T = 1
10-5 vor 10 microseconds
Figure 4-35.RC integrator circuit.
Since the time constant of the circuit is 10 microseconds and the pulse duration is 100 microseconds,
the time constant is short (1/10 of the pulse duration). The capacitor is charged exponentially through the
resistor. In 5 time constants, the capacitor will be, for all practical purposes, completely charged. At the
first time constant, the capacitor is charged to 63.2 volts, at the second 86.5 volts, at the third 95 volts, at
the fourth 98 volts, and finally at the end of the fifth time constant (50 microseconds), the capacitor is
fully charged. This is shown in figure 4-36.
Figure 4-36.Square wave applied to a short time-constant integrator.
Notice that the leading edge of the square wave taken across the capacitor is rounded. If the time
constant were made extremely short, the rounded edge would become square.
Medium Time-Constant Integrator
The time constant, in figure 4-36 can be changed by increasing the value of the variable resistor
(figure 4-35) to 10,000 ohms. The time constant will then be equal to 100 microseconds.
This time constant is known as a medium time constant. Its value lies between the extreme ranges of
the short and long time constants. In this case, its value happens to be exactly equal to the duration of the
input pulse, 100 microseconds. The output waveform, after several time constants, is shown in figure