
Concept explainers
In the op amp circuit of Fig. 10.118, find the closed-loop gain and phase shift of the output voltage with respect to the input voltage if C1 = C2 = 1 nF, R1 = R2 = 100 kΩ, R3 = 20 kΩ R4 = 40 kΩ and ω = 2000 rad/s.

Calculate the closed-loop gain and phase shift of the output voltage of the op amp circuit in Figure 10.118 using MATLAB.
Answer to Problem 75P
The closed-loop gain and phase shift of the output voltage are
Explanation of Solution
Given data:
Refer to Figure 10.118 in the textbook for op amp circuit.
The value of angular frequency
Formula used:
Write the expression to calculate impedance of the capacitor.
Here,
Calculation:
Let us assume that source voltage
Substitute
The frequency domain representation of given figure is shown in Figure 1.
Apply Kirchhoff’s current law at node
Substitute
Apply Kirchhoff’s current law at node
Apply voltage division rule at node
According to the properties of ideal op amp, the voltage at the input of the non-inverting terminal of the op amp is equal to the voltage at the input of the inverting terminal. Hence,
Substitute equation (5) in (2).
Substitute equation (5) in (3).
Represent the equations (6) and (7) in matrix form.
The MATLAB code to solve equation (8) is shown below.
A = [1+0.4*i -1-0.0667*i; 1 -0.3333+1.6667*i];
b = [2*i; 0];
x = A\b
The MATLAB result is shown below.
x =
-0.4166 + 2.0833i -1.2499 - 0.0000i
The polar representation of obtained results is shown below.
Write the expression for closed loop gain.
Substitute
Conclusion:
Thus, the closed-loop gain and phase shift of the output voltage are
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Chapter 10 Solutions
EBK FUNDAMENTALS OF ELECTRIC CIRCUITS
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