Electrical Engineering ⇒ Topic : Pulse Response

PULSE RESPONSE

A pulse E(t) shown in Figure 1 (a) is given by E(t) = E [u(t) - u(t - T)]. This pulse is applied to a series R-L circuit shown in Figure 1 (b) by closing the switch. Applying KVL to the loop of Figure 1 (b), we can write

                                        .............. (1)

           Figure (1) Series R-L circuit: (a) pulse and (b) circuit diagram to which the pulse is applied.

Taking the Laplace transform of Eq. (1),

                 L [s I(s) - i(0-)] + R I(s) = E(s)                   .............. (2)

                            .............. (3)

Using Eq. (2) and putting i(0 -) = 0, i.e. the circuit is initially relaxed, Eq. (3) can be written as

                         ............. (4)

Taking the inverse Laplace transform of Eq. (4), we get

                    ............. (5)