Coupling matrix-based co-design of filter-oscillators

Yang Gao, Fazhong Shen, Yingying Qiao, Haizhong Guo, Lei Li, Fan Zhang, Yi Wang

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This letter presents a methodology of designing integrated filter-oscillators using the coupling matrix technique. The N + 4 coupling matrix is developed for the first time to describe the filter-oscillator topology. Accordingly, the corresponding group delay, loop gain, loop phase, and complex quality factor of the feedback filter can be calculated using the matrix. This helps rapidly predict oscillating frequencies at group delay or complex quality factor peak frequencies to achieve lower phase noise. Moreover, since the transistor and the transmission line (TL) entries are incorporated in the coupling matrix, the physical geometries can be directly determined, resulting in improved design efficiency. Two third-order filter-oscillators are implemented at 2.91 GHz (group delay peak) and 3.15 GHz (complex quality factor peak) frequencies, respectively. The developed filter-oscillators are measured with -121 and -145 dBc/Hz phase noise at 1-MHz offset frequency, validating this coupling matrix-based co-design approach.

Original languageEnglish
Article number9712645
Pages (from-to)563-566
JournalIEEE Microwave and Wireless Components Letters
Issue number6
Early online date14 Feb 2022
Publication statusE-pub ahead of print - 14 Feb 2022

Bibliographical note

Publisher Copyright:


  • Active coupling matrix
  • Couplings
  • Delays
  • Microwave filters
  • Oscillators
  • Q-factor
  • Transistors
  • Transmission line matrix methods
  • filter-oscillator
  • resonator
  • transistor.

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electrical and Electronic Engineering


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