Cascade synthesis of polylithic crystal filters containing double-resonator monolithic crystal filter (MCF) elements

In crystal filter design the use of low-pass prototype networks containing frequency invariant reactances is well known. It is shown in this paper that if this concept is extended to the double-resonator monolithic crystal filter (MCF) section, then all the classical transmission zero producing networks, e.g., the Brune, Darlington C-type, and Darlington D-type, may be realized in a form containing low-pass prototype MCF sections. This result allows the techniques of reciprocal cascade synthesis to be applied to the direct synthesis of arbitrary lossless even degree transfer functions in crystal filter form. Explicit expressions are given by which the prototype MCF element values may be obtained