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1. Chapter 6Feedback Circuits
Analogue Electronics 电子2＋2

2. 6.1Introduction
6.2Types of feedback connection
Overall gain of the system
Input and output impedance
6.3 Practical feedback circuits
6.4 Feedback amplifier –phase and frequency considerations
Nyquist criterion
Ch6–Feedback circuits
Content

3. Introduction
Atypicalfeedbackconnectionisshownbelow.TheinputsignalVsisappliedtoamixer
network,whereitiscombinedwithafeedbacksignalVf.ThedifferenceofthesesignalsViis
thentheinputvoltagetotheamplifier.AportionoftheamplifieroutputVoisconnectedtothe
feedbacknetwork,whichprovidesareducedportionoftheoutputasfeedbacksignaltothe
inputmixernetwork.
Ch6–Feedback circuits

4. Introduction
Dependingontherelativepolarityofthesignalbeingfedbackintoacircuit,onemayhave
negativeorpositivefeedback.Negativefeedbackresultsindecreasedvoltagegain,forwhicha
numberofcircuitfeaturesareimproved.Positivefeedbackdrivesacircuitintooscillationasin
varioustypesofoscillatorcircuits
Ch6–Feedback circuits
•A(s)：open-loop amplifier or open-loop gain.
•β(s)：feedback loop gain.
•A(s)β(s)：overall gain. 
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5. Introduction
Ifthefeedbacksignalisofoppositepolaritytotheinputsignal,negativefeedbackresults.
Althoughnegativefeedbackresultsinreducedoverallvoltagegain,anumberofimprovements
areobtained,amongthembeing:
Ch6–Feedback circuits
1. Higher input impedance.
5. Reduced noise.
2. Better stabilized voltage gain.
3. Improved frequency response.
4. Lower output impedance.
6. More linear operation.

6. Feedback connection types
Therearefourbasicwaysofconnectingthefeedbacksignal.Bothvoltageandcurrentcanbe
fedbacktotheinputeitherinseriesorparallel.Specifically,therecanbe:
Ch6–Feedback circuits
1. Voltage-series feedback
2. Voltage-shunt feedback
Gain without feedback A
Feedback β
Gain with feedback Af
Gain without feedback A
Feedback β
Gain with feedback Af

7. Feedback connection types
3. Current-series feedback
Ch6–Feedback circuits
4. Current-shunt feedback
Gain without feedback A
Feedback β
Gain with feedback Af
Gain without feedback A
Feedback β
Gain with feedback Af

8. Feedback connection types
Ch6–Feedback circuits
Seriesfeedbackconnectionstendtoincreasetheinputresistance,whereasshuntfeedback
connectionstendtodecreasetheinputresistance.Voltagefeedbacktendstodecreasethe
outputimpedance,whereascurrentfeedbacktendstoincreasetheoutputimpedance.
Typically,higherinputandloweroutputimpedancesaredesiredformostcascadeamplifiers.
Bothoftheseareprovidedusingthevoltage-seriesfeedbackconnection.Weshalltherefore
concentratefirstonthisamplifierconnection.

9. Gain with Feedback -Voltage-Series Feedback
Thecircuitshowsthevoltage-seriesfeedbackconnectionwithapartoftheoutputvoltagefed
backinserieswiththeinputsignal.Ifthereisnofeedback(Vf=0),thevoltagegainofthe
amplifierstageis
Ch6–Feedback circuits
IfafeedbacksignalVfisconnectedinserieswiththeinput,then
Sothattheoverallvoltagegainwithfeedbackis
Therefore, an overall gain reduction is resulted.

10. Gain with Feedback -Voltage-Shunt Feedback
Forthevoltage-shuntfeedbackconnection,wehave
Ch6–Feedback circuits
Therefore, an overall gain reduction is resulted.

11. Input Impedance-Voltage-Series Feedback
Forthevoltage-seriesfeedbackconnection,theinputimpedancecanbedeterminedasfollows
Ch6–Feedback circuits
Theinputimpedancewithseriesfeedbackisthevalueoftheinputimpedancewithoutfeedback
multipliedbythefactor(1+βA).Thisconclusionappliestobothvoltage-seriesandcurrent-series
configurations.

12. Input Impedance-Voltage-Shunt Feedback
Forthevoltage-shuntfeedbackconnection,onecanobtain
Ch6–Feedback circuits
Theinputimpedancewithshuntfeedbackisthevalueoftheinputimpedancewithoutfeedback
dividedbythefactor(1+βA).Thisconclusionappliestobothvoltage-shuntandcurrent-shunt
configurations.

13. Output Impedance-Voltage-Series Feedback
Thisequationshowsthatwithvoltage-seriesfeedbacktheoutputimpedanceisreducedfrom
thatwithoutfeedbackbythefactor(1+βA).
Ch6–Feedback circuits
TheoutputimpedanceisdeterminedbyapplyingavoltageV,resultinginacurrentI,withVs
shortedout(Vs=0).Soaccordingtothis,wehave

14. Output Impedance-Current-Series Feedback
Theoutputimpedancewithcurrent-seriesfeedbackcanbedeterminedbyapplyingasignalV
totheoutputwithVsshortedout,resultinginacurrentI,theratioofVtoIbeingtheoutput
impedance.
Ch6–Feedback circuits
Thisequationshowsthatwithcurrent-seriesfeedbacktheoutputimpedanceisincreasedfrom
thatwithoutfeedbackbythefactor(1+βA).
+
-

15. Voltage gain and impedance with feedback
AsummaryoftheeffectoffeedbackoninputandoutputimpedanceisprovidedinTable
Ch6–Feedback circuits
•Theinputimpedancefortheconnectionsisdependentonwhetherseriesorshuntfeedback
isused.Forseriousfeedback,theinputimpedanceisincreased,whereasshuntfeedback
decreasestheinputimpedance.
•Theoutputimpedancefortheconnectionsisdependentonwhethervoltageorcurrent
feedbackisused.Forvoltagefeedback,theoutputimpedanceisdecreased,whereascurrent
feedbackincreasestheoutputimpedance.
Input impedance
Output impedance

16. Voltage gain and impedance with feedback -Example
Determinethevoltagegain,input,andoutputimpedancewithfeedbackforvoltage-series
feedbackhavingA=-100,Ri=10k,andRo=20kforfeedbackofβ=-0.1.
Ch6–Feedback circuits

17. Reduction in Frequency Distortion
Foranegative-feedbackamplifierhavingβA>>1.
Ch6–Feedback circuits
Itfollowsfromthisthatifthefeedbacknetworkispurelyresistive,thegainwithfeedbackis
notdependentonfrequencyeventhoughthebasicamplifiergainisfrequencydependent.
Practically,thefrequencydistortionarisingbecauseofvaryingamplifiergainwithfrequencyis
considerablyreducedinanegative-voltagefeedbackamplifiercircuit

18. Gain Stability with Feedback
Inadditiontotheβfactorsettingaprecisegainvalue,wearealsointerestedinhowstablethe
feedbackamplifieriscomparedtoanamplifierwithoutfeedback.
Ch6–Feedback circuits
Thisshowsthatmagnitudeoftherelativechangeingain isreducedbythefactor
comparedtothatwithoutfeedback1
f
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Differentiatingthefollowingequationleadsto

19. Gain Stability with Feedback –Example
Ifanamplifierwithgainof-1000andfeedbackofβ=-0.1hasagainchangeof20%dueto
temperature,calculatethechangeingainofthefeedbackamplifier
Ch6–Feedback circuits
Theimprovementis100times.Thus,whereastheamplifiergain|A|changesfrom1000to800
by20%,thegainwithfeedback|Af|onlychangesfrom10to9.98byonly0.2%.

20. Practical feedback circuits
Findtheoverallvoltagegainofthefollowingfeedbackcircuit(rdcanbeignored).
Ch6–Feedback circuits
Step 1: Identify the feedback loop, the input, output
and feedback variables
Step 2: Identify feedback connection type
Step 3: Calculate the overall gain

21. Practical feedback circuits
Findtheoverallvoltagegainofthefollowingfeedbackcircuit(rdcanbeignored).
Ch6–Feedback circuits
Apartoftheoutputsignal(Vo)isobtainedusinga
feedbacknetworkofresistorsR1andR2.The
feedbackvoltageVfisconnectedinserieswiththe
sourcesignalVs,theirdifferencebeingtheinput
signalVi.0
Feedback loop
Step 1: Identify the feedback loop, the input, output
and feedback variables

22. Practical feedback circuits
Findtheoverallvoltagegainofthefollowingfeedbackcircuit(rdcanbeignored).
Ch6–Feedback circuits
Step 2: Identify feedback connection type
Apartoftheoutputsignal(Vo)isobtainedusinga
feedbacknetwork.ThefeedbackvoltageVfis
connectedinserieswiththesourcesignalVs,their
differencebeingtheinputsignalVi.
0
Feedback loop
Voltage-series feedback connection√
0
Negative feedback:
Negative feedback:
?i s f
V V V

23. Practical feedback circuits
Findtheoverallvoltagegainofthefollowingfeedbackcircuit(rdcanbeignored).
Ch6–Feedback circuits
Step 3: Calculate the overall gain
Without feedback the amplifier gain is
RL= RD||Ro||(R1+R2)
Negative feedback:

24. Practical feedback circuits –Example
FindAf,Zif,Zofofthefollowingfeedbackcircuitusingthesevalues:R1=80k,R2=20k,Ro=10k,
RD=10k,andgm=4000μS.
Ch6–Feedback circuits 12
( )|| ||
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R R R R R (80 20 ) ||10 ||10k k k k 100 || 5kk 100 || 5kk mL
A g R 6
4000 10 4.76 19.05k
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k
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   1.89k

25. Practical feedback circuits -Voltage-Series Feedback
Ch6–Feedback circuits
A voltage-series feedback connection can also be built using an op-amp
Without feedback the amplifier gain is A
Vo= A (Vi1–Vi2)
Vo
Vi1
Vi2
With feedback the overall gain is reduced by the
feedback factor
0
Feedback loop
Apartoftheoutputsignal(Vo)isobtainedusinga
feedbacknetwork.ThefeedbackvoltageVfis
connectedinserieswiththesourcesignalVs,their
differencebeingtheinputsignalVi.

26. Practical feedback circuits -Voltage-Series Feedback
Ch6–Feedback circuits
A voltage-series feedback connection can also be built using an op-amp
0
Feedback loop
Calculate Afif A= 100,000 and R1= 1.8 k and R2= 200

27. Practical feedback circuits
Ch6–Feedback circuits
IfwetaketheinputvoltageandR1asthecurrentsource,andtheoutputvoltageisfedbackintothe
inputintermsofcurrent.Thenwehavebuiltavoltage-shuntfeedbackconnectionusingthe
constant-gainop-amp.
Voltage-shunt feedback

28. Feedback amplifier –phase and frequency considerations
Ch6–Feedback circuits
BecauseoftheRLbranch,theperformanceofthefollowingconnectionisdependent
uponthefrequencyofthesignalsource.Andthegainisacomplex,whichisactually
acombinationofanamplitudeandangle.

29. Feedback amplifier –phase and frequency considerations
Ch6–Feedback circuits
SincethefeedbackamplifierisalsoconsistedofanumberofRLbranches,theoverallgainwill
changewithfrequency.
If,asthefrequencyincreases,thephaseshiftchanges,thensomeofthefeedbacksignalwilladdto
theinputsignal.Itisthenpossiblefortheamplifiertobreakintooscillationsduetopositive
feedback.Properfeedback-amplifierdesignrequiresthatthecircuitbestableatallfrequencies,not
merelythoseintherangeofinterest.Otherwise,atransientdisturbancecouldcausesudden
oscillating.

30. Nyquist Criterion
Ch6–Feedback circuits
•Injudgingthestabilityofafeedbackamplifierasafunctionoffrequency,theβAproductandthe
phaseshiftbetweeninputandoutputarethedeterminingfactors.
•OneofthemostpopulartechniquesusedtoinvestigatestabilityistheNyquistmethod.ANyquist
diagramisusedtoplotgainandphaseshiftasafunctionoffrequencyonacomplexplane.

31. Nyquist Criterion
Ch6–Feedback circuits
ThuspointsonthisplotcanrepresentbothgainmagnitudeofβAandphaseshift.Ifthepoints
representinggainandphaseshiftforanamplifiercircuitareplottedatincreasingfrequency,thena
Nyquistplotisobtained.
Asastart,considerthecomplexplane.Afewpointsofvariousgain(βA)valuesareshownatafew
differentphase-shiftangles.Byusingthepositiverealaxisasreference(0°),weseeamagnitudeof
βA=2ataphaseshiftof0°atpoint1.Additionally,amagnitudeofβA=3ataphaseshiftof
135°isshownatpoint2andamagnitude/phaseofβA=1at180°isshownatpoint3.

32. Nyquist Criterion
Ch6–Feedback circuits
The amplifier is unstable if the Nyquist curve encloses (encircles) the –1 point, and it
is stable otherwise.
(a) stable (b) unstable

33. Nyquist Criterion -Gain and Phase Margins
Ch6–Feedback circuits
Gainmargin(GM)isdefinedasthenegativeofthe
valueof|βA|indecibelsatthefrequencyatwhich
thephaseangleis180°.
Phasemargin(PM)isdefinedastheangleof180°
minusthemagnitudeoftheangleatwhichthevalue
|βA|isunity(0dB).
FromtheNyquistcriterion,weknowthatafeedbackamplifierisstableiftheloopgain(bA)isless
thanunity(0dB)whenitsphaseangleis180°.Wecanadditionallydeterminesomemarginsof
stabilitytoindicatehowclosetoinstabilitytheamplifieris
Thus,0dB,equaltoavalueofβA=1,isonthe
borderofstabilityandanynegativedecibelvalueis
stable.