Dynamically Independent Equilibrium Equations for RLC Networks

This paper presents a systematic derivation of a system of first-order dynamically independent equilibrium equations for an RLC network. The dynamically independent equations are obtained from a set of topologically independent equilibrium equations which are written in terms of a judiciously chosen set of independent, current and voltage, network variables. It is thus shown that superfluous variables, which are the result of dynamic constraints on the network, can be eliminated by inspection. Finally a method for writing the dynamically independent equilibrium equations by inspection of the network is presented. Thus we show that by the above techniques the set of dynamically independent equations can be obtained with little more labor than the more conventional equilibrium equations whose variables are only topologically independent.