Electric Circuits and Networks

8.2 THE COMPLEX EXPONENTIAL FORCING FUNCTION

The method outlined in the previous section to determine the sinusoidal steady-state response of a dynamic circuit can be summarised as below:

1. Use the mesh or nodal analysis to obtain integro-differential equations of the circuit.
2. Differentiate the equations again to eliminate integrals, if needed.
3. Choose one of the mesh currents (or node voltages) as the describing variable for the circuit. Eliminate all the other variables and obtain an nth order linear constant-coefficient differential equation describing the chosen circuit variable.
4. Assume a solution in the form asinωt + bcosωt. Substitute the assumed solution in the differential equation. Equate the coefficients of cosine and sine on both sides ...