Complex Ladder Filter Realizations

Passive real ladder synthesis is extended to synthesize ladder filters realizing transfer functions with non-complex-conjugate loss-poles. The normal requirement on ladder filters of having lossless two-port impedance (or admittance) transfer functions being positive-real-functions and purely even or odd is over-restrictive and unnecessary. For ladder filters realizing complex transfer functions, this is replaced by the requirement that two-port transfer functions are reactive functions where numerator and denominator polynomials have s-term coefficients alternating between being purely real or purely imaginary for even and odd s-terms. This preserves maximum power transfer and good sensitivity properties. Design procedures are given; examples are used to demonstrate the procedures.