For the circuit in Fig. 15.56, (a) determine the transfer function H(jω) = Vout/Vin in terms of circuit parameters R1, R2, and C; (b) determine the magnitude and phase of the transfer function at ω = 0, 3 × 104 rad/s, and as ω → ∞ for the case where circuit values are R1 = 500 Ω, R2 = 40 kΩ, and C = 10 nF.
FIGURE 15.56
(a)
The transfer function
Answer to Problem 6E
The transfer function
Explanation of Solution
Given data:
The required diagram is shown in Figure 1.
Calculation:
The equivalent impedance of the capacitor is given as,
The Kirchhoff’s current law equation at node
Here,
The Kirchhoff’s current law equation at
The transfer function
Substitute
Substitute
Conclusion:
Therefore, the transfer function
(b)
The magnitude of transfer function
Answer to Problem 6E
The magnitude of transfer function
Explanation of Solution
Given data:
The resistance
The resistance
The capacitor
The angular frequency
The angular frequency
The angular frequency
Calculation:
The conversion of
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 magnitude of transfer function
Substitute
Substitute
The magnitude of transfer function
The magnitude of transfer function
Substitute
Substitute
Conclusion:
Therefore, the magnitude of transfer function
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