A variable capacitor with a range from 11 to 514 pF is used with a coil to form

Question

A variable capacitor with a range from 11 to 514 pF is used with a coil to form a variable-frequency LC circuit to tune the input to a radio. (a) What is the ratio of maximum frequency to minimum frequency that can be obtained with such a capacitor? If this circuit is to obtain frequencies from 0.77 MHz to 2.00 MHz, the ratio computed in (a) is too large. By adding a capacitor in parallel to the variable capacitor, this range can be adjusted. To obtain the desired frequency range, (b) what capacitance in picofarads should be added and (c) what inductance should the coil have?

Explanation / Answer

a)

Frequency of oscillation is

f=1/2pi*sqrt(LC)

Maximum frequency occurs when C is minimum

fmax=1/2pi*sqrt(LCmin)

Minimum frequency occurs when C is maximum

fmin=1/2pi*sqrt(LCmax]

=>fmax/fmin=sqrt[Cmax/Cmin]=sqrt[514/11]

fmax/fmin=6.84

b)

An additional capacitance C is chosen ,so the ratio of frequencies is

fmax/fmin=2/0.77=2.6

sqrt[C+514/C+11]=2.6

C+514/C+11=6.76

C+514=6.76C+74.36

C=76.33 pF

c)

for f=0.77 MHz minimum frequency is

C=514+76.33=590.33 pF

Inductance is

L=1/4pi2f2C =1/4pi2*(0.77*106)2*(590.33*10-12)

L=7.24*10-5 H or 72.37 uH

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