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Common mode feedback for fully differential amplifiers Differential amplifiers • Cancellation of common mode signals including clock feed-through • Cancellation of even-order harmonics • Double differential signal swing, SNR↑3dB Symbol: 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 Common Mode Output Voltage Stabilization Common mode drift at output causes differential signals move into triode region 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 Common mode equivalent VBP Vo1cm Vicm VBN I2 Vocm I1 If Vocm is too high, needs to increase Vo1cm for single stage, needs positive feedback Vo1cm I2 Vo1cm a little low Correct Vo1cm Vocm VBN I1 Vocm Vo1 actual Q point too high PMOS in triode If Vo1 Vo1CM need I x i.e. need to VBP From this single stage's point view, need positive feedback VBP Ix Vo1cm VO1CM Vicm Ix(Vo) Iy(Vo) VBN Iy Vo But we started by having Vocm too high need neg. feedback from Vo to VBP In both cases, the whole loop has negative loop gain VBP I1 I2 Vo1cm Vicm Vo Vicm VBN What about single ended? Does it have the same problem? Does it require feedback stabilization? VBP I3 Yes, to all three questions I4 Vo1cm Vi- I1 VBN I2 I6 Vo Vi+ I7 To match I1 and I3, the diode connection provides the single stage positive feedback to automatically generate Vg3. The match between I2 and I4, and I6 and I7 is a two stage problem and requires negative feedback: needs feedback from Vo to Vi-. All op amps must be used in feedback Viconfiguration! VBP I3 I4 Vo1cm I1 I2 I3 Vi- VBN Vi+ I4 Vo1cm I1 Vo I7 VBN VBP I6 I2 I6 Vo Vi+ I7 Buffer connection or resistive feedback provides the needed negative feedback Fully differential amplifiers are also used in feedback configuration. Vi Vp Ri Vp Vo Rb Vi Vi (Vp Vn ) Ri Vi Vn Vn Vo , Ri Rb Vi+ Vi- Vp Vn Vp Vn (Vo Vo ) Rb If amplifier gain is high, V p Vn is 0, Vi Vi (Vo Vo ) Rb , and Vo Vo (Vi Vi ) Ri Rb Ri Hence, differential signal is well defined. Vo+ Vo- But when you add the first two equations Vi Vp Ri Vp Vo Rb Vi Vn Vn Vo , Ri Rb You get: Vi Vi (Vp Vn ) Ri Vi+ Vi- Vp Vn Vo+ Vo- Vp Vn (Vo Vo ) Rb Solving for Vo Vo , Rb Rb Ri Vo Vo (Vi Vi ) (V p Vn ) Ri Ri Since Vp+Vn is undefined, Vo++Vo- is undefined. Basic concept of CMFB: Vo+ +Vo- Vo+ CM Vo- Dvb 2 measurement Voc CMFB e VoCM + desired common mode voltage Basic concept of CMFB: Vo+ +Vo- Vo+ CM Vo- Dvb 2 measurement Voc CMFB 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) example Vb2 CC Vi+ CC Vi- Vo+ VCMFB Vo- Vb1 VCMFB Voc + Vo+ Vo- Example Voc ? ? VoCM Need to make sure to have negative feedback VDD M7A 75/3 150/3 M2A 150/3 M2B BIAS4 300/3 300/3 M13A M13B 1.5pF 1.5pF M7B 75/3 averagerOUT- M3B BIAS3 OUT+ 300/2.25 300/2.25 M6C 20K M3A 20K 300/2.25 300/2.25 75/2.25 INM6AB 75/2.25 IN+ M1A Source M12B M12A 1000/2.25 1000/2.25 follower M1B 200/2.25 BIAS2 M11 150/2.25 M10 CL=4pF 4pF M9A 50/2.25 M9B 50/2.25 M4A 50/2.25 M4B 50/2.25 BIAS1 M8 150/2.25 200/2.25 M5 VSS Folded cascode amplifier Resistive C.M. detectors: Vo+ R1 R2 Vo- Vo Vo , if R1 R2 2 Prob : resistive loading effect. use R1 , R2 very large - difficult to achieve - especially when Vo is at an cascoded node Resistive C.M. detectors: Vo.c. Vo+ Vi+ R1 R1 Vo- Vi- Not recommended. The resistive loading kill gain. • 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) Buffer Vo+, Vo- before connecting to R1. Voc Vo+ VoR1 R1 Simple implementation: source follower Vo+ Vo.c. Vo- * Gate capacitance is added to your amp load. Why not: Vo+ Vo.c. Vo- * Initial voltage on cap. C1 C2 Vo Vo , if C1 C 2 2 Prob : at high freq. AC diff short Use buffer to isolate Vo node: gate cap is load or resistors Switched cap CMFB Vo+ Φ1 VCMFB Vo- Φ2 Φ1 VoCM. Vb-repl VoCM. In the normal balanced case, when Vo+=Vo- = desired Vocm, Vb-repl is supposed to generate the correct voltage for VCMFB Vxx Small copy of Vo- Vo+ Small copy Vb-repl of VCMFB Vyy Small copy of To increase or decrease the C.M. loop gain: e.g. Vo.c. Vo.c.d. VC.M.F.B. Another implementation • Use triode transistors to provide isolation & z(s) simultaneously. M1, M2 in deep triode. VGS1, VGS2>>VT Voc Vo+ VoM1 can be a c.s. M2 In that case, circuit above M1, M2 needs to ensure that M1, M2 are in triode. Vo Vo 2 deep triode oper Example: Input stage Vo- Vb M1 M2 e.g. Vo+, Vo-≈2V at Q & Vb ≈1V , Then M1&2 will be in deep triode. Vo+ If Vo ,Vo Vo- Vo+ Voc VG1 ,VG 2 Vb1 RM 1 , RM 2 Vb2 VX M1 M2 V X ( I const ) but V X to Vo ,Vo is cascoded C.G. Vo ,Vo Two-Stage, Miller, Differential-In, Differential-Out Op Amp M10 and M11 are in deep triode Vo++ Vo2 VoCM. VCMFB Vo Vo VCMFB 2 gain can be large Vo+ Vo- Note the difference from the book accommodates much larger VoCM range Small signal analysis of CMFB Example: IB M3 Vo+ M1 M4 IB M2 -Δi Vo- +Δi +Δi M5 +Δi -Δi VCM +Δi VCMFB Δi=0 2Δi Differential signal Common mode signal -Δi -Δi • Differential Vo: Vo+↓ by ΔVo, Vo-↑ by ΔVo • Common mode Vo: Vo+↑ by ΔVo, Vo-↑ by ΔVo DVo Di g m1 2 1 DVCMFB 2Di g m5 k DVo g m1 g m 2 g m3 g m 4 g m1 k g m5 IB M3 Vo+ M1 VCM M4 IB Vo- M2 +Δi +Δi M5 -Δi -Δi VCMFB Δi=0 2Δi Δi7 M7 + -2Δi M6 - 1 -2Δi gm6 To increase gain : 1 DVG 7 2Di g m6 Di7 DVG 7 g m 7 g m7 2Di g m6 g m7 Di5 2Di1 g m6 g m1 g m 7 1 DVo DVCMFB g m5 g m6 * gain by geometric ratios can be made accurate CMFB loop gain: example Vb2 CC Vi+ CC Vi- Vo+ VCMFB Vo- Vb1 VCMFB Voc + Vo+ Vo- Bandwidth of CMFB loop • Ideally, if CM and DM are fully decoupled, CM only needs to stabilize operating points. CM bandwidth only needs to be wide enough to handle disturbances affecting operating points. • Practically, there is CMDM conversion. CM loop needs to handle disturbances of bandwidth comparable to DM BW • But CM loop shares most of CM poles and have additional poles, difficult to achieve similar bandwidth, make CM loop bandwidth a few times low than DM Here Bandwidth = unity loop gain frequency Example VBP I1 I2 Vo1 Vo Vi++Vicm VBN Vi-+Vicm VCMFB VBN CM and DM equivalent circuit Comparison VBP VBP CM Vo1cm Vocm VCMFB ro1=rdsp||rcascode≈rdsp gm = ½gm5 ½Vo1d I2 Vid ½ M5 DM VBN I1 I2 -½Vid ½Vod AC GND VBN I1 ro1=rdsp||rdsn≈ ½rdsp gm = gm1 Low frequency pole p1 is about 2X lower in CM; DC gain is change by 2*½gm5/gm1, unity gain frequency gm/CC is changed by ½gm5/gm1, high frequency poles and zeros of DM remain in CM, CM has one additional node at D5 similar or worse PM at unity gain fre To ensure sufficient CMFB loop stability • CMFB loop gain = CM gain from VCMFB to Voc * gain of CMFB circuit • To ensure sufficient PM for CMFB loop – Make the DC gain of CMFB circuit to be a few time less than one – That make the CMFB loop UGF to be a few times lower than CM gain’s UGF – Make sure the additional pole in the CM gain and any additional poles from the CMFB circuit to be at higher frequency than DM UGF CM gain’s additional pole at D5 is given by: -gm1/(Cgs1+½Cdb5) This is close to fT of M1. So at very high fre. If the CMFB circuit below is to be used, then the following needs to be true: 1. IB and M5 sized to give desired VCMFB when Vo+=Vo-=desired 2. CMFB circuit DC gain ACMFB=2gm1f/gm5f is small. 3. Pole of CMFB – gm5f/(Cgs5+Cgs5f+Cdb5f+Cdb1,4f) >> ACMFB*UGF of DM VBP Vo+ M1f VCM IB M3f VBP M4f IB M2f Vo- Also, W/L of M1-4f should be small, so that their VEB is large to accommodate Vo+, Vo- swing. This is consistent with (1.) above VCMFB M5f Example DC gains 85dB 80dB AvCM(w) 70dB But does not mean CM Q point can be maintained with 70dB accuracy! AvDM(w) AvCMFBLoop(w) w -15dB Av(w) of CMFB circuit Why? Because op amp is always used in feedback configuration. DM feedback also kills CM gain, since DM and CM share the same path from vo1 to vo. VBP I1 I2 Vo1 Vo VBN VCMFB Ri Rf VBN Rf Ri VBP CM Vo1cm I2 Vicm = -bVocm Vicm Vocm -1 gm=gm1/(1+2gm1ro5) VCMFB ½ M5 Vocm AvCM (w )VCMFB AViCM (w )ViCM Vocm g m5 ro 5 AvCM (w ) VCMFB g m 5 ro 5 b AvCM (w ) VBN I1 g m1 1 2 g m1ro 5 AvCM (w )VCMFB AvCM (w )( bVocm ) 1 g m5 2 Vocm VCMFB g m5 ro5 when AvCM large b A (w ) when A vCM small vCM Example DC gains 85dB 80dB AvCM(w) 70dB New AvCM(w) AvDM(w) gm5ro5/b 40dB 25dB AvCMFBLoop(w) New AvCMFBLoop(w) -15dB Av(w) of CMFB circuit w Is it good enough to stabilize the CM Q points to -25 dB accuracy level? If not, what can be done? Increase the effective gm5ro5! That is: use cascode tail current source. This will improve the CMFB loop gain under DM feedback by about 30 to 35 dB. Or, increase the gain of CMFB circuit. In doing so, avoid introducing high impedance node, avoid introducing poles near or lower than DM GB. VDD M7A 75/3 150/3 M2A 150/3 M2B BIAS4 300/3 300/3 M13A M13B 1.5pF 1.5pF M7B 75/3 averagerOUT- M3B BIAS3 OUT+ 300/2.25 300/2.25 M6C 20K M3A 20K 300/2.25 300/2.25 75/2.25 INM6AB 75/2.25 IN+ M1A Source M12B M12A 1000/2.25 1000/2.25 follower M1B 200/2.25 BIAS2 M11 150/2.25 M10 CL=4pF 4pF M9A 50/2.25 M9B 50/2.25 M4A 50/2.25 M4B 50/2.25 BIAS1 M8 150/2.25 200/2.25 M5 VSS Folded cascode amplifier Voc variation range • Voc variation comes from two sources – Input common mode – Common mode PVT variations • Vicm induced Voc variation – Find closed-loop Vicm range – Find closed-loop gain from Vicm to Voc – Find contribution to Voc variation • PVT induced Voc variation – Refer all PVT variations to VBP variation – Find gain closed-loop from VBP to Voc – Find contribution to Voc variation VBP CM Vo1cm I2 Vicm V’icm Vocm -1 gm=gm1/(1+2gm1ro5) VCMFB ½ M5 VBN I1 CMFB circuit Vocm AvCM (w )VCMFB AViCM (w )ViCM AVBP (w)VBP VCMFB AVCMFBCircuit (w) Vocmdes Vocm ViCM V 'iCM b (w )(Vocm V 'iCM ) Vocm-Des Differences between CM and DM loop pole/zero At input node: Vi -Vi Vicm Vicm Current feedback eliminate one node in CMFB circuit. VDD 75/3 150/3 M2A M7A 150/3 M2B BIAS5 BIAS4 300/3 300/3 M13A M13B 1.5pF 1.5pF M3B BIAS3 OUT+ 300/2.25 300/2.25 OUT20K M3A 20K 300/2.25 300/2.25 M6C INM6A M6B IN+ M1A M1B M12A 1000/2.25 200/2.25 BIAS2 M11 150/2.25 M10 CL=4pF 4pF M9A 50/2.25 M9B 50/2.25 M4A 50/2.25 M4B 50/2.25 BIAS1 M8 150/2.25 200/2.25 M5 VSS What sizes should M6A-C be in order to maintain the same loop gain? M12B 1000/2.25 VDD=+1.65V M11 M12 M3 M4 Vo1 M27 M21 M22 M23 M24 Vo2 M1C M2C IDC=100υA VCM Vi1 M14 M26 M13 M1 M51 M2 M52 -VSS=-1.65V Vi2 M25 VDD + – Aocmc g m5 g m6 g ds 2 g ds 6 g ds 7 CMFB with current feedback M3 M4 Vo+ Vo- M1 IB CM Voc detect M2 VoCM M6 M7 M5 VDD VSS IB desired Q : I 3 I1 ,VoCM 4 2 If Vo Vo by DVo , Voc by DVo Di1 , Di2 by DVo g m 6 (equivalen t to VG1 , VG 2 by DVo )