Switched capacitor filters

Switched capacitor filters | Mechatronicsly

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.

Switched capacitor filters
Figure 1

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:

I=\frac{V_{IN}}{R}

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

Q=V_{IN}C

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.

Switched capacitor filters fig.2
Figure 2

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

I_{ave}=\frac{Q}{T}=\frac{V_{IN}C}{T}=V_{IN}Cf_{CLK}

where T is the time between S1 and S2 closing. The equivalent resistance can now be given by

R=\frac{V_{IN}}{I_{ave}}=\frac{V_{IN}}{V_{IN}Cf_{CLK}}=\frac{1}{Cf_{CLK}}

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.