Exact Synthesis of Unequal Power Division Filtering Rat-Race Ring Couplers

Po Jung Chou*, Chih Chuan Yang, Chi-Yang Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Exact synthesis of unequal power division filtering rat-race ring couplers is proposed. The power division property results from the half-symmetric core ring structure of the proposed couplers. The proposed core ring was modified from the equal power division rat-race ring in 2015 where the core ring in that circuit is fully symmetric. Due to the half-symmetry of ring and unequal power division characteristics, the signal excitation and circuit partition methods in 2015 cannot be applied. In this paper, the modified signal-excitation method and the source-division technique are proposed to reduce the original four-port rat-race ring couplers into the corresponding two-port networks. These two-port networks can be exactly synthesized by the S-domain filter synthesis method. Alternatively, the simplified design equations are proposed. Using these equations, the rat-race ring hybrid in 2015 can be transformed into the arbitrary power division rat-race ring couplers. Therefore, the final rat-race ring couplers are provided with some user-defined specifications, such as the unequal power division, the input/output impedance transformation, the center frequency, the fractional bandwidth, and the return loss level. Two fifth-order filtering rat-race ring couplers with 3- and 10-dB power division are implemented as examples; in addition, these couplers are with a center frequency of 2 GHz, a fractional bandwidth of 100%, a return loss level of 20 dB, and the input/output impedance transformation of 50/70 Ω. The measured and simulated results indicate good agreement.

Original languageEnglish
Pages (from-to)3277-3287
Number of pages11
JournalIEEE Transactions on Microwave Theory and Techniques
Issue number7
StatePublished - 1 Jul 2018


  • Arbitrary power division
  • couplers
  • exact synthesis method
  • power dividers
  • rat-race ring

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