A Mathematical Framework For Active Circuits Based On Port Equivalence Using Limit Variables

Infinity-variables (infinity-variables) have been used to allow symbolic description of any linear active element in an admittance matrix. This paper attempts a preliminary justification for such use of infinity-variables. We develop the idea of port equivalence and show that infinity-variables are a special case of limit-variables and can be used to imply limits in a set of matrix equations. We show that the presence of infinity-variables in an admittance matrix implies the existence of matrix equivalences which lead to theorems that provide a means for analysis and synthesis of active circuits.