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Q Factor in Band-Pass Filter

 

Q Factor - Bandpass Filter

Q Factor in Band-Pass Filter

Definition

The Q factor (Quality Factor) defines how selective a band-pass filter is. It determines how narrow or wide the frequency response is around the center frequency.

Formula

Q = f₀ / BW

Where:
f₀ = center frequency
BW = bandwidth = (fH - fL)

Circuit Form (RLC Bandpass)

Q = (1/R) √(L/C)

or

Q = ω₀L / R

Effect of Q Factor

Q Value Behavior
Low Q (< 1) Wide bandwidth, less selective
Medium Q (5–10) Balanced selectivity
High Q (> 20) Narrow bandwidth, highly selective

Summary

The Q factor controls the sharpness of the band-pass filter response. Higher Q means sharper peak and narrower bandwidth.

Cutoff Frequency & Q Factor

Effect of Cutoff Frequency (50 Hz) and Q Factor (Q = 1)

Given

Cutoff frequency (fc) = 50 Hz
Q factor = 1

Low-Pass Filter (LPF)

- Passes frequencies below cutoff
- Cutoff = 50 Hz

Range: 0 Hz → 50 Hz

High-Pass Filter (HPF)

- Passes frequencies above cutoff
- Cutoff = 50 Hz

Range: 50 Hz → ∞

Band-Pass Filter (BPF)

Q factor defines bandwidth:

Q = f₀ / BW

Given:
f₀ = 50 Hz
Q = 1

Bandwidth:

BW = f₀ / Q = 50 / 1 = 50 Hz

Cutoff frequencies:

fL = 50 - 25 = 25 Hz
fH = 50 + 25 = 75 Hz

Final BPF Range: 25 Hz → 75 Hz

Summary Table

Filter Type Frequency Range
Low-Pass Filter 0 – 50 Hz
High-Pass Filter 50 Hz – ∞
Band-Pass Filter (Q=1) 25 – 75 Hz

Summary

The cutoff frequency defines LPF/HPF boundaries, while Q factor controls bandwidth only in band-pass filters. Lower Q → wider bandwidth, higher Q → narrower bandwidth.

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