Modern network theory design of single-sideband crystal ladder filters

This paper presents modern network theory design data (rather than image parameter data) for one class of ladder network SSB crystal filters. The filter configuration involved uses crystals and capacitors only, so that the physical size of the resulting filters can be made quite small. A simple frequency transformation is first derived which enables the wealth of design data presently available for symmetrical response shape filters to be applied to the SSB response under consideration. It is shown that the transfer function being considered has n nonconjugate complex poles and n coincident zeros in the fractional bandwidth left half-plane. From the frequency transformation developed, graphs are presented for n-pole, n-coincident-zero SSB relative-attenuation shapes for n = 6, 8, 10, and 12, with a pass band peak-to-valley ratio of zero decibels; and a computation example shows how graphs may be prepared for any n, and any pass band peak-to-valley ratio. Specific design equations are presented for all the elements involved in both the upper and lower SSB filter structures, and from these an equation is derived which shows how crystal units limit the maximum fractional bandwidth which can be obtained.