Signals and Systems

4.19 STEP RESPONSE OF SERIES R–L–C CIRCUIT

Fig. 4.23 shows a series R–L–C circuit having zero initial conditions i.e., initially the circuit was relaxed. Let the switch K be closed at t = 0.

 

 

Fig. 4.23 Series RLC circ

 

The circuit equation is given by

 

 

Taking Laplace transform of Eq. (4.81), we can write

 

 

The three possible solution for I(s) are as follows,

Case (i) : Both a and bare real and a ≠ b i.e.,

 

 

 

∴ Using Eq. (4.85) ...