A load-pull technique for thedetermination of transistor S parameters

under large-signal conditionsM.A. Osborne, B.S.c. Ph.D., A.M.I.E.E., and G.B. Morgan. B.Sc, Ph.D..

C.Eng., M.I.E.E., M.lnst.P.

Indexing terms: Transistors, Mathematical techniques

Abstract: A novel method is presented for determining the large single S parameters of transistors under driveconditions using data obtained from load-pull measurements. The technique uses a load which can have avariable amplitude and phase, and can thus control the amplitude and phase of the signal at the device output.A mathematical analysis of the method is presented and typical results for the large-signal S parameters of anX-band FET are given. The gain compression and AM/PM conversion limits of a linearised power amplifier arethen calculated.

1 Introduction

At high power levels transistors show saturation in thetransfer characteristics which, in certain communication,radar and ECM type systems, can lead to unacceptabledistortion of the signals. In many cases circuits may bedesigned to partially compensate the distortion, and suchdesign techniques require a knowledge of how the S par-ameters of the transistor vary with signal power.

Despite inherent bandwidth limitations, the simplicityof load-pull measurements makes them an attractive wayof characterising microwave power transistors on accountof their directness and accuracy. Load-pull measurementsmay either be used to determine amplifier performancedirectly [1] or, alternatively, to obtain large signal S par-ameters under drive conditions [2]. In the methoddescribed in this paper the device under test (DUT) wasterminated in 50 Q at both input and output ports and apower splitter at the signal source output, which sent inci-dent signals to both the ports was used to simulate theload. In a recently reported alternative arrangement [3] asingle power source was used, and the output signal fromthe DUT was additionally amplified and returned to theoutput port via a phase shifter and circulator to maintain50 tl terminations throughout.

In the present work the DUT was a 100 mW X-bandGaAs MESFET (Plessey type GAT4/021 in a P103package) and the output of the transistor was terminatedin a variable attenuator followed by a sliding short circuit.The experimental arrangement is simpler than the tech-niques previously described but does not, however, havethe convenience of 50 O terminations. The results obtainedwere used to calculate large signal S parameters underdrive conditions. These S parameters were then used tocalculate the transfer functions of amplifiers using a seriesof successive approximations to determine the preciseoutput power for a given load and input power.

2 Theory of the method for characterising amicrowave transistor under drive conditions

Under large signal conditions it is not realistic to deter-mine the parameters S22 and S21 with an input port ter-minated in a passive 50 Q load. However, a transistor may

Paper 4225H (E12), received 11th July 1984

Dr. Morgan is, and Dr. Osborne was formerly, with the Department of Physics,Electronics & Electrical Engineering, University of Wales Institute of Science &Technology, Cardiff CF1 3NU, United Kingdom. Dr. Osborne is now withHMGCC, Hanslope Park, Northants, United Kingdom

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985

be characterised by incorporating it into an amplifier witha 50 Q source and a non 50 Q load, as represented by theflow graph shown in Fig. 1. (S12 and SX1 may still be deter-mined using well established techniques).

The transmission coefficient T of the amplifier rep-resented in Fig. 1 is given by eqn. 1 in terms of the tran-sistor parameters S2 2 , S2 i and the load F.

T =-rs

(1)22

Fig. 1 Flow diagram representing transistor and load

a and b are power waves

Eqn. 1 enables either S22 or S21 to be calculated, but,however, no relationship between the two parameters isspecified. It was thus necessary to treat S22 and S2J asfunctions of power incident on both ports in order toremove the phase dependency of S2 2 . The procedure isoutlined below and fuller details are given in Appendix 9.

Circles of constant gain may be drawn on a Smithchart, the radii and centres of which are determined fromthe transistor S parameters and gain. This process wasreversed to obtain S parameters as functions of power. Todetermine S22 and S2 1 , circles linking reflection coeffi-cients were plotted on a polar diagram, for which thepower incident on the output port was constant underconditions of constant power incident on the input port.

Referring to Fig. 1 it may be seen that

aS-,\r\:

I - r s= 9 (2)

22

where | a |2 and | b |2 are the incident powers. Loci of F maybe plotted for constant values of g which are circles of radiir given by

9 1/2

The centres of these circles, from which the phase of S22

419

was calculated, are at the point given by the co-ordinatesin eqn. 4

(4)x~ 1

where

S22 =

-

A

g s 2 2 2 '

+ JB

l - 9 \ S 2 2 V

(5)

The magnitudes of S22 and S21 may be calculated fromeqns. 6 and 7 where d is the distance separating the centreof a circle from the origin.

i c i1*22 I -

0 ='21 r\S 22

(6)

(7)

Finally, it can be shown that

b \ . ( rphase

aS21= phase

= tan

- rs22B\T\2

A\r\2 - uwhere

r = u+jv

(8)

(9)

The phase of S21 may thus be calculated from eqn,. 8.Under small signal conditions the S parameters are

independent of power and the theory described above isexact. Under large signal conditions the validity of thetheory was considered to have been assured on threecounts; with reference to Fig. 2, it may be seen that (a)

Fig. 2 Comparison between experimental and theoretical b — Y polarplots at 8.5 GHzb represents the power wave incident on the output port and T is theload. The power incident on the input port, \a\2, was 12 dBm. Thedashed lines are experimental results whilst the solid lines are theoreticalresults

circular loci were obtained for all values of r with whichthe transistor might be matched in practice, (b) eqn. 8 pre-dicted consistent values for the phase of S21 as the mea-surement point was varied and (c) the originalmeasurement points could be recalculated accurately fromthe S parameters.

In the measurement method adopted for 5 n and S12, a

similar dependence on the incident power levels to thatwhich had proved to exist for S22 and S21 was initiallyassumed. However, measurements demonstrated that S u

was essentially independent of the power incident on bothports, and that S12 was dependent on the ratio of thepower levels. Now the total power wave C reflected fromthe input port of the active circuit (represented in Fig. 3) is

Fig. 310

given by

C = a>

Flow diagram representation defining the characters used in eqn.

bSl2

(10)

So, if S n and Sl2 are assumed to be functions of the mag-nitudes of power waves a and b, the loci of C as the phaseof b is varied will be circular, as shown in Fig. 4 which alsoindicates how S n and S12 were obtained.

locus of c

Fig. 4 Locus ofC as the phase ofb is changed (see eqn. 10)

3 Experimental procedure

The S parameters of the transistors were determined usinga waveguide WG16 bridge and a Hewlett Packard 8410microwave network analyser. The signal source was aHewlett Packard 8602A sweep oscillator followed by awideband GaAs FET power amplifier which gave anoutput power of about 20 dBm. A harmonic frequencyconvertor processed the test and reference signals fordisplay. A diagram of the basic circuit is shown in Fig. 5,with the circuitry of the test arm, which is placed betweenports A and B, omitted. When transmission measurements

hp8620A

FETPA

10dB 10dB

signal generator 1powermeter

test arm

hp8A11A

_J ref. arm

display

/ l 3dB ^ 20dB

Fig. 5 Basic measurement system using a waveguide WG16 bridge and anetwork analyserThe test circuits were placed between ports A and B

420 1EE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985

were being undertaken the circuit shown diagrammaticallyin Fig. 6A was inserted between A and B, whilst whenreflection measurements were being made the circuit givenin the diagram of Fig. 6B was inserted between A and B.The determination of S12 required the use of the circuitshown diagrammatically in Fig. 6C.

networkanalyser B

Fig. 6A Test arm circuit for the determination ofS22 ond S2i

from sig gen.

Bnetworkanalyser power meter

Fig. 6 B Test arm circuit for the determination of Si, and \Si2\

frornsfg gen.DUT

analysermeasurementof c

analysermeasurementof b

B

Fig. 6C Test arm circuit for the determination ofSl2

The transistors were mounted in a 50 Q microstrip lineon 625 fi thick alumina substrate. High-low bias tees forthe gate and drain were integrated on the same substrateand the microstrip was transformed to the waveguideWG16 by means of microstrip to coaxial SMA transitions,followed by SMA coaxial to waveguide WG16 trans-formers.

As stated, the parameters S21 and S22 were determinedwith the waveguide test arm of the bridge set as shown inFig. 6A, so that the power waves a and b, and the load Fcould each be determined. The load consisted of a rotaryvane variable attenuator followed by a calibrated slidingshort which enabled the magnitude and phase of b to bevaried independently. For constant values of input powerlevel the values of F were determined as a function of b. Atypical set of results is shown in Fig. 7 where a polar plotof the load F is given for values of \b\2 of 8 dBm to18 dBm. At a value of 8 dBm the locus of F is seen to be'fairly circular' but deviates from a circular shape at higherpowers. The data presented in Fig. 7 correspond to a fre-quency of 8.5 GHz with a constant input power, | a |2, of14 dBm. Circles of constant radius correspond to fixedvalues of the magnitude of b while radial lines correspondto constant phase. Values of S22 were calculated from thedimensions of the cyclic paths and at the intersectionpoints the corresponding values of 5 2 1 were calculated.

The parameters S n and S12 were determined with thetest arm AB set as shown in Fig. 6B. The phase of thepower wave b was varied and the corresponding locus ofC, the reflected wave at the input port, was plotted. Thevalues of the magnitude and phase of Sl2 were determinedwith the bridge set as shown in Fig. 6C, with the network

analyser being switched from one side of the active deviceto the other.

18dBm _•!

120

U 0

180°

-20*

Fig. 7 Experimental b — F polar plots

F is represented on rectangular co-ordinatesCircular loci represent constant | b |2

Radial lines represent a constant phase of bExperimental results taken at 8.5 GHz with a constant power \a\2 of the 14 dBmincident on the input port

4 Results of large signal S parametermeasurements

Experimental results are presented for a frequency at8.5 GHz. The MESFET, which produced 1 dB of gaincompression for an input power of 14 dBm and 50 Q ter-minations had power levels of 8, 10, 12, and 14 dBmapplied to the input port.

The powers incident on the output port (determined bythe input power level, the active device gain and the load

1-8-

1-6

u

1-2

Ib I d B m

- 12

15

U

13

- 1 0 -0-8real S 21

-0-6 - 0

Fig. 8 Values ofS2ifor a transistor as a function of the power incidenton both ports

I a |2 is the power incident on the input portI b |2 is the power incident on the output portfrequency = 8.5 GHz

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985 421

reflection coefficient) lay in the region of 7-18 dBm. Mea-surements were taken at 2 dB intervals and the device wascharacterised over the range of power levels given abovefor 1 dB intervals.

In Fig. 8 the values of the parameter S21 are plottedagainst | b |2 for constant | b |2/l«I2 ratios.

S22 is shown plotted against \b\2 for constant \a\2 inFig. 9. The phase of S22 is approximately —60°. Values forthe phase of b which give useful gain are therefore in theregion of + 60° and the best possible curve fitting was pro-vided for (0 ^ phase of b ^ 120°).

The variation of the S parameters is clearly seen.

-O.IOr

-0.15

-0.20

-0.25

-0.30

-0.35

-0.40

dBm power incident on output port

power incident oninput port

|o|2

KdBm

13dBm

8 dBm

0.15 0.25 0300.20

real S22

Fig . 9 Values of S21for a transistor as a function of \b\2 for various

values of\ a \2

frequency = 8.5 GHz

-100*

- 90*

- 80*

- 70'

-3 -2 -1 0 1 2 3 A

b l 2 > dB

la I2

Fig. 10 Phase ofStl as a function of the ratio of the incident powers

All

SX1 was found to be virtually independent of powerover the range for which measurements were taken. Mag-nitude and phase variations lay within 0.75 dB and 10°ranges, respectively. Hence Sj t could be measured directly.Its value was found to be 0.52/ 58°.

The magnitude of S12 showed a similar independenceand was measured as 0.16. Its phase was found to be afunction of the ratio | b \2/\ a |2 and is shown plotted as suchin Fig. 10.

5 Power amplifier design

Non-linearity in the transfer function of an amplifier dis-torts the envelope of multi-carrier signals causing inter-modulation products which cannot be filtered out. Thelimits within which the gain varies will therefore initiallyaffect the intermodulation performance. In the designmethod adopted here the small signal gain is maximisedfor a set gain compression over a given range of inputpower levels [4]. Terminations were chosen using an iter-ative computer program which used device S parametersand incident power levels as data and included the follow-ing steps:

(a) Set a level, in dB, for the gain compression for inputpowers lying between 7 and 13 dBm.

(b) Define the first pair of reflection coefficients used toterminate the transistor.

(c) Set the input power to 7 dBm.(d) Assume transistor S parameters which describe its

performance for arbitrary incident powers.(e) Calculate the incident power levels at the transistor

ports.(/) Correct the device S parameters from the estimate

for the incident power levels obtained in step e and the Sparameters stored as data.

(g) Repeat steps e and/until the 5 parameters no longerneed correction (up to 3 times was found necessary).

(h) Calculate the amplifier gain.(i) If the input power is 7 dBm change it to 13 dBm and

return to step d, otherwise continue to step).(/) If the difference between the gains for input powers of

7 and 13 dBm is equal to the compression level set up instep a, store the loading details and gain.

(k) Repeat steps b-j, storing the details only of the cir-cuits with the best small signal gain.

(/) Calculate the amplifier gain of the final circuit forinput power levels at 1 dB intervals.

Transfer functions calculated for amplifier circuits usingthe GaAs MESFET which had previously been character-ised at 8.5 GHz are shown in Figs. 11 and 12. The curvesof both the gain and phase versus input power are num-bered 1-5, corresponding to small signal gains of 6.8, 6.3,

7r

m 6

8 9 10 11input power, dBm

12 13

Fig. 11 Gain of amplifiers at 8.5 GHz as a function of input power forvarious small signal gains

1 gain = 6.8 dB2 gain = 6.33 gain = 5.8

4 gain = 5.45 gain = 4.9

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985

5.8, 5.4, and 4.9 dB, and are plotted over a range corre-sponding to the gain being within 0.5 dB of the small

130'VI

i 120'

110'

137 8 9 10 11 12input power.dBm

Fig. 12 Phase of amplifiers at 8.5 GHz as a function of input power forvarious small signal gains1 gain = 6.8dB2 gain « 6.33 gain = 5.84 gain »• 5.45 gain - 4.9

signal value. An inspection of the curves shows that predis-tortion produces little effect on the maximum linearoutput.

6 Conclusion

A simple method of determining the large signal S par-ameters of transistors under drive conditions has beendeveloped. Experimental values of S parameters have beendetermined as a function of power for a X-band GaAsMESFET and the performance of predistortion linearisingcircuits have been investigated and found to give littleimprovement for class A biassing.

7 Acknowledgment

M.A. Osborne wishes to thank the Science & EngineeringResearch Council for a studentship which enabled him todo this work.

8 References

1 SECHI, F.N.: 'Design procedure for high-efficiency linear microwavepower amplifiers', IEEE Trans., 1980, MTT28, pp. 1157-1163.

2 MAJUMDER, S.R., and VAN DE PUIJE, P.D.: 'Two-signal methodof measuring the large-signal S parameters of transistors', ibid., 1978,MTT26, pp. 417-419

3 BAVA, G.P., PISANI, U., and POZZOLO, V.: 'Active load techniquefor load-pull characterization at microwave frequencies', Electron. Lett.,1982,18, pp. 178-179

4 MORGAN, G.B.: 'Linear microwave amplification using Impattdiodes', Radio & Electron. Eng., 1973,43, pp. 625-630.

9 Appendix

Proof of the equations used to determine S parameters fromexperimental dataThe proof starts from eqn. 2 which is repeated here:

i - r s , i2~9 (ID»22

aS2i

Let

r=U+jV (12)

and

S22 = A+jB (13)

Substituting for F and S22 in eqn. 11 and rearranging gives

u +i-g\s22\

,1/2(14)

Eqn. 14 represents circles with radii and centres given byeqns. 3 and 4. The distance separating the centre of thecircles from the origin is given in eqn. 15 and the radii ineqn. 16

d = 9\S22\ll-g\S22\2rl

Thus,

and

9 = r\S 22 aS21

Taking logs in eqn. 18 gives

10 log10 g = I b\2dB - I a \2dB - 20 log10 S2l

b\2dB-1 .,S21 = - ^ antilog10

a\2dB~\J

(15)

(16)

(17)

(18)

(19)

(20)

Finally,

phaseaS 21

= phase1 -FS22

Using the substitutions given in eqns. 12 and 13 it can beshown that

phase = tanL«S2iJ ~ " { (A\T\2-U)

phase S21 = phase b — phase a — tan ~1

(21)

(A\r\2-u)

IEE PROCEEDINGS, Vol. 132, Pt. H, No. 7, DECEMBER 1985 423