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
Y
of an
n
port obtained by imbedding an Esaki (tunnel) diode in a reciprocal lossless network are: 1)
- Y(-p)
is a positive-real matrix with either a pole or a zero at infinity. 2)
[Ev Y]
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
D
is even or odd. 4) The sum of the poles
(P)
does not exceed the reciprocal time constant
(l/T)
of the diode. 5) The ratio of
P
and
1/T
does not exceed the ratio of the determinants of
Y^q
and
Y_{sc}^q
at
p = \infty
for all
q
, or
PT \leq \frac {\det\cdot Y^q} {\det \cdot Y_{sc}^q} \arrowvert_{p = \infty}, q = 1,2,\cdots,n;
where
Ev
implies the "even part of," each element of matrix
Y
is defined as
Y_{ik}= \frac {N_{ik} {D} = \frac {p B_1^{ik} - A_1^{ik}} {A_2 - p B_2}
with polynomials
A_2, B_2, A_1^{ik}, B_1^{ik}
being even or odd as the degree of
D
is even or odd. The martix
Y_{sc}
is the admittance matrix obtained by short circuiting the diode. The superscript q represents all possible combinations of
q
accessible ports (the rest are short circuited).