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

8. Yes, to all three questions
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 negative 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-.

9. All op amps must be used in feedback configuration!
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

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

11. 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.

12. 4 equations: Vi = given value Vp = given value feedback relation
4 variables: Vi, Vo, Vn, Vp
4 equations: Vi = given value
Vp = given value
feedback relation
Vn~=Vp from A large
All 4 variables and internals fixed Vi Vn Vo Vp
6 variables: Vi+, Vi- Vo+, Vo-, Vn, Vp
5 equations: Vi+ = given value
Vi- = given value
feedback relation from Vo-
feedback relation from Vo+
Vn~=Vp from A large
Not sufficient to fix all variables
Vi+
Vo- Vp Vn
Vi-
Vo+

13. Basic concept of CMFB: Dvb e
Since diff feedback and diff input uses Vin+ and Vin-, CMFB has to be applied to somewhere else: like a bias current CM
measurement
Vo+ +Vo- 2
Vo+
Vo-
Voc -
CMFB
Dvb e
VocRef +
desired common mode voltage

14. Basic concept of CMFB: Dvb e e
measurement
Vo+ +Vo- 2
Vo+
Vo-
Voc -
CMFB
Dvb e e
VoCRef +
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)

15. example HW: When Vb2 changes by D, how much does Voc change?
When Vic changes by D, how much does Voc change?
What circuit design tricks can be used to reduce Voc change?
Vb2 M3 M4 M6 M8 CC CC
Vi+ M1
Vi-
Vo+
Vo- M2
VCMFB M5
Vb1 M9 M7
Vo+
VCMFB
Voc
ACMFB
1/2 -
Vo- +

16. Need to make sure to have negative feedback
Example
Voc ? ?
VocRef
Need to make sure to have negative feedback

17. Resistive C.M. detectors:
Vo+
Vo-

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

19. 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.

20. Why not:
Voc
Vo+
Vo-
Voc node is floating!!
Solution: add leakage to drain Voc node.
Voc
Vo+
Vo-

21. OUT+
M2A
M2B
BIAS3
IN-
M3A
M3B
IN+
M1A
M1B
M10 M5
CL=4pF
4pF
M9A
M4A
M9B
M4B
VDD
VSS
OUT-
BIAS2
BIAS1
BIAS4

22. BIAS4
1.5pF
M13A
M13B
20K
OUT+
OUT-
BIAS2
BIAS1
M7A
M7B
M6C
M6AB
M11 M8
M12A
VSS
VDD
Vref
M12B

23. Practical: Combine resistor, capacitor, and buffering
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

24. To increase or decrease the C.M. loop gain:
e.g.
Voc
VocRef
VCMFB

25. Another implementation
Use triode transistors to provide isolation & z(s) simultaneously.
M1, M2 in deep triode.
VGS1, VGS2>>VT
In that case, circuit above M1, M2 needs to ensure that M1, M2 are in triode. Vx
Vo+
Vo-
I1 = b((Vo+ – VT)Vx – 0.5Vx^2)
I2 = b((Vo- – VT)Vx – 0.5Vx^2)
I = 2b((Vo+ + Vo-)/2 – VT)Vx – 0.5Vx^2)
=2b((Voc – VT)Vx – 0.5Vx^2)
Vx = Voc–VT – ((Voc–VT)^2-I/b)^0.5
dVx/dVoc =– Vx/(Voc – VT – Vx)
 – Vx/(Voc – VT) M1 M2
can be a c.s.
When Vx small: I  {2b(Voc – VT)}*Vx
 M1&M2 together act as a Voc controlled resistor.

26. 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.

27. Vo-
Vo+
Vb1
Vb2 VX M1 M2

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

29. Vo++ Vo- 2
VocREF.
VCMFB
Vo+
Note the difference from the book
accommodates much larger Voc range
Vo-

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

31. M1 M3
VocREF M4 M2 M5 M6

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

34. Switched cap CMFB supports full Vo swing: VSS to VDDΦ1 Φ2 Φ1
VoCRef
VCMFB
Vb-repl
Vo-
VoCRef
During phi_1, the left cap are charged by the op amp output, and the right caps are charged by the reference and nominal bias voltage.
During phi_2, the charges are averaged.

35. One simplified implementation
VCM: desired Voc
VGS14: desired bias
Split for gain reduction
C1=C2

36. Points to consider If supply is high: If supply is very low:
S2 can be NMOS
S1 and S3 can be either NMOS or PMOS or transmission gates
S4 an S5 must be transmission gates
If supply is very low:
May need to use charge pump to boost the switch gate voltages
Error due to charge injection from switches
Intentionally offset VCM and VGS14
Use simulation to determine the right values

37. 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 DM poles and have additional poles,  difficult to achieve similar bandwidth,  make CM loop bandwidth a few times lower than DM
Here Bandwidth = unity loop gain frequency

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

39. 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

40. Vi
Vo1
VBP
VBN Vo I2 I1 M1 M2 CC CL Vi
Vo1
VBP
VBN Vo I2 I1 M1 M2 CC CL

41. 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 makes the CMFB loop UGF to be a few times lower than DM 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

42. 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+Cdb1,2f) >> ACMFB*(UGF of DM)
VBP
VBP IB
VCMRef 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

43. Also, W/L of M1-4f should be small, so that their VEB is large to accommodate Vo+, Vo- swing.
At Q-pt, Vo+, Vo- and VCMRef are all equal, and VS1f = VCMRef + VTP + VEB
When Vo+ is at Vomax, M1f turns off and all current goes to M3f, M3f has 20.5VEB, M1f has 0 VEB.
Hence, VS1f = VCMRef + VTP VEB, and VS1f = Vomax = VCMRef VEB.
Similarly, VS2f = Vomin = VCMRef – 20.5VEB.
Hence, Voswing = 2*20.5*VEB  VEB >= Voswing /2*20.5
But, IB need to be in saturation, hence VS1fmax = VCMRef + VTP + VEB <= VBP+VTP  VCMRef <= VBP – Voswing /2*20.5

44. AvCM(w) AvDM(w) AvCMFBLoop(w) Av(w) of CMFB circuit
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

45. Why?

46. 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
Vo1- I2
Vi+
Vo+
VBN
VCMFB
VBN Ri Rf Rf Ri
Vin+

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

48. AvCM(w) New AvCM(w) AvDM(w) AvCMFBLoop(w) New AvCMFBLoop(w)
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

49. 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.

50. 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

51. CM ½ M5 CMFB circuit VBP Vo1cm I2 Vicm Vocm V’icm gm=gm1/(1+2gm1ro5)-1
V’icm
gm=gm1/(1+2gm1ro5)
½ M5 I1
VCMFB
VBN
CMFB circuit
Vocm-Des