Crystal prototype C- and D-type all-pass networks

Prototype networks for the design of first- and second-degree all-pass sections using discrete quartz crystal resonators are given. The prototype all-pass networks, based on the Darlington and -type zero-producing sections, contain frequency-invariant reactances and, as such, are not directly realizable. Application of a suitable narrowband low-pass to bandpass frequency transformation, however, allows networks whose behavior approximates to an all-pass characteristic over a relatively narrow band to be built using crystals. A design example is given.