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5) Consider the RLC tank circuit shown in Figure 4 being driven by an AC current source. Current Source (→ Imn R_L V_Out a) Calculate the amplitude response Vout as a function of the frequency w of the current source. Use wo = 1/ Figure 4: RLC resonator for prelab Problem PL5. √LC for the resonant frequency (rad/sec). What is the magnitude of the complex amplitude response G(w) = |H(w)|? If the current has amplitude Io, what is the voltage V₁ on resonance at frequency wo? Note that in this case, H(w) = Vout(W)/Io (w), where Io(w) is the current emitted by the current source. b) Calculate the detuning Aw required to reduce G(w) by √√2, which is the 3dB point of the resonator. The detuning is the frequency shift away from the resonant frequency. Use this to determine the bandwidth BW and to calculate the Q of the filter. Express your results in terms of R₁, L, and C. Hint: you will want to set your expression for G(w) = 1/√√2 and evaluate your expression for small changes from the resonance frequency Aw = w-wo, where the detuning Aw is small compared to wo. You should then neglect terms of order (Aw/wo)² and solve for Aw. If you do not do this, your solution is likely to turn into an algebraic mess. Finally, remember that the detuning is only one half the bandwidth, so BW = 2^w.

5) Consider the RLC tank circuit shown in Figure 4 being driven by an AC current source. Current Source (→ Imn R_L V_Out a) Calculate the amplitude response Vout as a function of the frequency w of the current source. Use wo = 1/ Figure 4: RLC resonator for prelab Problem PL5. √LC for the resonant frequency (rad/sec). What is the magnitude of the complex amplitude response G(w) = |H(w)|? If the current has amplitude Io, what is the voltage V₁ on resonance at frequency wo? Note that in this case, H(w) = Vout(W)/Io (w), where Io(w) is the current emitted by the current source. b) Calculate the detuning Aw required to reduce G(w) by √√2, which is the 3dB point of the resonator. The detuning is the frequency shift away from the resonant frequency. Use this to determine the bandwidth BW and to calculate the Q of the filter. Express your results in terms of R₁, L, and C. Hint: you will want to set your expression for G(w) = 1/√√2 and evaluate your expression for small changes from the resonance frequency Aw = w-wo, where the detuning Aw is small compared to wo. You should then neglect terms of order (Aw/wo)² and solve for Aw. If you do not do this, your solution is likely to turn into an algebraic mess. Finally, remember that the detuning is only one half the bandwidth, so BW = 2^w.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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5) Consider the RLC tank circuit shown in Figure 4 being driven by an AC current source. Current Source (→ Imn R_L V_Out a) Calculate the amplitude response Vout as a function of the frequency w of the current source. Use wo = 1/ Figure 4: RLC resonator for prelab Problem PL5. √LC for the resonant frequency (rad/sec). What is the magnitude of the complex amplitude response G(w) = |H(w)|? If the current has amplitude Io, what is the voltage Von resonance at frequency wo? Note that in this case, H(w) = Vout(W)/Io (w), where Io(w) is the current emitted by the current source. b) Calculate the detuning Aw required to reduce G(w) by √√2, which is the 3dB point of the resonator. The detuning is the frequency shift away from the resonant frequency. Use this to determine the bandwidth BW and to calculate the Q of the filter. Express your results in terms of R₁, L, and C. Hint: you will want to set your expression for G(w) = 1/√√2 and evaluate your expression for small changes from the resonance frequency Aw = w-wo, where the detuning Aw is small compared to wo. You should then neglect terms of order (Aw/wo)² and solve for Aw. If you do not do this, your solution is likely to turn into an algebraic mess. Finally, remember that the detuning is only one half the bandwidth, so BW = 2^w.
Transcribed Image Text:5) Consider the RLC tank circuit shown in Figure 4 being driven by an AC current source. Current Source (→ Imn R_L V_Out a) Calculate the amplitude response Vout as a function of the frequency w of the current source. Use wo = 1/ Figure 4: RLC resonator for prelab Problem PL5. √LC for the resonant frequency (rad/sec). What is the magnitude of the complex amplitude response G(w) = |H(w)|? If the current has amplitude Io, what is the voltage Von resonance at frequency wo? Note that in this case, H(w) = Vout(W)/Io (w), where Io(w) is the current emitted by the current source. b) Calculate the detuning Aw required to reduce G(w) by √√2, which is the 3dB point of the resonator. The detuning is the frequency shift away from the resonant frequency. Use this to determine the bandwidth BW and to calculate the Q of the filter. Express your results in terms of R₁, L, and C. Hint: you will want to set your expression for G(w) = 1/√√2 and evaluate your expression for small changes from the resonance frequency Aw = w-wo, where the detuning Aw is small compared to wo. You should then neglect terms of order (Aw/wo)² and solve for Aw. If you do not do this, your solution is likely to turn into an algebraic mess. Finally, remember that the detuning is only one half the bandwidth, so BW = 2^w.
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