Introduction to Electric Circuits

186 Transient analysis

Response of the RC circuit to a pulse input voltage

Let the pulse of amplitude V and width T (>5~') shown in Fig. 8.8 be applied to

the circuit of Fig. 8.13. From t = 0 to t = ~" the conditions are similar to those

when a step input is applied and Equations (8.14), (8.15) and (8.16) apply. From

t = 5~" to t = T, the capacitor is fully charged so that Vc = V, i = 0 and VR = 0.

After the removal of the pulse at t = T the capacitor discharges and Equations

(8.19), (8.20) and (8.21) apply. These points are illustrated in the waveforms of

Fig. 8.19.

I,V

-V

VC

5~ T

~

~"~ 5~)

Ri

t

Figure 8.19

The R C integrator circuit

If the output voltage is taken across the capacitor as shown in the circuit of

Fig. 8.20, we have an integrator circuit, so called because the output voltage

approximates to the integral of the input voltage.

Figure 8.20

v( 3

R

I I -O

C Vo = Vc

0

Single pulse input

Following the application of the pulse's leading edge to the input terminals, the

capacitor charges up in accordance with Equation (8.14) so that the capacitor

voltage is given by

vc = V[1 - exp (-t//CR)]

If the pulse width T is greater than 5~" the capacitor will be fully charged before

the pulse is removed. After the pulse is removed, the capacitor discharges in