Concept explainers
Find the Thevenin equivalent to the left of the load Z in the circuit of Fig. 13.87.
Calculate the Thevenin equivalent to the left side of load Z in the coupled coils circuit.
Answer to Problem 18P
The Thevenin equivalent circuit parameters are
Explanation of Solution
Given data:
Refer to Figure 13.87 in the textbook for the circuit with coupled coils.
Calculation:
To the Thevenin’s voltage, open-circuit the impedance Z. Then, the current
Modify the Figure 13.87 by convert the circuit into the frequency domain and convert the coupled inductors into their dependent source equivalent. The modified circuit as shown in Figure 1.
Apply Kirchhoff's voltage law to the loop 1 contains current
Substitute 0 for
Modify the Equation as follows.
Write the expression for the open-circuit voltage.
Substitute
Consider the expression for the Thevenin voltage.
Substitute
Modify the Figure 1 by short-circuiting the load side contains current
From Figure 2, consider that the loops 1 and 2 contain the currents
Apply Kirchhoff's voltage law to the loop 1 in Figure 1.
Apply Kirchhoff's voltage law to the loop 2 in Figure 1.
Write equations (1) and (2) in matrix form as follows.
Write the MATLAB code to solve the equation (3).
A = [(4+j*7) -(4+j*11);-(4+j*11) (4+j*28)];
B = [440; 0];
I = inv(A)*B
The output in command window:
I =
61.069 - 121.926i
14.369 - 54.571i
From the MATLAB output, the currents
And
The short-circuit current
Substitute
Write the expression for Thevenin’s equivalent impedance.
Substitute
Conclusion:
Thus, the Thevenin equivalent circuit parameters are
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Chapter 13 Solutions
Fundamentals of Electric Circuits
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