Optimal Band-pass Ladder Design

Abstract

This chapter presents design techniques of switched-capacitor band-pass filters of the lossless-discrete-integrator (LDI) type (and wave digital filters with the same forms of transfer functions) which exhibit, simultaneously, good amplitude selectivity as well as good approximation to a constant group delay in the passband in an optimum manner. All the available degrees of freedom are exploited to shape both the amplitude and delay responses, by contrast with the available methods of delay equalization which yield sub-optimal designs. As noted earlier, due to the factor (1 — λ 2), which multiplies the delay functions,a standard frequency transformation from lowpass to bandpass will not transform a linear phase lowpass filter into a linear phase band-pass characteristic. This means that the design of SC band-pass filters with prescribed phase response, or on both amplitude and phase bases, should be dealt with independently. The technique preented here is a generalization of the low-pass case discussed in Chapter 3. However, the band-pass problem is a three-band approximation problem in the amplitude domain, and when combined with the requirement of phase linearity in the passband, it becomes much more difficult than the low-pass case. Hence, it requires special treatment and examination of the design parameters. Again, the technique is given in relation to switched-capacitor filters for the sake of brevity, but the resulting transfer functions are easily identified with the corresponding wave digital filters.