A State Variable Method of Circuit Analysis Based on a Nodal Approach

A method which is well suited for implementation on a digital computer is presented for the solutions of active circuits. Unlike many state variable approaches the state vector is defined as the set of voltages which exist between certain nodes and the reference node. An advantage of this approach is that degeneration in the order of complexity of the network caused by capacitance loops is handled automatically. Any type of controlled source can be specified. From the basic algorithm the circuit is specified in matrix form by inspection using standard nodal methods, and the solution is obtained by a systematic reduction of this one matrix equation. An upper bound on the order of complexity of the network is evident from the network topology or the partitioned form of the original matrix. Inductors are included in this approach by considering the equivalent gyrator-capacitor combination.