Large resistors in active RC filters are NOT practical in...
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HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters (S&S 12.10)
Large resistors in active RC filters are NOT practical in IC
Circuit technique to solve the problem
Replace resistors with capacitors: Switched capacitor
 Large area Accurate control of R very difficult
V1 V2
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
V1 V2
Assume initially φ2 ON, φ1 OFF and V1>V2
Q = CV2
When φ2 is OFF and φ1 is ON
Q=CV1
When φ1 is OFF and φ2 is ON
Q=CV2
∆Q = C(V1V2) supplied to V2
Switched capacitors deliver charges from V1 to V2
∆Q = C(V1V2) during Tc
1 2av
( )
c
C V Vi
T−
= 1 2
av
ceq
TV VR
i C−
= =
∆Q = C(V1V2) supplied by V1
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters (S&S 12.10)
V1 V2
Switches are usually realized with MOS switches having finite R, C
In this course, assume ideal switches
If 1/Tc >> frequency of interests, SW is acting as a resistor.
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
Switched Capacitor Amplifier
Q1 = C1Vi
Initially, assume Q1, Q2 = 0
When φ1 is ON, φ2 is OFF
Q2 = C2 (0Vo)
But Q1 = Q2
1 2
1
2
i o
o i
C V C VC
V VC
= −
∴ = −
Inverting Amplifier Gain determined by the ratio of C’s
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
Switched Capacitor Amplifier
Q1 = C1Vi
During φ1
Q2 = C2 (Vo 0)
But Q1 = Q2
1 2
1
2
i o
o i
C V C VC
V VC
=
∴ =
NonInverting Amplifier
Q2 = 0
During φ2
Q1 = 0
Switching phase can change the polarity signal
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
1 21 2o i
f f
C CV V V V
C C⎛ ⎞
= +⎜ ⎟⎜ ⎟⎝ ⎠
Noninverting weighted summer
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
Noninverting weighted summer
1 21 2o i
f f
C CV V V V
C C⎛ ⎞
= +⎜ ⎟⎜ ⎟⎝ ⎠
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
01 2
1R C
ω =1
02
21
1
CC
CT CT C
C
ω = =⎛ ⎞⎜ ⎟⎝ ⎠
Integrator
ωo can be more precisely determinedωo is tunable by TC
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
Influence of parasitic cap due tosource and drain of MOS switch
+ +

oV
iV
1φ2C
2φ
1C 2pC1pC
oV
+ +

iV 1φ
2C
2φ
1C
1pC 2pC
2φ1φ 2Q− 2Q+
1Q−1Q+
Robust to parasitic cap
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
Noninverting SC integrator
Inverting SC integrator
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
TowThomas Biquad
SC TwoThomas Biquad
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
TowThomas Biquad
SC TowThomas Biquad
HighSpeed Circuits and Systems LaboratoryElectronic Circuits 2
Lect. 18: Switched Capacitor Filters
Any active RC filter (such as biquad) can be replaced with equivalent SC filter Project #3
SC filters perform discrete time domain signal processing
sdomain analysis for continuous time signal processing
zdomain analysis for discrete time signal processing
However, SC circuits have speed limitations