A Compact Microstrip Second-Order Frequency-Variant Coupled Bandpass Filter with Simplified Composite Right-/Left-Handed Zeroth-Order Resonator

GONG Jianqiang; ZHANG Chenlei; LIAO Zihao; LIU Yirun; YU Hanchao; XIE Jian

doi:10.12263/DZXB.20250769

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A Compact Microstrip Second-Order Frequency-Variant Coupled Bandpass Filter with Simplified Composite Right-/Left-Handed Zeroth-Order Resonator

PAPERS | 更新时间：2026-05-28

- A Compact Microstrip Second-Order Frequency-Variant Coupled Bandpass Filter with Simplified Composite Right-/Left-Handed Zeroth-Order Resonator
- ACTA ELECTRONICA SINICA Vol. 54, Issue 2, Pages: 646-652(2026)
- 作者机构：
  
  南昌大学信息工程学院，江西南昌330031
- 作者简介：
- 基金信息：
  
  Natural Science Foundation of Jiangxi(20192BAB207006)
- DOI：10.12263/DZXB.20250769
  CLC： TN713;
- Received：05 September 2025，
  
  Accepted：04 February 2026，
  
  Published：25 February 2026
- 稿件说明：
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龚建强, 章晨磊, 廖梓豪, 等. 基于简化复合左右手零阶谐振器的二阶微带频变耦合带通滤波器[J]. 电子学报, 2026, 54(02): 646-652.

GONG Jianqiang, ZHANG Chenlei, LIAO Zihao, et al. A Compact Microstrip Second-Order Frequency-Variant Coupled Bandpass Filter with Simplified Composite Right-/Left-Handed Zeroth-Order Resonator[J]. Acta Electronica Sinica, 2026, 54(02): 646-652.
龚建强, 章晨磊, 廖梓豪, 等. 基于简化复合左右手零阶谐振器的二阶微带频变耦合带通滤波器[J]. 电子学报, 2026, 54(02): 646-652. DOI：10.12263/DZXB.20250769

GONG Jianqiang, ZHANG Chenlei, LIAO Zihao, et al. A Compact Microstrip Second-Order Frequency-Variant Coupled Bandpass Filter with Simplified Composite Right-/Left-Handed Zeroth-Order Resonator[J]. Acta Electronica Sinica, 2026, 54(02): 646-652. DOI：10.12263/DZXB.20250769

摘要

本文基于简化复合左右手零阶谐振器（Simplified composite right-/left-handed Zeroth-Order Resonator， SZOR）设计了一款小型化二阶微带频变耦合带通滤波器。小型化微带SZOR由高低阻抗线和并联枝节构成，结构对称，且具有可控的零阶主模和一阶寄生模。利用隐式空间映射可从SZOR的集总等效电路模型快速生成相应的微带版图。频变耦合由相邻微带SZOR低阻线间容性缝隙和并联枝节间感性条带提供的分立电磁耦合路径产生，电耦合与磁耦合皆可独立调控，易于实现目标频变耦合值。带通滤波器中心频率为3.1 GHz，相对带宽为4.5%，带内回波损耗为22 dB。滤波器初始物理参数基于二阶频变耦合矩阵生成。最优版图采用单纯形法最小化由S参数提取的频变耦合矩阵与理论频变耦合矩阵的绝对误差得到。优化过程完全自动化，无需人工干预。根据最优版图参数，加工并测试了滤波器原型，仿真与实测结果吻合良好。验证了磁主频变耦合传输零点位于上阻带以及电主频变耦合传输零点位于下阻带的关键特性。

Abstract

This paper presents a compact microstrip second-order frequency-varying coupled bandpass filter (BPF) based on a simplified composite right-/left-handed zeroth-order resonator (SZOR). The miniature microstrip SZOR is symmetrically composed of the high/low-impedance lines and the parallel stub

featuring the controllable zeroth-order dominant mode and the first-order spurious mode

of which layout can be quickly generated from its lumped equivalent circuit model by applying the implicit space mapping technique. The separate electric and magnetic coupling routes essential for the frequency-variant coupling (FVC) comprise the capacitive gap between the low-impedance lines and the inductive strip connecting the parallel stubs of two neighbouring microstrip SZORs

through which the electric and magnetic couplings can be independently controlled

facilitating to acquire the specified FVC value. The target BPF centers at 3.1 GHz with a fractional bandwidth of 4.5% and an inband return loss of 22 dB. Its design starts from the FVC coupling matrix synthesis. The finalized layout parameters are automatically optimized through the Nelder-Mead Simplex algorithm by minimizing the absolute error between the extracted FVC coupling matrix and the theoretically synthesized one. Good agreement between the full-wave simulation and the prototype measurement demonstrates when the FVC is magnetically dominant

the generated TZ will locate above 3.1 GHz

while as the FVC is electrically dominant

the resulted TZ will shift below 3.1 GHz.

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references

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