Synthesis of the transfer function of 2-terminal pair networks

The open-circuit transfer function θ(p) of the 2-terminal pair network, defined as the ratio of the output voltage to the input voltage, must be regular in the right-half p plane. Poles of θ(p) on the imaginary p axis, if any, must be simple with residues having zero real part. These conditions are sufficient to realize θ(p) to within a constant factor by a symmetrical lattice network. If, in addition, θ(p) has no zeros in the right-half plane, then θ may be realized to within a constant factor by a ladder network. If θ(p) is further restricted by the condition 0<θ<1 whenever θ is real in the right-half plane, then θ may be realized completely by an L network. An algorithm for factoring the product of two positive real functions is given also.