Design And Analysis Of Microwave Feedback Amplifiers

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Design and Analysis of Microwave Feedback AmplifiersGang Zhou and Lizhen ZhengDepartment of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA 94720Abstract--We have studied the basic theory of feedbackamplifiers. A broadband single stage MESFET amplifierhas been designed with 5 dB gain over the frequency rangefrom 500 MHz to 12 GHz. A gain flatness of 0.18 dB wasachieved. Meanwhile, the input VSWR and output VSWRwere controlled to be less than 1.88:1. Both negative andpositive feedback were used to extend the bandwidth. Theamplifier is unconditionally stable within the whole interested frequency region, while we checked the stability upto 60 GHz.I. INTRODUCTIONNegative feedback can be used in the broadband amplifiersto control gain flatness and reduce the input and outputVSWR at the same time. When the bandwidth requirementreaches a decade of frequency, the gain compensation basedon the matching network becomes very difficult, while thefeedback amplifier can be designed to have a very widebandwidth (more than two decades) with small gainvariations (tenths of a decibel). Also feedback can bedesigned to improve the circuit stability by reducing S12 overthe frequency. Another advantage of the feedback techniqueis that the modified transistor S matrix after feedback isrelatively insensitive to the device parameter variation, whichmakes the circuit more robust against process variations. Thecost is degradation of noise figure due to the introduction ofresistors, reduction of gain and reduced output powercapability.As shown in Figure 1, the two most common types ofRpRs(b)(a)(c)(d)Figure 1. (a) MESFET with series feedback (b) MESFET with parallel feedback (c) Bipolar transistor with series feedback (d) Bipolar transistor withparallel feedbackEE217 final project report, Spring, 1999.II. BASIC FEEDBACK AMPLIFIER CIRCUIT: MODEL, THEORYAND ANALYSISA. Device ModelRpRsfeedback are series feedback and parallel feedback. Theseries feedback is often used to improve S11 at the expense ofreduced stability. The parallel feedback is used to flattengain over frequency. A compound of both is often used.Reactive elements can also be used with the resistivefeedback to peak the high-frequency gain. We will illustratethis through our design example.Important efforts have been made in the past decades toextend these technique to higher frequency. Different designmethods are developed during the years. Niclas et al. havereported design methods and experimental results for GaAsMESFET feedback amplifier up to 18 GHz, obtaining five ormore octave bandwidth [1-2]. The design procedure relies ona known transistor model which works up to relative lowfrequency and then doing computer optimization at higherfrequency. Later on Perez and Ortega reported two graphicalmethods [3] controlling the gain flatness, amplifier stabilityand matching, which rely on the knowledge of the measuredS-parameters and need very little optimization to achieve thefinal design. And a method [4] based on rigorous calculationto achieve the optimum performance for stability andmatching was reported by Sheau-Shong Bor et al., whichprovides more insight into the effects of the feedback andmore control of the two-port amplifier for practicalapplications.We will follow the Niclas’ method in our design. Thescaled EE217 MESFET model was used. The goal of ourdesign is to achieve a wide bandwidth and excellent gainflatness and meanwhile to control the input and outputreflection. The basic theory for the feedback circuit design atlow frequency will be described in detail first. A few designissues and trade-offs will be discussed along with theanalysis and the design procedure.As shown in Figure 2, are the diagrams of the basicfeedback circuit we were using for the amplifier includingthe parallel feedback resistor and two associated inductorsLFB and LD.Figure 2(a) is the high-frequency model. Inside the dashedline box is the small signal model for the active device, theGaAs MESFET. A set of scaled standard EE217 MESFETparameter values were used in our project, which are listed inTable 1[5]. It is the parasitic reactive elements that restrict the

RFBi1Where,LFBLDCgdCgsRiG ds Rdsi2CdcidsV2Rsi ds g m Vgs(3)V gs V 1(4)Using elementary algebra, the admittance matrix converts tothe S matrix,(a)S RFBi1i2idsV1S 11 S 12(5)S 21 S 22Its elements are,RdsV2(b)Figure 2. Circuit diagram of the basic feedback amplifier. (a) High-frequencymodel. (b) Low-frequency model.Cdg 0.05 pF0 3 psecCdc 0.02 pFfroll-off 0 HzCds 0.14 pFCgs 0.47 pFRds 256.67 ohmRi 4.83 ohmRs 2.67 ohm1 R FBS 11 --- --------- ( 1 G ds Z 0 ) – ( g m G ds )Z 0 (6a)Z02S 12 --(6b)2S 21 – --- [ g m RFB – 1 ](6c)1 R FBS 22 --- --------- ( 1 – G ds Z 0 ) – ( g m G ds )Z 0 (6d)Z0TABLE 1. Parameter Values of the Transistor Modelgm 60 m mhos(2)AndCds RdsV1–1Withamplifier bandwidth ability. Two inductors, drain inductorLD and feedback inductor LFB are introduced to compensatethe capacitive output and bring positive feedback.Figure 2(b) is the low-frequency model when we ignorethe reactive elements and Ri, Rs, which can be used todetermine the amplifier’s dc gain, input and output VSWR,and reverse isolation. Further simplification will cause error,so Rds stays in our calculation below.R FB 2 ( g m G ds )Z 0 --------- ( 1 G ds Z 0 ) (6e)Z0The feedback resistor’s influence on the gain and theinput, output VSWR are implied in the S parameterexpression.The choice of RFB is clearly a compromisebetween gain and VSWR. We can consider three cases.Case 1: Input and output VSWR are identical for thefeedback resistor,2R FB ( g m G ds )Z 0(7a)and the S-parameters are:2S 11 – S 22G ds Z 0 --------------- ( g m G ds )(7b)B. DC Gain and Input and Output VSWR Calculation2S 12 ---(7c)Based on the simplified dc model of the feedbackamplifier, we can calculate its S-parameters.Assuming Ri, Rs are small compared with the feedbackresistor RFB, which is true in our case, and load resistor RL Z0, the relation between voltages and currents can bedescribed by the admittance matrix,22S 21 – --- [ gm ( gm G ds )Z 0 – 1 ](7d)i1i2 1 R FB– 1 R FBV1( g m – 1 R FB ) ( 1 RFB G ds ) V 2(1) 2 ( g m G ds ) ( 2 G ds Z 0 )Z 0(7e)Case 2: Perfect matching at the output, S22 0, whichrequires the feedback resistor,g m G ds 2R FB ------------------------ Z 01 – G ds Z 0(8a)

And the S-parameters are,g m Gds2S 11 ---------------------- G ds Z 01 gm Z0(8b)1 – G ds Z 0S 12 -----------------------1 gm Z 0(8c)S 21 1 – ( g m G ds )Z 0(8d)S 22 0(8e)resistances and matching network will come to the play. Butthere, the main effort will be made to maintain the flat gain tothe maximum frequency and to improve the degradedmatching. But the basic gain level and potential to a goodmatching are determined by the dc network. So the dcanalysis is very useful and important.C. Frequency Controlled FeedbackCase 3: Perfect matching at the input, S11 0, whichrequires the feedback resistor,g m Gds 2R FB ------------------------ Z 01 G ds Z 0(9a)and the S-parameters are,S 11 0(9b)1S 12 -----------------------------------------1 ( g m G ds )Z 0(9c)2S 212 g m ( g m G ds )Z 0 – --- --------------------------------------- – 11 G ds Z 0S 222 G ds ( g m G ds )Z 0 – --- ----------------------------------------1 G ds Z 0(9d)2(9e)By comparing these three cases, case 2 has highest gainbut also highest input reflection coefficient, while case 3yields lowest gain and best input match. Case 1 is acompromise with medium gain, and good control of both S11and S22. With a finite value of Rds, S11 and S22 can’t be zeroat the same time.Let’s look at a special condition for case 1 with Gds 0, orThe conventional negative resistive feedback can onlyoffer gain and VSWR to a relatively low frequency.“Frequency controlled feedback” is used to achieve widebandwidth. In Figure 2(a), two inductors are used toaccomplish this method. A feedback inductor LFB isconnected in series with the feedback resistor. And a draininductor LD is added before the output. These two inductorshave different functions. LD compensates the outputcapacitance at high frequency to recover the bandwidth. LFBcan reduce the feedback at high frequency to flatten the gainfurther. A good illustration will be given with the simulationof the design example in next section.III. SAMPLE DESIGNBased on the circuit theory and the chosen technology insection II, we designed a single-stage broadband microwavefeedback amplifier. Figure 3 shows a completed design,including the basic feedback amplifier in the dashed-linebox; a simple input matching network composed of L1, C1;and the biasing and decoupling circuits (Lbiasd, Lbiasg, Cin,Cout). Final circuit performance is evaluated with thetransmission line implementation without the biasing chokes.The design method and simulation results will beillustrated step-by-step to reveal how the design spec isachieved and to provide some insight to the feedbackamplifier.Finally, a simulation of the direct connection of two stagesdemonstrates the feedback amplifier can be easily cascadedto achieve higher gain while maintaining the bandwidth.Rds . Then perfect match can be achieved at both ends,S11 S22 0. And the tranceconductance gain is,S21R FB 1 – gm Z 0 1 – --------Z0VD(10)We can see the gain is determined by feedback resistanceinstead of the device parameters, which offers the immunityfor the circuit performance from the process variation.Because of the gain reduction caused by the feedback, a highgm transistor is favored in the microwave feedback design.As we noticed, this analysis is only valid for the lower endof the bandwidth. The design extended to higher frequencycan only be accomplished with the aid of the CAD tools,where all the device reactive parasitics, ignored parasiticRFBCinLFBLbiasdLDL1CoutC1LbiasgVgFigure 3. A single-stage feedback amplifier with input matching network andbiasing RF chokes. RFB 170 , LD 0.10 nH, LFB 0.73 nH, L1 0.76nH, C1 0.25 pF.

gm 200 mSgm 120 mSgm 40 mSCircuits with simple resistive feedback also demonstratethis trade-off as shown in Figure 5. With a dc gain of 10 dB,5 GHz bandwidth is achievable. With a higher bandwidth of10 GHz, the maximum dc gain would be about 5 dB. Since ahigher gain can be achieved by cascading two single-stageamplifier, we decide to design a single-stage with 5 dB dcgain. By further feedback technique and matching, we try topush the bandwidth as high as possible. Meanwhile, we wantto control the input and output VSWR to less than 2:1, whichimplies S11 and S22 should be less than 0.333.B. Amplifier Design and Simulation(a) Gain Flatness and Bandwidth EnhancementFigure 4. Gain magnitude vs. frequency of a bare MESFET of different gmvaluesgm 200 mSgm 120 mSgm 100 mSgm 90 mSgm 40 mSFrom the analysis of section IIB, we know when wechoose RFB, there is a trade-off between gain and VSWR. Inour design, we chose to get a relative good matching at bothinput and output. The main focus is to achieve a good gainflatness over a wide bandwidth. Simple matching networkwas adopted to compensate the degraded matching at highend of the bandwidth.From equation (7a) and (7d), we can calculate the gm to beused to get 5 dB dc gain and the feedback resistance. And wedid simulation similar as the one shown in Figure 5 with gmvalues near the calculated value and with corresponding RFBvalues. We found gm of 60 mS provides dc gain of 5 dB, thecorresponding RFB is 170 W. The gain response with onlyresistive feedback is shown in Figure 6, curve (a). 5 dB gainis achieved at dc, but it rolls down very quickly at thefrequency region we are interested. And its phase frequencyresponse is shown in Figure 8(b). The 3 dB point is around11 GHz, the gain phase is 90 degree.Positive feedback is used to compensate the gainFigure 5. Gain magnitude vs. frequency for a MESFET with simple resistivefeedback of different gm values(d)A. Gain-Bandwidth Trade-offFirst we studied the gain-bandwidth trade-off of the EE217MESFET and the resistive feedback circuit to determine areasonable spec for our design.,As shown in Figure 4, the gain response vs. frequency for abare EE217 MESFET of different gm values are studied. Byincreasing gm, the transistor dc gain is boosted. But veryclearly, for a certain technology, the gain-bandwidth is pair oftrade-off because by scaling gm up, the parasitic outputcapacitance scales up too. For a single-stage amplifier, with acertain bandwidth requirement, the maximum gain will belimited by the technology. So devicewise, eliminating thereactive parasitics can extend the circuit bandwidth.(c)(b)(a)Figure 6. Gain magnitude frequency response of the basic feedback amplifier shown in Figure 2(a). Curve (a) RFB 170 , LD 0, LFB 0, (b) RFB 170 , LD 0, LFB 0.5 nH, (c) RFB 170 , LD 0.35 nH, LFB 0, (d)RFB 170 , LD 0.35 nH, LFB 0.5 nH.

(a)(b)negative feedback(c)positive feedbackFigure 7. Comparison of gain magnitude frequency response among (a) baretransistor without feedback, (b) with only resistive feedback, (c) with bothresistive feedback and the inductors, LD 0.35 nH, LFB 0.5 nH.feedback basically works at very low frequency, by eliminatingthe dc gain. And it has very little effect on the phase frequencyresponse. However, by using the frequency controlled feedback.The gain flatness is maintained until 12 GHz. A positivefeedback frequency region appears as marked in the figures. Ifwe look at the phase curve (c), we know a zero is introduced tocompensate the pole which is at 11 GHz. That’s how we get thepositive feedback.LD was chosen to compensate the capacitive component ofthe output impedance so that the resonance occurs at the upperband edge. LFB was chosen to get the optimum positivefeedback. The final values of LD and LFB were obtained fromthe CAD tools optimization. We found in a large range, variouscombinations of LFB and LD produce good gain flatness andbandwidth. And the program doesn’t necessarily give theoptimal values which are practical for implementation. We keptin our mind a larger LFB value than that of the LD makes moresense in the layout since LFB connects from the output of thetransistor to the input of the transistor. So optimization wasterminated when the performance was achieved with a pair ofpractical parameters.(b) Input VSWR and Output VSWR(a)(b)(c)negative feedbackpositive feedbackFigure 8. Comparison of gain phase frequency response among (a) baretransistor without feedback, (b) with only resistive feedback, (c) with bothNow the broadband potential of the basic feedback amplifieras shown in Figure 2(a) or in the dashed-line box of Figure 3 isalmost exhausted. We want to come back to check the input andoutput VSWR. And a simple LC input matching network wasdesigned to improve the input matching, which is shown inFigure 3. Figure 9 and Figure 10 shows simulation resultsbefore and after the addition of the input matching network.Input and output reflection coefficients can be calculatedfrom equation 7(b). Comparing curve (a) and (b) in Figure 9 andFigure 10, the feedback does provide good matching at bothresistive feedback and the inductors, LD 0.35 nH, LFB 0.5 nH.degradation at the high end of the bandwidth. Two inductorswere added to achieve this. The connection is shown in Figure2(a). A comparison of the gain magnitude frequency response inFigure 6 well demonstrates the function of the two inductors. Asstated above, curve (a) shows gain in dB rolls down linearlywithout any inductor. Curve (b) shows LFB can reduce thenegative feedback at high frequency. At low frequency itdoesn’t affect the gain. Curve (c) shows the main contributionof the bandwidth recovery is from LD. Curve (d) is the gainresponse with both LFB and LD. Bandwidth is recovered to 12GHz, with gain 5 0.1 dB. The use of the two inductors in thefeedback is so called “frequency controlled feedback”.In Figure 7 and Figure 8, we compared both gain magnitudeand phase frequency response among three cases, (a) baretransistor, (b) resistive feedback, and (c) frequency controlledfeedback. Comparing (a) and (b), we can see the resistive(a)(c)(b)(d)Figure 9. Comparison of the input reflection coefficient S11. (a) Bare transistor, (b) Resistive feedback, (c) Frequency controlled feedback, RFB 170, LD 0.35 nH, LFB 0.5 nH, (d) Frequency controlled feedback withadditional input matching network.

(a)(a)(d)(b)(b)(d)(c)(c)Figure 10. Comparison of the input reflection coefficient S22. (a) Bare transistor, (b) Resistive feedback, (c) Frequency controlled feedback, RFB 170 ,LD 0.35 nH, LFB 0.5 nH, (d) Frequency controlled feedback with additional input matching network.input and output. S11 0.1463, S22 0.0130. But the matchingturn worse when the frequency increases. At 12 GHz, S11 0.5937, S22 0.3318. S11 is more problematic, At the frequencyband edge it is already out of the spec.Comparing curve (c) and (b) in Figure 9 and Figure 10, wecan see S11 is degraded a little near the frequency band edge,but S22 is improved above 1 GHz. At 12 GHz, S11 0.6438, S22 0.2548.So a simple LC matching network is added to the input toimprove S11. Since the concern here is reflection instead ofpower gain, we will pursue impedance match instead ofconjugate match. We chose the L section matching networkdescribed in Pozar’s book [6]. As shown in Figure 11, differentconfiguration should be used for different normalized loadimpedance we are trying to match. Given zL, the type ofconfiguration can be determined, and the required values of Band X can be calculated from the formula given in [6].In ourcase, ZL here is the input impedance Zin of the basic amplifierbefore matching. From the measurement by the software, at 12GHz, zin 0.28 - 0.52j, so type (b) should be used. As shown inFigure 3.Comparing curve (d) and (c), we can see, the LC networkjB(a)brings down S11 dramatically near its resonance frequency 11.5GHz. A local minimum S11 occurs at 10.5 GHz. At 12 GHz, S11 0.2922. And as we can see, the matching at input actuallydegrade the output match a little. At 12 GHz, S22 0.2555. So itis still within the spec. In this case, an output matching networkis not necessary.And overall, after some optimization, a design of 5 dB gain,12 GHz bandwidth, 0.15 dB gain flatness is achieved. InputVSWR is less than 1.8. Output VSWR is less than 1.7. Circuitparameters are listed in Figure3. Large value should be chosenfor the biasing and decoupling circuit elements.Curve (d) in Figure 12 shows with the input matchingnetwork, the amplifier remains a good gain flatness.(c) Transmission Line ImplementationSince the wide bandwidth and small inductance andcapacitance value we used in our design, it is possible to.implement the Ls and Cs by transmission line. The overalljXjXZ0Figure 12. Comparison of gain magnitude frequency response among (a) baretransistor without feedback, (b) with only resistive feedback, (c) with both resistive feedback and the inductors, LD 0.35 nH, LFB 0.5 nH, (d) frequencycontrolled feedback with additional input matching network.ZLZ0ZLjB(a)(b)(b)Figure 11. L section matching networks. (a) Network for zL inside the 1 jxcircle. (b) Network for zL outside the 1 jx circle.Figure 13. Gain magnitude frequency response of the complete design. (a) withideal Ls and Cs, (b) with transmission line implementation.

Table 2.(a)(c)(b)(e)S11(d)TABLE 2. Transmission line parameters(f)ElementImpedance ()Length at 12 (d) Circuit StabilityCircuit stability was checked step-by-step. A criteria forunconditional stability:Figure 14. Comparison of S11, S22 and stability parameter between the completed design with ideal Ls and Cs and the transmission line implementation.Curve (a), (c), (e) belong to the ideal case. Curve (b), (d), (f) are results of the

feedback amplifier can be designed to have a very wide bandwidth (more than two decades) with small gain variations (tenths of a decibel). Also feedback can be designed to improve the circuit stability by reducing S12 over the frequency. Another advantage of the feedback technique

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