The television 6 between frequencies 82 MHz and 88 MHz, with the video and audio

Question

The television 6 between frequencies 82 MHz and 88 MHz, with the video and audio using different parts of this frequency range. To watch (and listen) to the channel properly, the tuner circuit in a television must in the middle of this range (85 MHz) and produce a current over the whole range of at least 50% of the peak current at resonant frequency. A particular television tuning circuit is built with a 14.0 pF capacitor and a variable inductor. What value should the inductor have to watch channel 6? What value should the resistor be in order for the current at both 82 MHz and 88 MHz to be at least 50% of the current at the resonant frequency?

Explanation / Answer

A)

Resonate frequency

f=1/2pisqrt(LC)

=>L=1/4pi2f2C =1/4pi2*(85*106)2(14*10-12)

L=2.5*10-7 H or 0.25 uH

b)

at f=82 MHz

XL=2pifL =2pi*(82*106)(2.5*10-7)=129 ohms

XC=1/2pifC =1/2pi*(82*106)(14*10-12)=138.6 ohms

Impedance

Z=sqrt(R2+(XL-XC)2)=sqrt(R2+92.9)

Given

I=0.5Iresonant

V/Z =0.5(V/R)

2R=sqrt(R2+92.9)

4R2=R2+92.9

R=sqrt(92.9/3) =5.56 ohms

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