For the circuit in Fig. 15.57, (a) determine the transfer function H(s) = Vout/Vin in terms of circuit parameters R1, R2, R3, L1, and L2; (b) determine the magnitude and phase of the transfer function at ω = 0, 3 × 103 rad/s, and as ω → ∞ for the case where circuit values are R1 = 2 kΩ, R2 = 2 kΩ, R3 = 20 kΩ, L1 = 2 H, and L2 = 2 H.
FIGURE 15.57
(a)
The transfer function
Answer to Problem 7E
The transfer function
Explanation of Solution
Given data:
The required diagram is shown in Figure 1.
Calculation:
Assign the node intersecting the two resistors
The KCL equation at node
The KCL equation at node
Here,
Simplifying the equation (2) as,
The transfer function
Substitute
Substitute
Conclusion:
Therefore, the transfer function
(b)
The magnitude of transfer function
Answer to Problem 7E
The magnitude of transfer function
Explanation of Solution
Given data:
The resistance
The resistance
The resistance
The inductance
The inductance
The angular frequency
The angular frequency
The angular frequency
Calculation:
The conversion of
The conversion of
The conversion of
The magnitude of transfer function
The phase of transfer function
Substitute
Substitute
The magnitude of transfer function
The phase of transfer function
Substitute
Substitute
The magnitude of transfer function
The phase of transfer function
Substitute
Substitute
Conclusion:
Therefore, the magnitude of transfer function
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