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Sam PalermoAnalog & Mixed-Signal Center
Texas A&M University
Lecture 15: Fully Differential Amplifiers & CMFB
ECEN474/704: (Analog) VLSI Circuit Design Spring 2018
Announcements
• Project Report Due May 1• Email it to me by 5PM
• Exam 3 is on May 3• 3PM-5PM
2
Agenda
• Fully differential circuits
• Common-mode feedback circuits
• Multi-OTA stages CMFB
• OTA-C filter w/ CMFB example
3
TAMU-Elen-474 Jose Silva-Martinez-08
- 4 -
Basic Operational Transconductance Amplifier Topologies
SINGLE-ENDED
FULLY-DIFFERENTIAL
TAMU-ECEN-474 Jose Silva-Martinez_08
- 5 -
Fully-Differential Circuits
-vo1vin1
-
vo2vin2-+
+
In general:
Hence
ocodoooo
o
ocodoooo
o
vvvvvvv
vvvvvvv
222
222
21122
21211
ic
id
cccd
dcdd
oc
odvv
AAAA
vv
0Vidic
oddc
0Vicid
oddd v
vAvvA
Differential-mode output Common-mode output
0Vidic
occc
0Vicid
occd v
vAvvA
TAMU-ECEN-474 Jose Silva-Martinez_08
- 6 -
Fully-Differential Filters: Effects of current source inpedance and mismatches
-vo1vin1
-
vo2vin2-+
+
A very important parameter:dc
ddAACMRR
icm
sid
m
s
smm
mm
icm
sid
m
s
smm
mm
vgYv
gY
YggZggv
vgYv
gY
YggZggv
1121
22102
2221
12101
21
21
Example:
2IB
IBIB
v1 v2
v01v02
Z2Z1
M1 M2
Solving the circuit:
Ys is the admittance associated with the current source 2IB
212
12ii
iciiidvvvvvv
and w/
TAMU-ECEN-474 Jose Silva-Martinez_08
- 7 -
Fully-Differential Filters: Non-idealities
2IB
IBIB
v1 v2
v01v02
Z2Z1
M1 M2
Voltage gain: Note the effects of themismatches, especially in Adc and Acd
2
1
1
2
21
21
012
12
1
2
2
121
21
21
012
12
2
1
1
2
21
21
012
21
1
2
2
121
21
21
012
21
21
22
2212
2
2
mms
smm
mm
vii
oocc
mm
s
smm
mm
vii
oocd
mms
smm
mm
vii
oodc
mm
s
smm
mm
vii
oodd
gZ
gZY
Ygggg
vvvvA
gZ
gZYZZ
Ygggg
vvvvA
gZ
gZY
Ygggg
vvvvA
gZ
gZYZZ
Ygggg
vvvvA
id
ic
id
ic
22
11
2
11
1
1
ZgZgY
ZZg
AACMRR
m
ms
m
dc
dd
TAMU-ECEN-474 Jose Silva-Martinez_08
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Fully-Differential Circuits
-vo1Z1vin1
ZF
-
vo2Z1vin2 ZF
-+
+
112
0201
ZZ
vvvvA f
inindd
Ideal voltage gain
Ideally even-order distortions are cancelled
Ideally common-mode signals are rejected
What sets the output common-mode of these circuits?Function of the amplifier output resistance
-vo1Z1vin1
ZF
-
vo2Z1vin2 ZF
-+
+
IB
Common-mode offsets can impact the
performance of the following stages
• Can exceed the common-mode input
range of preceeding stages
• With finite Acc can accumulate in a
multi-stage amplifier circuit
TAMU-ECEN-474 Jose Silva-Martinez_08
- 9 -
Fully-Differential Amplifiers: COMMON-MODE DC offset
If IB is positive transistors M3 eventually will be biased in triode region (small resistance)
dc gain reduces drastically
Linear range is further minimized
THD increases
The common-mode output impedance is the parallel of the equivalent output resistance (M1 and M3) and the parasitic capacitors.
For large dc gain, the output impedance at nodes v01 and v02 are further increased and IB produces a dc offset = RoutIB. Large common-mode offsets!
How can this issue be fixed?
2IB
IB+IBIB+IB
v1 v2
v01 v02
Z1 M1 M1 Z1
M3M3Vb
TAMU-ECEN-474 Jose Silva-Martinez_08
- 10 -
Fully-Differential Amplifiers: Characterization
Common-mode current offset of 0.01 mAper side is added on purpose
Tail current is 0.5 mA while the current sources on top are 0.26 mA!
Differential input voltage is set at 0
TAMU-ECEN-474 Jose Silva-Martinez_08
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Fully-Differential Amplifiers: Characterization
Offset current is integrated, and output voltage moves upstairs and reach steady state when the current sources on top become equal to 0.25 mA!
Differential input voltage is set at 0
TAMU-ECEN-474 Jose Silva-Martinez_08
- 12 -
Fully-Differential Amplifiers: Common-mode Feedback
Gcmf=100 A/V.
If the current offset is 10 A, then the offset voltage needed for compensation is 100 mV.
Expected DC outputs after settling are 100 mV.
Adder
CM-Feedback
TAMU-ECEN-474 Jose Silva-Martinez_08
- 13 -
Fully-Differential Amplifiers: Common-mode Feedback
Gcmf=100 A/V.
If the current offset is 10 A, then the offset voltage needed for compensation is 100 mV.
Expected DC outputs after settling are 100 mV.
If necessary to reduce this 100mV offset further, then use a larger Gcmf
Agenda
• Fully differential circuits
• Common-mode feedback circuits
• Multi-OTA stages CMFB
• OTA-C filter w/ CMFB example
14
TAMU-ECEN-474 Jose Silva-Martinez_08
- 15 -
A common mode feed-back circuit is a circuit sensing the common-mode voltage, comparing it with a proper reference, and feeding back the correcting common-mode signal (both nodes of the fully-differential circuit) with the purpose to cancel the output common-mode current component, and to fix the dc outputs to the desired level.
What is a common-mode feed-back correction circuit ?
TAMU-ECEN-474 Jose Silva-Martinez_08
- 16 -
Fully-Differential Amplifiers: CMFB Principle
-vo1Z1vin1
ZF
-
vo2Z1vin2 ZF
-+
+
A common-mode feedback loop must be used: Circuit must operate on the common-mode signals only!
BASIC IDEA: CMFB is a circuit with very small impedance for the common-mode signals but transparent for the differential signals.
Use a common-mode detector (eliminates the effect of differential signals and detect common-mode signals)
Analyze the common-mode feedback loop: Large transconductance gain and enough phase margin
Minimum power consumption
2vvv 0201
cm
vo1 vo2vcm
Z Z
Simplest common-mode detector
TAMU-ECEN-474 Jose Silva-Martinez_08
- 17 -
CMFB Principles: Analysis of the loop for common-mode signals only
Analysis for common-mode noise; for instance noise due to power supplies:io1=io2=icm_noise
The two outputs can be connected together for the analysis of the CMFB loop!
mg
1Zcm
-
BASIC CONCEPTS:
The common-mode input noise is converted into a common-mode voltage (common-mode voltage noise) by the common-mode transconductance of the CMFB =1/Gm_fb.
common-mode voltage variations vcm_noise=icm_noise/Gm_fb !!
The larger Gm_fb the smaller the effects of the common-mode noise!
Gm_fb
vref
-
Gm_fb+
+
icm_noise vocm
Vref(define the common-mode level)
Effect of common-mode noise:
icm_noise
icm_noise
vcm_noise = icm_noise/Gm-fb
TAMU-ECEN-474 Jose Silva-Martinez_08
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Fully-Differential Amplifiers: CMFB
CMFB Characteristics:
Transconductance gain=gm2/2 (no PMOS mirror in CMFB OTA)
dominant pole at the output
3 additional poles in the loop
Zcm reduces the OTA dc gain, affecting the differential gain
NOTE THAT Vcm IS FORCED TO BE AROUND THE GROUND LEVEL.
DC OFFSET VOLTAGE IS AROUND 2*Ioff/gm2
2IB
IBIB
v1 v2
v01v02
Z1 M1 M1 Z1
2IBM2 M2
GNDVcm
M3 M3
M3M3
CMFB
Zcm Zcm
Control
TAMU-ECEN-474 Jose Silva-Martinez_08
- 19 -
Fully-Differential Amplifiers: CMFB
CMFB Characteristics:
DC Transconductance gain=gm2/2
Loop gain (ignoring poles)
dominant pole at the output
3 additional poles in the loop
DC OFFSET IS AROUND 2Ioff/gm2
i3voc
m
2M10.5 Z1
2IBM2 M2
GNDVcm
M3 M3
2M3
CMFB
0.5Zcm
Loop
Zcurrent_source
2221
2121
33
2 ZgZgg
g mm
m
m
TAMU-ECEN-474 Jose Silva-Martinez_08
- 20 -
Fully-Differential Amplifiers: CMFB Principles
Common-mode stability: DC gain and most relevant poles
1 pole at vcm (1/RC)1 pole at M2 source (2gm2/C2)1 pole at gate of M3 (gm3/CP3)1 pole at the output (g01/C1)
dc gain = 0.5 gm2R012IB
IBIB
v1 v2
v01v02
Z1 M1 M1 Z1
2IBM2 M2
groundVcm
M3 M3
M3M3
CMFB
Zcm Zcm
GBW
First non-dominantpole
Dominant pole
Can be removed for CMFB analysis
Be sure phase margin > 45º
TAMU-ECEN-474 Jose Silva-Martinez_08
- 21 -
Fig. 3 Common-mode feedback basic circuit concept. (a) Basic common-mode detector, (b) A CMOS CMFB Implementation.
Notice that the resistors R reduce the differential gain!
. . .
Mp Mp Mp Mp
v02v01.v1
Mn Mn
Mcm Mcm
2IB
2IB
CL
CL
v2GND
.A
ACv1
2IB
v2
vC
R R
IB(vC)IB(vC)
(a) (b)
OPAMP CMFB
vC
TAMU-ECEN-474 Jose Silva-Martinez_08
- 22 -
Fully-Differential Amplifiers: Common-mode pulse
A pulsed current is added to the tail current (common-mode pulse)
This current must be absorbed by the CMFB
Differential feedback does not reduce common-mode offsets and noise.
Differential Time Constant=5K*10P=50nsecs
TAMU-ECEN-474 Jose Silva-Martinez_08
- 23 -
Fully-Differential Amplifiers with CMFBDifferential input signals only
Single-ended outputs
Seems to be that the system is working fine, isn’t it?
Settling time
TAMU-ECEN-474 Jose Silva-Martinez_08
- 24 -
Fully-Differential Amplifiers with CMFBDifferential input signals + common-mode pulses
Single-ended outputs
TAMU-ECEN-474 Jose Silva-Martinez_08
- 25 -
Fully-Differential Amplifiers with CMFBDifferential input signals + common-mode pulses
Common-mode output
True pulse response of the CMFBEvidently PM<45 degreesGBW ~ 1/0.8us=1.2 MHzDC-CMFB resistance ~ 10mV/Ioffset
TAMU-ECEN-474 Jose Silva-Martinez_08
- 26 -
Fully-Differential Filters: Adding buffers to handle the resistive CM-detector
The stability conditions are exactly the same for OTA’s and OPAMP’s:1 pole at vcm (1/RC)1 pole at M2 source (2gm2/C2)1 pole at gate of M3 (gm3/CP3)1 pole at the output (g01/C1)1 pole at buffer outputIn OPAMP’s you can use resistors as common-mode detector due to the presence of the output buffersdc gain = 0.5gm2R01
2IB
IBIBv01v02
Z1
M1 M1
Z1
2IBM2 M2
groundVcm
M3 M3
M3M3
CMFB
Zcm Zcm
GBW
First non-dominantpole
Dominant pole
Isolated Common-Mode Sensing
• Source-Followers isolate the loading of the common-mode sensor resistors
• Need to have a replica source follower to set the appropriate reference level for the CMFB amplifier
27
[Gray]
Two Differential Pair CM Sensor
28
CMocm
mDCCMcmc
mcmf
CMocmACCMDCCMcms
VVggVV
gG
VVgIIII
5
2,
2
220,,
[Gray]
M2 M2 M2 M2
M5
Agenda
• Fully differential circuits
• Common-mode feedback circuits
• Multi-OTA stages CMFB
• OTA-C filter w/ CMFB example
29
TAMU-ECEN-474 Jose Silva-Martinez_08
- 30 -
2 IB
IB+icmfb
GND
VC
IB
IB
IBIB
GND
IB
VC
CMFB is required for Differential Structures
CMFB Requirements: Fixes the OTA output (low offset) ==> High dc loop gainReduction of common-mode noise==> Large Bandwidth
CMFB CMFB
Rg1g
Gm
mm
R Rmm gG
GND
CMFBicmfb = gcmfb(v01+v02-Vref)
IB+icmfbIB+icmfb
TAMU-ECEN-474 Jose Silva-Martinez_08
- 31 -
IB
VB1
IBIB
VREFIB
Common-mode loop gain = AV Gmp RL4 poles in the CMFB loop. Loop stability requires AV Gmp / CL < p2 @ VC, p3 @ VB1, p4 @ VD
IB
IBIB
IB
VB2
VDD
VSS
VC
Efficient CMFB for Differential Pair Based OTAs
+-AV
VD
TAMU-ECEN-474 Jose Silva-Martinez_08
- 32 -
IB
IBIB
IB
CMFB
IB
IBIB
IB
VDD
VSS
IB
GND
M1 M1R1 R1
M1
Efficient CMFB for Pseudo-Differential OTAs
common-mode detector
Agenda
• Fully differential circuits
• Common-mode feedback circuits
• Multi-OTA stages CMFB
• OTA-C filter w/ CMFB example
33
TAMU-ECEN-474 Jose Silva-Martinez_08
- 34 -
Filter is based on Biquadratic Cells:Biquad Realization in Gm-C topology
vi-
vi+
vo-
vo++ -
- +
+ -
- +
+ -
- +
+ -
- +
gm1 gm2 gm1
2C2
2C2
2C1
2C1
gm1
f0 (MHz) Gm1 (mA/V) Gm2 (mA/V)
Biquad 1 537.6 5.4 9.6Biquad 2 793.2 5.4 5.07
TAMU-ECEN-474 Jose Silva-Martinez_08
- 35 -
Time Domain characterization of the CMFBCommon-mode characterization using common-mode current pulsesOne CMFB circuit per pole
•Pulse response of the CMFB
•Phase margin is better than 45 degrees
CMFB
icm
icm
vi-
vi+
vo-
vo++ -
- +
+ -
- +
+ -
- +
+ -
- +
CMFB
TAMU-ECEN-474 Jose Silva-Martinez_08
- 36 -
OTA based on complementary differential pairs
-v1 v1v0 -v0
VCP
VCN
CLCL
M1 M1
M3 M3
M4 M4
M2 M2
VDD
VSS
Efficient OTA based on linear complementary differential pairs
Linear circuit due to source degeneration M3 and M4
Suitable for fast applications
11 22
2
31
1
Mm
m
Mm
mm Rg
gRggG
TAMU-ECEN-474 Jose Silva-Martinez_08
- 37 -
Optimized Class AB Common-mode Feedback
• Most important non-dominant pole at B
v03 v04-v1 v1v01 v02
VREF
Previous OTA CMFB Next OTA
A A'B
C
M1M3
M6
M5E'
E
• Class AB error amplifier is used• 4 non-dominant poles at A~E• 2 LHP zeros at A and C (Helpful in BW extension)
TAMU-ECEN-474 Jose Silva-Martinez_08
- 38 -
Analysis of Class AB Common-mode Feedback
CMFB can be simplified taking advantage of circuit’s symmetry
Class AB CMFB Analysis
39
103
6
5
5
56
6
1
1
1
103
6
5
5
111
21
21
1
1
1
111
21
m
EB
L
L
Lm
m
m
mm
C
m
C
m
A
m
gs
m
EB
L
L
Lm
m
m
VCMFB
gsC
gsC
gsC
ggg
g
ggsCgsC
gsCg
sC
gsC
gsC
gsC
ggg
g
A
• 2 pole-zero pairs (A and C) are very close to each other
• Allows for stable CMFB
TAMU-ECEN-474 Jose Silva-Martinez_08
- 40 -
Remarks• DC operating points for high impedances are difficult to fix
• Fully differential amplifiers with high output impedance nodes must use common-mode feedback circuits .
• Common mode circuits can fix the DC operating points as well as minimize the common mode output components.
• Low voltage constraints impose optimal bias conditions at both the input and output ports of an amplifier.
• Common mode circuits for LV should be used both at the input and output
Next Time
• Output Stages
41