The crossover circuit in Fig. 14.109 is a high-pass filter that is connected to a tweeter. Determine the transfer function H(ω) = Vo(ω)/Vi(ω).
Figure 14.109
Find the transfer function
Answer to Problem 97P
The transfer function
Explanation of Solution
Given data:
Refer to Figure 14.109 in the textbook.
Formula used:
Write a general expression to calculate the impedance of resistor in s-domain.
Here,
Write a general expression to calculate the impedance of an inductor in s-domain.
Here,
Write a general expression to calculate the impedance of a capacitor in s-domain.
Here,
Write the general expression to calculate the transfer function of the system
Here,
Calculation:
The given circuit is redrawn as Figure 1.
Use equation (1) to find
Use equation (1) to find
Use equation (2) to find
Use equation (3) to find
Use equation (3) to find
The s-domain circuit of the Figure 1 is drawn as Figure 2.
Refer to Figure 2, the series connected impedances
Therefore, the equivalent impedance is calculated as follows.
Simplify the above equation to find
The reduced circuit of the Figure 2 is drawn as Figure 3.
Apply voltage division rule on Figure 3 to find
Apply voltage division rule on Figure 2 to find
Substitute
Rearrange the above equation to find
Substitute
Simplify the above equation to find
Simplify the above equation to find
Substitute
Simplify the above equation to find
From equation (5), the equation (4) becomes,
Conclusion:
Thus, the transfer function
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Chapter 14 Solutions
Fundamentals of Electric Circuits
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