Common mode feedback for fully differential amplifiers

1. Common mode feedback for fully differential amplifiers

2. Differential amplifiers • Cancellation of common mode signals including clock feed-through • Cancellation of even-order harmonics • Double differential signal swing, SNR↑3dB Symbol:

3. 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

4. Common Mode Output Voltage Stabilization Common mode drift at output causes differential signals move into triode region

5. 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

6. Common mode equivalent VBP Vo1cm I2 Vicm Vocm VBN I1

7. If Vocm is too high, needs to increase Vo1cm for single stage, needs positive feedback Vo1cm Vo1cm a little low I2 Correct Vo1cm Vocm VBN I1 Vocm Vo1 actual Q point too high PMOS in triode

8. VBP Ix Vo1cm Ix(Vo) VO1CM Vicm Iy(Vo) VBN Iy Vo In both cases, the whole loop has negative loop gain

9. VBP I2 I1 Vo1cm Vicm Vo Vicm VBN What about single ended? Does it have the same problem? Does it require feedback stabilization?

10. VBP I4 I3 Yes, to all three questions Vo1cm I6 Vi- Vo I1 I2 Vi+ I7 VBN 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-.

11. VBP I4 I3 All op amps must be used in feedback configuration! Vo1cm I6 Vi- Vo I1 I2 Vi+ I7 VBN VBP I4 I3 Vo1cm Buffer connection or resistive feedback provides the needed negative feedback I6 Vi- Vo I1 I2 Vi+ I7 VBN

12. Fully differential amplifiers are also used in feedback configuration. Vi+ Vo+ Vp Vn Vi- Vo- Hence, differential signal is well defined.

13. But when you add the first two equations Vi+ Vo+ Vp You get: Vn Vi- Vo- Since Vp+Vn is undefined, Vo++Vo- is undefined.

14. Basic concept of CMFB: CM measurement Vo+ +Vo- 2 Vo+ Vo- Voc - CMFB Dvb e VoCM + desired common mode voltage

15. Basic concept of CMFB: CM 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)

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

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

18. 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

19. Resistive C.M. detectors: R1 R2 Vo+ Vo-

20. Resistive C.M. detectors: Vo.c. R1 R1 Vo+ Vo- Vi+ Vi- Not recommended. The resistive loading kill gain.

21. 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)

22. Buffer Vo+, Vo- before connecting to R1. Voc Vo+ Vo- R1 R1 Simple implementation: source follower Vo.c. Vo+ Vo- * Gate capacitance is added to your amp load.

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

24. C1 C2

25. Use buffer to isolate Vo node: gate cap is load or resistors

26. Switched cap CMFB Vo+ Φ1 Φ2 Φ1 VoCM. VCMFB Vb-repl Vo- VoCM.

27. 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+ VCMFB Small copy of Vb-repl Vyy Small copy of

28. To increase or decrease the C.M. loop gain: e.g. Vo.c. Vo.c.d. VC.M.F.B.

29. 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.

30. deep triode oper

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

32. Vo- Vo+ Vb1 Vb2 VX M1 M2

33. Two-Stage, Miller, Differential-In, Differential-Out Op Amp M10 and M11 are in deep triode

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

35. Small signal analysis of CMFB Example: IB IB VCM M4 M3 Vo+ Vo- M1 M2 -Δi +Δi +Δi +Δi M5 +Δi -Δi -Δi -Δi VCMFB Δi=0 2Δi Differential signal Common mode signal

36. Differential Vo: Vo+↓ by ΔVo, Vo-↑ by ΔVo • Common mode Vo: Vo+↑ by ΔVo, Vo-↑ by ΔVo

37. 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

39. CMFB loop gain: example Vb2 CC CC Vi+ Vi- Vo+ Vo- VCMFB Vb1 Vo+ VCMFB Voc - Vo- +

40. 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 CMDM 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

41. Example VBP I2 I1 Vo1 Vo Vi++Vicm Vi-+Vicm VBN VCMFB VBN

42. CM and DM equivalent circuit Comparison VBP VBP CM DM Vo1cm ½Vo1d I2 I2 Vid -½Vid Vocm ½Vod AC GND ½ M5 I1 VCMFB I1 VBN VBN ro1=rdsp||rdsn≈ ½rdsp ro1=rdsp||rcascode≈rdsp gm = gm1 gm = ½gm5 • 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

43. 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

44. 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: IB and M5 sized to give desired VCMFB when Vo+=Vo-=desired CMFB circuit DC gain ACMFB=2gm1f/gm5f is small. Pole of CMFB – gm5f/(Cgs5+Cgs5f+Cdb5f+Cdb1,4f) >> ACMFB*UGF of DM VBP VBP VCM IB IB 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 Vo+ Vo- M1f M3f M4f M2f VCMFB M5f

45. But does not mean CM Q point can be maintained with -70dB accuracy! Example DC gains AvCM(w) 85dB 80dB 70dB AvDM(w) AvCMFBLoop(w) w -15dB Av(w) of CMFB circuit

46. Why?

47. 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 I2 I1 Vo1 Vo VBN VCMFB VBN Ri Rf Rf Ri

48. VBP CM Vo1cm I2 Vicm = -bVocm Vicm Vocm -1 gm=gm1/(1+2gm1ro5) ½ M5 I1 VCMFB VBN

49. Example DC gains AvCM(w) 85dB 80dB New AvCM(w) 70dB AvDM(w) gm5ro5/b 40dB 25dB AvCMFBLoop(w) w New AvCMFBLoop(w) -15dB Av(w) of CMFB circuit

50. 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.