Switched-Capacitor Filters:The Principle of SC Technique

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The Principle of SC Technique

The principle of SC technique consists in simulating the resistor behavior with a switched-capacitor structure. In the structure of Figure 62.6, where an ideal opamp is used, the resistor Req is connected between Vi and a zero-impedance, zero-voltage node (as a virtual ground is). This means that

Switched-Capacitor Filters-0169

The alternative SC structure is shown in Figure 62.7(a). It is composed of an input sampling capacitor Cs (connected through four switches to the input signal Vi, to the opamp input node and to two ground nodes), an opamp, and a feedback (integrating) capacitor Cf. The clock phases driving the switches are shown in Figure 62.7(b). A switch is close (conductive) when its driving phase is high. It is necessary that the two clock phases are nonoverlapping, to connect each capacitor plate to only one low-impedance node for each time slot.

During phase f1, capacitor Cs is discharged. During phase f2, Cs is connected between Vi and the virtual ground. So a charge Q = –CsVi is collected on its right-hand plate. Owing to the charge conservation law applied at the virtual ground node, this charge collection corresponds to an injection in virtualb ground of the same amount of charge but with the opposite sign, given by

Switched-Capacitor Filters-0170

This means that the structure composed of Cs and the four switches operated at Fs is equivalent to a resistor Req. This approximation is valid for Vi equal to a DC value, as it is the case of the proposed example, and it is still valid for Vi slowly variable with respect to the clock period, otherwise the quantitative average operation of Eq. (62.5) is no more valid. The limits of the approximation between a resistor and an SC structure as expressed in Eq. (62.6) implies fundamental differences in the exact design of SC filters when derived from active-RC filters in a one-to-one correspondence.

Switched-Capacitor Filters-0171

The synthesis of active filters is based on the use of some elementary blocks interconnected in different ways depending on the type of the adopted design philosophy. The different strategies and approaches for designing analog filters are well known from the continuous-time domain and they are also used in the case of SC filters, although the sampled-data nature of the SC filters can be profitably used either for simplifying or improving the design itself. In any case, basic building blocks are used to compose high-order filters.

In the following the main basic blocks are described. They implement first- (active integrators, undamped and damped, summers) and second-order (biquads) transfer function in the z-domain (z is the state variable in the sample data domain).

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