In electrical engineering, the designer is often presented with the problem of synthesizing a circuit for which the mathematical specifications are unsuitable for physical realization. Hence, the engineer must approximate as well as possible the prescribed network function by another function which is realizable. This paper describes a new approximation method for solving the problem of realizing passive network transfer functions, where the realization is carried out through the use of passive, reciprocal,lumped, linear, and time-invariant elements.