Abstract
A necessary and sufficient condition for the existence of a solution to a set of linear circuit equations with dependent sources is shown to be that a submatrix derived from the coefficients of dissipative elements has rank equal to the number of dissipative elements. This result is particularly useful in computer-aided circuit analysis to determine a cause when a numerical solution does not converge. In the development a general systematic technique for reducing circuit equations to normal form is presented. It is also demonstrated that when dependent sources are present, the order of a circuit is not necessarily equal to the number of independent energy-storing elements. The techniques and conclusions are illustrated with some simple nontrivial examples.
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