- (a) For the circuit in Fig. 14.97, draw the new circuit after it has been scaled by Km = 200 and Kf = 104.
- (b) Obtain the Thevenin equivalent impedance at terminals a-b of the scaled circuit at ω = 104 rad/s.
Figure 14.97
(a)
Draw the new circuit for the circuit in Figure 14.97 after it has been magnitude scaled by a factor of
Explanation of Solution
Given data:
Refer to Figure 14.97 in the textbook.
The value of the magnitude scaling factor
The value of the frequency scaling factor
Formula used:
Consider the equations used in magnitude and frequency scaling.
Write the expression to calculate the scaled resistor.
Here,
Write the expression to calculate the scaled inductor.
Here,
Write the expression to calculate the scaled capacitor.
Here,
Calculation:
The given circuit is redrawn as Figure 1.
Refer to Figure 1, the value of the resistor
Substitute
Substitute
Substitute
The redesigned circuit is drawn as Figure 2 which is obtained by using the magnitude and frequency scaling on the circuit in Figure 1.
Conclusion:
Thus, the new circuit for the circuit in Figure 14.97 is drawn by using the magnitude and frequency scaling.
(b)
Find the value of the Thevenin equivalent impedance at terminals a-b of the scaled circuit.
Answer to Problem 80P
The value of the Thevenin equivalent impedance
Explanation of Solution
Given data:
The value of the angular frequency
Formula used:
Write the expression to calculate the impedance of the passive elements resistor, inductor and capacitor in s-domain.
Here,
Calculation:
Use equation (4) to find
Use equation (5) to find
Use equation (6) to find
Insert a
Apply Kirchhoff’s current law on Figure 3 to find
Rearrange the above equation.
Apply Kirchhoff’s current law on Figure 3 to find
Refer to Figure 3, the current
Substitute
By comparing the equations (7) and (9), the following equation is obtained.
Rearrange the above equation to find
Substitute
Simplify the above equation.
Simplify the above equation to find
Refer to Figure 3, the Thevenin equivalent impedance across the a-b terminals are calculated as follows.
Substitute
Substitute
Substitute
Simplify the above equation to find
Conclusion:
Thus, the value of the Thevenin equivalent impedance
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Chapter 14 Solutions
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