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TECHNICAL FEATURE

sign by analytically predicting oscillator feed-back parameters that allow the oscillator oper-ation mode to be realized very close to opti-

mum.2

A GENERAL ANALYTIC APPROACH

The general procedure for microwave tran-sistor oscillator design is to define the optimalvalues of feedback elements and load that cor-respond to the maximum power at a given fre-quency while in stable steady-state, large-sig-nal operation. The common-gate FET oscilla-tor configuration with positive series feedbackbetween gate and ground is shown in Figure1 where Zi = Ri +jXi, i = 1 or 2 and ZL = RL +

jXL. This circuit configuration was selecteddue to its inherent broadband negative resis-

tance. I f the correct feedback reactance isadded, oscillations can occur from very lowfrequencies to the approximate maximum os-cillation frequency fmax. The small-signal FETequivalent circuit, which characterizes the de-vice properties with good accuracy up to 50GHz, also is presented in the diagram.3

ANDREY V. GREBENNIKOVInstitute of MicroelectronicsSingapore

TECHNICAL FEATURE

Microwave FET oscillators havedemonstrated well-behaved opera-tion and easy integration capability in

both hybrid and monolithic integrated cir-cuits. The essential expansion of their applica-tion on the one hand and requirements forlow oscillator cost on the other call for newapproaches to transistor oscillator design. Inlarge-signal operation, it is necessary to defineappropriate parameters of the active two-portnetwork and external elements of the oscilla-tor circuit. Initially, the values of the externalcircuit elements are unknown and for a givenmicrowave oscillator with a required frequen-cy of oscillation it is difficult to directly choosetheir values without any preliminary calcula-tion. This process can be sufficiently time con-

suming and in a general case calls for muchsimulation. Therefore, it is con-venient to use an analyticmethod of optimum microwaveoscillator design that deter-mines the explicit expressionsfor feedback elements and loadimpedance in terms of the tran-sistor equivalent circuit para-meters.1 Such an approach hasbeen applied successfully to mi-crowave bipolar oscillator de-

M ICROWAVE FET

OSCILLATORS: AN ANALYTIC

APPROACH TO SIMPLIFY

COMPUTER-AIDED DESIGN

MIC

ROW

AVEJOURNAL

ED

ITORIAL BOARD

REVIEWED

gLg

Ls

Ld dRg

Rgs

Rds

Rs

RdCgd

Cgs

Z1 ZL

ZoutZ2

s

gm, Cds

Fig. 1 The series-feedbackFET oscillator equivalentcircuit.w

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The steady-state oscillation condi-tion for a single oscillation frequencycan be expressed as

Zout (I,) + ZL() = 0 (1)

where Zout (I,) = Rout (I,) +jXout(I,) is an equivalent one-port net-

work output impedance looking intothe FET drain where a series-tunedcircuit, ZL() = RL() +jXL(), isthe frequency-dependent load impe-dance. The output impedance Zoutcan be expressed through the transis-tor equivalent circuit and feedbackparameters as

It is advisable to optimize the os-cillator in terms of the maximum val-ue of the negative real part of theone-port network output impedance.1

In this case, the optimal values X1and X2 (at which the negative valueRout is maximum) can be defined bysolving the two equations

The analytic calculations show thatthe optimal values X1

0 and X20 depend

on the impedance parameters of theactive two-port network as

By substituting X10 and X2

0 into Equa-tion 2, the optimal real and imaginaryparts of the output impedance Z0out =R0out +jX

0out can be defined using

X

R R

X X

R RR R

XX X

X

R R R R R

X X

X X

10

21 12

21 12

12 2111 1

1112 21

20

2 12 21 21 12

21 12

12 21

2

2

2

2

24

=

+

++

=

+ +( ) ( )

( )

+

( )

=

=R

Xand

R

Xout out

1 2

0 0

3( )

Z

Z ZZ Z Z Z

Z Z Z

out =

++( ) +( )

+ +22 212 2 21 2

11 2 1

2

( )

SMALL-SIGNAL OSCILLATORCIRCUIT DESIGN

The internal FET in a common-source small-signal operation is conve-niently characterized with the help of

Y parameters, the frequency depen-dencies of which are determined as

where

= transit time in the FET channel

To significantly simplify the prelimi-nary theoretical calculations, it is ad-visable in some cases to neglect the

influence of gate-drain capacitanceCgd and transit time . By using well-known transformations of Y and Z pa-rameters and substituting the expres-sions for the real and imaginary partsof Z parameters from Equation 6 intoEquation 4, the optimum values ofthe imaginary parts of the feedbackelements X1

0, X20 and X0out, expressed

through the parameters of the FETequivalent circuit, are determined by

X

C

R

C R Rg

C

X R C Rg

C

X R C Rg

C

gs

ds

ds gs gm

gs

ds ds sm

gs

out ds ds outm

gs

10

20

0 0

1

2

2

2

7

= +

+( ) +

= +

= +

( )

Yj C

j C Rj C

Y j C

Yg j

j C Rj C

YR

j C C

gs

gs gsdg

dg

m

gs gsdg

dsds dg

11

12

21

22

1

1

16

=+

+

=

=( )

+

= + +( )

exp

( )

R R R

R R R X X

R R R

X X X

R R

X X R R R

out

out

out

02 22

2 12 21

2

21 12

2

11 2 1

020

22

21 12

21 12

0

2 22

2

4

5

= +

+ +( ) + ( )

+ +( )= +

( )

( )

To develop an optimal series-feed-back FET oscillator, the values of thereactances X1

0 and X20 should be in-

ductive and capacitive, respectively,in accordance with Equation 7. Theanalytic equation for the calculationof R0outcan be written as

Defining the differential drain resis-tance Rdsand expressing it through theoutput resistance R0out requires a solu-tion to the quadratic Equation 8. Thus,

where

LARGE-SIGNAL SIMULATION

One of the most popular ap-proaches for a nonlinear free-running

oscillator analysis is to use the har-monic balance equations developedfor the circuit and consider the oscil-lation frequency as an additional opti-mization variable.4 Such an algorithmis used in version 7.5 of MicrowaveHarmonica as a part of the circuitsimulator Serenade 7.5.5The basicidea in this method can be explainedstarting from the oscillation condi-tions described in Equation 1 whenan oscillator circuit is considered aone-port circuit. To determine theresonant frequency, the program

computes the circuit loop gain by im-posing a small test voltage source onthe circuit, as shown in Figure 2.

GR R R

g

C

R R C

dsog s gs

m

gs

out s ds

=+ +

+ ( )( )

1

2

2

0 2

R

R R G

Gds

out s dso

dso

=+

( )

1 1 4

29

0

( )

R RR

C R

R

R R R

g

C

out s ds

ds ds

ds

g s gs

m

gs

0 2

2

1

12

8

++ ( )

+ +

( )

TECHNICAL FEATURE

OSCILLATORCIRCUIT

V1

Y1

I1

Yload

Yosc

v Fig. 2 The principle of nonlinearcircuit simulation.

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The source fundamental current I1

= Re(I1) +jIm(I1) is a function of thezero-phase peak voltage V1 and fre-quency f. I f f is the circuits self-reso-nant frequency, then the phase of thecurrent I1 is zero and Im(I1) = 0 for anonzero Re(I1). For a nonzero volt-age V1 and a small Im(I1), the steady-state oscillations conditions (Equa-tion 1) are carried out for Re(I1) = 0when the circuit feedback loop gainequals unity. The starting oscillationconditions are found at Re(I1) < 0and Im(I1) = 0.

To verify the accuracy of the analyt-

ic approach used with reference to thecalculations of the oscillator externalfeedback parameters, a power mi-crowave MESFET (l = 1 m, w = 4 200 m) has been chosen.3To deter-mine the value of output resistanceRoout in consideration of the drain seriesresistance Rd for the chosen value ofload resistance RL, it is necessary touse the amplitude balance equationRoout + Rd + RL = 0. For a preliminarilydefined oscillation frequency f= 4GHz, the optimum oscillator feedbackparameters according to the theoreti-

cal calculations must be equal to L =5.0 nH and C = 0.4 pF when the loadresistance RL = 50 . To satisfy thephase balance condition Xoout + Ld +XL = 0 where Ld is the drain lead in-ductance, the value of XL should be in-ductive and LL = 4.0 nH. The small-signal parameters of the transistorequivalent circuit are listed inTable 1.

The nonlinear circuit simulationwas determined for a microwave se-ries-feedback circuit MESFET oscil-

lator, the equivalent circuit of which isshown inFigure 3. The starting oscil-lation conditions were determined bysweeping the frequency f of the exter-

nal test source from 3 to 5 GHz. Thecurves satisfy starting oscillation con-ditions under linear small-signal oper-ation where Re(I1) < 0 and Im(I1) = 0at 4.4 GHz, as shown in Figure 4. Inthe steady-state operation mode theoscillation frequency becomes equal

TECHNICAL FEATURE

TABLE I

TRANSISTOR EQUIVALENT CIRCUITSMALL-SIGNAL PARAMETERS

Lg (pH) 50.4

Ls (pH) 0.1

Ld (pH) 60.1

Rg () 2.0

Rgs () 2.0

Rs () 0.93

Rd () 1.1

Cgs (pF) 1.2

Cgd (pF) 0.087

Cds(pF) 0.199

gm (mS) 97.4

(ps) 4.8 to 3.85 GHz, which is in good agree-ment with the predicted theoreticalvalue. However, neglecting the gate-

drain capacitance Cgd and transit time leads to an inductive value of loadreactance. In the optimal oscillatorthe maximum output power is real-ized under the conditions of completephase compensation with a load reac-tance equal to zero.1

To increase the oscillation fre-quency to f= 12 GHz the optimal os-cillator feedback parameters accord-ing to theoretical calculations mustbe L = 0.35 nH and C = 0.5 pF, asshown in Figure 5. In this case, tosatisfy the phase balance condition

Xoout + Ld + XL = 0, the value of XLmust be capacitive and CL = 1 pF.

The simulated value of the oscillationfrequency is 10.72 GHz, which dif-fers from the theoretical value byonly 11 percent. The oscillation fre-quency dependence of RL is shown in

10 nH

10 nH

10 nH

5.0 nH

10 pF 0.4 pF

4.0 nH10 pFFET

MATERKA

S

G

D

V=0.6 V= 6

FREQUENCYSINGLE TONE

nHarm: 5FREQUENCY: 2 to 6 GHz

+

+

v Fig. 3 The simulated series-feedback 4 GHz FET oscillator equivalent circuit.

2

1

0

1

2654

FREQUENCY (GHz)

32

Y1(mA)

Fig. 4 The simulated startingoscillation conditions.w

10 nH

10 nH

10 nH

0.35 nH

10 pF 0.5 pF

1.0 pFFET

MATERKA

S

G

D

V=0.6 V= 6

FREQUENCYSINGLE TONE

nHarm: 5FREQUENCY: 7 to 15 GHz

+

+

v Fig. 5 The simulated series-feedback 12 GHz FET oscillator equivalent circuit.

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Figure 6 from which it follows thatmaximum output power Pout = 22.9

dBm can be realized for load valuesof 20 to 30. The constant bias draincurrent did not exceed 96 mA underthe simulation procedure.

The subsequent computer simula-tion shows that the large-signal oscil-lation conditions for various values offeedback elements L and C exist in avery broadband frequency range.Fig-ure 7 shows the frequency depen-dence of source feedback capacitanceC when RL = 25 and L = 0.35 nH.Capacitance tuning of 0.15 to 2.00 pFresults in frequency tuning of 8.3 to

13.6 GHz with an approximately con-stant level of output power of 23 to 24dBm. I mproved frequency tuningcharacteristics can be achieved by in-ductive tuning. F requency depen-dence of the gate feedback induc-tance L is shown in Figure 8 whereRL = 25 and L = 0.5 pF. In thiscase, inductive tuning of 0.2 to 7.0 nHresults in frequency tuning of 3.9 to13.3 GHz with an output power levelof 19 to 23 dBm. In addition, the os-

cillation conditions are satisfied undera subsequent increase of gate feed-back inductance up to 100 nH with anappropriate decrease of oscillation

frequency to 2.8 GHz.It was shown previously that a se-

ries-feedback MESFET oscillator wassuccessfully used as an octave band-width varactor-tuned oscillator in thefrequency range of 7.25 to 14.65GHz.6 In the case of the given powerMESFET, both the upper bandwidthfrequency and output power of theoscillator can be increased significant-ly. The equivalent oscillator circuit forwideband tuning is shown in Figure9. The values of source and gate biasinductances were preliminarily cho-

sen to maximize the frequency tuningbandwidth, and an additional capaci-tor of 1 pF in parallel with the loadresistance was used to provide stableoscillation conditions throughout theentire tuning range when RL = 50 .As a result, simultaneous gate andsource feedback capacitance tuning of0.09 to 2.0 pF produced a wide fre-quency tuning bandwidth of 10.1 to26.0 GHz with high output power, asshown inFigure 10.

TECHNICAL FEATURE

CONCLUSION

A simple analytic approach to mi-crowave FET oscillator design hasbeen used to define explicit expres-sions for optimum values of feedbackelements through transistor Z para-meters. A negative resistance conceptwas utilized to design a series-feed-back microwave FET oscillator withoptimized feedback elements andmaximum output power in terms ofthe transistor impedance parameters.Such an approach simplifies signifi-cantly the nonlinear circuit simula-

tion procedure. A very broadband ca-pacitor tuning of the series MESFEToscillator in the Ku and K frequencybands has been demonstrated. F inalsimulation results indicate the attrac-tiveness and advisability of the circuitparameter analytic evaluation fornonlinear computer-aided design. s

References1. A.V. Grebennikov and V.V. Nikiforov, An

Analytic Method of Microwave TransistorOscillator Design, International J ournalof Electronics, Vol. 83, December 1997,pp. 849858.

2. A.V. Grebennikov, Microwave TransistorOscillators: An Analytic Approach to Sim-plify Computer-aided Design, MicrowaveJournal, Vol. 42, No. 5, May 1999,pp. 292300.

3. J.M. Dortu, J.E. Muller, M. Pirola and G.Ghione, Accurate Large-signal GaAsMESFET and HEMT Modelling for Pow-er MMIC Amplifier Design, InternationalJournal of Microwave and Millimeter-waveComputer-aided Engineering, Vol. 5,March 1995, pp. 195209.

4. C.R. Chang, M.B. Steer, S. Martin and E.Reese, Computer-aided Analysis of Free-running Microwave Oscillators, IEEE

11.1

11.0

10.9

10.8

10.7

60504030

RL ()20100

23

20

17Pout(dBm)

f(GHz)

v Fig. 6 Output power and oscillationfrequency vs. load resistance.

14

13

12

11

10

9

82.42.01.61.2

C (pF)

0.80.40

f(GHz)

v Fig. 7 Oscillation frequencyvs. feedback capacitance.

15

13

11

9

7

5

36543

L (nH)

210

f(GHz)

v Fig. 8 Oscillation frequencyvs. feedback inductance.

0.8 nH

0.5 nH

10 nH

0.5 nH

0.09 pF 0.09 pF

1 pF

1 pFFET

MATERKA

S

G

D

V=0.6 V= 6

FREQUENCYSINGLE TONE

nHarm: 5FREQUENCY: 5 to 40 GHz

+

+

v Fig. 9 The simulated series-feedback-tuned FET oscillator equivalent circuit.

2623

20

17

14

11

8

f(GHz)

18

16

14

12

2.42.01.61.2

C (pF)

0.80.40

Pout(dBm)

v Fig. 10 Output power and oscillationfrequency vs. tuned capacitance.

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Transactions on Microwave Theory andTechniques, Vol. 39, October 1991,pp. 17351745.

5. Microwave Harmonica, Reference Vol-ume, Version 7.5/P.C., Ansoft Corporation,New Jersey, 1998.

6. J. Kitchen, Octave Bandwidth Varactor-tuned Oscillators, Microwave Journal,Vol. 30, No. 5, May 1987, pp. 347353.

Andrey ViktorovichGrebennikovreceivedhis Dipl Ing degreefrom Moscow Instituteof Physics andTechnology and hisPhD degree fromMoscow TechnicalUniversity ofCommunication and

Informatics in 1980and 1991, respectively.

In 1983, he joined the scientific researchdepartment of Moscow Technical University ofCommunication and Informatics as a researchassistant. Since October 1998 he has beenworking with the Institute of Microelectronics,Singapore. Grebennikov can be reached via e-mail at andrei@ime.org.sg.

TECHNICAL FEATURE