Differential Amplifier Common & Differential Modes

25
ESE319 Introduction to Microelectronics 1 Kenneth R. Laker update KRL 03Oct14 Differential Amplifier Common & Differential Modes Common & Differential Modes BJT Differential Amplifier Diff. Amp Voltage Gain and Input Impedance Small Signal Analysis – Differential Mode Small Signal Analysis – Common Mode

Transcript of Differential Amplifier Common & Differential Modes

Page 1: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

1Kenneth R. Laker update KRL 03Oct14

Differential AmplifierCommon & Differential Modes

● Common & Differential Modes● BJT Differential Amplifier● Diff. Amp Voltage Gain and Input Impedance● Small Signal Analysis – Differential Mode● Small Signal Analysis – Common Mode

Page 2: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

2Kenneth R. Laker update KRL 03Oct14

+-

Vo = A (V

1 - V

2)A

Most “Famous” Differential AmplifierV

CC

VEE

V1 & V

2 are single-ended input voltages defined w.r.t. ground.

Page 3: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

3Kenneth R. Laker update KRL 03Oct14

Common and Differential ModesConsider the two-input conceptual circuit shown below.

Z1

Z3

Z2

I1

I2

V2

V1

Define (convention) the voltages:

V d=V 1−V 2

Vc = “common mode voltage” Vd = “differential mode voltage”

+

+

±a

±a

V c=V 1V 2

2

1. Let V1 = V2 = V => Vc = V & Vd = 0

2. Let V1 = -V2 = V => Vc = 0 & Vd = 2V

Vc “common” to V

1 & V

2; V

d is split between V

1 & V

2 s.t. “difference” V

1 - V

2 = V

d

I1 + I2

Page 4: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

4Kenneth R. Laker update KRL 03Oct14

Replace V1, V2 with DM & CM Sources Vd , V

c

I1 + I2

V c=V 1V 2

2V d=V 1−V 2Definition Solve for V

1 and V

2

V 1=V cV d /2V 2=V c−V d /2

Page 5: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

5Kenneth R. Laker update KRL 03Oct14

+-

Vo = A (V

1 - V

2)

A

Our Most “Famous” Differential AmplifierV

CC

VEE

V1 & V

2 are single-ended input voltages defined w.r.t. ground.

+-

Vo = A (V

1 - V

2)

A

VCC

VEE

Vo V

o

V o=Av−dmV dAv−cm V c CMRR=∣Av−dm∣∣Av−cm∣

Page 6: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

6Kenneth R. Laker update KRL 03Oct14

Z1

Z3

V 1=V cV d /2

V 2=V c−V d /2

Vx

<=>R

C1R

C2

RE1

RB1

RB2

RE2

Vd/2

-Vd/2V

d/2

-Vd/2

Vc

Vc

Typical Op-Amp Input Stage

vo1 vo2

Page 7: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

7Kenneth R. Laker update KRL 03Oct14

Common and Differential Mode Currents

Solving for I1 and I

2:

I 1= I c /2 I d

I 2= I c /2−I d

Z1

Z3

Z2

I1 = I

c/2 + I

d

Vc

Vd/2

- Vd/2

Ic

I2 = I

c/2 - I

d

Definition: I c= I 1 I 2I d=I 1−I 22

+

++

±.

±.

±.

Page 8: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

8Kenneth R. Laker update KRL 03Oct14

CM-DM Circuit Description

Z1

Z3

Z2

Ic/2

Vc

Vd/2

- Vd/2 Ic Ic/2

Id

1. Voltage sources defined as common and differential mode quantities.

2. Differential mode currents take “blue” path.

3. Common mode current takes “red” path.

4. When Z1 = Z

2 = Z, the differential

circuit is said to be balanced.

OBSERVATIONSi. No DM I

d flows through Z

3.

ii. No CM Ic flows around Z

1, Z

2 loop

+

++

±.

±.

±.

I1

I2

I 1= I c /2 I d I 2= I c /2−I d

Page 9: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

9Kenneth R. Laker update KRL 03Oct14

Z1

Z3

Vx

<=>R

C1R

C2

RE1

RB1

RB2

RE2

Vd/2 -V

d/2

Typical Diff Amp Op-Amp Input Stage

Z2

Z 1=Z 2=Zbalanced circuit => Z1 = Z2 => Q1 = Q2, RC1 = RC2,RE1 = RE2 and RB1 = RB2

Balanced Circuit Differential Mode (VC = 0)

vo −vo

Page 10: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

10Kenneth R. Laker update KRL 03Oct14

Analyze Circuits by SuperpositionBalanced Circuit Differential Mode (V

C = 0)

Z1

Z3

Z2

I1 = Id

Vd/2

- Vd/2

I2 = -Id

Id

Z 1=Z 2=Z

V x

I c=0⇒V x=0

+

+

±.

±.

I c= I 1 I 2=

V d

2−V x

Z1

−V d

2−V x

Z 2=−2V x

Z

balanced circuit =>

+ -VZ1

+- VZ2

Z i n−dm=V d

I d=2 Z

NOTE: If , then => Vx ≠ 0.Z 2=Z 1Z Ic ≠ 0

Ic = 0

I c=I 1I 2=I d−I d=0

I d=I 1− I 22

=

V d

2−V x

2Z 1−

−V d

2−V x

2 Z 2=

V d

2Z

Page 11: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

11Kenneth R. Laker update KRL 03Oct14

Analyze Circuits by SuperpositionBalanced Circuit Common Mode (V

d = 0)

Z1

Z3

Z2

Ic/2

Vc

IcIc/2

Id = 0

Z 1=Z 2=Z

I c=V c

Z 1∣∣Z 2Z 3=

V c

Z2Z 3

+ ±.

balanced circuit =>

I1

I2

Z i n−cm=V c

I c=

Z2Z 3

I 1= I c /2I 2=I c /2

=> I d=0

Page 12: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

12Kenneth R. Laker update KRL 03Oct14

Summary

<=>

Definitions:

V c=V 1V 2

2V d=V 1−V 2

I c= I 1 I 2 I d=I 1−I 22

V 1=V cV d /2V 2=V c−V d /2I 1= I c /2 I d

I 2= I c /2−I d

I c

I 1

I 2

All V's & I's have differential & com-mon mode com-ponents

Z 1

Z 2

Z 3

I 2

Id

Page 13: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

13Kenneth R. Laker update KRL 03Oct14

Summary cont.In a balanced differential circuit (Z1 = Z2 = Z): 1. Differential mode voltages result in differential mode currents.2. Common mode voltages result in common mode currents.

The differential mode input impedance of a balanced circuit is: Z i n−dm=Z 1Z 2=2ZThe common mode input impedance of a balanced circuit is: Z i n−cm=Z 1∥Z 2Z 3=

Z2Z 3

Id Id = 0

Page 14: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

14Kenneth R. Laker update KRL 03Oct14

BJT Differential Amplifier – DC Bias View

I C= I cm /2 I cm /2

I BI B

I B=I cm

21

RC1=RC2=RC

RB1=RB2=RB

Collector bias path inherentlycommon mode.

I C=I cm

2≈

I cm

2

Choose Icm and RC for approximate½ VCC drop across RC.

balanced circuit

Icm

Q1=Q2

IE

IE

I E=I cm

2

RB1 RB2

RC2RC1

I 1=I c /2 I d

I 2= I c/2−I d

Recall00

for dc bias

Page 15: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

15Kenneth R. Laker update KRL 03Oct14

vid/2

-vid/2

vic

BJT Differential Amplifier – AC Signal View

RB1 RB2

RC1 RC2

vo1

vo2+-v

od

vod=vo2−vo1

vi1

vi2

v ic=v i1v i2

2v id=v i1−v i2

ro

Page 16: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

16Kenneth R. Laker update KRL 03Oct14

vid /2

rin-dm

+-

Z in−dm=v id

ib1d

Avdm=vodm

v idvo1d

Single-ended DM outputs: vo1d, vo2d

Differential DM output: vodm

=vo1d

- vo2d

vid /2

RC1

Avdm1 ,2=vo1 ,2d

vid

(diff Adm

)

(s-e Adm

)+

-

ro

NOTE: ib1d=ib1

; ib2d

=-ib2

ib1d i

b2d

RC2

RB1RB2

vodm vo2d

BJT Differential Amplifier – AC Diff Mode View

ro

ie1d

ie2d

DM input impedance

vidm=vid

Page 17: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

17Kenneth R. Laker update KRL 03Oct14

ro

vic

ib1c

rin-cm

+-vocm

Avcm=vocm

vicm

Single-ended CM outputs: vo1c

, vo2c

Differential CM output: vocm

= vo2c

- vo1c

vo1c vo2c

RB2Avcm1 ,2=

vo1 ,2c

vic

(diff Acm

)

(s-e Acm

)

NOTE: ib1c

=ib1

; ib2c

=ib2

BJT Differential Amplifier – AC Cmn Mode View

RB1

RC1RC2

ICM

ib2c

Z in−cm=v ic

ib1c

CM input impedance

Page 18: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

18Kenneth R. Laker update KRL 03Oct14

BJT Differential Amplifier – Small-signal View

ICM current source output impedance

ib1 ib2ie1

ic1ic2

ie2

vic

vid /2 vid /2

NOTE: 1. ro for amplifier Q1 & Q2 is ignored.2. vid /2 and vic are ac small signals

Z 1=Z 2=1re

Z 3=1r o

RB RB

RCRC

βib1re

ro

re

βib2V

x

Z1

Z2

Z3

vid

/2

vic

Vx

-vid

/2

re1=re2=re

RC1=RC2=RC

RB1=RB2=RB

ie1=ie1d1i ic /2 ie2=−ie2d1 i ic /2&

ib1=i ic /2iid

iic

/2

iid iid

ib2=i ic /2−i id

iic

/2

Page 19: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

19Kenneth R. Laker update KRL 03Oct14

Superposition Small-signal AnalysisDifferential Mode (vic = 0)

DM Path (ignoring both RB):

Balanced circuit

+-vo-dm

ie

icib

ied

vid=2 re ied=21r e ibd

Z 3=1roZ 1=Z 2=Z=1r e

vid

2=ied reied r e−

v id

2

ib1ib

vid /2 vid /2

ied

ie

RB

ro

βib-dm β ib-dm

RCRC

RBre re

⇒ ie2=−ie1=ie , ib2=−ib1=ib , ic2=−ic1=ic

Z i n−dm=2 ZRecall:

ibdibdic

icdicd

ie1−dm=ie−dm=ie1=i e

ib1−dm=ib−dm=i b1=i b

ie2−dm=ie−dm=−i e2=−ie

ib2−dm=ib−dm=−i b2=−ib

ic1−dm=ic−dm=ic1=ic ic2−dm=ic−dm=−ic2=−i c

vx

Z i n−dm=vid

ibd=21 re

Z in−dm=vid

ibd

Z Z

Z3

vid

/2

vic

Vx

-vid

/2

Page 20: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

20Kenneth R. Laker update KRL 03Oct14

Superposition Small-signal AnalysisDifferential Mode (vic = 0) cont.

+- vodm

ie ie

icib

iedied

Balanced circuit

DM Differential voltage gain:

Avdm=vodm

vid=

RC 1r e

≈RC

r e

vodm=RCibd −−RC ibd

vodm=vo2d−vo1d

ibd=v id

21

1r e

Avdm2=−Avdm1=vo2d

v id=

RC

21re≈

RC

2 re

vodm=2RC

1 re

v id

2

DM Single-ended voltage gains:

ib

ie1−dm=ie−dm=ie1=i e

ib1−dm=ib−dm=i b1=i b

−ie2−dm=−ie−dm=i e2=ie

vid /2

RB

ro

RC RC

βibd β ibdre re RB

vo2d vo1d

icicd

icdibd ibd

−ib2−dm=−ib−dm=i b2=ib

ic1−dm=ic−dm=ic1=ic −ic2−dm=−ic−dm=ic2=ic

ic−dm= i b−dm

vid /2vx

ibd=v id

21

1r e

Page 21: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

21Kenneth R. Laker update KRL 03Oct14

Superposition Small-signal AnalysisCommon Mode (vid = 0)

CM path: both re are in parallel

vic

+-ibc

iec

icm /2=ie−cm=i e1=i e

.=1[r e2ro]ibc

Z 1=Z 2=1re Z 3=1r o

Balanced circuit

Z in−cm=vic

icm=

vic

2 ibc=1

re

2ro≈1r o

ib1−cm=i b−cm=ib1=ib

RB

βibcβibcre

re

ro

RB

RC RC

i ic /2=ibc

Recall:ic1−cm=ic−cm=ic1=ic

icm /2=ie−cm=i e2=ie

ib2−cm=ib−cm=i b2=ib

ic2−cm=ic−cm=ic2=ic

vo-cm

Z i n−cm=Z∥ZZ 3=Z2Z 3

ibc

icc i

cc

vic=1 re ibc21 ro ibc

Note:

iec

ibc=i ic /2 ibc=i ic /2

Z Z

Z3

vid

/2

vic

Vx

-vid

/2

Page 22: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

22Kenneth R. Laker update KRL 03Oct14

Superposition Small-signal AnalysisCommon Mode (vid = 0)

vic

+-ibc

iec

ibc

icc vocm=−RC ibc−−RC ibc=0

ibc=v ic

1 re2 ro ≈

v ic

2 1 ro

CM Differential voltage gain:

vocm=vo2c−vo1cBalanced circuit

Avcm=vocm

vic=0

CM Single-ended voltage gains:

Avcm2=Avcm1=vo1c

v ic=−

RC 2 1 ro

≈−RC

2 ro

vo2c=vo1c=−RC ibc=−RC 2 1r o

vic

ro

RC RC

RB RBre re

βibcβibc

icm /2=ie−cm=i e1=i e icm /2=ie−cm=i e2=ieib1−cm=i b−cm=ib1=ib ib2−cm=ib−cm=i b2=ib

ic1−cm=ic−cm=ic1=ic ic2−cm=ic−cm=ic2=ic

ic−dm= i b−dm

vocm

ic−dm= i b−dm

icc

iec

ibc=i ic /2 ibc=i ic /21i ic

vic=1 r e2 ro ibc

Page 23: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

23Kenneth R. Laker update KRL 03Oct14

Summary Differential mode:

Z i n−dm=21r e

Avdm=vodm

vid≈

RC

re

Differential DM Voltage gain:

Common mode:

Z i n−cm=1 r e

2 ro≈1ro

Differential CM Voltage gain:

Avcm=vocm

v ic=0

Single-Ended DM Voltage gain:

Avdm1=−Avdm2=vo1d

v id≈−

RC

2 reAvcm1=Avcm2=

vo1c

v ic≈−

RC

2 ro

Single-Ended CM Voltage gain:

CMRR=Avdm1 ,2

Avcm1 , 2≈20 log10 ro

re Single-ended-output (balanced)Differential-output

CMRR=Avdm

Acdm=∞ i.f.f. Balanced

Page 24: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

24Kenneth R. Laker update KRL 03Oct14

v i

Practical Signal Excitation to Test CM

vo2vo1

Page 25: Differential Amplifier Common & Differential Modes

ESE319 Introduction to Microelectronics

25Kenneth R. Laker update KRL 03Oct14

Practical Signal Excitation to Test DM

vo1 vo2

vo1 vo2