Introduction to Electric Circuits

178 Transient analysis

The response to the application of a pulse

Suppose that the pulse of width T seconds (T >i 5r) shown in Fig. 8.8 is applied

to the circuit of Fig. 8.1. The effect upon the circuit can be considered to be a

combination of the conditions in the previous two sections.

0 T "-t
Figure 8.8

For the period from 0 to T seconds, the current in the circuit and the voltages

across the resistor and the inductor will be given by Equations (8.2), (8.5) and

(8.6), respectively, while for the period following T, these quantities are given

by Equations (8.9), (8.10) and (8.11), respectively. The corresponding wave-

form of current may be obtained by combining Fig. 8.3 with Fig. 8.6(a), putting

0 >I 5z in the latter. Those of VR and Ve can be obtained by combining Fig. 8.4

with Fig. 8.6(b), again changing the origin of the latter to 5z. When you have

done this you should obtain graphs similar to those of Figs 8.10 and 8.12.

The RL integrator circuit

If the output voltage of the RL circuit shown in Fig. 8.9 is taken to be the

voltage across the resistor, then the circuit is called an integrator because the

output waveform approximates to the integral of the input voltage.

vC)

_~,..j,-,~ryy~ i L

F

"]R

0

Vo --

0

VR

Figure 8.9

Example 8.4

A pulse of magnitude 5 V and width 40 txs is applied to an integrator circuit

consisting of an inductor of 8 mH in series with a resistor of 2 kf~. Draw the

waveforms of the output voltage, Vo, and the current, i.

Solution

The circuit is as shown in Fig. 8.9 with R - 2 kl), L - 8 mH and V = 5 V. First