Enlargement of piezoelectric filter bandwidth by parallel connection of coupled resonators

Parallel connection of coupled-resonator piezoelectric filters of different frequencies can provide increased bandwidth without additional insertion loss, at the expense of extra coupled resonators. A theory of two such methods of connection is presented, for two biquartic filters placed in parallel, with and without phase inversion before interconnection. Standard amplitude responses may be obtained from both methods; with phase inversion, standard amplitude and phase responses based on a third order, all-pole prototype can be obtained with bandwidth increases of up to 50%; without phase inversion, standard amplitude response based on a second-order prototype may be obtained with bandwidth increases of up to 100%.