Signals and Systems

4.23 PULSE RESPONSE OF SERIES R–C CIRCUIT

A pulse e(t) shown in Fig. 4.15(a) is applied to a series RC circuit shown in Fig. 4.27. The switch K is closed at t = 0. Using KVL in the loop of Fig. 4.27, the following is obtained,

 

 

Fig. 4.27 Series RC circuit with pulse input

 

 

Taking Laplace transform of Eq. (4.104), it can be written as

 

 

Assuming, the capacitor is initially discharged i.e., q₀ = 0 Eq. (4.105) can be written as