Lattice Phase Equaliser - Design

Design

Parts of this article or section rely on the reader's knowledge of the complex impedance representation of capacitors and inductors and on knowledge of the frequency domain representation of signals.

The essential requirement for a lattice filter is that for it to be constant resistance, the lattice element of the filter must be the dual of the series element with respect to the characteristic impedance. That is,

Such a network, when terminated in R₀, will have an input resistance of R₀ at all frequencies. If the impedance Z is purely reactive such that Z = iX then the phase shift, φ, inserted by the filter is given by,

The prototype lattice filter shown here passes low frequencies without modification but phase shifts high frequencies. That is, it is phase correction for the high end of the band. At low frequencies the phase shift is 0° but as the frequency increases the phase shift approaches 180°. It can be seen qualitatively that this is so by replacing the inductors with open circuits and the capacitors with short circuits, which is what they become at high frequency. At high frequency the lattice filter is a cross-over network and will produce 180° phase shift. A 180° phase shift is the same as an inversion in the frequency domain, but is a delay in the time domain. At an angular frequency of ω = 1 rad/s the phase shift is exactly 90° and this is the midpoint of the filter's transfer function.