Passive Filters

Abstract

The Nyquist plot shows real and imaginary components of the signal and the LTspice cursor shows phase. Pole-zero plots are applied to first-order RC filters and then cascaded RC and RL low-, high- and band-pass filters to find the frequency response, breakpoints, amplitude and phase. LCR filters are similarly dealt with but can have complex poles and a resonance peak or a sharp notch, the analysis is aided by pole-zero plots.

We find the image impedance and propagation constant for prototype ‘T’ and ‘Π’ filters and hence the frequency response, phase shift and attenuation for low-, high- and band-pass and band-stop constant-K filters and the more complex m-derived filters. We note that double-tuned circuits can create a narrow pass band.

Higher-order Butterworth, Chebyshev and Elliptic low-pass filters are handled using published design tables then high-pass and band-pass filters are derived by transformation, and the chapter concludes with all-pass filters.