4-47
At the first instant of time, a pulse of 100-volts amplitude with a duration of 100 microseconds is
applied. Since the capacitor cannot respond instantaneously to a change in voltage, all of the applied
voltage is felt across the resistor. As time progresses, the capacitor will charge and the voltage across the
resistor will be reduced. Since the time that the capacitor is permitted to charge is 100 microseconds, the
capacitor will charge for only 1/10 of 1TC or to 9.5 percent of the applied voltage. The voltage across the
resistor must be equal to the difference between the applied voltage and the charge on the capacitor (100
-
9.5 volts), or 90.5 volts.
At the end of the first 100 microseconds of input, the applied voltage suddenly drops to 0 volts, a
change of 100 volts. Since the capacitor is not able to respond to so rapid a voltage change, it becomes the
source of 9.5 volts. This causes a
-
9.5 voltage to be felt across the resistor in the first instant of time. The
sum of the voltage across the two components is now 0 volts.
During the next 100 microseconds, the capacitor discharges. The total circuit voltage is maintained at
0 by the voltage across the resistor decreasing at exactly the same rate as the capacitor discharge. This
exponential decrease in resistor voltage is shown during the second 100 microseconds of operation. The
capacitor will now discharge 9.5 percent of its charge to a value of 8.6 volts. At the end of the second 100
microseconds, the resistor voltage will rise in a positive direction to a value of
-
8.6 volts to maintain the
total circuit voltage at 0 volts.
At the end of 200 microseconds, the input voltage again suddenly rises to 100 volts. Since the
capacitor cannot respond to the 100-volt change instantaneously, the 100-volt change takes place across
the resistor. This step-by-step action will continue until the circuit stabilizes. After many cycles have
passed, the capacitor voltage varies by equal amounts above and below the 50-volt level. The resistor
voltage varies by equal amounts both above and below a 0-volt level.
The RC networks which have been discussed in this chapter may also be used as coupling networks.
When an RC circuit is used as a coupling circuit, the output is taken from across the resistor. Normally, a
long time-constant circuit is used. This, of course, will cause an integrated wave shape across the
capacitor if the applied signal is nonsinusoidal. However, in a coupling circuit, the signal across the
resistor should closely resemble the input signal and will if the time constant is sufficiently long. By
referring to the diagram in figure 4-42, you can see that the voltage across the resistor closely resembles
the input signal. Consider what would happen if a pure sine wave were applied to a long time-constant
RC circuit (R is much greater than XC). A large percentage of the applied voltage would be developed
across the resistor and only a small amount across the capacitor.
Q23. What is the difference between an RC and an RL differentiator in terms of where the output is
developed?
COUNTERS
A counting circuit receives uniform pulses representing units to be counted. It provides a voltage that
is proportional to the frequency of the units.
With slight modification, the counting circuit can be used with a blocking oscillator to produce
trigger pulses which are a submultiple of the frequency of the pulses applied. In this case the circuit acts
as a frequency divider.
The pulses applied to the counting circuit must be of the same time duration if accurate frequency
division is to be made. Counting circuits are generally preceded by shaping circuits and limiting circuits
(both discussed in this chapter) to ensure uniformity of amplitude and pulse width. Under those
conditions, the pulse repetition frequency is the only variable and frequency variations may be measured.
