Differential Amplifier Common & Differential Modes

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ESE319 Introduction to Microelectronics

Differential Amplifier

Common & Differential Modes

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Common & Differential Modes

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BJT Differential Amplifier

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Diff. Amp Voltage Gain and Input Impedance

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Small Signal Analysis – Differential Mode

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+

-

A Vo = A (V1 - V2)

Most “Famous” Differential Amplifier

V_CC

V_EE

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Common and Differential Modes

Consider the two-input conceptual circuit shown below.

Z₁ Z₃ Z₂ I₁ I₂ V₂ V₁

Define (convention) the voltages:

V _d_=V₁_−V ₂ V_c = “common mode voltage”

V_d = “differential mode voltage”

+ + ±a ±a V_c₌V 1V 2 2 1. Let V₁ = V₂ = V => V_c = V & V_d = 0 2. Let V₁ = -V₂ = V => V_c = 0 & V_d = 2V V_c “common” to V₁ & V₂; V_d is split between V₁ & V₂ s.t. “difference” V₁ - V₂ = V_d

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Replace V

₁

, V

₂

with DM & CM Sources V

_d

, V

_c

I₁ + I₂

V _c₌V 1V 2

2 V d=V 1−V 2

Definition Solve for V₁ and V₂

V ₁₌V _c_V _d_{/ 2}

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+

-V_o = A (V₁ - V₂)

A

Our Most “Famous” Differential Amplifier

V_CC

V_EE

V₁ & V₂ are single-ended input voltages defined w.r.t. ground.

+

-V_o = A (V₁ - V₂) A V_CC V_EE V_o V_o V _o₌A_v−dmV _d_A_v_−cmV _c CMRR₌∣Av−dm∣ ∣A_v_−cm_∣

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ESE319 Introduction to Microelectronics Z₁ Z₃ V ₁₌V _c_V _d_{/ 2} V ₂₌V _c₋V _d_/2 V_x <=> R_C1 R_C2 R_E1 R_B1 RB2 R_E2 V_d/2 -V_d/2 V_d/2 -V_d/2 V_c V_c

Typical Op-Amp Input Stage

v_o1 _v

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Common and Differential Mode Currents

Solving for I₁ and I₂:

I₁₌I_c_/2_I_d I ₂₌I_c_/2₋I _d Z₁ Z₃ Z₂ I₁ = I_c/2 + I_d V_c V_d/2 - V_d/2 I_c I₂ = I_c/2 - I_d Definition: I _d= Ic=I1I2 I₁_−I ₂ 2 + + + ±. ±. ±.

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CM-DM Circuit Description

Z₁ Z₃ Z₂ I_c/2 V_c V_d/2 - V_d/2 Ic/2 I_c I_d

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 = Z₂ = Z, the differential

circuit is said to be balanced. OBSERVATIONS

i. No DM I_d flows through Z₃.

ii. No CM I_c flows around Z₁, Z₂ loop

+ + + ±. ±. ±. I₁ I₂ I₁₌I_c_/2_I_d I ₂₌I_c_/2₋I _d

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ESE319 Introduction to Microelectronics Z₁ Z₃ V_x <=> R_C1 R_C2 R_E1 R_B1 RB2 R_E2 V_d/2 _-V d/2

Typical Diff Amp Op-Amp Input Stage

Z₂

Z₁_=Z₂_=Z

balanced circuit => Z1 = Z2 => Q1 = Q2, RC1 = RC2, R_E1 = R_E2 and R_B1 = R_B2

Balanced Circuit Differential Mode (V

_C

= 0)

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Analyze Circuits by Superposition

Balanced Circuit Differential Mode (V

_C

= 0)

Z₁ Z₃ Z₂ I₁ = I_d V_d/2 - V_d/2 I₂ = -I_d Id Z₁_=Z₂_=Z V _x I_c_=0⇒V _x₌₀ + + ±. ±. I_c=I1I2= V_d 2 −V x Z₁  −Vd 2 −V x Z₂ = −2V _x Z balanced circuit => + VZ1 -+ - V_Z2 Z_{i n}_−dm₌Vd I_d =2 Z NOTE: If , then => Z₂_=Z₁_{ Z} _I V_x ≠ 0. c ≠ 0 I_c = 0 I_c_=I₁_I ₂₌I_d₋I _d₌₀ I_d= I1−I₂ 2= V_d 2 −V x 2 Z₁ − −Vd 2 −Vx 2 Z₂ = V_d 2 Z

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Analyze Circuits by Superposition

Balanced Circuit Common Mode (V

_d

= 0)

Z₁ Z₃ Z₂ I_c/2 V_c I_c I_c/2 I_d = 0 Z₁_=Z₂_=Z I_c= Vc Z₁∣∣Z2Z3 = V c Z 2 Z3 + _±_. balanced circuit => I₁ I₂ Z_{i n}_−cm₌V c I_c = Z 2 Z3 I₁₌I_c_/2 I₂₌I_c_/2 => Id=0

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Summary

<=> Definitions: V _c₌V1V 2 2 Vd=V1−V 2 I_c_=I₁_I₂ _I _d₌ I1−I 2 2 V ₁₌V _c_V _d_{/ 2} V ₂₌V _c₋V _d_/2 I₁₌I_c_/2_I_d I ₂₌I_c_/2₋I _d I_c I₁ I₂

All V's & I's have

differential & com-mon mode com-ponents Z₁ Z₂ Z₃ I₂ I_d

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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: Zi n_−dm=Z1Z2=2 Z

The common mode input impedance

of a balanced circuit is: Zi n−cm=Z1∥Z2Z3=

Z

2 Z3

I_I_d

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BJT Differential Amplifier – DC Bias View

IC=Icm/2 I_cm/2 I_B I_B I _B₌ Icm 2_{1} R_C1_=R_C2_=R_C R_B1_=R_B2_=R_B

Collector bias path inherently

common mode.

I_C_= Icm 2 ≈

I_cm

2

Choose I_cm and R_C for approximate

½ V_CC drop across R_C. balanced circuit I_cm Q1_=Q2 I_E I E I_E₌ Icm 2 R_B1 R_B2 R_C2 R_C1 I₁₌I_c_/2_I_d I₂₌I_c_{/ 2}₋I_d

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v_id/2 -v_id/2

v_ic

BJT Differential Amplifier – AC Signal View

R_B1 R_B2 R_C1 R_C2 v_o1 -vod + v_o2 v_od_=v_o2_−v_o1 v_i1 v_i2 v_ic₌vi1vi2 2 vid=vi1−vi2 r_o

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ESE319 Introduction to Microelectronics v_id/2 r_in-dm + -Z_in_−dm₌ vid i_b1d A_vdm₌ vodm v_id v_o1d

Single-ended DM outputs: v_o1d, v_o2d

Differential DM output: v_odm=v_o1d- v_o2d v_id/2 R_C1 A_{vdm1 ,2}₌vo1 ,2d v_id (diff A_dm) (s-e A_dm) + -r_o NOTE: i_b1d=i_b1; i_b2d=-i_b2 i_b1d _i b2d R_C2 R_B1 R_B2 v_odm vo2d

BJT Differential Amplifier – AC Diff Mode View

r_o

i_e1d i_e2d

DM input impedance

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ESE319 Introduction to Microelectronics r_o v_ic i_b1c r_in-cm + -v_ocm Avcm= v_ocm v_icm

Single-ended CM outputs: v_o1c, v_o2c

Differential CM output: v_ocm = v_o2c - v_o1c

v_o1c v_o2c R_B2 A_{vcm1 , 2}₌ vo1 ,2c v_ic (diff A_cm) (s-e A_cm) NOTE: i_b1c=i_b1; i_b2c=i_b2

BJT Differential Amplifier – AC Cmn Mode View

R_B1 R_C1 R_C2 I_CM i_b2c Z_in_−cm₌ vic i_b1c CM input impedance

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BJT Differential Amplifier – Small-signal View

I_CM current source output impedance i_b1 i_e1 i_b2 i_c1 i_c2 i_e2 v_ic v_id/2 _v id /2 NOTE:

1. r_o for amplifier Q1 & Q2 is ignored. 2. v_id/2 and v_ic are ac small signals

Z₁_=Z₂_{=1r}_e Z₃_{=1r}_o R_B _R B R_C RC βi_b1 r_e r_o r_e βi_b2 V_x Z₁ Z₂ Z₃ v_id/2 v_ic V_x -v_id/2 r_e1_=r_e2_=r_e R_C1_=R_C2_=R_C R_B1_=R_B2_=R_B

i_e1₌i_e1d_{1}i_ic_/2 _& i_e2₌₋i_e2d_{1}i_ic_/2

i_b1₌i_ic_/2_i_id

i_ic/2

i_id _i_id

i_b2₌i_ic_/2₋i_id

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Superposition Small-signal Analysis

Differential Mode (v

_ic

= 0)

DM Path (ignoring both R_B):

Balanced circuit + -vo-dm i_e i_c i_b i_ed v_id_{=2 r}_ei_ed_{=21r}_ei_bd Z₃_{=1r}_o Z₁=Z2=Z =1re v_id 2 =ied reied re− v_id 2 ib1i b v_id/2 v_id/2 i_ed i_e R_B r_o βi_b-dm βi_b-dm R_C RC R_B r_e r_e

⇒ie2=−ie1=ie,ib2=−ib1=ib,ic2=−ic1=ic

Z_{i n}_−dm_{=2 Z} Recall: i_bd icd icd i_c i_b_d i_e1_−dm₌i_e_−dm_=i_e1=i_e i_b1_−dm₌i_b_−dm_=i_b1=i_b i_e2_−dm₌i_e_−dm_=−i_e2_=−i_e i_b2_−dm₌i_b_−dm_=−i_b2_=−i_b

i_c1_−dm₌i_c_−dm_=i_c1=ic i_c2_−dm₌i_c_−dm_=−i_c2_=−i_c

v_x Z_{i n}_−dm₌vid i_bd =21 re Z_in_−dm₌ vid i_bd Z Z Z₃ v_id/2 v_ic V_x -v_id/2

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Superposition Small-signal Analysis

Differential Mode (v

_ic

= 0) cont.

+ - v_odm i_e i_e i_c i_b i_ed i_ed Balanced circuit

DM Differential voltage gain:

A_vdm₌vodm v_id = R_C _ 1re ≈ RC r_e v_odm_=RC_i_bd_{−−RC} _i_bd_

v_odm₌v_o2d₋v_o1d

i_bd=vid 2 1 1re A_vdm2=−A_vdm1=vo2d v_id =  R_C 21r_e≈ R_C 2 r_e v_odm= 2 RC  1 re v_id 2

DM Single-ended voltage gains:

i_b i_e1_−dm₌i_e_−dm_=i_e1_=i_e i_b1_−dm₌i_b_−dm_=i_b1=i_b −i_e2_−dm₌₋i_e_−dm_=i_e2=ie v_id/2 R_B r_o R_C R_C βi_bd βi_bd r_e r_e _R B v_o2d v_o1d i_c i_cd icd i_bd _i bd −i_b2_−dm₌₋i_b_−dm_=i_b2=i_b i_c1_−dm₌i_c_−dm_=ic1=i_c −i_c2_−dm₌₋i_c_−dm_=i_c2=i_c i_c_−dm_=i_b_−dm v_id/2 v_x i_bd=vid 2 1 1re

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Superposition Small-signal Analysis

Common Mode (v

_id

= 0)

CM path: both r_e are in parallel

v_ic + -i_bc i_ec i_cm_/2₌i_e_−cm_=i_e1_=i_e .=1[re2ro]ibc Z₁_=Z₂_{=1r}_e Z3=1ro Balanced circuit Z_in_−cm₌vic i_cm= v_ic 2 i_bc=1 r_e 2 ro≈1ro i_b1_−cm₌i_b_−cm_=i_b1_=i_b R_B βi_bc βi_bc r_e r_e r_o R_B R_C _R_C i_ic_/2₌i_bc Recall: i_c1_−cm₌i_c_−cm_=i_c1_=i_c i_cm_/2₌i_e_−cm_=i_e2_=i_e i_b2_−cm₌i_b_−cm_=i_b2_=i_b i_c2_−cm₌i_c_−cm_=i_c2_=i_c v_o-cm Z_{i n}_−cm=Z∥ZZ3= Z 2 Z3 i_bc i_cc i_cc v_ic_{=1 r}_ei_bc_{21}r_oi_bc Note: i_ec i_bc₌i_ic_/2 ibc=iic/2 Z Z Z₃ v_id/2 v_ic V_x -v_id/2

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Superposition Small-signal Analysis

Common Mode (v

_id

= 0)

v_ic + -i_bc i_ec i_bc i_cc v_ocm=−R_C i_bc−−R_Ci_bc=0 i_bc₌ vic 1r_e_2r_o≈ v_ic 2_{1}r_o

CM Differential voltage gain:

v_ocm₌v_o2c₋v_o1c

Balanced circuit

A_vcm=v_vocm

ic

=0

CM Single-ended voltage gains: A_vcm2₌A_vcm1₌vo1c v_ic =− R_C _ 2_{1}r_o≈− R_C 2r_o v_o2c=v_o1c=−RC ibc= −RC  21r_o vic r_o R_C _R C R_B re re R_B βi_bc βi_bc i_cm_/2₌i_e_−cm_=i_e1_=i_e _i_cm_/2₌_i_e_−cm_=i_e2_=i_e i_b1_−cm₌i_b_−cm_=i_b1_=i_b i_b2_−cm₌i_b_−cm_=i_b2_=i_b i_c1_−cm₌i_c_−cm_=i_c1_=i_c i_c2_−cm₌i_c_−cm_=i_c2_=i_c i_c_−dm_=i_b_−dm v_ocm i_c_−dm_=i_b_−dm i_cc i_ec i_bc₌i_ic_/2 1i_ic i_bc₌i_ic_/2 v_ic_{=1}r_e_2r_oi_bc

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Summary

Differential mode: Z_{i n}_−dm_{=21r}_e A_vdm₌vodm v_id ≈ R_C r_e

Differential DM Voltage gain:

Common mode: Z_{i n}_−cm_{=1}



re

2 ro



≈1ro

Differential CM Voltage gain: A_vcm₌vocm

v_ic =0

Single-Ended DM Voltage gain:

A_vdm1₌₋A_vdm2₌vo1d v_id ≈− R_C 2 r_e Avcm1=Avcm2= v_o1c v_ic ≈− R_C 2 r_o

Single-Ended CM Voltage gain:

CMRR₌ Avdm1 ,2 A_{vcm1 , 2}≈20 log10



r_o r_e



Single-ended-output (balanced) Differential-output CMRR₌ Avdm A_cdm=∞ i.f.f. Balanced

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v_i

Practical Signal Excitation to Test CM

v_o2 v_o1

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Practical Signal Excitation to Test DM

v_o1 v_o2