A band-pass filter has a bandwidth of 250Hz and center frequency of 866Hz. Find the quality factor of the filter?a.6.42b.3.46c.4.84d.None of these

Break Down the Problem

1. Identify the parameters given for the band-pass filter:
   • Bandwidth (BW) = 250 Hz
   • Center Frequency (f₀) = 866 Hz

Relevant Concepts

2. The quality factor (Q) for a band-pass filter can be calculated using the formula: $Q = \frac{f₀}{BW}$ where $f₀$ is the center frequency and $BW$ is the bandwidth.

Analysis and Detail

3. Substitute the given values into the formula: $Q = \frac{866 \, \text{Hz}}{250 \, \text{Hz}}$ Performing the division: $Q = 3.464$

Verify and Summarize

4. Rounding the value obtained gives us:
   • $Q \approx 3.46$

Final Answer

The quality factor of the filter is approximately $3.46$. Thus, the correct answer is b. 3.46.