Table of Contents
International Journal of Microwave Science and Technology
Volume 2009, Article ID 184895, 8 pages
Research Article

On the Relation between Composite Right-/Left-Handed Transmission Lines and Chebyshev Filters

1The School of Electronics and Information Engineering, Sichuan University, Chengdu 610064, China
2The Institute of Microwave Techniques, University of Ulm, 89069 Ulm, Germany

Received 16 July 2009; Accepted 23 October 2009

Academic Editor: Kamya Yekeh Yazdandoost

Copyright © 2009 Changjun Liu and Wolfgang Menzel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Composite right-/left-handed (CRLH) transmission lines have gained great interest in the microwave community. In practical applications, such CRLH sections realized by series and shunt resonators have a finite length. Starting from the observation that a high-order Chebyshev filter also exhibits a periodic central section of very similar structure, the relations between finite length CRHL transmission lines and Chebyshev filters are discussed in this paper. It is shown that a finite length CRLH transmission line in the balanced case is equivalent to the central part of a low-ripple high-order Chebyshev band-pass filter, and a dual-CRLH transmission line in the balanced case is equivalent to a low-ripple high-order Chebyshev band-stop filter. The nonperiodic end sections of a Chebyshev filter can be regarded as matching sections, thus leading to an even better amplitude and phase response. It is also shown that, equally to a CRHL transmission line, a Chebyshev filter exhibits negative phase velocity in part of its passband. As a consequence, an improved behavior of finite length CRLH transmission lines may be achieved adding matching sections based on filter theory; this is demonstrated by a simulation example.