Switched capacitor
From Wikipedia, the free encyclopedia
Switched Capacitor (SC) is a circuit made of one capacitor and two switches which connect the capacitor with a given frequency alternately to the input an output of the SC. This simulates the behaviour of a resistor, so SCs are used in integrated circuits instead of resistors. The resistance is set by the frequency.
S1 S2
/ /
o--/ ---/ --o
|
in | out
===
| Cs
|
o-----------o
Often you will find this structure in place of the resistance of an integrator; see Operational amplifier applications. In turn, filters implemented with these integrators are termed Switched capacitor filters.
Let us analyze what happens in this case. Denote by T=1/f the switching period. Recall that in capacitors charge = capacitance x voltage. Then, at the instant when S1 opens and S2 closes, we have the following:
1) Because Cs has just charged:
2) Because the feedback cap, Cfb, is suddenly charged with that much charge (by the opamp, which seeks a virtual shortcircuit between its inputs):
Now dividing 2) by Cf:
And inserting 1):
This last equation represents what is going on in Cf -- it increases (or decreases) its voltage each cycle according to the charge that is being "pumped" from Cs (thanks to the op-amp, sure). This is what you must store in your brain.
However, there is a more elegant way to formulate this fact if T is very short. Let us introduce 
and 
and rewrite the last equation divided by dt:
Therefore, the op-amp output voltage takes the form:
Note that this is an integrator with an "equivalent resistance" 
. This allows its on-line or runtime adjustment (if we manage to make the switches oscillate according to some signal given by e.g. a microcontroller).
