
Demystifying Switched-Capacitor Circuits
96
schematic shows that the integrating capacitor of the fi rst integrator, C
1
, is split into
three capacitors, namely C
11
, C
12
, and C
13
. Let us assume that the input signal comes
into the circuit through the M
1
C
1
path—that is, the SC circuit realizes a low-pass
fi lter. During the idle case (Φ
2
= 1), the op-amp’s output at node A is given by
Vz
MC
CC
Vz
Aidlein
(
)
=−
+
(
)
11
12 13
(4.13)
Next, Φ
1
= 1, and the capacitor C
13
is discharged to ground while the stored charge
on C
12
is transferred to C
11
. Based on the charge reservation rule, we can write the
following expression of V
A
(z):
Vz
MCC
CCC z
V
Aactive i
(
)
=−
+
(
)
⋅