- Switched capacitor
Switched capacitor is a circuit design technique for discrete time
signal processing. It works by moving charges between different capacitors when switches are opened (off) and closed (on). Usually, non-overlapping signals are used to control the switches, so that not all switches are on simultaneously.
Voltage amplification can be achieved by moving a charge from a large capacitor to a small capacitor. Fact|date=May 2008
Voltage amplification can be achieved by repeatedly switching capacitors from a parallel arrangement with regard to the supply to a series arrangement with regards to the load. This arrangement is called a
The simplest switched capacitor (SC) circuit is made of one capacitor and two switches which connect the capacitor with a given frequency alternately to the input and output of the SC. This simulates the behaviour of a
resistor, so SCs are used in integrated circuitsinstead of resistors. The resistance is set by the frequency.
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 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 has just charged:
2) Because the feedback cap, , is suddenly charged with that much charge (by the opamp, which seeks a virtual shortcircuit between its inputs):
Now dividing 2) by :
And inserting 1):
This last equation represents what is going on in -- it increases (or decreases) its voltage each cycle according to the charge that is being "pumped" from (due to the op-amp).
However, there is a more elegant way to formulate this fact if 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).
Switched-mode power supply
* Mingliang Liu, "Demystifying Switched-Capacitor Circuits", ISBN 0-7506-7907-7
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