c. In Figure 41D, the input to the differentiator circuit of
Figure 41A is a sine wave. When the input voltage is zero, its rate
of change is maximum, and the differentiated output voltage is
maximum. When the input voltage is maximum, the rate of change of
current is zero, and the differentiated output voltage is zero. As a
result, the differentiated output voltage is a sine wave that is 90
degrees out of phase with the input sine wave.
d. In Figure 42B, the input to the differentiator circuit is a
sawtooth wave. Since the voltage rises at a constant rate to some
maximum amplitude, the input voltage rate of change remains constant.
The differentiated output voltage during this time is a positive DC
voltage whose amplitude is proportional to the voltage rate of change
and the time constant. When the maximum value of the input voltage
is reached, the input voltage begins to decay toward zero. The input
voltage rate of decrease is constant, and the differentiated output
during this time is a negative DC voltage. Since the input voltage
rate of change is greater during the decay time, the amplitude of the
negative DC differentiated output voltage is greater.
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