Minimal Realizations of the Biquadratic Minimum Function

The purpose of this paper is to obtain rigorously minimal realizations of the biquadratic minimum positive real function without the use of transformers. For this purpose a few theorems are proved about the structure of the network realizing a minimum pr function. This is followed by an exhaustive search of networks in increasing order of number of elements. It is proved that the modified Bott-Duffin (or the Reza-Pantell-Fialkow-Gerst) realization using seven elements is rigorously minimal in number of elements, except for the special cases
Z(0) = 4 Z(\infty)
and
Z(\infty) = 4 Z(0)
. These two special cases have five element realizations.