Question

FM radio stations have carrier frequencies that are separated by 0.20 MHz. When the radio is tuned to a station, such as 100.4 MHz, the resonance width of the receiver circuit should be much smaller than 0.2 MHz so that adjacent stations are not received. If f0 = 100.4 MHz and delta_f = 0.05 MHz, what is the Q factor for the circuit?

Q = ____

Answer 1

The Q factor for an FM radio receiver circuit with a resonance frequency of 100.4 MHz and a resonance width of 0.05 MHz is calculated using the formula Q = f0 / delta_f, which gives a Q factor of 2008.

Step-by-step explanation:

The Q factor, also known as the quality factor, of a circuit is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is calculated as the resonance frequency of the circuit divided by the resonance width (delta_f). Therefore, for an FM radio receiver circuit with a resonance frequency (f0) of 100.4 MHz and a resonance width (delta_f) of 0.05 MHz, the Q factor can be calculated using the formula Q = f0 / delta_f.

By plugging in the given values:

Q = 100.4 MHz / 0.05 MHz = 2008

Thus, the Q factor for the circuit should be 2008. It's important to have a high Q factor for an FM receiver to filter out adjacent station frequencies and avoid interference.