Microstrip BPF Design with Coupling Matrix Method

Gülmez H. N. , Ertay A. O. , Döken B., Kartal M.

INTERNATIONAL GRADUATE RESEARCH SYMPOSIUM IGRS’22, İstanbul, Turkey, 1 - 03 June 2022, pp.1

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.1
  • Erzincan Binali Yildirim University Affiliated: Yes


In this paper, we provide an overview of coupling matrix synthesis and design of a microstrip bandpass filter for the 5G n77 (3700 MHz) band based on the coupling matrix approach. 5G radio equipment strictly requires high filtering performance to prevent adjacent channel interference. Asymmetrical pseudo elliptic filter approximation with finite transmission zeros is providing optimal in-band, out-band performance together with sharp cut-offs at the passband edges. Microstrip technology may employ filter designs up to 100 GHz. Unlike waveguide and coaxial cavity filters, microstrip filters are cost-effective and provide ease of manufacture. 

The coupling matrix is a compact tool that represents a certain topology of the bandpass filters. It represents the filter prototypes without being required to extract reactive components’ values in advance. The coupling matrix incorporates both inter-resonator coupling coefficients and frequency offsets in the vicinity of center resonances. The direct synthesis approach, mostly, ends up with physically unrealizable coupling matrices. Instead, a realizable coupling matrix is obtained by means of successive similarity transformations applied to the synthesized matrix. Similarity transformations may emerge in singlet, triplet, and quadruplet topologies which comprise a finite number of prescribed transmission zero either real or complex.

This paper begins with design specifications. In order to fulfill n77 specifications, 0.1 dB passband ripple and a decent amount of out-band rejection is may be realized by a 3rd order filter with 1 finite transmission zero. Next, the characteristic polynomial and filtering function is derived via utilizing a recursive method. Once the set of polynomials is known, the 2-port short circuit admittance matrix is defined by the ratio of certain characteristic polynomials. Afterward, a nodal admittance matrix is formed for the transversal low pass prototype. Coupling matrix synthesis is ended up by equating the short circuit admittance matrix and corner elements of the nodal admittance matrix. Diagonal elements of the coupling matrix represent the frequency offset of each resonator section while off-diagonals are direct and cross-couplings. Appropriate similarity transform is applied to the synthesized matrix for reconfiguring its topology from transversal to triplet. In this work, we deploy a square open-loop resonator. Any coupling can be implemented by changing the orientation and distance between the resonators. A square loop resonator may support a dual-mode of operation which is realized by adding perturbations on the resonator rings.