On the Realization of 2-Port Immittance Matrices Without Transformers

The realization of immittance matrices of passive, bilateral two-ports without transformers is discussed. It is shown that given any symmetric, positive real, immittance matrix, as for example the open-circuit impedance matrix with entries , , and , provided only that the driving functions have nonzero real parts when the variable is imaginary, a RLC network without coupled coils can always be found such that the parameters of are , and where is any positive number no greater than . The value is determined by the given parameters and may or may not exceed unity. A simple rule for determining is given. The realization procedure makes use of available approximation techniques which give rise to nonunique solutions. All solutions, however, are in the form of general lattice networks.