In this chapter, the operational amplifier is used to realize simple functions used in active filters, such as summing amplifiers, integrators, inductor simulations, and FDNRs. Although in our pencil-and-paper analyses, for simplicity, assume ideal Op Amp with infinite gain, the omission of their finite gain-bandwidth products results in some degree of error. Depending on the frequency of operation and the form of compensation used, this error may or may not be negligible. When the error is nonignorable, designs can frequently be nominally predistorted to minimize the error.

In this chapter, the design and performance of single-amplifier and multiple-amplifier active-RC and active-R(C) biquad circuits has been considered. Negative-feedback single-amplifier circuits have been shown to have low-Q sensitivities to passive components but large ω_o and Q sensitivities to the Op Amp GB. The latter property restricted negative feedback circuits to low Q. On the other hand, positive-feedback circuits have been shown to offer the ability of trade-off between active and passive sensitivities and can be designed for higher Q than the negative-feedback circuits.

In this chapter we describe and demonstrate techniques for the analysis and design of active switched capacitor networks. Because of their sampled-data character, switched capacitor networks are most conveniently analyzed and designed, in the z-transform domain, like digital filters. However, SC filters are analog networks; thus, the analog concepts of impedance and loading, which are absent in digital filters, are retained. In this chapter a library of z-domain equivalent circuits will be developed to facilitate the analysis, design, and, more importantly, to aid the reader's understanding of switched capacitor networks. With these equivalent circuits, the familiar circuit theory tools, which we use routinely in the analysis of continuous active networks, are extended for use in switched-capacitor networks. Like active-RC networks, there are many SC topologies that can be used to realize a given z-domain transfer function. We will examine some of the more interesting and useful ones.

This book chapter presents the table for filter function with different filter types discussed. Ideal low-pass filter characteristics is approximated by an all-pole function. Butterworth filters table B-1 gives the polynomials for n up to 10 and a_o normalized to unity. For n < 4, see Table 1-1. Chebyshev filters when the Chebyshev filter requirements call for 1/2-dB ripple, the polynomials for n up to 10 and a_n normalized to unity are listed in Table B-2. For n < 4, see Table 1-3. The corresponding polynomials for 1-dB ripple are in table B-3 and for 2-dB ripple, in Table B-4. Thomson filters the Bessel polynomials for Thomson filters for n up to 10 are given in table B-5 for τ = a₁/a_o = 1. For n < 4, see Table 1-4. The coefficients of the elliptic filters for one zero pair and two poles, one zero pair and three poles, and two pairs of zeros and four poles are given in Tables B-6, B-7, and B-8, respectively [P1]. The parameters A₁, A₂, and ω_s are defined in Fig. B-1. The reader is referred to many excellent tabulations for elliptic filter data [B1-B4].