Derivation of Transfer Function for the Cross-Coupled Filter Systems Using Chain Matrices

  • Um, Kee-Hong (IT Department, Hansei University)
  • Received : 2018.01.16
  • Accepted : 2018.02.11
  • Published : 2018.03.31


In this paper, we derive a transfer function of cross-coupled microwave filter systems by using a characteristics of chain matrices. Depending on the lumped element of capacitor or inductor, the cross-coupled system is negatively- or positively system. We used a ladder network as a starting system composed of several subsystems connected in chain. Each subsystem is descrived by Laplace impedance. By solving the transmission zero characteristic equation derived from the cascaded subsystems, we can find the zeros of filter system with externally cross-coupled lumped elements. With the cross-coupled elements of capacitors, the numerator polynomial of system transfer function is used to locate the quadruplet zeros in complex plane. We show the polynomoials of numerator and denominator of cascaded transfer function, obtaining the zeros of the cross-coupled system.


Ladder network;Negative cross-coupling (NCC);transmission zeros;Cross-coupling;Bridged-T subsystem


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