A ${Z}$-Transform Method for Synthesis of Unequal-Length Multisection Transmission Lines for Multiband Applications

Joonsuk Kim, Yongshik Lee

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


A method based on the $Z$-transform is demonstrated to cascade transmission line sections of unequal lengths and achieve multiband and/or wideband properties. Unlike previous methods based on the $Z$-transform, the proposed method associates the $z^{-1}$ term with the infinitesimal length of the unit segment. Consequently, any electrical length can be expressed in the $z^{-1}$ form. Therefore, while the previous methods are restricted to cascading lines of a commensurate length only, the proposed method can be applied to those of incommensurate lengths. Furthermore, the $z$-polynomials for triple or more bands can be constructed by multiplying a combination of single- A nd dual-band polynomials, which remarkably simplifies the entire procedure to develop multiband and/or wideband circuits with virtually no limitation in terms of the number and/or combination of frequencies. The validity and practicality of the proposed method is verified with experimental results for various impedance transformers for real loads and Wilkinson power dividers; the results show the independence in the number and combination of operating frequencies as well as a dual-band operation with a center frequency ratio as large as 7.75.

Original languageEnglish
Article number7886282
Pages (from-to)3200-3210
Number of pages11
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number9
Publication statusPublished - 2017 Sept

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

All Science Journal Classification (ASJC) codes

  • Radiation
  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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