15.9 THE s-DOMAIN EQUIVALENT CIRCUIT
Yes, it can. Laplace transform technique tells us that we do not even have to derive the circuit differential equation and initial values required to solve it. Let us see how.
The circuit equations arising out of applying KVL in loops and KCL at nodes are equations that remain true at all values of t. Therefore, such equations can be differentiated and integrated with respect to time without changing their truth content. And, of course, being equations they can be multiplied by the same constant or function on both sides.
We choose to multiply all KCL and KVL equations in a linear time-invariant circuit by a function e –st, where s is a complex frequency value drawn from s-plane, with a real part of suitable ...