The design of parallel connected filter networks with non-uniform Q resonators

A method of designing parallel connected lossy filter networks is introduced. In a transversal filter network, each resonator represents one of the global eigenmodes and is independent of the others, thus the dissipation of each resonator can be considered separately. It is observed that some of the resonators are more critical than the others in determining the filter performance. These resonators have to be designed with high Qu technologies while the Qu of the others can be reduced. Gradient based optimization is used for determining the Qu distribution that provides a good passband insertion loss as well as a good return loss. The design theory will be presented along with examples of networks which clearly show that high performance filters may be constructed with a minimum number of high Qu resonators. An example using mixed coaxial and microstrip technology is presented.