Feedback Voltage & Transconductance...

Willy Sansen 10-05 131

Willy Sansen

KULeuven, ESAT-MICASLeuven, Belgium

[email protected]

FeedbackVoltage & Transconductance

Amplifiers


Table of contents

DefinitionsSeries-shunt FB for Voltage amplifiers.Series-series FB for Transconductance amps.


Ideal feedback

G

H

Σ

if the loop gain LG = GH >> 1

vε = vIN - H vOUT

1 + GH≈ 1

H

vIN vOUTvε

vOUT = G vε

vOUT

vIN

=G

Gray, Hurst, Lewis, Meyer: Design of analog integrated circuits, Wiley 2001

-


Shunt-shunt feedback configurations

+- vOUT

RF

iIN

AR = RF

RIN ≈ 0

IN : shunt FB : RIN OUT : shunt FB : ROUT

LG =vOUT

vIN

A0 ≈ 104 … 106

Output shunt : ROUT =ROUTOL

OL Open Loop

1+LG

Input shunt : RIN =RINOL

1+LG

A0

vIN = AvOL= A0


Calculation loop gain or return ratio

+- vOUT

RF

vIN

LG =vOUT

vIN

A0 ≈ 104 … 106

= AvOL= A0

OL Open Loop

Low output resistance !

Independent sources : voltage source to zerocurrent source to infinity

Break loop where impedances are very differentFind the loop gain = return ratio

A0


Calculation loop gain - alternate

+-

RF

vIN

vOUT LG =vOUT

vIN

A0 ≈ 104 … 106

OL Open LoopIdeal separation!

= AvOL= A0

A0


Shunt-shunt FB pair in CMOS

+vOUTiIN-

RF

M1

M2

VDD

AR = RF

LG = gm1ro1


Shunt-shunt FB pair in bipolar

+vOUTiIN-

RF

Q1

Q2

VDD

AR = RF

LG = gm1ro1 RF + rπ1

rπ1


Loop gain or return ratio

vOUT

RF

Q1Q2

VDD

ro1gm1vIN

+

-rπ1

LG = gm1ro1 RF + rπ1

rπ1

Ideal separation!


Series-shunt feedback configurations

+-

vOUT

R2R1

vIN +-

vOUTvIN

Av = 1 +R1

R2

RIN = ∞RIN = ∞Av = 1

IN : series FB : RIN OUT : shunt FB : ROUT

IN : series FB : RIN OUT : shunt FB : ROUT


Calculation loop gain

+-

vOUT

R2R1 vIN

Av = 1 +R1

R2

RIN ≈ ∞IN : series FB : RIN OUT : shunt FB : ROUT

LG =R1+ R2

R1vOUT

vINAvOL

AvOL ≈ A0 ≈ 104 … 106

=

Output shunt : ROUT =ROUTOL

OL Open Loop

1+LG

Input series : RIN = RINOL (1+LG)

A0


Shunt & series at input & output

Shunt

Output

Series

RIN

Input

IIN

A

RF

+

RE

vIN

A

RFRE

RIN +-

A

RFROUT

vOUT

A

RF

ROUT

iOUT


Shunt FB decreases the impedance

+vOUT-

RF

ROUT =

+vOUT-

iOUT = iTT iTT iOUT > iTT

iF

iOUT

vOUT


Series FB increases the impedance

+

vIN > vGS

-

RL

RS+

-

vS

vGS+

RL

-

vIN = vGS

RIN = iIN

vIN

iIN iIN


Input- & output impedances

RIN = RINOL(1+LG)

Shunt

Input

SeriesOutput Shunt

Series

ROUT =ROUTOL

1+LGROUT = ROUTOL(1+LG)

RIN =RINOL

1+LG

1H

=

= AR vOUT

iIN= AI

iOUT

iIN

= AG iOUT

vIN= AV

vOUT

vIN


Shunt vs series feedback

Shunt feedbacklowers impedance levels : higher bandwidths

Series feedback increases impedances : lower node poles

Ouput shunt best for interconnect to next stage !

Output series acts as current source !


Shunt versus series for sensors

vIN Microphoneis a voltage sourcerequires a high Rin amplifier

+ Pixel-, photodiode , radiation detectors are current sources, require a low Rin amp.

+

Pressure- , temperature sensors are voltage sourcesrequire a high Rin amp.

iIN

vINR

RR

R


Table of contents

DefinitionsSeries-shunt FB for Voltage amplifiersSeries-series FB for Transconductance amps


Series-shunt FB configuration

AV = =

vOUT

vIN

R2

RIN +

-

vIN

A0vIN A0 ≈ 104 … 106

vOUT

vIN

ROUT

RO << R2

RIN ≈ ∞ ROUT ≈ 0

R2 + R1

R1R1

RNP

+-

R1 << RNP


Series-shunt FB : loop gain

AV =

vOUTLG

vIN= 0

R2

+

-

vIN

A0vIN A0 ≈ 104 … 106

RO << R2R2 + R1

R1R1

LG =vOUTLG

vINLG

vINLG

= R2 + R1

R1 A0

RNP

+-

R1 << RNP


vOUT

vIN

R2

RIN +

-

vIN

A0vIN A0 ≈ 104 … 106

RO << R2

R1

AV = R2 + R1

R1

RINOL = RIN (A0 = 0) = RNP + R1//R2

RNP

RIN = vIN

iIN= RINOL LG ≈ ∞

Series-shunt FB : input resistance


vOUT

R2

+

-

vIN

A0vIN A0 ≈ 104 … 106

ROUT

RO << R2

R1

AV = R2 + R1

R1

ROUT = ≈ 0ROUTOL

LGROUTOL = ROUT (A0 = 0)

= RO//(R2+…) ≈ RO

vIN= 0

Series-shunt FB : output resistance


Series-shunt FB pair : loop gain

+vOUT-

R2 LG = ?M3

VDD

M1

M2

R1

vIN

AV = R2 + R1

R1

R1 > 1/gm1


Series-shunt FB pair : series input

+

R1

+

R1

RL

++

RL

R1 > 1/gm

RL < ro

RIN ≈ 1/gm

1/gm

1/gm

R1

RIN = 1/gm

∞ ∞

∞

∞

R1

RIN = R1

RIN = ∞


Series-shunt FB pair : gain input stage

+

R1

vOUTvIN

+

R1

vOUT

RL

+vOUT

+vOUT

RL

R1 > 1/gm

RL < ro

vOUT

vIN= = gmroR2

RL

R2

R2 > 1/gm

vIN

vIN

vIN

R2 R2

R2

= RL

R2

R1

R1+R2

= gmro


Series-shunt FB pair : input & output resistance

+vOUT-

R2 LG =

RIN ≈ ∞

ROUT = ≈ 01/gm3

LG

M3

VDD

M1

M2

R1

vIN

AV = R2 + R1

R1

R1 > 1/gm1

gm1ro1 gm2ro2 R1+R2

R1


Series-shunt FB pair : loop gain

+vOUT-

R2M3

VDD

M1

M2

R1

vINR2M1

R1

vIN

LG = gm2ro2 R2

RL LG = gm1ro1 gm2ro2 R1 + R2

R1

RL


Series-shunt FB pair : output loading

+vOUT-

R2

RIN ≈ ∞

ROUT = ≈ 0 ??(R1+R2)//ro2

LG

VDD

M1

M2

R1

vIN

AV = R2 + R1

R1

Output loading : R2 ≈ ro2

R1 > 1/gm1

LG =

gm1ro1 gm2R1+R2+ro2

ro2 R1


+vOUT-

R2

RIN ≈ ∞

ROUT = (R2+R1)//ro2//R3

LG

VDD

M1

M2

R1

vIN

AV = R2 + R1

R1

Output loading : R2 ≈ R3 ≈ ro2

R1 > 1/gm1

LG =

gm1ro1 gm2R1+R2+ro2//R3

ro2//R3 R1

R3

≈ 0 ??

Series-shunt FB pair : output loading with R


Series-shunt pair in BiCMOS

+vOUT

R1 > 1/gm1

Q1

VDD

ROUT =LG

1/gm3

R2

M2

vIN

-

M3

R1

Input loading : RIN < ∞

RIN = RINOL LG ≈ ∞

AV = R2 + R1

R1

LG =

gm1ro1 gm2ro2 R1+R2

R1

RINOL = rπ1+ β (R1//R2 )

≈ 0

RS


Series-shunt FB pair with resistances

+vOUT-

R2

LG = gm2ro2

RIN = RINOL LG ≈ ∞ RINOL = rπ1+ β (R1//R2 )

ROUT = ≈ 0ROUTOL

LG

Q3

VDD

Q1

Q2

R1

vIN

AV = R2 + R1

R1

R1 > 1/gm1


RL1RL2

RL2 + ro2

RL2RL1//rπ2

R2

ROUTOL = +gm3

1β

RL2//ro2

RERD CD


Table of contents



Series-series feedback : gain

+-

iOUT

R2

R1

vIN

RE

VDD

AG = R2 + R1

R1

1RE12

ROUT

LG = A0

A0R2 + R1

R1

RE12 = RE // (R1 + R2)

AGOL = A01

RE12

= R2 + R1 + RE

R1

1RE


Series-series feedback : in- & output resistances

+-

iOUT

R2

R1

vIN RIN = ∞

ROUT = ROUTOL LG ≈ ∞

RE

VDD

ROUT

ROUTOL = ro (1 + gmRE12)

A0

LG = A0 R2 + R1

R1

RE12 = RE // (R1 + R2)


Series-series feedback with load RL

+- iOUT

R2

R1

vIN

RIN = ∞ROUT = RL

RE

VDDRL

+

-

AV = - R2 + R1

R1

RL

RE12

A0

AG = R2 + R1

R1

1RE12

vOUT

= -R2 + R1 + RE

R1

RL

RE

RE12 = RE // (R1 + R2)


Ideal current source

+-

+

- vIN

iOUT

RE

ROUT = ROUTOL LGROUTOL ≈ ro (1+gmRE )

RIN

RIN ≈ ∞

iOUT =vIN

REA0

LG = A0

ROUT


Series-series feedback : two outputs

+- vOUT1R2

R1

vIN

ROUT1 = RL

RE

VDDRL

+

-

AV1 = - R2 + R1

R1

RL

RE12

A0

+vOUT2

ROUT2 =

LG = A0 R2 + R1

R1

RE12 = RE // (R1 + R2)

AV2 = R2 + R1

R1

1/gm

LG


Series-series FB triple

+vOUT1

-

R2

LG = A1A2

RIN ≈ ∞ ROUT1 = RL

M3

VDD

M1

M2

R1

vIN

AV1 = - R2 + R1

R1

R1 > 1/gm1

RE

RL

RL

RE12

vOUT2+

ROUT2 =

AV2 = R2 + R1

R1

≈ 01/gm2

LGRE12 = RE // (R1 + R2)

Ai = gmiroi

R2 + R1

R1


Series-series FB triple

+vOUT1

-

R2

LG = gm2ro2

RIN ≈ ∞ ROUT1 = RL

M3

VDD

M1

M2

R1

vIN

AV1 = - R2 + R1

R1

R1 > 1/gm1

RE

RL

RL

RE12

vOUT2+

ROUT2 =

AV2 = R2 + R1

R1

≈ 01/gm2

LGRE12 = RE // (R1 + R2)

R2

RD

RD


Series-series triple

+

vOUT

-

R2

gm2(ro2//RL2)

RIN = RINOL LG ≈ ∞ RINOL = rπ1+ β (R1//R2)

ROUT = RL3

Q3

VDD

Q1Q2

R1

vIN

AV = - R2 + R1

R1

R1 > 1/gm1


RL1RL2

RL1//rπ2

R2RE

Wooley, JSSC Feb.71, 24-34

RL3 RE12

RL3

R2 > ROUTQ3

RE12 = RE // (R1+R2)

LG ≈


Nonideal single-transistor FB

+

vOUTvIN

-

LG = gmRE (>>1)

RIN = rπ + β RE

ROUT = RL//roL

VDD

Output loading : RL ≈ roL roL = ro (gmRE)Input loading : RS < RIN RIN = rπ + βRE

RL

RS

Av ≈ -RL

RE

RE

AG ≈1

RE

iOUT


Decreasing distortion by feedback

M1Vid/2 -Vid/2

2Ibias

-ioutiout

M1 M1Vid/2 -Vid/2

Ibias

-ioutiout

M1

IbiasR R 2R

AG ≈LG = gmR (>>1)1R


By tunable feedback

M2Vid/2 -Vid/2

IbiasIbias

Itune -ioutiout

M1

Ref.Torrance etal CAS Nov.85, 1097-1104

R = 1/gm2

AG ≈

LG = gmR (>>1)

1R

M1M2


Decreasing distortion by more feedback

Additional local FB

2R

More FB with opamps

2R

A0 A0

iout -iout

iou -iout


Low-pass filter

vIN

vOUT

CL

RL RL

Av0 = 2 RL/RE

fp = 1

2π 2RLCLAv =

RE

f

|Av|

φ (Av) fp f

f

-90o

0o

-20 dB/dec

90o

Av0

(1 + j )

Av0

fp


High-frequency booster

vIN

vOUT

CE

RL RL

Av0 = 2 RL/REfz =

1

2π RECEAv = Av0 (1 + j )

RE

fz

f

|Av|

φ (Av) fz f

f

-90o

0o

20 dB/dec

90o

Av0


Single-transistor FB with two outputs

+ vOUT1

vIN

-

LG = gmRE (>>1)

RIN = rπ + β RE

ROUT1 = RL//roL

VDD

Output loading : RL ≈ roL roL = ro (gmRE)Input loading : RS < RIN RIN = rπ + βRE

RL

RS

Av1 ≈ -RL

RE

RE

iOUT

+ vOUT2

Av2 ≈ 1

ROUT2 = 1/gm + RS/β


Table of contents


Feedback Voltage & Transconductance...

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