Mixed Signal Techniques - Signal Processing Systems - page 809

C 2

φ 1 φ 1

a

C 1

V i

V o

−

+

φ 2 φ 2

C 2

φ 2

φ 1

b

C 1

V i

V o

−

+

φ 2

φ 1

Fig. 20 ( a ) Inverting SC integrator. ( b ) Noninverting SC integrator

5.3 Integrators

Integrators are used as the basic building blocks in SC filters. Figure 20 a showsan
inverting and Fig. 20 b shows a noninverting SC integrator circuit that form the basis
of many SC networks. Notice that although the switches are drawn as single NMOS
transistors, a PMOS transistor is usually connected in parallel. The transfer function
of the inverting integrator is given by

V o ( z ) C 1

C 2 )

1

H i ( z )=

) = − (

(34)

z − 1 V i ( z 1 −

and the transfer function of the noninverting integrator is

z − 1 V o ( z ) C 1

C 2 )

( )=

) =( z − 1 .

H n z (35)

V i ( z 1 −

The unit delay z − 1 in the numerator is due to the fact that it takes the time of both
clock phases for V i to have an effect on V o . Both of these integrator circuits are
insensitive to stray capacitances that may be present at the capacitor plates.