Broad-band impedance matching of the RLC generator and load

A simple theory is presented for the design of a broadband impedance matching network which, when operating between a given RLC generator z₁(s) and an RLC load z ₂(s), yields a maximum Chebyshev lowpass or bandpass response. Using realizability conditions for the double frequency-dependent terminations, a theorem is presented, which states that if there exists a second-order all-pass function such that the resulting reflection coefficients are bounded-real and satisfy Youla´s (1964) conditions at each zero of transmission of z₁(s) and z₂(s), a ladder equalizer exists. A method to realize such a ladder is described. After choosing the order of the transfer function at least equal to the total number of the energy storage elements of z₁(s) and z ₂(s), the result can easily be extended to any all-pole lowpass response for any non-Foster positive-real impedances z₁(s) and z₂(s) except for the case where z ₁(s) and z₂(s) have a common finite zero on the jω-axis