Derivation of Zeros from Externally-loaded Feed-forward Element of Filter Network

We present a mathematical method for calculation of transmission zero locations, determining a filtering characteristics of two-port systems. By adjusting element values based on the zero locations, the frequency-selectivity is characterized. The characteristic polynomial of ladder networks in externally-loaded feed-forward systems is considered by adopting chain matrices for subsystems. This method can be extended to other types of lumped systems with cross-coupled sections. We find out the zeros by solving characteristics polynomials of closed-form expressions in terms of Laplace impedances of elements. The pairs of complex zeros are shown to be solely from the cross-coupled portion of the system.