l
tn
Designof RF and Microwave Amplifiers and Oscillators
r0.12
BALANCED AMPLIFIERS
Srln a balancedamplifier, the input signalis split into two or moreamplifiers,andthe output :nals of theseamplifiers are combinedto a single load, with isolation betweenthe Ddividual amplifierportsin bothcases.Themostcommonlyusedconfigurationis shown b Figure10.57. The S-parameter matrix of a 3-dB, 90" hybrid divider is given by [13], with the prts numberedas in Figure 10.57. For the divider, the energyincidentat port l, therefore,is deliveredto the loads coorcted to ports2 and3 with a 90' phaseshiftbetweenthetwo components. Theenergy :-cident at ports2 and3 in the combineris routedto port l, againwith a 90' phaseshift -:iseenthe two components.
l Su
outpl refle indiv ampl ampl
Gr=
j '-l [o =0.107 li o ol
(10.139)
L l 0 o J
Gr=
I hd ftd for a 3-dB, 90'hybrid combinerby
whicl
[t o o- i 1l
sr=0.707 0 rl 10
(lo.t4o)
li 1oJ
t -
The S-parametermatrix of the amplifier is given in termsof theS-parameters of the . nro individual amplifiersby [13]
I
indiv only r
be re< (10. decid
10.
3-dB 90" hybrid coupler
3-dB 90" hybrid
Oscil or the gain. at sta to ens
feedb 10.5
ftrrc
10.57
The most commonly usedbalancedamplifier configuration.
to the first n the se
The Designof Radio-Frequencyand Microwave Amplifiers and Oscillators
S r = 0.,I
srr,r- s,,.2 ,l(srz,r+ s r r r ) l
[f(szr,r+ szr,z) sz2,l*
Snl
I
441
(l0.l4l)
I
It is clearfrom this equationthat if amplifiersI and2 areidentical,the input and outputreflectionparameters of thebalancedamplifierwill beequalto zero,evenwhenthe reflectionpararneters of the individual amplifiersare not equalto zero.As long as the individual amplifiersare almost identical,the input and output VSWRs of a balanced amplifier will thereforebe very low, independentof the vSWRs of the individual amplifiers. The tansducer power gain of the balancedamplifier is given by
Gr = 0.25''s rr,,* r rr,rl'
(r0.r42\
When the individual amplifiers are identical, this reducesto t P ur = lszr,rl
(10.143)
which is identicalto the gain of a singleamplifier. Although the gain of the balancedamplifier is thereforeidenticalto that of each individual amplifier in the idealcase,the outputpower is twice that obtainableby using only a single-endedstage. Shouldoneof the amplifierscomprisingthe balancedamplifierfail, the gainwill reduced be to one-fourthofits originalvalue.This canbe provedeasilyby settingszr,rin (10.142)equalto zero.Insomeapplications thisadvantage canbeanimportantfactorwhen decidingwhethera balancedor single-ended amplifiershouldbe used.
10.13 OSCILLATORDESIGN Oscillatorscanbe designedby controllingthe reflectioncoefficient(negativeresistance) or theloop gainof thetransistor[1- 4]. Thebetteraltemativeusuallyis to controlthe loop gain.At steady-state,both conditionswill be satisfied,but this doesnot necessarilyfollow at start-up.Independentofhow the designwasdone,both conditionsshouldbe checked to ensurethat spuriousoscillationswill not occur. The two basicoscillatorconfigurationsareshownin Figure 10.58.Voltage-shunt feedbackis used in Figure 10.58(a),while current-seriesfeedbackis used in Figure 10.58(b). In orderto control the outputpowerof an oscillator,the loadterminationpresented to thetransistorshouldbe controlledtoo. Theloadterminationcanbe controlledeasilyby fust modifring thebasicconfigurationsto thoseshownin Figure10.59[4]. In thecaseof the seriesfeedback,the original groundconnectionwasfloatedanda virtual groundwas
442
Designof RF and Microwave Amplifiers and Oscillators
(b) Figure 10.58
The basic configurationsfor oscillatorswith (a) shuntfeedbackand (b) seriesfeedback.
introduced.No physical changeis requiredin the shuntfeedbackcircuit. In the seriesfeedbackcase,any transmissionlinesusedshouldfirst be converted to lumpedT- or Pl-sectionequivalentsbeforethe groundconnectionis changed. Any extensionlines shouldbe kept as short as possible.The extra phaseshift aroundthe loop will reducethefrequencyrangeoverwhich oscillationis possibleandwill alsoincreasethe start-uptime. A simplifiedflow diagramofthe oscillatordesignprocessis shownin Figure10.60. In order to control the output power,power contourscan be generatedfor the transistorby using the power parameterapproachdescribedin Chapter2 or by using a nonlinearsimulator.A suitableload line can then be selected,after which a feedback networkcanbedesignedto providethis loadterminationto thetransistorwith theloop gain shouldbecontrolled,butexcellentresultscan required.Ideally,theloadline at steady-state if the loop gainrequiredis low. alsobe obtainedwith the small-signalparameters
The Design of Radio-Frequencyand Microwave Amplifiers and Oscillators
443
(a)
(b) *
ZLr
Zn= Zt r
(c) Figure 10.59
(a), (b) The two oscillatortopologiesshownin Figure 10.58modified for the purposeof calculating the transistorload-terminationand the loop gain [l]. (c) The voltage and impedanceat steady-state.
The output power of an oscillator will increaseinitially as it is driven harder into compression, after which it will decrease. The transistor will be driven harder into compression as the loop gain or the negative resistancein the input loop (series feedback case) is increased. The gain compressionassociatedwith the maximum effective output power can be estimatedby assumingthe power saturationcharacteristicto be governedby an exponential law function [5]. Under the assumptionsmade, this point is only a function of the smallsignal gain associatedwith the load termination chosen.The relevant equationsare derived i n S e c t i o n1 0 . 1 3 . 1 .
F
F
444
Design of RF and Microwave Amplifiers and Oscillators
Selecta transistor.
Find a suitableload termination for the transistor.
Decide on the constraintsto be imposedon the three T- or PIsection impedances(only four ofthe six parametersare requiredto control the loop gain and the load terminationofthe transistor).
Determinethe valuesofthe three impedancesin the T- or Pl-sectionfeedbacknetwork.
Design the resonatorcircuit to be used(if any).
Synthesizenetworksto realizethe impedancesrequired.
Analyze the oscillator and check for and eliminate any spuriousoscillations.
Veri! the performancewith a nonlinear simulator and optimize the performanceif an accuratenonlinear model for the transistoris available.
Figure 10.60
A simplified flow diagramof the oscillatordesignprocessoutlined [].
If the compressionrequiredis relativelylow (a few decibels),the compressionat steady-statewill be approximatelythe sameas the loop gain at start-up.In this casethe loop gain at start-upcanbe useddirectlyto forcethe transistorto its peakpowerpoint. Substantialcompressionis frequently required to extract the maximum output powerfrom an oscillator.It is importantto realizethat in thesecasesthe loadtermination presentedto the transistorand the oscillatorfrequencywill changeas the transistoris driven into compression.In order for this changeand the changein the oscillation
us
The Design of Radio-Frequencyand Microwave Amplifien and Oscillators
frequencyto be small,the conditionslistedin Section10.13.1mustapply. If theseconditionsdo not apply,a betterapproachwouldbeto makeuseofthe fact that, with a well-behavedload line, the main nonlineareffect in the transistorwould be the (G,). Thetransconductance in thesmall-signalmodel compression ofthe transconductance asrequired. canthereforebe reduceduntil the large-signaloperatinggain is compressed instead setof S-parameters Thefeedbacknetworkcanthenbedesignedwith theassociated is controlled instead load line parameters. In case the steady-state this small-signal of the of the load line at start-up. When the goal is low phase-noiseand not power, the steady-statecompression shouldbe kept low. If this is done,theconversioneffrciency(mixing effects)will be low, of theflickernoise.A well-behavedload efflecton theup-conversion with a corresponding line for the transistoris still desirableas it will preventrunning into nonlineareffects with a poor choiceof the loadline. associated is required,extracareshouldbe takento maximizethe loaded If low phase-noise ofthe oscillator.This (or the slope in thephaseofthe loop gainresponse) equivalently Q will reflecton thechoiceof theresonatorto beused,aswell astheloadline chosen(higher with higherQs).In simplecasesthe will be associated parallelor lower seriesresistance by using( I 0.44).Instead loadedQ at start-upcanbeestimatedfrom theloopgainresponse of trying to estimatethe loadedQ, abetteroption seemsto be to controlthe slopein the loop phasedirectly. The feedbacknetwork (refer to Figure 10.58)must be designedto provide the (or an approximationof requiredload line and loop gain at start-upor at steady-state
Table 10.19 An exampleof a table of the T-sectionimpedancesrequiredat a specificfrequency(3.5 GHz) as a function of the loop gain [] Loop gain
(dB)
RL
(o)
XL
Ln Cr
Lo C"
v
(o)
(o)
(nH, pF)
(o)
(nH, pF)
-1.952 -2.t90 -2.457 -2.757 -3.093 -3.471 - 3.894
4.651nH 4.665nH 4.677nH 4.691nH 4.706nH 4.723nH 4.743nH
t02.356 t02.594 I 02.861 t 0 3 l.6 l 103.494 103.875 104.298
-4.902 -5.500 -6.172 -6.925 -7.770 - 8.718
4.81n 6H 4.846nH 4.881nH 4.919nH 4.962nH
105.905 106.576 r0'1.329 108.t74 109.122
-0.0927 0.9073 1.9073 2.9073 3.9073 4.9073 5.9073
49.620 49.5'73 49.521 49.463 49.39'l 49.324 49.24r
l.808 2.029 2.277 2.555 2.866 3.216 3.608
23.300pF 20.765pF pF 18.508 pF 16.495 pF 14.701 1 3 . 1 0p3F
7.9073 8.9073 9.9013 10.9073 I 1.9073 t2.9073
49.015 48.928 48.798 48.651 48.486 48.30t
5.097 5.719 6.417 7.200 8.078
8.267pF 7.368pF 6.567pF 5.853pF 5.216pF
@trc
xF
11 . 6 7 8
Note: The highlighted loop gain is equal to the estimatedcompressionrequiredto maximize the output power.
u6
b
r
Design of RF and Microwave Amplifiers and Oscillators
steady-state).Two of the three impedances(seriescase)or admittances(shunt feedback case)areusuallyassumedto bepurelyreactive(i.e.,at leastduringthe initial stagesof the design),while the outputpoweris extractedfrom the third impedanceor admittance. ofthe transistoris alsoknown, Becausetheloadline is known,theinputimpedance andit follows that the terminationsfor the T- or Pl-sectionfeedbackareknown.With the terminationsand the gain of the transistorknown, equationscan be derived for the componentsthat will provide the required loop gain, as well as the required load termination.This is donein Section10.13.2[1,. An exampleof a tableof the2,.,Zr, andZ valuesrequired(seriesfeedbackcase) GHz to realizedifferentvaluesof the loop gainanda specifiedload terminationis at 3.5 given in Table10.19.In this edsa,ZpandZ, were chosento be purely reactive.The highlightedloop gain is equalto the estimatedcompressionrequiredto maximizethe output power. for this oscillatorfrom 3.5to Table 10.20givesthe2,.,Zr, andZ valuesgenerated 4.5 GHzafterselectingthe loop gainestimatedfor peakpower.Therequiredterminations are displayedon a Smith Chart in Figure 10.61.Table 10.19showsthe T-section requiredat a specificfrequencyasa functionof the loop gain. impedances to be usedmustrotate Note thatthe tracefor at leastoneof the setsof impedances aroundthe Smith Chartin orderto ensurefrequencystability (i.e.,the counterclockwise oscillatormust lock at the frequencyof interestand not drift aroundin frequency).Such will be referredto asof varactortype. impedances The equivalentstatementin termsof the loop phaseversusfrequencyresponse (displayedon a rectangularplot) is thatthephasetracemustpassthroughzerowithoutany jiner and must not crossthe zero-degree line againbeforethe loop gain is too low for oscillation. With the T- or Pl-sectionimpedancesknown over the frequencyrangeof interest, networksmust be synthesizedto approximateeachof the impedancesover the frequency rangeof interest.Onewould generallyselecta combinationthatwouldresultin onefixedvalued component,a varactor,or a resonatorcircuit and a complex impedance(to be network). realizedwith an impedance-matching oscillator(VCO) is designed,betterresultscanusually Whena voltage-controlled network. be obtainedwith t'wovaractorsandoneimpedance-matching The impedanceassociatedwith the load terminationis often takento be the actual network load (50O),but this is clearlynot optimum.In general,an impedance-matching is requiredto realizethe impedancerequired. The reactancesrequired can be realizedwith capacitors,inductors,transmission ThedesignofhighQ dependingon therequirements. lines,varactordiodes,or resonators, resonatornetworksis consideredin Section10.13.3,while that of varactornetworksis in Section10.13.5. considered If a resonatoris used,the resonatorimpedancemustbe transformedto presentthe impedancerequiredat the relevantposition. This can often be doneby simply using a impedanceandlength.This is illustrated transmissionline with the correctcharacteristic in Section10.13.4. Onewould generallyuseseriestunedvaractornetworksin a seriesfeedbackoscil-
447
The Design of Radio-Frequencyand Microwave Amplifiers and Oscillators
Table 10.20 An exampleof a table of the T-sectionimpedancesrequiredto providethe specifiedload termination and the specifiedloop gain over the oscillationband (VCO with two varactors)[] Frequency (GHz)
3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50
L"'C'
x"
(o)
(nH, pF)
(o)
-4.369 -4.430 -4.497 -4.564 -4.639 - 4.715 -4.820 -4.935 -5.046 -5.166 -5.290
4.764nH 4.452nH 4.1't'tnH 3.916nH 3.684nH 3.464nH 3.273nH 3.095nH 2.925nH 2.772nH 2.630nH
104.773 100.707 97.O97 93.492 90.275 87.051 84.305 81.683 79.038 76.645 74.352
XL
L1,C1
XF
(cl)
(0)
(nH, pF)
49.149 49.114 49.078 49.041 49.004 48.965 48.923 48.878 48.832 48.786 48.738
4.049 4.085 4.126 4.165 4.212 4.257 4.327 4.403 4.475 4.552 4.632
pF 10.408 9.979pF 9.565pF 9.178pf 8.797pF 8.438pF 8.053pF 7.679pF 7.335pF 7.002pF 6.68spf
RL
lator and parallel tuned networks in a shunt feedbackoscillator. The particular choice would dependon the componentvaluesand the behavioroutsidethe oscillationband. Whena seriestunednetworkis usedin a shuntfeedbackoscillator,andvice versa,losses in the varactornetwork could havea seriousstabilizingeffect on the circuit. If sucha choicewas made,be sureto checkthe effect of suchlosseson the performanceof the circuit.
MEASSYreE lru.4.ffi
Figure 10.61
ml: ru2
A.@ $.6
The T-sectionimpedancesin Table 10.20displayedon a SmithChart[]. Note that at least one of the setsof impedancesshouldrotatecounterclockwisearoundthe Smith Chart to ensurefrequencystability (Zo in this case).
448
Design of RF and Microwave Amplifiers and Oscillators
Care shouldbe takenwhen decidingon the impedanceto be approximatedwith a fixed capacitoror inductor.Ideally,thechoicemadeshouldresultin a topologythatcannot sustainoscillationsat very low or very high frequencies. Whensuitablenetworkshavebeenfitted to the targetimpedances, the oscillator shouldbe analyzedto confirm its performanceandto checkfor anyspuriousoscillations. Becauseloopsmay be present,the analysisshouldbe donefairly densely.Both the loop gain andthe reflectiongainperformanceshouldbe checked. If an accuratenonlinearmodel for the transistorusedis available,the oscillator performanceshouldbe verified andoptimizedwith a nonlinearsimulator. An exampleof a dielectricresonatoroscillator(DRO) designedasdescribedhere is shown in Figure 10.62(Courtesyof PlesseyAvionics, Retreat,SouthAfrica). The topologyis shownin Figure 10.63.Theoscillatorwasdesignedto oscillateat 15.65GHz with theoutputpowerhigherthan l0 dBm (Biaspoint: 2V,20 mA). Theperformance was in the supplyvoltageandthepuck position. realizedwith slight adjustrnents Note that becausea nonlinearmodel for the transistorusedwas not available,a nonlinearsimulatorwasnot used. The loop gainperformance ofthe oscillatoris shownin Figure10.64.Oscillations seemto be possiblearound6 GHz too. However,a modificationwas madeto the basic oscillatorcircuit (a gap capacitorwas insertedbetweenthe transistorandthe resonator circuit) to delaythe changein the loop phasein this area,andthe gain margin in this case
Figure 10.62
AnexampleofaDROoscillator(CourtesyofPlesseyAvionics, Reheat,SouthAfrica). The oscillationfrequencyis 15.65GHz andthe outputpoweris aroundI1.6 dBm. The puck is coupled to a line connectedto the gate ofthe transistor.
The Design of Radio-Frequencyand Microwave Amplifiers and Oscillators
Thc currnt-senes feedbackapplied to thc two sources
The gap capacitor used to eliminate the spurious oscillations at 6GHz
Figure 10.63
The schematicof the oscillatorshownin Figure 10.62[l].
450
Design of RF and Microwave Amplifiers and Oscillators
DROOSC
8i l:1999 8:al:13
dE 3!.00
r95.0
22.20
165.0
n
11.40
135.0
6.607
105.0
- 1.190
75.00
v\,
Lsp_G
PHASE
- 16.70
15.0O
- 24.5t
- 15.00
- 3:L3E
- ,15.00
t
"l V
-,o.t8 - 47.96 0.100
9.mo
3.000
- 75.d!
V 12.250
- 105.0
20.000
FREO(GHz)
Fos15.6435GH2 Gloop-6.9€ t dB
66..Eg5.2tS5.rGHr
(a)
DROOSC
8: t:1999 8:4'.49
dB 25.O
,{0.0o
21.U
31.50
'tE.67
23.00
15.51
14.50
12_y
6.000
tfip_G
PHASE
6.010
- | 1.00
2.U5
- 19.50
---\
- 0.320
- 28.00
\
- 3.,184 - 6.6,19
'15.000
15.500
16.m0
16.500
>a \ 17.OOO
.,'
./
- 36.50 - 45.00
18.000
FREO(GHz) F6c=l 5.6,135GH2 GloP=5.96169
64..tg5.2t55'lGHz
(b) Figure 10.64
(a), (b) The theoreticalloop gain andphaseofthe oscillatorshownin Figure10.62[l].
The Design of Radio-Frequencyand Microwave Amplifrers and Oscillators
451
is actually quite large.Interestinglyenough,the circuit doesoscillate around6 GHz if the the fact that changeintroducedis not made.While the spuriousoscillationis undesirable, with relative ease servesas be it canbe predictedwith suchaccuracyandcan eliminated a validationfor the loop gain approach. The spurious oscillation can also be eliminated by using a different (more expensive)transistor.
Associatedwith the 10.13.1 Estimationof the Compression Maximum EffectiveOutput Power If the power gain of a transistoris consideredasa function of the drive level, it is clearthat the gain is equalto the small-signaloperatingpowergain (G^) whenthe input power is low andthe outputpowerwill approachthe saturationlimit whenthe input poweris high (seeFigure 10.65).Assumingthe transitionto be exponential,the outputpowercould be describedby the following equation[5]: /P* Pou,= Pr* [1 - e-G* 4" 1
(10.144)
Pin t
-l
Figure 10.65
Typical saturationcharacteristicsfor a transistor.
452
Design of RF and Microwave Amplifien and Oscillators
Themaximumeffectiveoutputpower(Pou,- P;")is deliveredby thetransistorwhen
l
l i
r l
0(P"*- 4") -,^, 0P^ that is, when dPou,-,
oPn aboveyields Applyingthisto theequation (10.r45)
4" = P."[n(G.")/G."] and Poot_-o = P.", (l - I / G.")
",
(10.146)
from which it follows that - p rDo s c m a - ' o u t
_ p ma< 'in
= P,",[1-l I G,, - ln(G.,) / G,"]
(10.147)
The correspondingvalue of the large-signaloperatingpower gain (G"y)at this maximum effectiveoutputpowerpoint is givenby G.t = Pou,_.o/P^ = (G," - l) / ln(G,")
(10.148)
The ratio of the small-signalandthe large-signaloperatingpowergainis therefore G,, I G,r = [G." I (G,, - l)]ln(G,")
(10.149)
a first order with a setof small-signalS-parameters, If an oscillatoris synthesized power is possible output gain in the maximum will result that the loop for approximation is, ratio, that root of this the square
tc-
=.1# G*r-oo, s
