Concept explainers
If the input impedance is defined as Zin = Vs/Is, find the input impedance of the op amp circuit in Fig. 10.116 when R1 = 10 kΩ, R2 = 20 kΩ, C1 = 10 nF, C2 = 20 nF, and ω = 5000 rad/s.
Figure 10.116
Calculate the input impedance
Answer to Problem 73P
The value of input impedance
Explanation of Solution
Given data:
Refer to Figure 10.116 in the textbook for the op amp circuit.
The values of resistance
The values of capacitance
The value of angular frequency
Formula used:
Write the expression to calculate impedance of the capacitor.
Here,
Write the formula for input impedance of the given op amp circuit.
Here,
Calculation:
Substitute
Substitute
The frequency domain representation of given circuit with the node voltage is shown in Figure 1.
Apply Kirchhoff’s current law at node
According to the properties of an ideal op amp, the voltage appear across the input terminals of the op amp is zero.
The voltage at the inverting terminal will be appear at the non-inverting input terminal. Since the output voltage is fed back to the inverting terminal, the voltage
Substitute equation (4) in (3).
Reduce the equation as follows.
Apply Kirchhoff’s current law at node
Substitute equation (5) and (7).
Simplify the equation as follows.
Substitute equation (7) in (5).
Simplify the above equation as follows.
Substitute equation (8) in (7).
From Figure 1, write the expression for current
Substitute equation (10) in (2).
Conclusion:
Thus, the value of input impedance
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Chapter 10 Solutions
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