EECS 240 Lecture 18: Offset Cancellation V. Petkov 1
Offset Cancellation Overview• Techniques:
– Autozero (sampled)– Chopper stabilization (continuous-time)
• Objective:– Reject offset and 1/f noise
• Reference– Ch. Enz and G. C. Temes, “Circuit Techniques for Reducing the
Effects of Op-Amp Imperfections,” Proc. IEEE, Nov. 1996, pp. 1584-1614.
EECS 240 Lecture 18: Offset Cancellation V. Petkov 2
Outline• Autozero technique:
– Offset cancellation• Output• Input• Using auxiliary amplifier
– Flicker noise rejection– Design example: capacitive sensor interface
• Chopper stabilization– Principle of operation– Residual offset and nested chopper stabilization
• Comparison and summary
EECS 240 Lecture 18: Offset Cancellation V. Petkov 3
Output Offset Cancellation
• Output still corrupted by switch charge injection
bottom plate sampling
• Requires
( )in
Cosinout
osC
AVVVVAV
AVV
=−−=
−=
:2 Phase
:1 Phase DDos VAV <
EECS 240 Lecture 18: Offset Cancellation V. Petkov 4
Multistage Implementation
R. Poujois and J. Borel, "A low drift fully integrated MOSFET operational amplifier," IEEE Journal of Solid-State Circuits, vol. 13, pp. 499 - 503, August 1978.
EECS 240 Lecture 18: Offset Cancellation V. Petkov 5
Input Offset Cancellation
( )
( )
1AVV
1AVVAV
VVVAV:(b) Phase
1AAVVV
VVAV:(a)Phase
osres,os
osino
cosino
osoc
ooso
+−=
+−=
+−=
+=−=
+−=
EECS 240 Lecture 18: Offset Cancellation V. Petkov 6
Multistage Cancellation
• Open switches left to right• Residual offset from S1 … SN-1 cancelled by final stage• Capacitive coupling reduces gain• Application: comparators
EECS 240 Lecture 18: Offset Cancellation V. Petkov 7
Example: Offset Compensated SC Gain Stage
S1
S2
C1
S1
C2
S2 S1
S2ViVo
Vos
VC1
VC2
EECS 240 Lecture 18: Offset Cancellation V. Petkov 8
SC Gain Stage: Φ1
Assuming infinite open-loop gain.
S1C1
S1
C2
S1
S2ViVo
Vos
VC1
VC2
( ) osi
CCtot
osC
osiC
VCCVCVCVCQ
VVVVV
211
2211
2
1
1
+−=+=
−=−=
Φ
EECS 240 Lecture 18: Offset Cancellation V. Petkov 9
SC Gain Stage: Φ2
( )( )
io
tottot
ositot
osotot
osoC
osC
VCCV
VCCVCQ
VCCVCQ
VVVVV
2
1
211
212
2
1
12
1
2
=
→=
+−=
+−=
−=−=
ΦΦ
Φ
Φ
S2
C1
C2
S2
S2Vo
Vos
VC1
VC2
• Charge on C1, C2 is redistributed• Total charge stays same!• At end of phase 2:
EECS 240 Lecture 18: Offset Cancellation V. Petkov 10
SC Gain Stage Implementation
S1
S2
C1
S1
C2
S2 S1
S2ViVo
Vos
VC1
VC2
Cx
• Amplifier must be unity-gain stable
• Output pulled back to Vos in each cycle
• No feedback during clock non-overlapCx (deglitching capacitor)
• Charge injected at input node
EECS 240 Lecture 18: Offset Cancellation V. Petkov 11
Offset Cancellation Options
M. Degrauwe, E. Vittoz, and I. Verbauwhede, "A micropower CMOS-instrumentation amplifier," IEEE Journal of Solid-State Circuits, vol. 20, pp. 805 - 807, June 1985.
At input Charge injection degrades performance
At outputRequires low-gain amplifier or two stages
At input of auxiliary amplifier
EECS 240 Lecture 18: Offset Cancellation V. Petkov 12
Auxiliary Amplifier Offset Cancellation( ) ( )
( )
( )
++
+++
=
+−+=
++
+++
=
−−==
−−−−=
444444 3444444 21
44 344 2144 344 21
offset referredinput
2sw1
2
2
2OS
1
2
2
1sw1OS1
2OS2221sw11OS1out
2sw2OS2
21sw1OS
2
12
2OS221OS1o2
ampaux
2OS22
ampmain
1OS11out
VAA
A1V
AA
A1VVA
VAVAVAVAV
VVA1
AVVA1
AV
VVAVAVV
VVAVVAV
2 node b, phase :1 node a, phase :
:Injection Charge Switch
2
1
sw
sw
VV Offset, charge injection attenuated if A1 >> A2
EECS 240 Lecture 18: Offset Cancellation V. Petkov 13
Aux Amp Options
M. Degrauwe, E. Vittoz, and I. Verbauwhede, "A micropower CMOS-instrumentation amplifier," IEEE Journal of Solid-State Circuits, vol. 20, pp. 805 - 807, June 1985.
EECS 240 Lecture 18: Offset Cancellation V. Petkov 14
CDS and Flicker Noise
S1
S2A . S/H Σ
S2Vi Vo
V1 V2
V1/f
S1
S2
T = 1/fstime[kT]
EECS 240 Lecture 18: Offset Cancellation V. Petkov 15
Flicker Noise Analysis
( ) ( ) ( )
( ) ( )
( )43421
4444 34444 21321
sH
Ts
fnieq
st
V
ffio
n
d
nieq
esVsV
e
TkTVkTVkTVAkTV
−=
→
−−+=
−
−
2/1
d
error referredinput
/1/1
signal
1
by tDelay
Transform Laplace
2
EECS 240 Lecture 18: Offset Cancellation V. Petkov 16
Flicker Noise Frequency Response
( )
2sin
2cos1
1
1
2
2
TjTe
esHTj
Ts
n
ωω
ω
+−=
−=
−=
−
−
( )
( )s
jsn
jsn
ffTsH
T
T
TTT
TTsH
2sin2
4sin2
4sin4
2cos12
2sin
2cos
2cos21
2sin
2cos1
2
1
22
222
πω
ω
ω
ωωω
ωω
ω
ω
==
=
−=
++−=
+
−=
→
→
444 3444 21
EECS 240 Lecture 18: Offset Cancellation V. Petkov 17
Flicker Noise SpectrumK 1:= fs 1:=
Sf f( )Kf
:= Hf f( ) 2 sinπ f⋅2 fs⋅
⋅:=
0 1 2 3 4 50
1
2
3
4
5
Hf f( )2
Sf f( ) Hf f( )2⋅
f
• Flicker noise is differentiated
• Essentially removed at low frequency
• Choosing fs/2 sufficiently large effectively removes flicker noise
• Noise above fs/2 folds to baseband
• Thermal noise folded to 0 … fs/2
EECS 240 Lecture 18: Offset Cancellation V. Petkov 18
Design Example:Capacitive Sensor Interface
S+
S-
MM
S+
S-
CSo - ∆C
CSo + ∆Cxo- ∆x
xo+ ∆x
∆x
CS+
CS-
(a) (b)
Principle of capacitive sensing:
EECS 240 Lecture 18: Offset Cancellation V. Petkov 19
Capacitance-to-Voltage (C/V) Conversion
CS - ∆C
CS + ∆C
CI
CI
VMVO
S+
S-M
MechanicalElement
MI
O VC
C2V ∆=
EECS 240 Lecture 18: Offset Cancellation V. Petkov 20
Correlated Double-Sampling (CDS)
Phase 1 Phase 2
Reset
Phase 3
kT
∆C(kT-T/2) ∆C(kT)
(k-1)T kT-T/2
Noisecancelation
SensingPhase 1
Phase 2
Phase 3For DC signal: M
IO V
CC2V ∆
=
For AC (low-frequency) signal:
( )( )
ErrorC
2TkTCVkTCV
2kTVI
12
o +
−∆−∆
=
CI+
CI-
V1
(a)
CH+
CH-
CS+
CS-
CI+
CI-
V1
CS+
CS-
CH+
CH- Vo
CI+
CI-
V2
CS+
CS-
(b)
V1
(c)
M
M
M
EECS 240 Lecture 18: Offset Cancellation V. Petkov 21
CDS Front-End Schematic
EECS 240 Lecture 18: Offset Cancellation V. Petkov 22
Initial Design Decisions• Process: 0.5µm 5V CMOS
• Electrostatic force-feedback – allocate feedback phase in timing diagram
• Sampling frequency – chosen based on resolution and stability requirements- fs=500kHz for this example
• Input common-mode feedback (ICMFB) for the C/V converter
- Advantages: reduces DC offset and drift
- Disadvantages: additional amplifier; increases Cp; affects settling
- Can be omitted if common-mode voltage step at input is small(typically the case in two-chip solutions with large Cp)
• Amplifier topology
EECS 240 Lecture 18: Offset Cancellation V. Petkov 23
Amplifier Topology
• Small sensor output:
Small signal swing in the front-end
• Telescopic double-cascoded amplifier:
High DC gain
Few noise contributing devices
• Sensing on negative edge of VM:
PMOS input
• Choice of VICM :
Equal to V1 (minimize delay)
( )( )
I
12
o C2TkTCVkTCV
2kTV
−∆−∆
=
EECS 240 Lecture 18: Offset Cancellation V. Petkov 24
• Settling accuracy:
- Accelerometer with full-scale range of 5g and noise floor of 150µg
- Settling error: ε=3x10-5
• Phase A: tA=(3/16)Ts=375ns
- Only C/V converter operates
- Single-pole stage settling:
• Phase B: tB=(1/4)Ts=500ns
- Three stages in series
- Use C/V bandwidth from Phase A (maximally relaxed conditions)
- Second and third stages require 5.3MHz bandwidth
Amplifier Design - Settling
T S=2µs
φM
φR ST
φ1
∆C 2
FeedbackPhase A
∆C 1
Phase B
( )MHz5.4
1lnt2
12
1fA
CVCV_BW =
επ
=πτ
=
EECS 240 Lecture 18: Offset Cancellation V. Petkov 25
Amplifier Design – Noise Analysis
++=
∆ P_Leff
CV_LeffePrPP
SCV
CV_Leff
B
CV
2xn
CC
NRN1f1n
CTk
F1
316
fv
RP
CI
VOutCPACPSCS
2nav2
nRpv2
pre_nvVXPreamp
MechanicalElement
CL
2preCV
P
P
CVePr
CV_BW
2
T
PSS
CV
CV_LeffCVP
A1
nn
FF
21N
fC
CCnCF
3N
=
π
+=
Noise factors:
EECS 240 Lecture 18: Offset Cancellation V. Petkov 26
Amplifier Design – Noise Analysis
++=
∆ P_Leff
CV_LeffePrPP
SCV
CV_Leff
B
CV
2xn
CC
NRN1f1n
CTk
F1
316
fv
• Choosing CI – tradeoff between SNR and speed
• CL is scaled according to noise requirements (tradeoff with power)
• Parasitics (Rp and Cp) should always be minimized
• This example:
Noise contributions:
- Amplifier (C/V): 60%
- Rp: 35%
- Preamp: 5%
Capacitance resolution:
HznV330f
v2xn =
∆
HzaF08.0
EECS 240 Lecture 18: Offset Cancellation V. Petkov 27
Chopper Stabilization
EECS 240 Lecture 18: Offset Cancellation V. Petkov 28
Chopper Amp Bandwidth & DelayExample 1:
Amplifier is ideal LPF• Gain Ao• BW 2 fs
DC gain ~ 0.8 Ao
Example 2: Amplifier introduces 90o phase shift
DC gain is 0
( ) ( )[ ]( ) ( )[ ]yxyxyx
yxyxyx++−=
++−=
sinsincossincoscoscoscos
2121
EECS 240 Lecture 18: Offset Cancellation V. Petkov 29
Chopper Results
K. Hsieh, P. R. Gray, D. Senderowicz, and D. G. Messerschmitt, "A low-noise chopper-stabilized differential switched-capacitor filtering technique," IEEE Journal of Solid-State Circuits, vol. 16, pp. 708 - 715, December 1981.
EECS 240 Lecture 18: Offset Cancellation V. Petkov 30
Chopper Residual Offset
A. Bakker, K. Thiele, and J. H. Huijsing, "A CMOS nested-chopper instrumentation amplifier with 100-nV offset," IEEE Journal of Solid-State Circuits, vol. 35, pp. 1877 - 1883, December 2000.
Spikes from input chopper due to charge injection mismatch.
EECS 240 Lecture 18: Offset Cancellation V. Petkov 31
Nested Chopper Amplifier
• Inner chopper runs at high frequency to remove 1/f noise• Outer chopper runs at low frequency to minimize “spiking” and remove
residual offset from inner chopper. 1/f-noise is no issue since it has been reduced by inner chopper.
EECS 240 Lecture 18: Offset Cancellation V. Petkov 32
Results
EECS 240 Lecture 18: Offset Cancellation V. Petkov 33
ComparisonAutozero
• Samples Signal– No continuous time
operation
• Flicker noise removed– No need for LPF
• Increased baseband noise due to thermal noise folding
Chopper Stabilization
• Modulates Signal– Compatible with continuous
time operation
• Flicker noise to high frequency– Requires LPF to remove noise
• Virtually no thermal noise folding if fclk >> B
• Finite BW amp reduces gain
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