1590 IEEE TRANSACTIONS ON MICROWAVE THEORY...

1590 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 54, NO. 4, APRIL 2006

A New Feedback Method for Power Amplifier WithUnilateralization and Improved Output Return Loss

Zuo-Min Tsai, Student Member, IEEE, Kuo-Jung Sun, George D. Vendelin, Life Fellow, IEEE, andHuei Wang, Fellow, IEEE

Abstract—Given a device with a conventionally optimized 1 dB

point, this paper proposes a new theory for feedback amplifiers tooptimize gain and improves 22 (ideally resulting in 22 = 0).The design procedure only requires the small-signal -parame-ters and the measured load–pull data of the transistor. To verifythis theory, two 800-mW 2-GHz GaAs MESFET amplifiers withand without the lossless feedback were implemented and evaluated.The feedback amplifier achieved significant improvement in lineargain (6 dB), reverse isolation (12 dB), and output return loss (5 dB)with the same output 1 dB for both types of amplifiers.

Index Terms—Feedback, output power 1-dB compression( 1 dB), power amplifier (PA).

I. INTRODUCTION

FEEDBACK techniques were used to implement unilateral-ized amplifiers [1]–[6]. There are basically three types of

feedback amplifiers, which are: 1) high gain amplifier (HGA),which was presented by Mason in 1954, which gives the highestpossible gain of a stable amplifier (unilateral gain) with both

and equal to 0 at a particular frequency [2], [4]; 2)low-noise amplifier (LNA), which was presented by Vendelinin 1975, which gives the lowest noise figure (NF) and[7]–[9]; and 3) high power amplifier (HPA), which is proposedin this paper, and can improve gain and return loss (ideally re-sulting in ) with a given conventionally optimizedpoint of a device. The second and third designs are not exactlyduals of each other, although we are treating the HPA in a linearsense. We have successfully predicted the power performanceof the HPA even though it is really a nonlinear design in our de-sign examples.

The theory provides two essential advantages when designingpower amplifiers (PAs). First, a design approach of the feed-back PA without a nonlinear device model was proposed. Inthis paper, the feedback amplifier can be designed for maximum

with only load–pull measured data and linear network pa-rameters of the device without feedback. The other advantage isto avoid the tradeoff between output power and output returnloss. With this theory, the load admittance can be equal

Manuscript received October 17, 2005. This work was supported in part by theNational Science Council of Taiwan, R.O.C., under Grant NSC 93-2752-E-002-002-PAE, Grant NSC 93-2219-E-002-016, Grant NSC 93-2219-E-002-024, andGrant NSC 93-2213-E-002-033.

The authors are with the Graduate Institute of Communication Engineeringand the Department of Electrical Engineering, National Taiwan University,Taipei, Taiwan 10617, R.O.C. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TMTT.2006.871347

Fig. 1. Given linear two-port device. (a) Matched to source and load impedancewith input and output matching network. (b) Embedded within a linear losslessreciprocal four-port.

to the conjugate match, thus the output return loss can be im-proved. Moreover, the reverse isolation can also be improved sothe power gain can be enhanced to even higher than the max-imum transducer power gain of the device withoutfeedback.

To realize the feedback PA, a new feedback topology is pro-posed based on the requirement of the HPAs. The design pro-cedure is also developed according to the proposed feedbacktopology. Two 800-mW 2-GHz GaAs MESFET amplifiers withand without lossless feedback were implemented to verify thisnew theory. Both theoretical and experimental results show thatsignificant improvements are achieved for the linear gain, outputreturn loss, reverse isolation, and stability without a tradeoff ofoutput power and efficiency.

II. UNILATERIZATION OF AMPLIFIERS

Fig. 1(a) shows the circuit block diagram of a typical linearamplifier without a feedback topology. Using input and outputmatching networks, both input and output impedances can bematched to the source and load impedance when . Thus,the maximum transducer power gain is defined underthis simultaneous conjugate match conditions. In other words,

is the upper bound of power gain from a linear active

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TSAI et al.: NEW FEEDBACK METHOD FOR PA WITH UNILATERALIZATION AND IMPROVED OUTPUT RETURN LOSS 1591

device when the input and output matching networks are bothoptimal designs [1].

In Mason’s paper [2], the power gain of the linear two-portdevice with a lossless feedback network was discussed. Fig. 1(b)shows the block diagram of a linear feedback amplifier. A linearactive device is embedded in a linear lossless reciprocal four-port network. With the four-port networks, the power gain canbe optimized to the unilateral gain ( ) where

(1)

and the -parameters of the complete amplifier becomes

(2)

This is the most ideal amplifier that can be achieved theoret-ically. With ideal input and output return loss and perfect re-verse isolation, the input power is amplified to the output portwithout any reverse pass. Thus, is always higher than .In a typical design procedure, the embedded four-port structurecan be divided into feedback and matching networks. The func-tion of the feedback networks is to make the reverse isolation ofthe transistor zero. With the matching networks, the input andoutput impedance mismatch can be eliminated. The feedbacknetwork can be determined first, and then the matching networkscan be designed accordingly.

III. OUTPUT POWER IN UNILATERALIZED FEEDBACK PAS

When designing an HPA, the nonlinear effect of the transistorhas to be taken into consideration. Fig. 2(a) shows the block di-agram of a load–pull measurement system [1]. For a nonlineartwo-port device, is a function of load admittance, andthe optimum admittance and the optimumcan be obtained via the load–pull measurement system. Thesource matching network can then be determined by the con-jugate match to the input of the loaded transistor, therefore, aPA can be easily designed by small-signal network parametersand .

In a feedback PA design, the load–pull data should be useddifferently. Based on the following assumptions , the outputpower can be predicted by the linear network parameters andmeasured load–pull data.

• The device is linear when the output power is lower than.

• of the device only depends upon load admittance, while the gain of the transistor is high enough, and

both the voltage and current swing at the transistor inputport are much lower than those at the output port.

Fig. 2(b) illustrates the circuit schematic of a feedback PA.A nonlinear two-port device is embedded in a four-port feed-back network. and denote the load and source admit-tances, respectively, and are transformed from system character-istic impedance by two different passive lossless matchingnetworks. The amplifier is driven by a given voltage source .Based on the first assumption, the equations for the currents and

Fig. 2. (a) Load–pull setup of the PA without feedback. (b) Circuit schematicof a feedback PA.

voltages can be obtained from the linear network admittance pa-rameters of the device and feedback network

(3)

(4)

Using (3) and (4), the admittance at the output of thetransistor can be solved in terms of , , , , andin (5). It is interesting to observe that the output admittance ofthe transistor is independent of . The result shows that, witha given transistor and specified feedback networks, the outputadmittance is only determined by , shown in (5) at bottom ofthe following page.

To obtain to the load, the transistor has to delivermaximum power in the linear region. According to the secondassumption, another condition for , , and optimum ad-mittance for the optimum 1-dB compression outputpower is needed in addition to (3) and (4), i.e.,

(6)



From (5) and (6), is evaluated in (7), shown at the bottomof this page. In the PA design, for at plane

is . Since is a function of , , and ,at plane A in Fig. 2(b) can be transformed to from

the device and the feedback network and . The powerdelivered to the plane of Fig. 2(b), namely, , can becalculated from the measured , the output power deliv-ered to plane , and the linear network parameters, as shown in(8), at bottom of this page.

Using (7) and (8), the power performance of the feedbackamplifier can be predicted. In the feedback amplifier, the reverseisolation is perfect and, thus, the output impedance of the devicewith feedback at plane of Fig. 2(b) is independent of

. Therefore, making be conjugate to the optimum loadadmittance of can achieve a unilateral PA with simultaneouspower and impedance match.

IV. FEEDBACK STRUCTURE FOR PA

Fig. 3 illustrates the block diagram of the proposed feed-back structure. Since the feedback structure is lossless, the shuntfeedback can only eliminate the imaginary part of of thecircuit. Thus, additional series feedback elements ( and )are added to make the real and imaginary parts of both 0.

Fig. 3. Schematic of the proposed feedback structure.

Moreover, the shunt connected elements ( and ) was usedto increase the design flexibility to improve the return loss of theunilateralized PA. It is noted that the source pads of the transistorneed to be connected to ground directly for heat sink and, thus,no source feedback should be used in this design.

(5)

(7)

(8)



Fig. 4. 2-GHz load–pull measurement of Hexwave 1686 MESFET at V =

10 V and I = 200 mA.

By definition of the unilateralized device, is 0. In Fig. 3,it is observed that plays the role to cancel the imaginarypart of ,

(9)

With proper selection of , , , and , the realpart of can also be eliminated. (shown in Fig. 3) can beevaluated in terms of , , , , and as

(10)By simplifying (10), can be evaluated as

(11)

In (11), making the real part of 0, we have

(12)

To obtain perfect output return loss, the load admittance ofthe feedback device , which can be expressed in terms

Fig. 5. G and S of the device with and without feedback network.

Fig. 6. Conjugate match point and the output power match point of the tran-sistor with and without feedback.

of , , , , , and , is the complex conjugate ofin Fig. 3, i.e.,

(13)

By equating (7) and (13), we can obtain

(14)



Fig. 7. Circuit schematic of feedback PA.

and, thus, optimum at plane and perfect output returnloss can be achieved simultaneously.

To design the lossless feedback network, , , , , andneed to satisfy (9), (12), and (14). It is obvious that the solu-

tions of , , , , and are not unique. The nonuniquesolutions give the flexibility to improve the output impedancematching of the PA, and the conjugate match admittancecan be close to (the optimum admittance for ). Thus,the output match of the unilateralized transistor is improved.

V. EXPERIMENTAL RESULTS

To verify the theory of the lossless feedback amplifier, a2-GHz feedback amplifier was implemented using the Hex-awave 1686 MESFET 1-W power transistor [10]. Fig. 4 isthe measured load–pull data at 10-V drain voltage and200-mA drain current . The optimum admittanceis when the 1-W is achieved. Thelinear network parameters of the transistor are obtained basedon the measured small-signal -parameters.

The lossless feedback network should be designed first. Usingthe design equations of feedback networks (9), (12), and theoutput power constraint (14), to can be designed andrealized with two short stubs, two series microstrip lines, anda 0.1-pF gap capacitor, respectively. The gate and drain biasesare supplied from the bias networks to the two short stubs in thefeedback network. Fig. 5 illustrates and for the tran-sistor with and without the lossless feedback network from 1 to3 GHz based on the measured transistor -parameters. By ap-plying feedback networks, of the transistor was enhancedfor 5.9 dB (from 18.8 to 24.7 dB) at 2 GHz and the reverse iso-lation becomes 49 dB, which is 16.9 dB better than thetransistor without feedback.

Regarding output matching consideration, Fig. 6 illustratesthe conjugate match points and the output power match pointsof the transistor with and without the feedback network. It canbe observed that the conjugate match point and the outputpower match point for the transistor with feedback are muchcloser to each other than those points for the transistor withoutfeedback, therefore, the output return loss can be greatly im-proved with the feedback network.

Fig. 8. Feedback PA.

Fig. 7 shows the complete circuit schematic diagram of thefeedback PA including the input and output matching networks.Fig. 8 shows the photograph of the feedback PA. The amplifierwas implemented using 1.6-mm-thick FR4 board.

For comparison, another 2-GHz PA using the same transistorwithout a feedback network was also implemented at the samebias condition ( V, mA). Fig. 9 shows thecircuit schematic diagram of this PA. It was designed based onthe conventional PA design procedure in [1] and also imple-mented using 1.6-mm-thick FR4 board. The output matchingnetwork was designed for from measuredof the load–pull data, and the input match network was conju-gate-matched to the input of the transistor, thus, it has a pooroutput return loss, but a very good input return loss. The photo-graph of the PA without feedback is shown in Fig. 10.

Figs. 11 and 12 shows the simulated -parameters from 1.5to 2.5 GHz of the PAs with and without feedback, respectively.Again, the measured -parameters of the transistors were usedin the simulations. Both amplifiers were designed for 2 GHz. Itis observed that, with the lossless feedback network, the gain isimproved from 13.4 to 19 dB, the output return loss is improvedfrom 3.0 to 11.0 dB and the reverse isolation is improved from



Fig. 9. Circuit schematic of PA without feedback.

Fig. 10. PA without feedback.

Fig. 11. Simulated S-parameters of the feedback PA.

28.3 to 41.59 dB. The simulations are consistent with our theoryfor the feedback PA design.

Figs. 13 and 14 illustrate the measured -parameters of thefeedback PA and the PA without feedback, respectively, from1.5 to 2.5 GHz. Although both amplifiers were designed for2 GHz, the measured performances shifted a little to lower fre-quencies for both amplifiers. The peak gain (12.6 dB) and best

Fig. 12. Simulated S-parameters of the PA without feedback.

Fig. 13. Measured S-parameters of the feedback PA.

input return loss (12.2 dB) of the PA without feedback occurredat 1.92 GHz, while the PA with feedback has peak gain (18.8 dB)and best input return loss (29 dB) at 1.96 GHz. The perfor-mances at the frequencies of peak gain and best input return lossfor the two amplifiers were then compared against each other.The power gain is improved 6.2 dB from 12.6 to 18.8 dB, andthe reverse isolation is improved from 30 to 43.1 dB. The outputreturn loss, improved from 3.8 to 8.6 dB, is not as good as ex-pected due to the loss of the matching and feedback network.It is observed that the feedback structure presents significantimprovements of all four small-signal -parameters for the PAwith a feedback network.

Fig. 15 presents the measured output power versus inputpower for the feedback PA at 1.96 GHz and the PA withoutfeedback at 1.92 GHz. It is observed that both the feedbackamplifier and the amplifier without feedback have the sameoutput of 29 dBm. The theory in Section III is thenverified with the results. The power-added efficiency (PAE) forboth the amplifiers was also measured and shown in Fig. 16.



Fig. 14. Measured S-parameters of the PA without feedback.

Fig. 15. P versus P of feedback PA and PA without feedback.

Fig. 16. PAE versus P of feedback PA and PA without feedback.

Since both amplifiers have similar output power and enoughgain, they have a similar PAE of 37% at .

TABLE IPERFORMANCE SUMMARY OF MEASURED FEEDBACK

AND PA WITHOUT FEEDBACK

Table I summarizes the performances of the PAs with andwithout feedback at the frequencies of peak gain and best inputreturn loss. It can be observed that the power performance ofboth amplifiers are the same, but with significant improvementof the power gain, isolation, and output return loss for the feed-back PA.

VI. CONCLUSION

In this paper, a new theory and design procedure of the loss-less feedback amplifiers based on load–pull measurements andlinear network parameters has been proposed. The design pa-rameters of the feedback amplifiers for can be evalu-ated by the linear network parameters without a nonlinear de-vice model. A feedback structure to realize the feedback PA hasalso been proposed. To verify the theory, two 2-GHz 800-mWMESFET amplifiers were implemented and measured. Based onthe comparison of the PAs with and without feedback, the powergain, reverse isolation, and output return loss can be improvedfor the feedback PA with the same output power performance.

ACKNOWLEDGMENT

The authors would like to thank Hexawave, Hsin-Chu,Taiwan, R.O.C., for providing the power transistors andP.-S. Wu, National Taiwan University, Taipei, Taiwan, R.O.C.,for his helpful advice. The authors would also thank to K.Vaesen and N. Van Hoovels , both of the Interuniversity Micro-electronics Center (IMEC), Leuven, Belgium, for their help inthe PA measurement.

REFERENCES

[1] G. Gonzalez, Microwave Transistor Amplifiers Analysis and Design,2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1997.

[2] S. J. Mason, “Power gain in feedback amplifiers,” IRE Trans. CircuitTheory, vol. CT-1, no. 2, pp. 20–25, Jun. 1954.

[3] C. Cheng, “Neutralization and unilateralization,” IRE Trans. CircuitTheory, vol. CT-2, no. 2, pp. 138–145, Jun. 1955.

[4] M. S. Gupta, “Power gain in feedback amplifiers, a classic revisited,”IEEE Trans. Microw. Theory Tech., vol. 40, no. 5, pp. 864–879, May1992.

[5] G. D. Vendelin, A. M. Pavio, and U. L. Rohde, Microwave CircuitDesign Using Linear and Nonlinear Techniques. New York: Wiley,1990.

[6] ——, Microwave Circuit Design Using Linear and Nonlinear Tech-niques, 2nd ed. New York: Wiley, 2005.



[7] G. D. Vendelin, “Feedback effects on the noise performance of GaAsMESFETs,” in IEEE MTT-S Int. Microw. Symp. Dig., May 1975, pp.324–326.

[8] L. Besser, “Stability considerations of low-noise transistor amplifierswith simultaneous noise and power match,” in IEEE MTT-S Int. Mi-crow. Symp. Dig., May 1975, pp. 327–329.

[9] M. P. Van der Heijden, L. C. N. De Vreede, and J. N. Burghartz, “Onthe design of unilateral dual-loop feedback low-noise amplifiers withsimultaneous noise, impedance, and IIP3 match,” IEEE J. Solid-StateCircuits, vol. 39, no. 10, pp. 1727–1736, Oct. 2004.

[10] “Manual of HWF1686RA,” Hexawave, Hsin-Chu, Taiwan, R.O.C.,2002.

Zuo-Min Tsai (S’01) was born in Mailo, Taiwan,R.O.C., in 1979. He received the B.S. degree in elec-tronic engineering from National Taiwan University,Taipei, Taiwan, R.O.C., in 2001, and is currentlyworking toward the Ph.D. degree at National TaiwanUniversity.

His research interests are the theory of microwavecircuits.

Kuo-Jung Sun was born in Tainan, Taiwan, R.O.C.He received the B.S. degree in electrical engineeringfrom National Tsing Hua University, Hsinchu,Taiwan, R.O.C., in 1991, and the Masters degreein business and administration (MBA) and M.S.degree in communication engineering from NationalTaiwan University, Taipei, Taiwan, R.O.C., in 1997and 2005, respectively.

His research interests include the design of RF in-tegrated circuits (RFICs)/monolithic microwave in-tegrated circuits (MMICs), CMOS sensors, and data

converters.

George D. Vendelin (M’61–SM’70–F’99–LF’04)received the B.S.E.E., M.S.E.E., and Eng.E.E.degrees from Stanford University, Stanford, CA, in1959, 1961, and 1963, respectively.

From 1963 to 1968, he was with Texas InstrumentsIncorporated. In 1968, he joined the Research Depart-ment, Signetics, Sunnyvale, CA. In 1972, he joinedFairchild MOD, Palo Alto, CA. In 1974, he was withthe Microwave Amplifier Department, Varian Asso-ciates, which lead to the publication of the feedback(FB) LNA design. From 1975 to 1977, he was a Mi-

crowave Consultant until he joined the startup Dexcel. From 1979 to 1985, hewas the Technical Director for the Eaton Instrumentation Division, where heauthored his first book in 1982. In 1985, he joined the Semiconductor Division,Avantek, as Application Manager of semiconductors. Since 1989, he has beenPresident of the consulting firm Vendelin Engineering. He was recently a Vis-iting Professor with the University of Aveiro, Aveiro, Portugal, and NationalTaiwan University, Taipei, Taiwan, R.O.C., where he was involved with grad-uate electrical engineering teaching and research. He authored Microwave Cir-cuit Design Using Linear and Nonlinear Techniques, 2nd edition (Wiley, 2005).He continues his research in microwave nonlinear circuits.

Huei Wang (S’83–M’87–SM’95–F”06) was born inTainan, Taiwan, R.O.C., on March 9, 1958. He re-ceived the B.S. degree in electrical engineering fromNational Taiwan University, Taipei, Taiwan, R.O.C.,in 1980, and the M.S. and Ph.D. degrees in electricalengineering from Michigan State University, EastLansing, in 1984 and 1987, respectively.

During his graduate study, he was engaged inresearch on theoretical and numerical analysis ofelectromagnetic radiation and scattering problems.He was also involved in the development of mi-

crowave remote detecting/sensing systems. In 1987, he joined the ElectronicSystems and Technology Division, TRW Inc. He has been an MTS and StaffEngineer responsible for monolithic-microwave integrated-circuit (MMIC)modeling of computer-aided design (CAD) tools, and MMIC testing evaluationand design, and became the Senior Section Manager of the Millimeter-WaveSensor Product Section, RF Product Center. In 1993, he visited the Institute ofElectronics, National Chiao-Tung University, Hsinchu City, Taiwan, R.O.C.,where he taught MMIC-related topics. In 1994, he returned to TRW Inc.In February 1998, he joined the faculty of the Department of ElectricalEngineering, National Taiwan University, Taipei, Taiwan, R.O.C., where he iscurrently a Professor.

Dr. Wang is a member of Phi Kappa Phi and Tau Beta Pi. He was the re-cipient of the Distinguished Research Award presented by the National ScienceCouncil, R.O.C. (2003–2006). He was also elected as the first Richard M. HongEndowed Chair Professor of National Taiwan University in 2005.


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