For an FM radio receiver, when the consumer changes the channel, the oscillator frequency changes. The frequency of 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 capacitance if the total inductance is 2.5 µH. -

The output of the mixer stage is the difference of the two input frequencies.

$f_{station}=f_{oscillation}-f_{mixer}=99.2MHz-10.7MHz=88.5MHz$

The formula for the frequency for the oscillation is:

$$f=\dfrac{1}{2 \pi \sqrt{LC}}$$

Solving for C we have

$$C=\bigg(\dfrac{1}{2 \pi f}\bigg)^2\bigg(\dfrac1L\bigg)$$

If f=99.2 MHz and L=2.5 µH, C=1.03pF