Question
What is the half-power bandwidth of a resonant circuit that has a resonant frequency of 7.1 MHz and a Q of 150?
Answer Options
- A) 157.8 Hz
- B) 315.6 Hz
- C) 47.3 kHz
- D) 23.67 kHz
Correct Answer: C
Explanation
The half-power bandwidth (\Delta F) of a resonant circuit is the measure of its selectivity. It is the frequency range between the two points where the circuit’s power response drops to half (-3 \text{ dB}) of the maximum response at the resonant frequency. The relationship between bandwidth, resonant frequency (F_R), and the Quality factor (Q) is given by the formula \Delta F = F_R / Q.
Using the given values, F_R = 7.1 \text{ MHz} and Q = 150, the half-power bandwidth is calculated as: \Delta F = \frac{7,100,000 \text{ Hz}}{150} \approx 47,333 \text{ Hz}. This means the bandwidth is approximately 47.3 kHz. This wide bandwidth suggests the circuit may be used as a broadband RF filter or in a low-Q impedance matching network.
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