Synthesis of Wideband Bandpass Filter With Cross-Coupled or Inline Topology for Direct Circuit Implementation Using Lumped Elements

Abstract

A synthesis method of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> th-order wideband bandpass filter (BPF) with cross-coupled or inline topology using inductive- and capacitive-coupling components is presented. The synthesized admittance matrix can fully represent the frequency-dependent characteristics of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${J}$ </tex-math></inline-formula> -inverters and resonators that are used to implement the wideband BPF. All negative inductive-coupling elements in the trisection, quadruplet, or conjoined trisection blocks can be transformed into negative capacitive-coupling elements by using the proposed similarity transformation matrix and the corresponding transformation conditions. As a consequence, the resulted admittance matrix can be directly implemented using lumped elements. All values of the lumped elements can be calculated without any optimization. The transformation method of cascaded blocks filter with trisection, quadruplet, and two conjoined trisections is demonstrated through several numerical examples. The fundamental transformation of third-order and fourth-order cross coupled or inline topologies is proposed first. Cascaded block synthesis for higher order wideband BPF with multiple transmission zeros (TZs) is then carried out based on the proposed fundamental transformation. The proposed synthesis method can be applied to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${N}$ </tex-math></inline-formula> th-order wideband BPF with multiple TZs. To validate the proposed method, a fifth-order cascaded triplets (CTs) filter with fractional bandwidth (FBW) of 66.7%, one TZ at the lower stopband, and two TZs at the upper band are synthesized, designed, and fabricated.