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.