A mathematical framework for active circuits based on port equivalence using limit variables

Infinity-variables (infin-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 co-variables. We develop the idea of port equivalence and show that co-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 co-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