### 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**.

Question

### 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**.

Knowee AI · Accepted Answer

### 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**.

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

Question

Solution

Break Down the Problem

Relevant Concepts

Analysis and Detail

Verify and Summarize

Final Answer

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