Design of Reflectionless Bandpass Filters Based on Asymmetric Reciprocal Filtering Network
Qing‐Yuan Lu, Jianpeng Wang, Lei Zhu, Zhipeng Xia, Wen Wu
Abstract
This article presents a concise two-port asymmetric reciprocal filtering network, which mainly consists of short-and open-ended coupled lines for designing reflectionless bandpass filters (RBPFs). The network form is evolved from the lumped-element circuit to the distributed-element one. According to our theoretical analysis, it can be found that the network has the same transmission coefficients, i.e., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\mathbf{12}}$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\mathbf{21}}$</tex-math> </inline-formula> . However, the reflection coefficients at the two ports are opposite. In other words, the magnitudes of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\mathbf{11}}$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\mathbf{22}}$</tex-math> </inline-formula> are the same ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{\mathbf{11}}$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert S_{\mathbf{22}}\vert)$</tex-math> </inline-formula> while their phase difference is 180 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> . Remarkably, this special 180 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> relationship is frequency-independent. By resorting to this property, an asymmetric reciprocal filtering network can be developed by incorporating the filtering sections into the coupled lines. As a result, balanced-circuit-based RBPFs have been constructed without adding an extra phase shifter by arranging two filtering networks in a rotationally symmetrical manner. Benefiting from the frequency-independent antiphase reflection, the reflection signals of the two paths are canceled out in the stopband of the RBPF and absorbed by the isolation resistor of the employed power dividers (PDs). For demonstration, second-and fourth-order RBPFs using interdigital line resonators and split-ring resonators are, respectively, designed. Good agreements between the measured and simulated results can be observed.