from 2.0 to 2.5.

The required minimiun length for the lower frequency cutoff requirementsshould next be examined. A consearvative empirical relation which holds quiteclosely is :

40~a Inches (o

where A~ Is the load roesistance (n ohZ'")jthe lowest operating frequency inM~z., aný e, the relative permeability of the ferrite at fSL' This expression"relates a Ingth corresponding to the input Impedance having a i0lto 150 in-ductive phase angle at fL when the transformer is terminated in a real loadRt, A typical ferrite for use at 30 MHz (e.g., Q-2 Ferramic) will have A/ of15, With RL.- 50 .9L., and f, - 30 MHz, equation (9) gives -. 2.08 in."Reference to the curves for the low Z port (Fig. 7) with Zo - Zo optimum254 1 at .08 A P Rin is about 6% down from the ideal 12.5 d- value and Xin isessentially zero.

Using equation (8) with f 4 - 80 MHz and n - 0.08 it follows that T1= 7.5in. Therefore, any length between 2.5 in. and 7.5 in. wound on a ferritetoroid will offer excellent performance. Arbitrarily let the choice be alength of 4 in. It is apparent that for this frequency range of 30 MHz to80 MHz the design of the transformer is quite flexible. If the frequency"range were expanded (e.g., 2 M1z to 80 MHz the length determined from equation(8) would converge upon that of equation (9).

"The curves are very useful in other ways. For example, assume it to bemore convenient to use transmission line of Zo = 504.t. than the optimum valueof 25AL. At n = 0.08 and observing the Zo = 2 Zo optimum curves, Rin isalmost ideally equal to 1%or 12.5 .&, Xin is about 5 A. inductive. Theeffect of this value of reactance may be difficult to place in percpectivewhen attempting to estimate performance. The insertion loss curves of Fig. 8will be useful for this. Note that at 0.08 A on the Zo = 2 Zo optimum curvethe insertion loss is less than 0.2 dB. This gives more specific meaning tothe effect of the 54.•inductive reactance. Figure 9 illustrates the outputmatching circuit in block diagram.

Measurements

To verify calculated resulte measurements were made over a frequency rangeof 1 through 108 MH'z using an HP 4815A Vector Impedance Meter. A 9-in, lengthof RG-58 cable (Zo = 50 L and L= 0.25 A at 200 MHz) with outer insulationremoved was interconnected as a 4:i impedance step-down transformer. Ferritetoroids, CF 102 size of type Q-1 meterial, covered the entire transmissionline section. With this fixed Zo = 50-iLline terminated in RL of 50 4L.,lOOJand 200A-, the 0.5 Zo optimum, Zo optimum and 2.0 Zo optimum conditionswere simulated. Measured and calculated insertion loss with frequency are

7

compared in Fig. 9. Differences between measured and calculated were lessthan 0.2 d3 at 100 MHz for the 0.5 and 2.0 Zo optimum conditions. The Z0optimum simulation gave performance hardl7 distinguishable from the theoret-ical from 10 to 108 MHz.

The measured curves evidence low frequency effects. As apparent fromequation (9) low frequency cutoff is a function of the load impedance, thelength of the ferrite covered section, and the permeability of the ferrite atthe lower frequencies. The lower 1 dfl frequencies were 1 MlIz or less.

Input Matching

The broadband input matching of the transistor is considerably more diffi-cult than the matching at the output. The transistor base input is a lowimpedance which makes it impractical to select the value of characteristicimpedance considered optimum for the transformer. The input impedance appearsto be an R-L-C series circuit from 30 to 80 MHz. Larga-signal base inputimpedance measurements of this transistor at 30, 40, 60, and 80 MHz indicatethe resistance RH - 2A.-, the inductance La = 3nH and the capacitance Cb =2500 pF. The L is due to parasitic lead inductance in the transistor pack-age plus any contributed by circuit interconnections. Extreme care in circuitconstruction is required to minimize this series base input inductance. Thisinput circuit is resonant at about 58 MHz and has a Q = 0.55. Minimized in-put Q is desirable for transistors intended for broadbanding. Figure 15depicts the transistor input circuit.

Universal design curves for the 4:1 transformer, with -vrious reactiveterminations, are not practical, but design attitudes evident from this ex-ample are applicable to other transistors and other frequency ranges. Theequations (6) and (7) can always be applied to any particular design situation.

Some general 4:1 transformer characteristics apparent from Fig. 6 and 7with real loads may be used to guide design attitudes. The transistor inputimpedance is inductive above 58 MHz. The design curves for reactance at thehigh impedance port suggest that the use o: low Zo (i.e., Zo optimunm or less)would lend an increasingly capacitive phase with frequency. This would off-set the increasingly inductive attitude of the transistor input impedancn withfrequency. Unfortunately, this specifies Zo values from 1 to h.IL. Suchunusually low values have been achieved with homemade coaxial and strip trans-mission line, but have not been useful because of the unavoidably bulkyconstruction. The minimum interconnection lengths contribute parasitic in-ductance that more than offsets the improvements anticipated over higher Zolines with compact interconnections.

The lowest practical values of Zo are 10A0 to 12JtL. Assuming the use of12AL for design, the previous curves indicate that inductive reactance contri-buted by the transformer is minimized by minimum length. The smallest practi-cal construction length of transmission line with Zo = 12.L is about 2 in.Figures 10 and 11 show the variation of R#14 and XH, with Zc = 12 AN trans-mission line of lengths 2.0, 2.5 and 3.0 in. The differences in performanceare seen to be relatively minor. These curves were developed from computercalculations using equations (7) with Z1 being the transistor input impedance.

8

The transistor input. was cnrefully simulated with z ' L carbon resistor,three leadless capacitor chips totaling 2500 IF with in~rconnecting induct-ance of 3 to 4 nrl. The dotted curve shows measured performance for a 4:1transformer constructed with a 2. 5 in. length of Zo = 12J. line. The trans-former was identical in structure to the strip line unit at the lower rightof Fig. Id. Measurements for these curves were made vith a HP 4815A VectorImpedance Meter. Corrections must be made in low impedance measurements toaccount for the parasitics in the probe. These values are typically resist-ance of 0.6-4Land inductance of 12 to 15 nH in the probe. The exceptionallyclose correlation of measured and calculated curves emphasizes that thecalculated values for these transformers are reliably accurate in predictingperformance.

Curves of calculated R•gI and XwNg for various values of Zo with linelength fixed at 2.5 in.are shown in Fig. 12 and 13. These calculations donot include the effects of parasitic series inductances. It is 11kely thatlarger parasitics would accompany the lower Zo values thereby nullifying muchor all of the slight performance edge indicated by the curves.

It is always desirable to maintain an operating load line as purely resist-ive as possible. Where this is not possible best stability often favorscapacitive rather than inductive reactance. Asstming this to be true, theaddition of a parallel capacitor added as shown at point 1 in Fig. 15 canmaintain effectively the phase of Z 111 capacitive over the entire 30 to 80MHz range rather than growing increasingly inductive about 50 MHz. For zerophase at 80 MHz:

ifvhere 44 X 1• 1 , and R1f1 are determined at 80 MHz. This gives C close to100 pF. The use of a variable capacitor would allow trimming to the fixedvalue for the best overall operation. The cascading of an additional 4:1transformer to step up Z1#1 paralleled by the capacitor gives an input Zjgz.at point 2 as shown in Fig. 15.

The large-signal dynamic swing of a transistor stage is limited &, avail-able voltage. For this reason load lines are conventionally represented bythe equivalent parallel resistanci for partly reactive loads. Real outputpower can be defined easily by YP/ where R1 is the equivalent parallel loadresistance.LL

R, .L represents the equivalent parallel resistance looking in at point 2.Figure 15 gives a clear representation of this. Figure 14 shows the behaviorof R11 • and the phase of Zp• with frequency for two values of Zo. The trans-mission line length is 2.5 in.A Zo of 8AI gave results hardly distinguishablefrom the 16-A value plotted. From Fig. 14 the better choice of Zo is the16.Avalue which produces the smaller overall variation in Re1j. and phase.These variations must be accepted as a consequence of the low impedance R-L-Cinput of the transistor. The use of the capacitor has preserved the non-inductive character of this load line.

If the efficiency of the driver stage is critical the value of this load

line (between 32 and 40-.D) is somewhat low. An additional 4:1 transformer

9

kI

would give a load line resistance too large to develop sufficient drive powerfor the output stage (I,,- 4 watts). The use of a 9:1 transformer in placeof the second 4:1 between points 1 and 2 would be suitable. The resultantload line would have very similar trends to Fig. 14 but with the approximateresistive value between 72 and 90-&.. This load line would permit deliveringthe 4 W of input power to the 2N5071 transistor at good efficiency.

PUSH-FULL DESIGN

Assume it is desired to operate two 2N5071 transistors for an output powerof 60 W. Two 1800 phase hybrids as previously described are necessary; onefor splitting single-ended input power source into two out of phase sourcesdriving the transistor inputs, the other for adding the outputs from the twotransistors. Figure 16 shows a typical arrangement.

Output Matching

The output matching offers no particular problems. Assuming the antennaload to be 50.Lit must be partially transformer 2:1 by the low-pass filterto either a 25-A or 1004Lvalue for efficient output matching. Figure 16shows the load as 25A. . The hybrid can easily be constructed with the opti-mum values of Zo as indicated. Under the conditions shown each transistoroperates into a 12.51. load line suited to 30 W output power from each. Thetransmission line lengths are not critical. A length of 4 in.for each wind-ing is adequate.

Input Matching

The input hybrid is conistructed of the lowest practical characteristicimpedance line Zo = 12. 5•4. The shortest practical length of 2.5 in.willminimize mismatch effects. During push-pull operation one transistor is con-ducting while the second is biased off. The conducting transistor has a lowimpedance as described previously. The off transistor appears as a relativelyhigh impedance due to the reverse biased base emitter junction. This affectsthe impedance of the input port of the power splitter. With balanced loads ofRe = 24 Aeach the input would be approximately 4 11. However, with one outputport terminated in an open circuit the input impedance approaches three timesthis value. For transistor loads the input impedance is somewhere betweenthese extremes. Figure 15 indicates Rjg could be between 6 and lO..Ltypi-cally. The 4:1 transformer would step this up to a 25 to 40.-Oload line forthe driver. This is a suitable load line for developing 10 W of drive powerwith good efficiency.

CONCLUSIONS

A group of transmission line transformers and by brids useful for mitunedbroadband R' transictor amplifiers has been presented together with the funda-mental principles underlying their operation. Design curves and expressionsfor realizing predictable performance from 4:1 transformers terminated in re-sistive loads were presented. The typical behavior of RF power transistorinput impedance over the VHF range of 30 to 80 MHz was described. A means fortransforming this input impedance to a non-inductive load line was

demonstrated. Finally the push-pull power adding of two transistors through

the use of the 1800 hybrid was illustrated.

ACKNOWLEDGEMNTS

The authors wish to acknowledge the assistance of Mr. Dave Huisman for thenecessary computer programming for this work. Mr. Robert Horn and Mr. DennisBowman contributed noteworthy ideas and observations during the course ofseveral stimulating discussions.

PkWEPENCES

1. G. Guanella, "New Method of Impedance Matching in Radio FrequencyCircuits," Brrown-Boveri Review, vol. 31, pp. 327-329, 1944.

2. C. L. Ruthroff, "Some Broad-Band Transformers," Proc. IRE, vol. 47,pp. 1337-1342, August 1959.

3. W. Doherty and W. Hatley, "Broadband Transmitter Techniques," ECOTechnical Report Contract Number DA28-O4aC-OI829( E), April 1967.

4. D. R. Lohrman, "High Efficiency CW HF Power Amplifier," USAEC4Technical Report 2836, May 1967.

5. 0. Pitzalis and T. Couse, "Practical Design Information for Broad-Band Transmission Line Transformers," Proc. IEEE, April 1968.

6. H. M. Schlicke, Essentials of Dielectromagnetic lbaineering, N. Y.,Wiley, 1961.

7. W. C. Johnson, Transmission L-nes and Networks, N. Y., Mc Graw-Hill,1950.

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Secunty Classificatton

DOCUMENT CONTROL DATA - R & Dt'S..ureti closs JeaI tion of title, body of a.betrct and indehing ennotaflon muor be entered when the overall repot I/a classified)

I. ORIGINATING ACTIVITY (Coepeeete 4a4141# ) a,. REPORT SECURITY CLASSIFICATION

U. S. Army Electronics Command UNCLASSIFIEDFort Monrouth, N. J. 2b. .RouP

3. REPORT TITLE

Broadband Transformer Design for RF Transistor Power Amplifiers

4. OESCMIPTIVI NOTES (7•'pe of iseot ow,] .*nchwivo date*)

Technical ReportS. AUTNORIis) (First a•ain. mlje initial. lost nem.)

Octavius Pitzalis, Jr.Thomas P. Couse

0I. REPORT OATtE 7411, TOTAL NO. o0 PA^&C 76b. 0e. OF RrS

July 1968 27I 78. CONTRACT OR GRANT NO. SD. ORIGINATORI11 "4EPORT NUW4M9R(S1

6. PO.jeCT NO. lH6-2200l-A-o56 ECOM 2989

S . Task No. -01 Ob. OT-ER REPORT NIhos 'Any obt inre ,tt, -sy baeeisd

d. Subtask No. -13DISTRIBUTION STATEMENT (1)

This document has been approved for public

release and sale; its distribution is unlimited.

I I. SUPPLEMENTARY NOTES 12. SPONSOPING MILITARY ACTIVITY

U.S. Arqr Electronics CommandFort Monmouth, N. J. 07703Attn: AMSEL-KL-SS

IS. ABSTRACT

Various forms of broadband transmission line transformers for use through VHF andconcepts basic to their operation are summarized and described. Broadband power add-ing and power dividing hybridn for push-pull amplifiers and parallel additive uses aregiven similar attention. The design of broadband input and output matching elementsfor a single-ended stage using a 2N50T1 transistor for 30 W of output power from 30 to80 MHz is illustrated. Useful curves for guiding the design of 4:1 transformers withresistive loads are given. Curves showing typical input impedance versus frequency ofa pair of cascaded 4:1 transformers loaded by the large signal R-L-C equ.'valent inputcircuit of the 2N5071 are included. The use of hybrids to operate a pair of thesetransistors in push-pull operation is described.

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