Electric Circuits and Networks

15.15 SUMMARY

• Let v(t) be a right-sided function that is bounded by Me^αt with some finite value of M and α. Then the Laplace transform pair is defined as

   

  

   

  where s = σ + jω is the complex frequency variable standing for the complex exponential function e^st with σ value ≥ α. The ROC of V(s) is the entire plane to the right of Re(s) = α line.

• Laplace transform expands a transient right-sided time-function in terms of infinitely many complex exponential functions of infinitesimal amplitudes. The ROC of such a Laplace transform will include the right-half of s-plane and hence the time-domain waveform gets constructed by the growing complex exponential ...