We want to design a tuner (actually a band pass filter) for an AM radio station

Question

We want to design a tuner (actually a band pass filter) for an AM radio station whose frequency is f= 700 kHz. The tuner must be able to detect the AM sidebands which are located at ±5 kHz (695 kHz and 705 kHz) from the central frequency. An easy way to achieve the above is to use a series RLC circuit and take VR for the output voltage. The resonant frequency of this circuit is that of the radio station. The rest of the circuit parameters are fixed by matching the 3 dB points of the circuit to the upper and lower sidebands. Calculate the value of R and L necessary for the above circuit if C 300 plF

Explanation / Answer

Resonant frequemcy

fr=1/2pisqrt(LC)

Therefore Inductance

L=1/4pi2f2C =1/4pi2*(700*103)*(300*10-12)

L=0.1723 mH

quality factor

Q=fr/BW=700/(705-695)=70

since

Q=2pfrL/R

therfore resistance

R=2pi*(700*103)*(0.1723*10-3)/70

R=10.83 ohms

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