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Numerical: To find frequency and capacitance of Oscillator for an FM radio receiver

For an FM radio receiver, when the consumer changes the channel ,the oscillator frequency changes. The frequency of the radio signal coming out of the mixer will be always be 10.7 MHz regardless of the channel selected. If the oscillator frequency is 99.2 MHz. What is the frequency of station selected? If a Hartley tuned oscillator is being used with a variable capacitor in the LC tank circuit, what is the value of the capacitance if the total inductance is 2.5 micro Hz.

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$I_f = 10.7MHz$

$f_o = 99.2MHz$

$I_f = f_o - f_s$

$f_s = f_o - I_f$

$\hspace{0.5cm} = 99.2 - 10.7$

$\hspace{0.5cm} = 88.5MHz$

$88.5 = \frac{1}{2 \pi \sqrt{LC}}$

$\sqrt{LC} = \frac{1}{2\pi \times 88.5 \times 10^6} = 1.29pF$

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