State-Variable Techniques

The concept of states is closely related to the order of complexity of the circuit. When compared with other circuit descriptions, the state-variable representation is not necessarily the simplest. The state equation is also particularly suitable for analysis by numerical techniques. Another distinct advantage of the state-variable approach is that it can be easily extended to nonlinear and/or time varying circuits. In writing a state equation for networks, the same systematic procedure can be applied with the selection of a modified proper tree. The response of the circuit depends on the solution of the state equation. Once the state transition matrix is known, the solution of the state equation can be obtained from. In general, it is rather difficult to obtain a closed-form solution from the infinite series representation of the state transition matrix. When independent sources are present in the circuit, the complete response depends on the initial states of the circuits as well as the input sources.