Switched capacitor filters have become popular mainly because they require no external components such as capacitors or inductors.
Besides offering a very sharp cut-off frequency, these filters have the following advantages: low cost; high accuracy; good temperature stability; and few external components are required. The main disadvantage is that they generate more noise than standard active filters.
The operation of any RC filter depends on the value of the selected resistors and capacitors. Briefly, the switched capacitor filter simulates the resistance by using a capacitor and a few switches. In Figure 1(a) the value of the simulated resistor is proportional to the rate at which the switches are opened and closed in Fig. 2(b). If a voltage Vin is applied to the resistor then the current through it is given by:
Figure 1(b) consists of a capacitor and two switches, which, in practice, would be MOS transistors etched on the integrated circuit. When S1 is open Vin is applied to the capacitor C and hence the total charge on the capacitor is
When S1 is open and S2 closed, the charge Q flows to ground. Furthermore, if the switches have no resistance, i.e. they are ideal switches, C will charge and discharge instantly.
Figure 2 shows the current into and out of the switched capacitor filter as a function of time. If the switches are opened and closed at a faster rate, the bursts of current will have the same amplitude but will occur more often. Hence the average current will be greater for a higher switching rate. The average current flowing through the capacitor is
where T is the time between S1 and S2 closing. The equivalent resistance can now be given by
This expression indicates that R is dependent on the clock frequency as C is constant. It should be noted that Vin must change at a rate much slower than fclk especially when Vin is an AC signal.