The crossover circuit in Fig. 14.108 is a low-pass filter that is connected to a woofer. Find the transfer function H(ω) = Vo(ω)/Vi(ω).
Find the transfer function
Answer to Problem 96P
The transfer function
Explanation of Solution
Given data:
Refer to Figure 14.108 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.
The s-domain circuit of the Figure 1 is drawn as Figure 2 using the equations (1), (2), and (3).
Refer to Figure 2, the resistor
The Figure 2 is redrawn as Figure 3.
Refer to Figure 3, the inductor
Substitute
Simplify the above equation to find
The Figure 3 is redrawn as Figure 4.
Apply voltage division rule on Figure 4 to find
Apply voltage division rule on Figure 3 to find
Substitute
Rearrange the above equation to find
Substitute
Simplify the above equation to find
Substitute
From the equation (5), the equation (4) becomes,
Conclusion:
Thus, the transfer function
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Chapter 14 Solutions
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