A band-pass filter has a bandwidth of 250Hz and center frequency of 866Hz. Find the quality factor of the filter?

Question

A band-pass filter has a bandwidth of 250Hz and center frequency of 866Hz. Find the quality factor of the filter?

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Solution

1. Break Down the Problem

To find the quality factor (Q) of a band-pass filter, we need to use the formula: $Q = \frac{f_c}{BW}$ where:

$f_c$ = center frequency
$BW$ = bandwidth

2. Relevant Concepts

Center frequency $f_c$ is given as 866 Hz.
Bandwidth $BW$ is given as 250 Hz.

3. Analysis and Detail

Substituting the known values into the formula: $Q = \frac{866 \, \text{Hz}}{250 \, \text{Hz}}$

4. Verify and Summarize

Now, we perform the calculation: $Q = \frac{866}{250} \approx 3.464$

Final Answer

The quality factor $Q$ of the filter is approximately 3.464.

This problem has been solved

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