A medium-wave receiver uses a series resonant circuit: the emf induced in the antenna…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electronics, Instrumentation & Communication · Circuit foundations and passive networks

Electricity, Magnetism and Electromagnetism, Ch AC circuits: phasors, complex impedance, resonance and power

Problem

A medium-wave receiver uses a series resonant circuit: the emf induced in the antenna coil drives the coil (inductance

L = 0.10\,\mathrm{mH}

, resistance

R

) in series with a tuning capacitor

C

, which is assumed lossless. The circuit is to be tuned to a station at

1.20\,\mathrm{MHz}

, and the stations in this band are spaced

9.0\,\mathrm{kHz}

apart, so the half-power bandwidth of the circuit must be

9.0\,\mathrm{kHz}

. ((a)) Find the capacitance

C

needed. ((b)) Find the quality factor

Q_{\mathrm{f}}

the circuit must have. ((c)) Find the total loop resistance

R

that gives this bandwidth. ((d)) After detection the audio signal is passed through a first-order RC low-pass filter with

R_1 = 4.7\,\mathrm{k}\Omega

, to be given a corner frequency of

5.0\,\mathrm{kHz}

. Find the capacitance required.

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