Concept explainers
An op amp integrator with R = 4 MΩ and C = 1 μF has the input waveform shown in Fig. 6.88. Plot the output waveform.
Figure 6.88
For Prob. 6.69.
Sketch the output voltage waveform of an op-amp integrator.
Explanation of Solution
Given data:
The value of the resistor
The value of the capacitor
Refer to Figure 6.88 in the textbook.
Formula used:
Write the expression to calculate the output voltage of an op-amp integrator.
Here,
Calculation:
Substitute
The given input voltage waveform is redrawn as Figure 1.
Refer to Figure 1, the input voltage
Case (i): For
Substitute
Simplify the equation to find
Substitute
Case (ii): For
Equation (2) can be rewritten as following equation to find the output voltage for
Substitute
Simplify the equation to find
Substitute
Case (iii): For
Equation (2) can be rewritten as following equation to find the output voltage for
Substitute
Simplify the equation to find
Substitute
Case (iv): For
Equation (2) can be rewritten as following equation to find the output voltage for
Substitute
Simplify the equation to find
Substitute
Case (v): For
Equation (2) can be rewritten as following equation to find the output voltage for
Substitute
Simplify the equation to find
Substitute
Therefore, the output voltage function for Figure 1 is expressed as,
The output voltage waveform is drawn as Figure 2.
Conclusion:
Thus, the output voltage waveform of an op-amp integrator is sketched.
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