Electric Circuits and Networks

15.6 METHOD OF PARTIAL FRACTIONS FOR INVERTING LAPLACE TRANSFORMS

Any Laplace transform can be inverted by evaluating the synthesis integral in Eqn. 15.2-2 on a suitably selected vertical line extending from –∞ to ∞ in the s-plane within the ROC of the transform being inverted. But simpler methods based on Residue Theorem in Complex Analysis exist for special Laplace transforms. We do not take up the detailed analysis based on Residue Theorem here. However, the reader has to bear in mind the fact that the ‘method of partial fractions’ for inverting certain special types of Laplace transforms is based on Residue Theorem in Complex Analysis.

Linear time-invariant circuits are described by linear constant-coefficient ordinary differential equations. ...