9) Suppose an RLC circuit must be created by choosing an inductor and capacitor

Question

9) Suppose an RLC circuit must be created by choosing an inductor and capacitor to place in series with a 1200 ohm resistor. It will be used in an AM radio in which the RLC circuit will filter out all but the AM band of frequencies, which is 530 kHZ to 1150 kHz. The capacitor will have a variable capacitance while the inductor will have a fixed value.

a) To tune in the AM band frequencies, calculate an appropriate value for the inductance and determine the max and min capacitance of the capacitor.

b) If the capacitance has a resonant frequency of 800 kHz, estimate the fraction of the max power if the circuit was ran at 1000 kHz.

Explanation / Answer

a)

W^2 =1/LC

530*530*10^6 = 1/4*pi^2*L*C1

1150 *1150*10^6 = 1/4*pi^2*L*C2

assume L=0.01H

now we can solve for C1 and C2

b)

power = V^2/Z1

so fraction would be = Z(800) / Z(1000) = R+1/jw1c + jw1L / R + 1/jw2C + jw2L

where W1 = 2pi*800*10^3

w2 = 2pi*1000*10^3

so now we can calculate fraction also

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