System-theoretic realization of active RC networks - The case of RC ladder networks

The transformation matrix between the adjoint and tridiagonal matrices for the state variable expression of RC driving point impedance is reported. A technique for realizing RC transfer functions with RC ladder networks is discussed noting the realization of arbitrary zeros and arbitrary transfer functions. It is shown that by changing the weighted factors, arbitrary characteristics may be realized with equal element values for the RC ladder network. The theory is developed in terms of the generalized Routh table.