The Design of Parallel Connected Filter Networks With Nonuniform $Q$ Resonators

A method of designing parallel connected lossy filter networks is introduced. In a parallel connected filter network, each resonator represents one of the poles of the admittance parameters 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-Q technologies while the unloaded Q of the others can be reduced. Gradient-based optimization is used for determining the Q distribution that provides a flat 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-Q resonators. Examples using mixed coaxial and microstrip technology are presented.