For the following filter circuit with component values below the circuit; what is the amplitude of the transfer function if the frequency is 100 rad/s? Vi(s), R, sL, 1/sC, Vo(s) L = 100 mH, R = 1 k?, C = 10 ?F Select one: a. 107.0682 b. None of these c. 701.792 d. 13.55
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ZL = jωL = j(100)(0.1) = j10 Ω ZC = 1/(jωC) = 1/(j100)(10^-5) = -j10 Ω Show more…
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An active bandpass filter circuit is shown in Figure Q4(b). The transfer function of the circuit is given by the following equation: Av(Δ) = Vo / Vi = -(1/R1) / (1/R2 + j(ωC - 1/(ωC(R3)^2))) Figure Q4(b) (i) Analyse the transfer function at two extreme frequencies and draw the frequency response of the circuit. (ii) Determine the maximum overall gain of the circuit at pass band. (iii) Design the circuit by finding the value for resistor R1, R2 and R3. The design specifications are: • The magnitude of the maximum overall gain (|Av(max)|) of the circuit is 50. • The centre frequency is 5 kHz.
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a) Show that if the low-pass filter circuit illustrated in Fig. 15.1 is scaled in both magnitude and frequency, the transfer function of the scaled circuit is the same as Eq. 15.1 with $s$ replaced by $s / k_{f}$ where $k_{f}$ is the frequency scale factor. b) In the prototype version of the low-pass filter circuit in Fig. $15.1, \omega_{c}=1 \mathrm{rad} / \mathrm{s}, C=1 \mathrm{F}$ $R_{2}=1 \Omega,$ and $R_{1}=1 / K$ ohms. What is the transfer function of the prototype circuit? c) Using the result obtained in (a), derive the transfer function of the scaled filter.
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