Concept explainers
The triangular waveform in Fig. 6.91(a) is applied to the input of the op amp differentiator in Fig. 6.91(b). Plot the output.
Figure 6.91
For Prob. 6.74.
Sketch the output voltage waveform of an op amp differentiator.
Explanation of Solution
Given data:
Refer to Figure 6.91 in the textbook.
Formula used:
Write the expression to calculate the straight line equation for two points
Refer to Figure 6.91(a) in the textbook.
From the given voltage graph, substitute
Write the expression to calculate the output voltage of an op amp differentiator.
Here,
Calculation:
The given circuit is redrawn as Figure 1.
Substitute
The given input voltage waveform is redrawn as Figure 2.
Refer to Figure 2, split up the time period as three divisions such as
Case (i):
The two points
Substitute
Simplify the equation to find
Case (ii):
The two points
Substitute
Simplify the equation to find
Case (iii):
The two points
Substitute
Simplify the equation to find
Therefore, the input voltage function
For
Substitute
Simplify the equation to find
For
Substitute
Simplify the equation to find
For
Substitute
Simplify the equation to find
Therefore, the output voltage function
The output voltage waveform is drawn as Figure 3.
Conclusion:
Thus, the output voltage waveform of an op amp differentiator
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Chapter 6 Solutions
Fundamentals of Electric Circuits
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