# Switched capacitor filter

Switched-Capacitor-Filter (German: filter with switched capacitors ) or often just short SC-Filter describes electronic filters in which ohmic resistances have been replaced by switched capacitors . These are time-discrete filters.

The transfer function of active analog filters is usually determined by capacitors and electrical resistors in the form of an external circuit of an operational amplifier . This brings with it the following problems:

• Difficult to integrate, since process steps for both capacitors and resistors have to be used.
• different tolerances of resistors and capacitors
• different temperature coefficients of resistors and capacitors
• difficult to produce for different frequencies.

These problems can be avoided by replacing resistors with switched capacitors. Resistors are replaced by switched capacitors, filters can be freely tuned by changing the switching frequency. Depending on the circuit or external wiring, low-pass, high-pass, band-stop and band-pass filters can be configured.

Circuit diagram of an SC resistor

By varying the switching frequencies at which the capacitors are switched, the filter parameters of the SC filters can be changed very easily. The replacement of the ohmic resistances R in a given circuit such as a low-pass filter by capacitors C S , which are operated with the switching frequency f s , can be calculated using the following equation:

${\ displaystyle R = {\ frac {1} {C_ {s} \ cdot f_ {s}}}}$

Since this type of filter is a scanning system, the switching frequency f s must be sufficiently higher than the cutoff frequency of the filter in order to avoid aliasing . SC filters are therefore mostly only suitable for low-frequency applications and, if necessary, require downstream low-pass filters that filter out the high-frequency signal components from the switching frequency. This is one of the disadvantages of this circuit technology.

A major advantage of these filters is that the filter time constant is only slightly dependent on the component tolerances of the capacitors used. Only the relationships between the component values ​​have to remain constant, since the filter accuracy is primarily determined by the switching frequency. Exact switching frequencies can easily be ensured technically by means of quartz oscillator circuits .

## Literature sources

• Ulrich Tietze, Christoph Schenk: Semiconductor circuit technology , Berlin: Springer 2002. ISBN 3-540-42849-6