The Esaki Diode as a Network Element

The following basic theorem is proved: Theorem: Necessary and sufficient conditions for the physical realizability of a short-circuit admittance matrix of an port obtained by imbedding an Esaki (tunnel) diode in a reciprocal lossless network are: 1) is a positive-real matrix with either a pole or a zero at infinity. 2) is of rank one or less. 3) (A_1^{kk} A_2 - p^2 B_1^{kk}B_2)^{1/2} is a polynomial which is even or odd as the degree of is even or odd. 4) The sum of the poles does not exceed the reciprocal time constant of the diode. 5) The ratio of and does not exceed the ratio of the determinants of and at for all , or where implies the "even part of," each element of matrix is defined as with polynomials being even or odd as the degree of is even or odd. The martix is the admittance matrix obtained by short circuiting the diode. The superscript q represents all possible combinations of accessible ports (the rest are short circuited).