Simulation of ionospheric dispersion

Clark C. Watterson

Abstract: An ideal dispersion filter for simulating ionospheric dispersion is defined as one with constant dispersion in a channel frequency band and zero dispersion outside the band. An optimum lumped-element all-pass filter that approximates this ideal has a constant amplitude characteristic and a dispersion characteristic that has an equal-ripple variation about a constant nominal dispersion in the filter band. The pole-zero values required by optimum narrowband dispersion filters are presented with the corresponding nominal dispersions for 70 combinations of filter orders n = 1, 2, ... , 10 and ripple factors = .001, .002, .005, .01, . 02, . OS, and . 1. These results are applicable for narrowband filters. The maximum fractional bandwidths for which the narrowband solutions apply and the dispersion efficiencies of the filters are presented; both increase with increasing filter order, n, and ripple, O. A limited set of wideband solutions shows that while larger fractional bandwidths are possible with wideband designs, there is a limiting bandwidth beyond which the wideband filters are not physically realizable. A description is given of an active all-pass network that avoids several undesirable features of lattice networks, and an easy method of using the tabulated solutions to synthesize filters of this type is described.

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