ABSTRACT
The need to have monolithic high-performance analog filters motivated circuit designers in the late 1970s to investigate alternatives to conventional active-RC filters. A practical alternative appeared in the form of switched-capacitor (SC) filters [1-3]. The original idea was to replace a resistor by an SC simulating the resistor. Thus, this equivalent resistor could be implemented with a capacitor and two switches operating with two-clock phases. SC filters consist of switches, capacitors, and op-amps. They are characterized by difference equations in contrast to differential equations for continuous-time filters. Simultaneously, the mathematical operator to handle sample-data systems such as SC circuits is the z-transform, while the Laplace transform is used for continuous-time circuits. Several key properties of SC circuits have made them very popular in industrial environments:
1. Time constants (RC products) from active-RC filters become capacitor ratios multiplied by the clock period T. That is
RC) C CR
T ¼ C CRfc
where fc is the clock frequency used to drive the SC equivalent resistor. 2. Reduced silicon area, since the equivalent of large resistors can be simulated using small-size
capacitors. Furthermore, positive and=or negative equivalent resistors can be easily implemented with SC techniques.
