Exploiting Redundancy in Direct Synthesis for Inline Filters

The generalized Chebyshev (pseudoelliptical) filter functions may not be optimal for certain applications due to physical constrains. With redundancy in filter polynomials, this article breaks down the "mental barrier" in conventional synthesis and directly synthesizes the "Chebyshev-like" functions to achieve desired filter performance under physical limitations. By exploiting the redundant restrictions on exact equal-ripple response, the reflection zeros can be moved to the complex plane, thus forming the "Chebyshev-like functions." A class of inline filters with a block of second-order dangling resonators is synthesized, which can generate a pair of symmetric transmission zeros (Tzs) but is considered unrealizable using standard Chebyshev functions. With the proposed theories, an accurate and much improved filter prototype is directly derived from the "Chebyshev-like" polynomials, avoiding additional optimization in the design process. For verification, a group of examples with synthesis results are elucidated. Eight ten-pole filters with four Tzs are synthesized and fabricated. The simulated and measured results demonstrate the effectiveness and application of the proposed theories.