Concept explainers
For the op amp circuit of Fig. 7.138, let R1 = 10 kΩ, Rf = 30 kΩ, C = 20 μF, and v(0) = 1 V. Find v0.
Find the output voltage
Answer to Problem 73P
The output voltage
Explanation of Solution
Given data:
Refer to Figure 7.138 in the textbook.
The value of capacitance
The source voltage
The value of resistance
The value of feedback resistance
The initial voltage v(0) or
Formula used:
Write the expression to find the time constant for an RC circuit.
Here,
C is the capacitance of the capacitor.
Write the general expression for the unit step function.
Calculation:
The given Figure 7.138 is redrawn as shown in Figure 1.
The given source voltage is,
Apply the unit step function in equation (2) to equation (3).
For
Since the source voltage
For
The source voltage is,
In Figure 1, apply Kirchhoff’s current law at node
In Figure 1, apply Kirchhoff’s current law at node
From Figure 1, the voltages are,
Substitute
Substitute
Rearrange the equation as follows,
The equation is similar to the equation (7.42) in the textbook.
Hence,
In Figure 1, the Thevenin resistance
Substitute
Substitute the units
Substitute 1 V for
On differentiating the above equation as follows,
Substitute
Substitute
Apply the unit step function in equation (2) to equation (9).
Conclusion:
Thus, the output voltage
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Chapter 7 Solutions
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