Design technique for broadband microwavetransistor power amplifiers

K.L. Kotzebueand E.R. Ehlers

Indexing terms: Microwave amplifiers, Power amplifiers, Solid-state microwave circuits, Transistor circuits

Abstract: A technique for the design of broadband microwave transistor power amplifiers is presented thatutilises the powerful methods of network synthesis to achieve optimum large-signal performance. Only twolarge-signal transistor measurements per frequency are required to achieve a good analytic model of thetransistor's variation of added power with load impedance, and a mapping function is presented that trans-lates this added-power characteristic into an equivalent linear-circuit reflection-coefficient characteristic.With this representation, methods of linear-network synthesis are used to obtain circuits which optimise theamplifier's added-power efficiency over a broad range of frequencies. The design technique has been exper-imentally verified by the characterisation, design and construction of a b.j.t. amplifier of near-octave band-width centred at 1 GHz, with the large-signal performance in good agreement with that predicted by thedesign theory.

1 Introduction

Within the last few years, network-synthesis techniqueshave been successfully employed in the design of small-signal broad-band microwave amplifiers.1"3 Using thistechnique, a circuit is synthesised with a specified magni-tude of reflection coefficient over a band of frequencies,often with the reflection coefficient varying with frequencyin such a manner as to compensate for the transistor'sintrinsic roll off of gain at high frequencies. The endresult is an amplifier design of optimum gain-bandwidthproduct, achieved with little or no need for computer-aided search routines. This paper presents a similar tech-nique, which has been modified to apply to the case ofmicrowave-transistor power-amplifier design. In the case ofsuch large signal design, optimisation of gain-bandwidth isno longer the primary goal; instead, it is desired to optimisea large-signal quantity such as efficiency, output power, oradded power over the frequency band of interest. In thedesign technique presented here, emphasis is placed uponthe synthesis of output circuits which directly optimisethe amplifier's added power over a wide frequency band.The approach is to employ an analytic representation of atransistor's added-power characteristic as a function of loadimpedance ,4>s and to then map this into an equivalentreflection-coefficient characteristic, thus formulating theproblem in a manner suitable for the use of network-synthesis procedures. This design technique has beenexperimentally verified by the characterisation, designand construction of a bipolar-junction-transistor (b.j.t.)amplifier of near-octave bandwidth centred at 1 GHz,with a large-signal performance in good agreement withthat predicted by the design theory.

2 Transistor modelling

Transistor modelling for the purpose of broadband power-amplifier design involves the determination of the requiredload impedance for optimum large-signal performance atvarious frequencies, together with the determination ofhow the large-signal performance deteriorates as the loadimpedance departs from its optimum value. (This latter

Paper T351 M, first received 10th October 1978 and in revised form7th March 1978Prof. Kotzebue and Mr. Ehlers are with the Department of ElectricalEngineering and Computer Science, University of California, SantaBarbara, Ca. 93106, USA

MICROWA VES, OPTICS AND ACOUSTICS, MA Y 1979, Vol. 3, No. 3

information is necessary for broadband design because itis impossible to maintain the optimum-load terminationover a large frequency range.) Such a determination oflarge-signal performance under nonoptimum load con-ditions is the primary purpose of the experimental tech-nique of load-contour mapping.

Load-contour mapping is essentially the experimentaldetermination of transistor output power under manydifferent load conditions; however, if manual load-contourmapping is employed, the procedure can be tedious andtime consuming, since a large number of measurements arerequired, and if automated techniques are used, extensiveand complex test equipment is involved.6 In Reference 6 itis stated that if only three frequencies and three outputpower levels were used, more than 300 measurementswould have to be made for every device. Based upon ourexperience, each of the measurements could take up to30min when using a conventional measurement scheme.Clearly, there is great incentive to investigate alternativeapproaches which offer the possibility of less time con-sumption in the characterisation of the large-signal behav-iour of microwave transistors. In this paper, such an alterna-tive approach is used, and it is experimentally shown toyield a good large-signal characterisation with only twomeasurements per frequency required. Thus, only sixlarge-signal measurements are required to characterise thetransistor at three frequencies, instead of the 300 measure-ments suggested in Reference 6.

Quite apart from considerations of time, it would bedifficult to apply network-synthesis techniques to a large-signal design based upon a conventional load-contourcharacterisation for the following reasons:

(a) The load-contour approach yields numerical dataonly; a curve-fitting procedure would have to be im-plemented to arrive at a suitable mathematical represen-tation of the numerical data.

(b) The load-contour data, even when represented insuch a mathematical model, is not directly usable since thedata involve large-signal parameters such as power output,whereas the synthesis procedure specifies a small-signalquantity such as a circuit reflection coefficient. The transis-tor characterisation used in this study overcomes these twodifficulties. A mathematical representation of the large-signal behaviour is employed, and a mapping procedureis developed which translates the large-signal propertiesinto an equivalent linear reflection-coefficient characteristic.

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0308-6976/79/030121 + 07 $01-50/0

In the conventional load-contour mapping technique,loci of constant-output-power load impedances are ob-tained for a fixed incident input power, and quite oftenthe transistor is operated under selfbias conditions; incommon-emitter operation the collector is held at a con-stant bias voltage, and the base is returned to earth throughan r.f. choke, with biasing of the base-emitter junctionaccomplished entirely by rectification of the input r.f.signal. This mode of bias is commonly referred to as 'classC operation, although it should be noted that such adesignation should not be taken to imply highly nonlinearoperation of the output port of the transistor. Harrison,7

for example, shows a computed case of such an amplifier.The internal collector current is shown to be nonzero overa full cycle of operation, with a near elliptic dynamiccollector load line, which implies near linear behaviour ofthe collector port of the transistor. Leighton et al.,8 alsocomment on the suitability of linear analysis for class Coperation. The load-contour mapping procedure itselfwould be inaccurate if the output of the transistor were tobe operating in a highly nonlinear fashion, for then theeffects of harmonic terminations would be significant. Theload-contour mapping technique ignores such harmoniceffects, and useful results are, in fact, still obtained.

This approximation of near linear behaviour of theoutput port of a 'class C microwave transistor under large-signal operation is not valid at low frequencies (low com-pared to /T, for example), as it is well known that theefficiency of a low-frequency selfbiased transistor amplifier(the conventional class C operation) is highly dependenton the value of the load impedance at harmonic frequencies.One basic difference between the low-frequency case andthe high-frequency case may be summarised as follows. Atlow frequencies, the gain is high, small signals are presentat the transistor input port, and saturation occurs primarilyas a result of the clipping of the large signals present at theoutput port. At high frequencies, the gain is low andlarge-amplitude signals are present at the transistor input.Because of this low gain, saturation effects will occurfirst at the input, while the output voltage is below the levelnecessary to generate significant additional nonlinearity.

In the design procedure reported here, fixed-bias oper-ation is used; under common-emitter operation both thecollector bias voltage and collector bias current are heldconstant, even in the presence of large r.f. signals. Thismode of operation is similar to 'class A' operation, althoughsuch a designation for the case treated here should notimply that only small r.f. signals are involved, or thatsaturation effects are excluded. As with selfbias operation,harmonic effects may be neglected under fixed-bias oper-ation if the frequency of operation is sufficiently high.Fixed-bias operation is used as the basis of the designprocedure reported here to reduce the degrees of freedom,and to make possible the use of a linear circuit theorypreviously developed for the design of microwave transistorpower amplifiers.4'5 Because of this bias constraint, thedesign method is not rigorously applicable to selfbiasconfigurations; however, the experimental results to bepresented indicate that this method can, in practice, alsobe useful for the design of such selfbiased broadbandpower amplifiers.

The transistor modelling procedure used in this study isin some respects the conceptual equivalent of the load-contour mapping technique, but instead of experimentallyobtaining contours of constant output power, this pro-

cedure uses analytic techniques to calculate contours ofconstant added power. Added power, which is the differ-ence between output and input r.f. power, is felt to be ofmore fundamental importance for transistor characteris-ation than total output power, since the added powergives only the r.f. power contributed by the transistor,whereas total output power also includes the power con-tributed by the input r.f. signal source. In a typicalmicrowave-transistor power-amplifier stage, where powergain is low, the use of total output power can give a toooptimistic picture of a transistor's performance. Forexample, an amplifier with an output power of 10 W at apower gain of 3 dB has an added power of only 5 W, withthe remaining 5W supplied by the signal source. The addedpower of an amplifier will typically reach a maximum valueas a function of r.f. drive, and will decrease as the r.f.drive is increased further. This condition of maximumadded power indicates the optimum utilisation of thetransistor as a power amplifier. The total power output willusually continue to increase with increasing r.f. drive, butan ever increasing percentage of this output power will haveto come from the signal source itself.

The full application of the linear circuit theory of poweramplifier design presented in Reference 4 requires thecharacterisation of the transistor by a set of large-signal^-parameters at each frequency of interest. This completecharacterisation, however, is not required for the designmethod used here. In the interests of minimising thenumber and complexity of the required large-signal measure-ments, no large-signal ^-parameters are measured. Instead,direct measurements are made of the maximum addedpower at several frequencies and load terminations ofinterest. These measurements can be made by the standardtechnique of optimising tunable test amplifiers, and thendisassembling and evaluating the resulting terminations;alternatively, the 'active load-pull' method described byTakayama9 can be used to make these evaluations withoutthe need to build test amplifiers. The maximum-added-power performance of the transistor under an arbitrarynonoptimum termination is then modelled analyticallyusing the results of the theory presented in Reference 4.In this way, the number of experimental measurementsis greatly reduced, and the large-signal performance ofthe transistor is characterised in an analytic form.

The procedure used to translate the transistor's added-power performance into a form suitable for use in networksynthesis is to compare the theoretical added-power con-tours in the _y-parameter representation presented inReference 4, with an analogous representation of circuitreflection loss with respect to the optimum load for maxi-mum added power.

The equations for circles of constant added power, asgiven in Reference 4, are repeated below in a normalised^-parameter Linvill plot set of co-ordinates (x,y):

centre of circles x0 = —

radii of circles r = 1 +

y0 = 0 0)

~Pc

1/2

(2)

where pa is a normalised added power defined in Reference4.

122 MICROWA VES, OPTICS AND A COUSTICS, MAY 19 79, Vol. 3, No. 3

The analogous representation for circles of constant reflec-tion loss, with respect to the optimum load for maximumadded power, is given by Reference 10 as follows:

ILcentre of circles x0 =

1 - (1-1//L)

radii of circles r —. - - I 11-

yvi

l -

(3)

(4)

where IL is the 'insertion loss' (actually a reflection losswith IL > 1 for passive loads) which results from an outputmismatch with respect to the optimum output load.

The two sets of circles are not the same; physically thismeans that a termination which yields an 'insertion loss' of3 dB does not yield added power which is 3dB below thebest value of added power. Moreover, the two sets of circlesare not concentric, which means that the relation betweenIL and added power is a function of the phase angle of theoutput termination reflection coefficient. This phasedependence, if significant, would mean that conventionalinsertion-loss synthesis techniques could not be used sinceonly the magnitude of the reflection coefficient is specified.However, if [y2l | > 4[y12|, the two sets of circles becomenearly concentric and the phase dependence diminishes;fortunately, this condition is almost always satisfied inpractice for both microwave power b.j.t.s and f.e.t.s. Whenthis approximation is justified, a simple relation betweenIL and the resulting decrease in added power can be derivedas follows:

IL{Gp-\)Gp -IL

(5)

where Gj. is the large-signal operating power gain at maxi-mum added power with the optimum load termination,IL is the output circuit reflection loss, and ILA is thenormalised change in added power which results. A plotof eqn. 5 for various values of Gp is shown in Fig. 1.

Under these conditions, it is a straightforward procedureto draw circles of constant added power on a conventionalSmith chart. The circles are the usual constant reflectionloss circles 'centred' about the optimum load impedancefor maximum added power. However, eqn. 5 must beemployed to provide the proper specification of the re-

£5 2

1

co KWB6dB

Gn=3dB

0 1 2 3 U 5 6 7decrease in added power, dB

Fig. 1 Relation between output reflection loss IL and resultingdecrease in added power ILA as a function of parameter Gp

duction in added power below the maximum value. Forexample, if the maximum added power for the optimumtermination is 1W, and the operating power gain is 3(or 4-8 dB), and if an output circuit is used with a reflectionloss of IL = 2 (or 3 dB), then eqn. 5 predicts ILA = 4(or 6 dB), which yields an added power of only \ W.

This method of large-signal characterisation was exper-imentally investigated using a b.j.t. rated at 1 W outputpower at 1 GHz (CTC D-28Z). Although this transistor isnot representative of the current state of the art, relativelyprecise measurements can be conveniently made at thisfrequency and power range. The transistor was operatedunder common-emitter, fixed-bias conditions with Ic —100 mA, KC£ = 20V. For the purpose of verifying theaccuracy of the analytic approach to large-signal character-isation, a relatively large number of measurements weremade at 1 -3 GHz. Power-output/power-input data weretaken for a variety of load terminations, and the maximumvalue of added power at each termination was determined.The results of this experimental investigation are plottedin Fig. 2. It should be noted that each measured point ofadded power shown in Fig. 2 represents the maximumadded power obtained for a particular load termination,and that, in general, different r.f. drive levels are requiredfor different load terminations. This is in contrast withmore conventional load-contour data where the input r.f.drive level is held constant.

Fig. 2 Comparison of measured maximum-added-power character-istic of test transistor at 1-3 GHz with analytic model

Model based on eqn. 5, with Gp — 1-65Experimental datao maximum added power• — 1 dB below maximumA —2 dB below maximumA — 3 dB below maximum

The theoretical model used to predict the added-powercharacteristic at a given frequency for an arbitrary loadtermination requires only a single measured point at theoptimum load termination which yields the highest valueof added power; in practice however, we are interested inthe maximum added power for each load termination. Ithas been determined experimentally that the results of thepreviously developed theory can be used for the case ofsuch maximum added power if the value of the parameterGp is selected on the basis of a second measured point at anonoptimum termination. The measured point at the

MICRO WA VES, OPTICS AND ACOUSTICS, MA Y 1979, Vol. 3, No. 3 123

optimum load termination is used to establish the 'centre'point of the characterisation as depicted on a Smith chartor reflection-coefficient plane, and the measured pointunder a nonoptimum termination is used to select thevalue of Gp to be used in the mapping function, eqn. 5.In the example shown in Fig. 2, Gp = 1-65 was selectedto yield a fit between the analytic model and the measureddata at an added power 3 dB below the maximum value.

The circles shown in Fig. 2 are conventional constantreflection loss circles drawn on a 50 £2 Smith chart,10

but the mapping function, eqn. 5, has been used to 'relabel'the curves in terms of the relative decrease in maximumadded power. Thus the outer circle, which represents a3 dB decrease in maximum added power, is a circle of0-95 dB reflection loss, as determined by using Gp = 1-65in eqn. 5. (This example illustrates the experimentally-observed phenomenon that a transistor power amplifiermust be 'well-matched' at the output for good large-signalperformance.) All three circles drawn in Fig. 2, which arefor values of ILA of 1 dB, 2 dB, and 3 dB, use the samevalue of Gp, illustrating that the simple analytic modelpredicts with good accuracy the maximum-added-powercharacteristics of the transistor, using a minimum of twomeasured points at each frequency. These circles of con-stant maximum added power, which are analogous to thecircles obtained from load-pull measurements, need not beconstructed when using the circuit-design approach to bedescribed next.

3 Circuit design

In the case of broadband power amplifiers, it would bedesirable to 'match' perfectly the output circuit overthe operating frequency range so that added-power ef-ficiency could be maintained. However, such matchingover a large range in frequency is not possible in the pres-ence of reactance, and some decrease in efficiency must beaccepted to achieve a wide frequency range. The centralfeature of the design approach used in this study is a'mapping' of an amplifier's large-signal maximum-added-power characteristic into an equivalent linear circuit mis-match problem through the use of eqn. 5, making availableto the designer of such power amplifiers all the procedureswhich have been developed for small-signal broadbandamplifier design.

One design method which can be used for this purposeis described in the work of Mellor and Linvill.2'3 In thisdesign of small-signal amplifiers, an impedance-matchingnetwork is synthesised which yields the best possible gainover a band of frequencies; when adapted to the case ofpower amplifiers, a similar impedance-matching networkis synthesised which yields the best added-power efficiencyover a band of frequencies. The procedure may be outlinedas follows:

(a) From the results of the experimental measurementson the transistor, an output-circuit model is derived whoseimpedance over the frequency band of interest is a close fitto the complex conjugate of the measured terminationswhich yield maximum added power.

(b) A design decision is made regarding an acceptablevariation of maximum added power with frequency. Twocommon possibilities are:(i) accept a constant percentage decrease in maximumadded power across the band (this corresponds to a uniformmismatch across the band)

(ii) accept the minimum decrease in maximum added powerat the high end of the band, and design for a constant valueof added power across the band (this corresponds to anincreasing mismatch with decreasing frequency). These twopossibilities are illustrated in Fig. 3.

(c) The variation in maximum added power ILA whichis considered acceptable is translated into an equivalentinsertion loss IL variation with frequency through the useof eqn. 5, using the values of Gp obtained in the exper-imental transistor characterisation.

(d) The techniques described in References 2 and 3 areused to synthesise a broadband matching circuit whichyields the insertion loss variation obtained in (c) when oneend of the matching circuit is terminated by the outputcircuit model of (a) and the other end is terminated by thedesired external load impedance (usually 50 £2).

As discussed in Reference 3, some cut and try iteration isneeded to ensure that the best insertion-loss function isbeing used in this step. If the proposed insertion-lossfunction is too optimistic a choice, the circuit will not bephysically realisable, although if the choice is too pessi-mistic, unnecessary additional reactance will have to beadded to the output of the transistor, and performancewill be less than optimum. The details of the synthesisprocedure are too lengthy to be included here, but theyare well covered in References 1, 2 and 3.

(e) With the output circuit of (d) constructed and inplace, the power gain and input impedance of the partiallyconstructed amplifier are measured at the required r.f.drive level. An input-matching network can then be de-signed to yield the correct input-power variation withfrequency. If flat transducer power gain over the frequencyband is desired, an input matching network is designedwhich has a sloped-insertion-loss characteristic that com-pensates for the variation of power gain across the fre-quency band of interest. This network is used for theinput-matching circuit.The amplifier bandwidth that can be obtained is determinedby the same factors as in the conventional small-signalnetwork synthesis approach; i.e. it is a function of thetransistor model reactance slope, or 'Q', the insertion-lossslope, the allowable insertion loss at the high end of theband, and the complexity of the matching circuits used.

maximum added power(matched condition)

frequency

Fig. 3 Schematic representation of two possible variations ofadded power with frequency as design objectives

a Constant mismatch with frequencyb Variable mismatch condition, constant added power with fre-quency

124 MICROWA VES, OPTICS AND ACOUSTICS, MA Y 1979, Vol. 3, No. 3

4 Experimental results

The 1 W b.j.t. (CTC D-28Z) described in Section 3 wasused in the experimental verification of the design theory.Two large-signal measurements were required at each ofthree frequencies to obtain the necessary transistor charac-terisation over an octave frequency centred at 1 GHz. Thesemeasurements gave a slope in maximum added power undermatched conditions of —2dB per octave (as shown inFig. 6), with Gp varying from 21 at 0-7 GHz to 1-6 at1 -4 GHz. By curve fitting the optimum load-impedancedata, the output circuit model shown in Fig. 4 was ob-tained.

It was decided to design the amplifier for the bestconstant value of maximum added power over the fre-quency band of 0-7—1-4 GHz. Using the experimentaltransistor data together with eqn. 5, it was determined thatan insertion-loss function with 1-0 dB per octave slope wasrequired for the output circuit. Since little insertion-lossslope was needed, the output circuit was synthesisedstarting from a maximally-flat prototype of octave band-

100A ±A6pF

Fig. 4 Experimental large-signal model of test transistor used forsynthesis of matching networks

50H r

50A

i i

input matchingnetwork

I I

output matchingnetwork

Fig. 5 Schematic representation of amplifier with synthesisedmatching networksC , = 3 - 8 p F C 2 = 5 - 3 p F C 3 = 4 - 5 5 p F/, : Z o = 50 SI, 6 = 1 8-8° at 1 GHz' • Z o = 87 SI, 6 = 1 5-2° at 1 GHz

: Zo = SO SI, 0 = 7-2° at 1 GHz: Z o = 87 0 , 0 = 18-0° at 1 GHz

Z o = 87 SI, Q = 2 7 1 ° at 1 GHz

31-

30

£29

I 28

•n 27

O26

§ 25X

t 24

23

i50'

30 o

20 a.

1007 08 0-9 10 1-1 12 13 U

frequency, GHz

Fig. 6 Experimental values of maximum added power of testtransistor for both optimum ('matched') load terminations andbroadband circuit based on Fig. 5, as compared with theoreticalresults predicted for this circuit

A optimised narrowband circuit (matched condition)o broadband circuit (experiment)

broadband circuit (theory)

Fig. 7 Complete broadband amplifier circuit

width with a midband insertion loss of 0-8 dB. Afterscaling to the correct frequency and impedance level, andreplacing the lumped-element inductors by transmissionlines, the element values were adjusted to yield the requiredslope of 10 dB per octave. This theoretical insertion losswas converted through the use of eqn. 5 into a corre-sponding variation of maximum added power as a functionof frequency. The output circuit element values are shownin Fig. 5, and the resulting theoretical maximum-added-

t power characteristic is shown plotted in Fig. 6. The actualcircuit was fabricated from a glass-reinforced p.t.f.e. dielec-tric microstrip using miniature chip capacitors and 5012and 87 £1 characteristic-impedance transmission lines forthe inductors. 2-section, £-wavelength lowpass filterswere fabricated on the microstrip for both the base andcollector bias lines. Because of the need to introduce bias,the first shunt inductor of the output circuit could notexactly be realised. Instead, this element was created byplacing a lOOpF miniature chip capacitor between the r.f.earth and the collector bias line at an appropriate distancefrom the transistor. A photograph of the amplifier configur-ation is shown in Fig. 7.

The experimentally-measured maximum-added-powercharacteristic of this transistor with the output circuitin place is shown in Fig. 6. (The values for added-powertransistor efficiency are obtained by dividing the addedpower by the bias power of 2 W). The agreement betweenthe measured performance and the theoretically-predictedperformance also shown in Fig. 6 is considered to be good.Over most of the band, the agreement is within ±0-25dB,which corresponds to an agreement in output circuitreflection loss of ±0-1 dB. An investigation of the differ-ences between the measured and predicted performance,which occur primarily at the band edges, has shown thatthe major sources of error are the approximations involvedin modelling the transistor output by a simple parallelcircuit of a single resistor and a single capacitor, and theinability to perfectly fabricate the circuit theoreticallyspecified (primarily because of the need to introducebias). The errors involved in the analytic large-signal model-ling technique appear to be of less consequence.

When the output circuit is designed to achieve a constantvalue of maximum added power over a frequency band, itdoes not necessarily follow that the resultant amplifierwill have an operating-power-gain characteristic constant

MICROWA VES, OPTICS AND ACOUSTICS, MA Y 1979, Vol. 3, No. 3 125

with frequency, since different values of r.f. input poweras a function of frequency will, in general, be required toachieve the prescribed maximum-added-power character-istic. In the present experimental example, the requiredr.f. input power level increased with frequency with a slopeof approximately 3 dB per octave. At midband, the requiredinput power was approximately 200 mW.

If desired, an input matching network with an oppositeslope of — 3 dB per octave could be used to ensure anoptimum input power level over the band when driven bya frequency-independent source. However, the added poweris not a strong function of input power in the vicinity ofits maximum, and some departure from the optimum inputpower level does not seriously degrade the efficiency. In thepresent example, the input-matching circuit was selected toyield a flat transducer-power-gain characteristic, whichrequired a slope of — 2dB per octave instead of the — 3 dBper octave slope required for best added power. An incidentpower of lOOmW was selected (deemed a suitable compro-mise between small-signal and large-signal operation) tocharacterise the input impedance of the transistor; theresulting input model of the transistor is shown in Fig. 4.Again a maximally-flat prototype was selected for thestarting point of the network synthesis, and it was deter-mined that an insertion-loss slope of 2 dB per octave witha high-end insertion loss of 0-5 dB would result in the besttransducer-gain characteristic over a bandwidth equal tothat obtained with the output matching network. As withthe case of the output network, the inductors were replacedby sections of transmission line, and the element valuesaltered until the required theoretical insertion-loss slopewas achieved. The input matching network which resultedis shown in Fig. 5.

The measured transducer gain of the overall amplifier soconstructed is shown in Fig. 8 for fixed-bias operation at

7

6

5

CD•o 3

bV

0

-1

-2

-3

K• i

i i i

1

/

\\\\\ -

-3

-2

07 0-8 09 10 11 12 13 1 Ufrequency, GHz

Fig. 8 Measured transducer-gain characteristics of completebroadband amplifier

Transducer gaino fixed bias, lOOmW incident powera fixed bias, 310mW incident powerX selfbias, 310mW incident powerInput reflection lossA fixed bias, lOOmW incident power

both lOOmW and 310mW incident power, and for selfbiasoperation ('class C) at 310mW incident power. (An inputincident power level of 310mW is close to that required toyield the maximum added power.) The selfbias configur-ation was obtained by keeping VCE = 20 V and earthingthe base lead through the input bias network. Also shownin Fig. 8 for the case of 100 mW incident power level isthe measured input-circuit reflection loss, showing excellentagreement with the calculated characteristic of 0-5 dB lossat the high end of the band and a slope of 2 dB per octave.The two curves for 310mW of incident power are useful forcomparing fixed-bias and selfbias operation. At this drivelevel the selfbias collector current at midband was approxi-mately equal to the fixed-bias collector current of 100 mA.It is observed that the amplifier performance under selfbiasoperation is nearly equal to the performance under fixed-bias operation, with the bandwidth only slightly reduced.Hence this design approach, although based upon a fixed-bias characterisation of the transistor, should also proveuseful for the design of selfbiased broadband amplifiers.

5 Conclusion

An approach to the design of broadband microwave transis-tor power amplifiers has been presented which makes itpossible to use network-synthesis procedures to obtaincircuits that optimise the added-power performance of theamplifier over a broad range of frequency. Most of thelarge-signal measurements involved in a conventionalload-contour characterisation are not required; instead,a minimum of only two measurements per frequency areneeded to obtain an accurate representation of the transis-tor's added-power characteristic under nonoptimum termin-ations. A mapping function is presented which convertsthis added-power characteristic into an equivalent linear-reflection-coefficient problem, thus making possible the useof linear-network-synthesis techniques to optimise large-signal performance. Although this technique is based upona fixed-bias transistor characterisation, experimental resultsshow that good performance can also be achieved when thetransistor is in selfbiased operation mode (class C oper-ation). More recent experiments have shown that thisgeneral approach to large-signal design is also applicable tothe case of microwave power f.e.t. amplifiers.11

6 Acknowledgment

This work was supported by the National Science Foun-dation under Grant ENG76—12252.

7 References

1 KU, W.H., and PETERSEN, W.C.: 'Optimum gain-bandwidthlimitations of transistor amplifiers as reactively constrainedactive two-ports', IEEE Trans., 1975, CAS-22, pp. 523-533

2 MELLOR, D.J., and LINVILL, J.G.: 'Synthesis of interstagenetworks of prescribed gain versus frequency slopes', ibid,1975,MTT-23,pp. 1013-1020

3 MELLOR, D.J.: 'Computer-aided synthesis of matching net-works for microwave amplifiers'. Ph.D. thesis, Stanford Univer-sity, 1975

4 KOTZEBUE, K.L.: 'Design technique for microwave-transistorpower amplifiers', Electron Lett., 1976, 12, pp. 74-75

5 KOTZEBUE, K.L.: 'A quasi-linear approach to the design ofmicrowave transistor power amplifiers', IEEE Trans., 1976,MTT-24, pp. 975-978

6 CUSACK, J.M., PERLOW, S.M., and PERLMAN, B.S.: 'Auto-matic load contour mapping for microwave power amplifiers',ibid., 1974.MTT-22, pp. 1146-1152

126 MICROWA VES, OPTICS AND A COUSTICS, MAY 19 79, Vol. 3, No. 3

7 HARRISON, R.G.: 'Computer simulation of a microwave power f o r microwave power amplifiers'. IEEE-MTT-S Internationaltransistor', IEEE J. Solid-State Circuits, 1971, SC-6, pp. 226- Microwave Symposium, Digest of Technical Papers, 1976,235 pp. 218-220

8 LEIGHTON, W.H., CHAFFIN, R.J., and WEBB, J.G.: 'RF 10 CARSON, R.S.: 'High-frequency amplifiers'(Wiley, New York,amplifier design with large-signal S-parameters', IEEE Trans., 1975)1973,MTT-21,pp. 809-814 ] 1 KOTZEBUE, K.L., and EHLERS, E.R.: 'Simple model of the

9 TAKAYAMA,' Y.: 'A new load-pull characterisation method large-signal properties of a 1 W FET at 5 GHz'(to be published)

MICROWA VES, OPTICS AND ACOUSTICS, MA Y1979, Vol. 3, No. 3 127