Synthesis of Wideband Cross-coupled Resonator Filter for Direct Circuit Implementation Using Lumped Elements

A synthesis method of wideband cross-coupled resonator filter with both inductive and capacitive coupling components is presented using similarity transformation. The synthesized admittance matrix can fully represent the frequency-dependent characteristics of the J-invertors that are used to implement the coupling components. All negative inductive-coupling elements obtained from the conventional filter synthesis method can be transformed to positive capacitive coupling elements by solving the equation from similarity transformation, so that the resulted admittance matrix can be directly implemented using lumped elements. All values of the lumped elements can be calculated without any optimization. A third-order triplet with fractional bandwidth (FBW) of 50% and one transmission zero (TZ) in the lower stopband, and a fourth-order quadruple with FBW of 50% and two symmetric TZs are synthesized to demonstrate the proposed method.