albert comerma (pi)

Advanced Analog Building Blocks

Differential amplifiers

Albert Comerma (PI)([email protected])

Course web

SoSe 2017

http://www.kip.uni-heidelberg.de/~shen/Advanced_Analog_Building_Blocks/

• Next lectures after holidays:• 25.5 → lecture Friday 26th

• 15.6 → lecture Friday 16th

Should we proceed as normal days (attendance)?

Run some more cadence lab on one of those days?

IntroductionAmplifier configurations

Miller EffectDifferential amplifier key elementsThe Differential Pair

Introduction: Miller Effect

i1 = v1−v2Z = v1+Kv1

Z = 1+KZ v1

v1i1

= Z1+K = 1

(1+K)Cs

i2 = v2−v1Z =

v2+v2K

Z =1+ 1

KZ v2

v2i2

= Z1+ 1

K

= 1

(1+ 1K )Cs

C1 = (1 + K )CC2 =

(1 + 1

K

)C

for K >> 1→ C1 >> C , C2 ≈ C

Caution!

Miller effect is usually calculated forK(w) at medium frequencies.Extrapolation to high frecuenciesproduces error.

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Introduction: Differential amplifier key elements

• Two terminals input (differential).

• Flexibility in configuration / feedback options (OPamp).

• Commmon mode: DC voltage present at both inputs.

• Differential input: small signal present at input: V+ − V−• Common Mode Rejection Ratio, CMRR: immunity to changes in

common mode.

• Power Supply Rejection Ratio, PSRR: immunity to changes in powersupply.




The Differential Pair: circuit basics

• Usually a difference of voltages need to be amplified.

Assuming both in saturation:V1 = V2 → ID1 = ID2 = Ib

2

V1 >> V2 → ID1 ≈ Ib → ID2 ≈ 0

Differential voltage:Vd = V1 − V2

Common-mode:

Vc = V1−V22

V1 = Vc + Vd2

, V2 = Vc − Vd2




The Differential Pair: small signal analysis

• Intrinsic gain in differential mode.

Av1 = vd1vd

= −gm1rds12

Transconductance amplifier (voltage to current conversion);

g1 = id1vd

= gm12

Caution!

Devices must be kept in saturation.



Active loadTelescopic cascodeFolded cascode N inputFolded cascode P input

Amplifier configurations: active load

Av1 = vo1vd

= −gm1(rds1//rds3)2

= −gm12(go1+go3)

Assuming M1 = M2,M3 = M4 thengm1 = gm2, go1 = go2, go3 = go4 the

differential gain is;

Avd = vo2−vo1vd

= −gm1go1+go3

Caution!

VG must guarantee that ID3 + ID4 = Ib




Amplifier configurations: common mode gain

• Intrinsic gain in differential mode.

Neglecting the current flow in rds1;

Avc1 = vo1vc≈ −gm1rds3

1+2gm1rb




Amplifier configurations: CMRR

CMRR =∣∣∣ Avd

Avc1

∣∣∣ = −go3(1+2gm1rb)2(go1go3

If go1 = go3,CMRR ≈ gm1rb2

CMRR

Increasing the differential pair transconductance or rb, the CMRRraises!.




Amplifier configurations: assymetric

• Current mirror ensures currents are the sameand half Ib

Avd ≈ gm1go2+go4




Amplifier configurations: assymetric frequency response

C1 = CGD1 + CBD1 + CGS3 + CGS4 + CBD3

C2 = CGD2 + CBD2 + CGD4 + CBD4 + CL

R1 = 1gm3

,R2 = 1go2+go4

Then (with gm1 ≈ gm2):

Av ≈ gm12

R2ω2s+ω2

(1 + gm4R1ω1

s+ω1

)where ω1 = 1

R1C1, ω2 = 1

R2C2

Av = Av (0)

(s

ω′1

+1

)(

sω1

+1)(

sω2

+1)

Av (0) = gm1R22

(1 + gm4R1) ≈ gm1go2+go4

, ω′1 = ω1(1 + gm4R1) ≈ 2ω1

A pole-zero pair is obtained, with the zero at double frequency of the pole.The dominant pole is: ω2 = go2+go4

C2c©[email protected] Advanced Analog Building Blocks: Differential amplifiers 9 / 13



Telescopic cascode amplifier

VB ,VBCN ,VBCP are DC biasvoltages generated externally toset stauration opperation point.

• Gain: Ad = (gmrds )2

2

• Cuttoff frequency: ωt = gm1CL

(other poles also)

• Output swing: VDD − 5Veff

(Veff = VGS − VTH)

Low Gain, Low output swing butfast and low power.




Folded cascode N input

• Slower

• Wider outputswing




Folded cascode N input

• Gain: Ad = (gmrds )2

2

• Cuttoff frequency: ωt = gm1CL

(other poles also)

• Output swing VDD − 4Veff

• Wider output swing




Folded cascode P input


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