12
Introduction to SwitchedCapacitor
Circuits
Our study of amplifiers in previous chapters has dealt with only cases where the input signal is
continuously available and applied to the circuit and the output signal is continuously observed.
Called “continuoustime” circuits, such amplifiers find wide application in audio, video, and high
speed analog systems. In many situations, however, we may sense the input only at periodic instants
of time, ignoring its value at other times. The circuit then processes each “sample,” producing a
valid output at the end of each period. Such circuits are called “discretetime” or “sampleddata”
systems.
In this chapter, we study a common class of discretetime systems called “switchedcapacitor
(SC) circuits.” Our objective is to provide the foundation for more advanced topics such as filters,
comparators, ADCs, and DACs. Most of our study deals with switchedcapacitor amplifiers but
the concepts can be applied to other discretetime circuits as well. Beginning with a general view
of SC circuits, we describe sampling switches and their speed and precision issues.
Next, we
analyze switchedcapacitor amplifiers, considering unitygain, noninverting, and multiplybytwo
topologies. Finally, we examine a switchedcapacitor integrator.
12.1
General Considerations
In order to understand the motivation for sampleddata circuits, let us first consider the simple
continuoustime amplifier shown in Fig.
12.1(a).
Used extensively with bipolar op amps, this
circuit presents a difficult issue if implemented in CMOS technology. Recall that, to achieve a
high voltage gain, the openloop output resistance of CMOS op amps is maximized, typically
approaching hundreds of kiloohms. We therefore suspect that
2
heavily drops the openloop
gain, degrading the precision of the circuit. In fact, with the aid of the simple equivalent circuit
395
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Chapter 12. Introduction to SwitchedCapacitor Circuits
396
R
R
1
2
out
V
in
V
R
R
1
2
out
V
in
V
A
V
R
out
X
V
X
v

(a)
(b)
Figure 12.1.
(a) Continuoustime feedback amplifier, (b) equivalent circuit of (a).
shown in Fig. 12.1(b), we can write
1
2
1
1
2
12 1
and hence
2
1
2
1
1
2
1
12 2
Equation (12.2) implies that, compared to the case where
0, the closedloop gain suffers
from inaccuracies in both the numerator and the denominator. Also, the input resistance of the
amplifier, approximately equal to
1
, loads the preceding stage while introducing thermal noise.
In the circuit of Fig. 12.1(a), the closedloop gain is set by the ratio of
2
and
1
. In order to
avoid reducing the openloop gain of the op amp, we postulate that the resistors can be replaced by
capacitors [Fig. 12.2(a)]. But, how is the bias voltage at node
set? We may add a large feedback
out
V
in
V
(a)
C
C
1
2
X
out
V
in
V
(a)
C
C
1
2
X
R
F
Figure 12.2.
(a) Continuoustime feedback amplifier using capacitors, (b) use of resistor to define
bias point.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Bazgei
 Operational Amplifier, Fig., Vout, SwitchedCapacitor Circuits, in0 Vout

Click to edit the document details