مرکز منطقه ای اطلاع رساني علوم و فناوري

Abstract :

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 $PT \\leq {det. Y^q \\over det. Y_{sc}^q} \\Bigg{\\vert}_{p = \\infty}, \\hbox{ } q = 1,2,\\cdots ,n;$ where $Ev$ implies the "even part of," each element of matrix $Y$ is defined as $Y_{ik}= {N_{ik} \\over D} = {pB_1^{ik} - A_1^{ik} \\over A_2 - pB_2}$ 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).