Sharp rejection low-pass filter using three-section stub and Z-transform technique

Chain-scattering-parameter matrices of equal-length multiple-section open stubs are developed in the z domain. All the zeros of the transfer scattering parameters of the multi-section stubs are examined in detail. The values of the characteristic impedances of the transmission lines synthesising the low-pass filter are adjusted according to the autoregressive process by optimisation algorithms. A Chebyshev-type II low-pass filter with high rejection is designed and implemented in the form of microstrip, and its frequency response is measured to validate the design method.