Insertion Loss Design of Symmetrical Lattice Piezoelectric Resonator Filters with Symmetrical or Unsymmetrical Pass Bands

The problem of designing symmetrical lattice filters whose arms consist of a number of piezoelectric resonators plus a broad-banding inductor is solved. The solution proceeds from a statement of the low-pass prototype transmission function which must be of the form1/1+(P/Q)^2wherePandQare polynomials in frequency which are neither even or odd. Although this low-pass prototype is not realizable in terms of resistors, inductors and capacitors, it is realizable if an additional element, a constant reactance, is introduced. The low-pass filter is transformed to a band-pass filter realizable with piezoelectric resonators by the use of low-pass to band-pass transformations together with O'Meara's transformation. Examples are given.