The Exact Design of Two Types of Single-Crystal, Wide-Band Crystal Filters

It is shown how a low-pass ladder filter may be transformed to one of two equivalent band-pass, unbalanced, crystal filter structures with three poles and two transmission zeros. The first structure is the bridged T, previously discussed by Mason on an image parameter basis, and the second is a ladder filter. Either type may be designed on an exact insertion loss basis, and both types are equivalent if the Q\´s of the associated inductors are infinite. With finite inductor O\´s one may "exactly" compensate for inductor losses with the bridged T while one may only partly compensate for inductor losses with the ladder. In spite of this, it is shown that the ladder filter does not suffer too large a degradation in its insertion loss function with reasonable Q\´s. Practical constraints on both types of filters are discussed.