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**Differential Amplifiers and common mode feedback**

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**Differential amplifiers**

Cancellation of common mode signals including clock feed-through Cancellation of even-order harmonics Increased signal swing Symbol:

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**Two-Stage, Miller, Differential-In, Differential-Out Op Amp**

peak-to-peak output voltage ≤ 2·OCMR Output common mode range (OCMR) = VDD-VSS - VSDPsat - VDSNsat

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**Two-Stage, Miller, Differential-In, Differential-Out Op Amp with Push-Pull Output**

Able to actively source and sink output current Output quiescent current poorly defined

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**Cascode Op Amp with Differential-Outputs, push-pull output**

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**Differential-Output, Folded-Cascode**

OCMR = VDD -VSS - 2VSDP(sat) -2VDSN(sat) Quite limited

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**Two-Stage, Differential Output, Folded-Cascode**

M11-M13 and M10-M12 provide level shift

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**Common Mode Output Voltage Stabilization**

Common mode drift at output causes differential signals move into triode region

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**Common Mode feedback All fully differential amplifier needs CMFB**

Common mode output, if uncontrolled, moves to either high or low end, causing triode operation Ways of common mode stabilization: external CMFB internal CMFB

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**Cause of common mode problem**

Unmatched quiescent currents Vbb=VbbQ+Δ Vbb I2 Vin=VinQ Vbb=VbbQ Vo1 Vo2 Vin I1 Vo1Q Vo1 Vin=VinQ+ΔVin actual Q point M2 is in triode

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Vxx Ix Vo Ix(Vo) VOCM Vin Iy(Vo) Vyy Iy Vo

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**Basic concept of CMFB: Dvb e desired common mode voltage CM**

measurement Vo+ +Vo- 2 Vo+ Vo- Voc - CMFB Dvb e VoCM + desired common mode voltage

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**Basic concept of CMFB: Dvb e e**

measurement Vo+ +Vo- 2 Vo+ Vo- Voc - CMFB Dvb e e VoCM + Find transfer function from e to Voc, ACMF(s) Find transfer function from an error source to Voc Aerr(s) Voc error due to error source: err*Aerr(0)/ACMF(0)

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example Vb2 CC CC Vi+ Vi- Vo+ Vo- VCMFB Vb1 Vo+ VCMFB Voc - Vo- +

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**Need to make sure to have negative feedback**

Example Voc ? ? VoCM Need to make sure to have negative feedback

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**Folded cascode amplifier**

VDD M7A 150/3 150/3 M2A M2B 300/3 300/3 75/3 M13A M13B BIAS4 averager 1.5pF 1.5pF M7B 75/3 M3B BIAS3 OUT+ OUT- 20K 20K M3A 300/2.25 300/2.25 300/2.25 300/2.25 M6C 75/2.25 IN- IN+ Source follower M1A M1B M12B M6AB M12A 1000/2.25 75/2.25 1000/2.25 200/2.25 BIAS2 M11 M10 M9A M9B CL=4pF 4pF 150/2.25 50/2.25 50/2.25 BIAS1 M8 M5 200/2.25 M4A M4B 150/2.25 50/2.25 50/2.25 VSS Folded cascode amplifier

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**Resistive C.M. detectors:**

Vo+ Vo-

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**Resistive C.M. detectors:**

Vo.c. R1 R1 Vo+ Vo- Vi+ Vi-

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**O.K. if op amp is used in a resistive feedback configuration**

& R1 is part of feedback network. Otherwise, R1 becomes part of g0 & hence reduces AD.C.(v)

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**Buffer Vo+, Vo- before connecting to R1.**

Voc Vo+ Vo- R1 R1 Simple implementation: source follower Vo.c. Vo+ Vo- * Gate capacitance is your load to Amp.

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Why not: Vo.c. Vo+ Vo- * Initial voltage on cap.

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C1 C2

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**Use buffer to isolate Vo node:**

gate cap is load or resistors

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Switched cap CMFB Vo+ Φ1 Φ2 Φ1 VoCM. Vo- VoCM.

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**To increase or decrease the C.M. loop gain:**

e.g. Vo.c. Vo.c.d. Vo.c. Vo.c.d. VC.M.F.B. VC.M.F.B.

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**Another implementation**

Use triode transistors to provide isolation & z(s) simultaneously. M1, M2 in deep triode. VGS1, VGS2>>VT Voc Vo+ Vo- M1 M2 In that case, circuit above M1, M2 needs to ensure that M1, M2 are in triode. can be a c.s.

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deep triode oper

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Example: Input state Vo+ Vo- Vb M1 M2 e.g. Vo+, Vo-≈2V at Q & Vb ≈1V , Then M1&2 will be in deep triode.

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Vo- Vo+ Vb1 Vb2 VX M1 M2

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**Two-Stage, Miller, Differential-In, Differential-Out Op Amp**

M10 and M11 are in deep triode

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Vo++ Vo- 2 VoCM. VCMFB Vo+ Note the difference from the book accommodates much larger VoCM range Vo-

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**Small signal analysis of CMFB**

Example: IB IB VCM M4 M3 Vo+ Vo- M1 M2 -Δi +Δi +Δi M5 +Δi -Δi -Δi VCMFB Δi=0 2Δi

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**Differential Vo: Vo+↓ by ΔVo, Vo-↑ by ΔVo**

Common mode Vo: Vo+↑ by ΔVo, Vo-↑ by ΔVo

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IB IB VCM M4 M3 Vo+ Vo- M1 M2 +Δi +Δi M5 -Δi -Δi VCMFB Δi=0 2Δi M7 Δi7 + - 1 gm6 -2Δi -2Δi M6

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**CMFB loop gain: example**

Vb2 CC CC Vi+ Vi- Vo+ Vo- VCMFB Vb1 Vo+ VCMFB Voc - Vo- +

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-gm5vro2 -gm5vro2gm6 Vo gm5v v Poles: p1 p2 z1 same as before

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**Folded cascode amplifier**

VDD M7A 150/3 150/3 M2A M2B 300/3 300/3 75/3 M13A M13B BIAS4 averager 1.5pF 1.5pF M7B 75/3 M3B BIAS3 OUT+ OUT- 20K 20K M3A 300/2.25 300/2.25 300/2.25 300/2.25 M6C 75/2.25 IN- IN+ Source follower M1A M1B M12B M6AB M12A 1000/2.25 75/2.25 1000/2.25 200/2.25 BIAS2 M11 M10 M9A M9B CL=4pF 4pF 150/2.25 50/2.25 50/2.25 BIAS1 M8 M5 200/2.25 M4A M4B 150/2.25 50/2.25 50/2.25 VSS Folded cascode amplifier

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**Removing the CM measurement**

Vo+ VoCM Vo- VCMFB Directly connect Vo+, Vo- to the gates of CMFB diff amp.

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VDD=+1.65V M11 M12 M3 M4 M26 M27 Vo1 Vo2 M21 M22 M23 M24 M1C M2C IDC=100υA VCM M13 Vi1 M2 Vi2 M1 M14 M51 M52 M25 -VSS=-1.65V

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**CMFB with current feedback**

IB Vo+ Voc CM detect VoCM Vo- M5 M6 M7 M1 M2

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