microelectronic circuits ii ch9 :...

CNU EE 9.1-1

Microelectronic Circuits II

Ch 9 : Feedback

9.5 The Feedback Transconductance Amplifier (Series-Series )9.6 The Feedback Transresistance Amplifier (Shunt-Shunt)9.7 The Feedback Current Amplifier (Shunt-Series)Appendix C Two-port Network Parameters

CNU EE 9.1-2

- b circuit samples short-circuit output current Io& provides a feedback signal Vf à Vi=Vs-Vf

- zero resistance to output load à b circuit doesnot load the amplifier output

- Ideal voltage source Vf = b Io à b circuit doesNot load the amplifier input

- A : transconductance & b : transresistanceà Loop gain Ab = dimensionless quantity

- Ideal structure : load and source resistancesare absorbed inside the A circuit, and b circuitdoes not load the A circuit

- Closed loop gain Af :

- Af =short-circuit transconductance

Feedback Transconductance Amplifier (Series-Series)§Ideal case

bAA

VIA

s

of +

=º1

- Stabilize Io/Vs à transconductance amplifier- Unilateral open loop amplifier (A circuit) +

ideal feedback network (b circuit)- A circuit : input resistance Ri, short-circuit

transconductance A=Io/Vi, output resistance Ro

Ideal structure

Equivalent circuit for series-series feedback amplifier

CNU EE 9.1-3

- Negative feedback increases the output resistance in the current (series) sampling- Negative feedback à Io is constant in spite of changes in output voltage à increase in output resistance- While voltage (shunt) sampling reduces the output resistance, current (series) sampling increases it.- Series-series feedback topology increases the input and output resistance

§ Output Resistance Rof of feedback transconductance amplifier (Series-Series)

x

xof I

VR º

- Vs à 0 & breaks the output loop (at OO/) toapply a test current Ix

- Output resistance Rof :

xofi IIVV bb -=-=-=

( ) ( ) oxxoixx RIAIRAVIV b+=-=

( ) oof RAR b+=\ 1

Feedback Transconductance Amplifier (Series-Series)

( )bARR iif +=\ 1Equivalent circuit for series-series feedback amplifier

§Input resistance with feedbackSeries mixing always increases the inputresistance by a factor equal to the amount offeedback

CNU EE 9.1-4

- Feedback network is not an ideal currentcontrolled voltage sourceà resistive and hence, load the basic

amplifierà affect A, Ri & Ro

- Rs & RL affect A, Ri & Ro

- Simple method for finding A circuit & bcircuit from a given series-series feedbackamplifier

•Practical series-series feedback amplifier- Source and load resistances should

be lumped with the basic amplifier- Two-port feedback network is

represented in terms of z parameters- z parameter : a series circuit at the input and a series circuit at the output

Feedback Transconductance Amplifier (Series-Series)Ideal structure

Practical caseRi & Ro vs. Rin & Rout vs. Rif & Rof

CNU EE 9.1-5

§ Derivation of A Circuit & β Circuit

use of z parameters (appendix C)

úû

ùêë

éúû

ùêë

é=ú

û

ùêë

é

2

1

2221

1211

2

1

II

zzzz

VV

Feedback CircuitInput Impedance(w/ Output open)

Feedback CircuitOutput Impedance(w/ input open)

negligible

β

Feedback network isrepresented by a seriesnetwork at port 1 and aseries network at port 2

Feedback Transconductance Amplifier (Series-Series)Ri & Ro vs. Rin & Rout vs. Rif & Rof

CNU EE 9.1-6

à Dispense with the voltage source z21I1

- Forward transmission through the feedback networkis negligible in comparison to that through the basicamplifier

- A circuit is composed of the basic amplifieraugmented at the input with Rs and z11 andaugmented at the output with RL and z22.

- z11 & z22 : impedance looking into ports 1 & 2 ofthe feedback network while the other port is open-circuited or short-circuited so as to destroy thefeedback (open if series & short if shunt)

- b is measured with port 1 open

- Feedback network samples the output current [I2 =Io) & provides a voltage [Vf = V1] that is mixed inseries with the input source

§ Derivation of A Circuit & β Circuit

02

112

1 =

º=II

Vzb

amplifierbasic

networkfeedback zz 2121 <<

networkfeedback

amplifierbasic zz 1212 <<

- Includes z11 and z22 with the basic amplifier- If basic amplifier is unilateral,


CNU EE 9.1-7

§ Summary of the rules for finding A and β Circuit

- Ri & Ro : input & outputresistance of the A circuit- Rif & Rof : input & outputresistance of the feedbackamplifier, including Rs & RL- Actual input & outputresistance of the feedbackamplifier usually exclude Rs& RL à Rin & RoutI2=0 I1=0

I1=0


Lofout

sifin

RRRRRR

-=

-=

Ro by breaking the output loop at YY/ & measuring theresistance between Y & Y/

CNU EE 9.1-8

- b circuit samples open-circuit output voltage Vo& provides a feedback signal If à Ii=Is-If

- infinite resistance to amplifier output à b circuit does not load the amplifier output- Ideal current source If = bVo à b circuit does not

load the amplifier input- A : transresistance & b : transconductanceà Loop gain Ab = dimensionless quantity



- Af : open-circuit transresistance

Feedback Transresistance Amplifier (Shunt-Shunt)§Ideal case

bAA

IVA

s

of +

=º1

- Stabilize Vo/Isà transressitance amplifier- Unilateral open loop amplifier (A circuit) +

ideal feedback network (b circuit)- A circuit : input resistance Ri, open-circuit

transresistance A=Vo/Ii, output resistance Ro

Ideal structure

Equivalent circuit for shunt-shunt feedback amplifier

CNU EE 9.1-9

- Shunt connection in the input à a reduced currentIi into the A circuit : Ii = Is – If

- Shunt mixing reduces the input current by the amount of feedback (Vi/Ii = Ri)

- Shunt connection at the input lowers the input resistance by a factor equal to the amount of feedback

§ Output Resistance Rof of feedback tranresistacne amplifier (Shunt-Shunt)

Shunt connection at the output lowers the output resistance by a factor equal to the amount of feedbackà The output voltage will change less as we draw current from the amplifier output

- Shunt feedback connection, whether at the input or at the output, always reduces the correspondingresistance

( ) bb AR

IAV

IVR i

i

i

s

iif +

=+

=º11

Equivalent circuit for series-series feedback amplifier

§Input resistance with feedback

Feedback Transresistance Amplifier (Shunt-Shunt)

bbb

AIIAIVI s

iiof +===

1>

bARR o

of +=

1

CNU EE 9.1-10

- Simple method for finding A & b circuit - Assume the basic amplifier is unilateral &

the feedforward transmission through the feedback network is negligibly small

- A circuit includes Rs across the input terminals of the amplifier & RL across its output terminal

- Loading effect of the feedback network onthe amplifier input à R11 is obtained by looking into port 1 of the feedback networkwhile port2 is shorted (shunt connected output)

- Loading effect at the output à R22 is foundby looking into port 2 while port 1 is shorted(shunt connected input)

- Since the feedback network senses Vo & is fedby Vo; delivers a current If that is mixed in shunt at the input, its port 1 is short-circuitedàb is found as If/Vo, where If flows through

the short circuit

úû

ùêë

éúû

ùêë

é=ú

û

ùêë

é

2

1

2221

1211

2

1

VV

yyyy

IIy parameter

Ri & Ro vs. Rin & Rout vs. Rif & Rof

Feedback Transresistance Amplifier (Shunt-Shunt)Ideal structure

Practical case

CNU EE 9.1-11

§Summary of the rules for finding A and β Circuit

÷÷ø

öççè

æ-=

sifin RR

R 11/1

÷÷ø

öççè

æ-=

Lofout RR

R 11/1

networkfeedback

amplifierbasic yy 1212 <<

amplifierbasic

networkfeedback yy 2121 <<

Condition for Reverse yparameter of the basicamplifier & feedbacknetwork

Condition for Forward yparameter

Actual input & outputresistance of the feedbackamplifier usually exclude Rs& RL

V2=0 V1=0

V1=0

Feedback Transresistance Amplifier (Shunt-Shunt)

CNU EE 9.1-12

- b circuit samples short-circuit output current Io& provides a feedback current If à Ii=Is-If

- zero resistance to the output loop à b circuit does not load the amplifier output

- Ideal current source If = bIo à b circuit does notload the amplifier input

- A & b : current gainà Loop gain Ab = dimensionless quantity



- Af : closed-loop current gain

§Ideal case

bAA

IIA

s

of +

=º1

- Stabilize Io/Isà current amplifier- Unilateral open loop amplifier (A circuit) +

ideal feedback network (b circuit)- A circuit : input resistance Ri, short-circuit

current gain A=Io/Ii, output resistance Ro

Ideal structure

Equivalent circuit for shunt-shunt feedback amplifier

Feedback Current Amplifier (Shunt-Series )

CNU EE 9.1-13

- Shunt mixing reduces the input current by the amount of feedback (Vi/Ii = Ri)

- Shunt connection at the input lowers the inputresistance by a factor equal to the amount offeedback

§ Output Resistance Rof of feedback current amplifier (Shunt-Series)

- By setting Is = 0, breaking the short-circuit output loop, at say OO/, and measuring the resistancebetween the two terminals à Output Resistance Rof

- Series connection at the output always raises the output resistance by a factor equal to the amount of feedback

bARR i

if +=

1

Equivalent circuit for shunt-series feedback amplifier

§Input resistance with feedback

( ) oof RAR b+= 1


CNU EE 9.1-14

- Simple method for finding A & b circuit - Assume the basic amplifier is unilateral &

the feedforward transmission through the feedback network is negligibly small

- A circuit includes Rs across the input terminals of the amplifier & RL in series withits output terminal

- Loading effect of the feedback network onthe amplifier input à R11 is obtained by looking into port 1 of the feedback networkwhile port2 is open (series connected output)

- Loading effect at the output à R22 is foundby looking into port 2 while port 1 is shorted(shunt connected input)

- Since the feedback network senses Io & is fedby Io; delivers a current If that is mixed in shunt at the input, its port 1 is short-circuitedà b is found as If/Io, where If flows through

the short circuitRi & Ro vs. Rin & Rout vs. Rif & Rof

Ideal structure

Practical case


úû

ùêë

éúû

ùêë

é=ú

û

ùêë

é

2

1

2221

1211

2

1

IV

gggg

VIg parameter

(inverse hybrid)

CNU EE 9.1-15

§ Summary of the rules for finding A and β Circuit

÷÷ø

öççè

æ-=

sifin RR

R 11/1

Lofout RRR -=

amplifierbasic

networkfeedback gg 2121 <<

networkfeedback

amplifierbasic gg 1212 <<

Most of the forwardtransmission occurs in thebasic amplifier

Most of the reversetransmission takes place inthe feedback network

Actual input & outputresistance of the feedbackamplifier usually exclude Rs& RL

I2=0 V1=0

V1=0


Ro by breaking the output loop at YY/ & measuring theresistance between Y & Y/

CNU EE 9.1-16

Summary for four Feedback-Amplifier Topologies

h

g

z

y

CNU EE 9.1-17

Summary of the Feedback Analysis Method

1. Always begin the analysis by determining an approximate value for the closed-loop gain Af, assuming that the loop gain Ab is large and thus

Af ~ 1/b : the approximate value depends on how large Ab is compared to unity

2. The shunt connection at input or output always results in reducing the corresponding resistance (inputor output). The series connection at input or output always results in increasing the correspondingresistance (input or output).

3. In utilizing negative feedback to improve the properties of an amplifier under design, the starting pointin the design is the selection of the feedback topology appropriate for the application at hand.Then the required amount of negative feedback (1+ Ab) can be ascertained utilizing the fact that it isthis quantity that determines the magnitude of improvement in the various amplifier parameters.Also, the feedback factor b can be determined from

b ~ 1/ Af

CNU EE 9.1-18

Two-port Network Parameters§ Characterization of Linear two-port networks

2221212

2121111

VyVyIVyVyI

+=+=

§ Four port variables of two-port network- V1, I1, V2, I2

§ Linear two-port network- two of the variables à excitation variables - the other two à response variables

§ Example : excited by V1 & V2, responded by I1 & I2 - V1, V2 : independent variables - I1, I2 : dependent variables- network operation is described by the two equations

§ y11, y12, y21, y22 : admittances à completelycharacterized the linear two-port network

§ Depending on which two of the four port variables areused to represent the network excitation, a different setof equations (and a correspondingly different set ofparameters) is obtained for characterizing the network

§ Four parameters sets commonly used in electronics§ Independent Variable : Shunt à V, Series à I§ Dependent Variable : Shunt à I, Series à V

CNU EE 9.1-19

y Parameters

2221212

2121111

VyVyIVyVyI

+=+=

§ Excitation by V1 & V2

§ Short-circuit admittance (or y-parameter) characterization

(b) y11 : input admittance atport 1 with port 2 short-circuited01

111

2 =

ºVV

Iy

02

112

1 =

ºVV

Iy(c) y12 : transmission fromport 2 to port 1, internalfeedback

01

221

2 =

ºVV

Iy(d) y21 : transmission fromport 1 to port 2, forwardgain or transmission

02

222

1 =

ºVV

Iy

(e) y22 : admittance lookinginto port 2 with port 1short-circuited, outputshort-circuit admittance

CNU EE 9.1-20

z Parameters

2221212

2121111

IzIzVIzIzV

+=+=

§ Excitation by I1 & I2

§ Open-circuit impedance (or z-parameter) characterization

- Duality between the z- and y-parameters characterization

CNU EE 9.1-21

h Parameters

2221212

2121111

VhIhIVhIhV

+=+=

§ Excitation by I1 & V2

§ Hybrid (or h-parameter) characterization

(b) h11 : input impedance atport 1 with port 2 short-circuited01

111

2 =

ºVI

Vh

02

112

1 =

ºIV

Vh(c) h12 : reverse orfeedback voltage ratio withinput port open-circuited

01

221

2 =

ºVI

Ih(d) h21 : current gain withoutput port short-circuited,short-circuit current gain

02

222

1 =

ºIV

Ih(e) h22 : output portadmittance with input portopen-circuited

CNU EE 9.1-22

g Parameters

2221212

2121111

IgVgVIgVgI

+=+=

§ Excitation by V1 & I2

§ Inverse-hybrid (or g-parameter) characterization

- Duality between the g- and h- parameters characterization

CNU EE 9.1-23

Equivalent-circuit representation§ Four possible equivalent circuits

microelectronic circuits ii ch9 :...

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