Electric Circuits and Networks

13.1 PERIODIC WAVEFORMS IN CIRCUIT ANALYSIS

Let us consider the first question.

Expansion in terms of sinusoids is not the only expansion possible for a periodic waveform. However, this expansion turns out to be of a great utility in Circuit Analysis.

Complex exponential functions of the form e^st, where s is a complex number, are eigen functions of linear time-invariant circuits. This means that the total response of the circuit when v_S(t) = e^st for all t is applied, is a scaled copy of e^st itself. The scaling factor will be a function of s and circuit parameters and hence it will be a complex number (this complex number is called an eigen value). We note that e^st has to be applied from t = –∞ for this to be true. Since the waveform is applied ...