Systems with Initial Conditions
Most of the treatment so far in the text assumed systems/circuits with zero initial conditions. This means capacitors had zero initial charge and inductors had zero initial current. While this is the most often case, it is not the only one! In the chapter we outline a simple method how to deal with initialized circuits. For capacitors we replace the cap with a zero-pre-charged cap in series with a unit step voltage source. For inductors we replace the inductor with zero-pre-charged one in parallel with a unit step current source. We show that so far as the external world is concerned these substitute topologies can replace the pre-charged ones. Once the pre-charged elements have been replaced with zero-charged ones, and in conjunction with the additional sources, we can now use our standard set of spectral/convolution techniques to solve the system. We illustrate the process on a few examples.