Question

We would like to build an AM radio receiver using a series RLC circuit working as a bandpass filter. We have decided to use a 240 μH inductor with an internal resistance of 12Ω, and a variable capacitor whose capacitance varies between 40 to 360 pF. A radio “tunes” into a certain frequency by adjusting its receiver circuit so that it resonates at that frequency, and it only catches that specific frequency.

1. Determine the range of channel frequencies that we can tune into with this receiver;

2. Determine the receiver’s bandwidth;

3. AM radio broadcasting has assigned channels, ranging from 540 kHz to 1,700 kHz and spaced at 10-kHz intervals. What is the largest value of the internal resistance that would would allow us to avoid adjacent channel interference (i.e., listening to more than one channel at once)?

(For simplicity, assume that the bandwidth of the RLC circuit is symmetric around the resonance frequency)

Problem 3 We would like to build an AM radio receiver using a series RLC circuit working as bandpass filter. We have decided to use a 240 inductor with an internal resistance of 12, and a variable capacitor whose capacitance varies between 40 to 360 pF. A radio "tunes" into a certain frequency by adjusting its receiver circuit so that it resonates at that frequency, and it only catches that specific frequency. a (t) Figure 3: AM radio receiver 1. Determine the range of channel frequencies that we can tune into with this receiver; 2. Determine the receiver's bandwidth Problem 3 continued 3. AM radio broadcasting has assigned channels, ranging from 540 kHz to 1,700 kHz and spaced at 10-kHz intervals. What is the largest value of the internal resistance that would would allow us to avoid adjacent channel interference (i.e., listening to more than one channel at once)? carrier frequency of the station 530 kHz 1700 kHz 10 kHz Figure 4: AM radio band (For simplicity the resonance frequency) assume that the bandwidth of the RLC circuit is symmetric around :

Answer 1

L-240H R-12 c40pFto 360 pF

1. Resonant frequency of a series RLC circuit

fo 2πνLC

Where L = Inductance = 240 $\mu$H = 240 x 10^-6 H

    and C = capacitance = 40 pF to 360 pF = 40 x 10^-12 F to 360 x 10^-12 F

Minimum resonance frequency is obtained for the maximum value of capacitance and maximum resonance frequency is obtained for the minimum value of capacitance.

. fomin2TV240 x 10-6 x 360 x 10-12

             

=5.4146 x 103 H

             

0.54 MH

H 240 x 10-6 x 40 x 10-12 . fomaz

             

=1.6244 x 10 H

            

1.62 x MHE

2. Bandwidth of RLC circuit:

122 7.96 kH BW = 2T L 2T x 240 x 10-6H

3. If the channel frequencies are spaced at 10 kHz intervals and the RLC circuit bandwidth is symmetric about resonant frequency, Then to avoid interference between two adjacent channels the bandwidth must be $\small \leqslant$ 10 kHz. Below figure explains this phenomenon.

foi+1 foi |for-1 BW BW BW

i.e.

R 10 kH 2T L BW =

R 10 x 10H x 2T x 240 x 10 H15.08