(decay time). Since the waveform does not level off at a constant
value, the duration time is zero. The triangular waveform thus is
different from the square wave in which the voltage rises quickly and
then levels off. Likewise, the response of RC and RL circuits to a
triangular wave is different from their response to a square wave.
b. Response of an RC circuit. The response of an RC circuit to a
triangular wave input is illustrated in Figure 30. Figure 30C shows
the voltage waveforms enlarged several times for easier study. When
a square wave is applied, the capacitor charges gradually towards the
value at which the square wave levels off; with the application of a
triangular wave, the voltage continues to increase as the capacitor
charges toward it, and the capacitor must continuously charge toward
a new, higher value. Initially, when the voltage E is applied to the
circuit, the current rises with the voltage because the capacitor is
uncharged. The current charges the capacitor to a voltage that
opposes the applied voltage. This action should decrease the circuit
current, but since the input voltage is continuously increasing, the
opposing voltage across the capacitor is more than overcome by the
applied voltage, and the current actually increases, but at a slower
rate than it did initially. As the current continues to increase,
the capacitor becomes charged to a higher voltage and the rate of
current increase is reduced further until, finally, the current is
high enough to raise the capacitor voltage at the same rate as the
increase in the input waveform. At this point, the current becomes
constant, and the capacitor voltage slope is essentially the same as
the input voltage slope.
(1) The current curve is the same as the curve ER. At the end
of 1 time constant, the resistor voltage is equal to approximately
63.2 percent of the voltage applied at that time, and the current is
equal to 63.2 percent of the voltage applied at that time divided by
the value of the resistance in the circuit. After 7 time constants,
ER will level off at a value equal to the voltage applied at the end
of the firsttime constant, and the current will be equal to this
voltage divided by the resistance. The capacitor continues to charge
at the same rate as the rise in input voltage, until the rise of
decreasing during the second half of the cycle, the charging rate of
the capacitor decreases, until the applied voltage drops to the same
value as the capacitor voltage (Figure 31B). At this point, the
current in the circuit is zero. As the applied voltage continues to
decrease, it falls below the capacitor voltage, and the capacitor
starts to discharge.
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