High-Speed 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

High-Speed 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(V1-V2) supplied to V2

Switched capacitors deliver charges from V1 to V2

∆Q = C(V1-V2) during Tc

1 2av

( )

c

C V Vi

T−

= 1 2

av

ceq

TV VR

i C−

= =

∆Q = C(V1-V2) supplied by V1

High-Speed 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.

High-Speed 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 (0-Vo)

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

High-Speed 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

=

∴ =

Non-Inverting Amplifier

Q2 = 0

During φ2

Q1 = 0

Switching phase can change the polarity signal

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 18: Switched Capacitor Filters

1 21 2o i

f f

C CV V V V

C C⎛ ⎞

= +⎜ ⎟⎜ ⎟⎝ ⎠

Non-inverting weighted summer

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 18: Switched Capacitor Filters

Non-inverting weighted summer

1 21 2o i

f f

C CV V V V

C C⎛ ⎞

= +⎜ ⎟⎜ ⎟⎝ ⎠

High-Speed 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

High-Speed 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

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 18: Switched Capacitor Filters

Non-inverting SC integrator

Inverting SC integrator

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 18: Switched Capacitor Filters

Tow-Thomas Biquad

SC Two-Thomas Biquad

High-Speed Circuits and Systems LaboratoryElectronic Circuits 2

Lect. 18: Switched Capacitor Filters

Tow-Thomas Biquad

SC Tow-Thomas Biquad

High-Speed 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

s-domain analysis for continuous time signal processing

z-domain analysis for discrete time signal processing

However, SC circuits have speed limitations