Reference no: EM132287998
Questions -
Question 1 - Design a series RLC high-Q and a parallel RLC high-Q circuits from the listed component in Table 1. Both circuits must have 20 krad/s bandwidth and 200 krad/s resonant frequencies.
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Table 1
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Resistor
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Inductor
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Capacitor
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1kΩ
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2.5 mH
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2.5 nF
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5 kΩ
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5 mH
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50 nF
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10 kΩ
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10 mH
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2.5 pF
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15 kΩ
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50 mH
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50 pF
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20 kΩ
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0.5 H
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2.5 μF
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Show calculation or state the reason for each selected or neglected component. Draw and label the components used for both circuits clearly.
Question 2 - The student wants to use series RLC circuit to tune to 89.7MHz to set FM radio station. The student would like to avoid the objectionable frequency modulation station, which broadcast at 89.5MHz. In order to attain abovementioned issue, for a given input voltage signal from antenna, the student want the width of resonance to be narrow enough at 89.7MHz such that the current flowing in the designed circuit will be 10-2 times less at 89.5MHz than at 89.7MHz. Assume R = 0.1and use minimum L for practical considerations. Determine the following for abovementioned issues:
(i) The amplitude of your current in your circuit as a function of the angular frequency of the input signal (LR in terms of your circuit parameters, L, R, and C).
(ii) The ω0 (angular frequency) of the input signal.
(iii) LC values.
(iv) The quality factor for resonance.
(v) The ratio of the amplitude of the voltage across the inductor with the driving signal amplitude is the quality of the resonance and show that at resonance.
(vi) At resonance, the ratio of the amplitude of the voltage across the capacitor with the driving signal amplitude is the quality of the resonance.
(vii) The time averaged power at resonance that the signal delivers to the circuit.
(viii) The phase shift for the input signal at 89.5MHz.
(ix) The time averaged power for the input signal at 89.5MHz.