Bandpass Bandwidth
BW = f2 − f1
Quick answer
This calculator solves BW = f2 - f1 for Bandwidth. With Lower Cutoff 2.2 kHz, Upper Cutoff 4.7 kHz, the result is 2.5 kHz. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The bandwidth of a bandpass filter is simply the difference between the upper and lower -3dB cutoff frequencies. It defines the range of frequencies that pass through the filter with less than 3 dB of attenuation. A narrow bandwidth means the filter is highly selective (high Q factor), while a wide bandwidth passes a broader range of frequencies. The center frequency is the geometric mean of the cutoff frequencies: f0 = √(f1 × f2), and the quality factor is Q = f0 / BW. Bandpass filters are essential in radio receivers, spectrum analyzers, and communication systems.
Variables
- BW — Bandwidth (Hz)
- f1 — Lower -3dB cutoff frequency (Hz)
- f2 — Upper -3dB cutoff frequency (Hz)
Practical Notes
In communication systems, channel bandwidth determines the maximum data rate (Shannon's theorem). Voice channels use 3.1 kHz bandwidth (300-3400 Hz), AM radio uses 10 kHz, FM radio uses 200 kHz, and WiFi uses 20-160 MHz channels. Narrower bandwidth also means less noise power captured by the receiver.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| BW | Bandwidth | Hz | Hz, kHz, MHz, GHz |
| f1 | Lower Cutoff | Hz | Hz, kHz, MHz, GHz |
| f2 | Upper Cutoff | Hz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Lower Cutoff 2.2 kHz, Upper Cutoff 4.7 kHz
- 2. The relation: BW = f2 - f1
- 3. Substitute: f1 = 2.2 kHz, f2 = 4.7 kHz
- 4. Result: Bandwidth = 2.5 kHz
Worked examples
Minimum range
Given: Lower Cutoff 11 Hz, Upper Cutoff 23.5 Hz
Result: Bandwidth = 12.5 Hz
Low range
Given: Lower Cutoff 110 Hz, Upper Cutoff 0.235 kHz
Result: Bandwidth = 125 Hz
Typical
Given: Lower Cutoff 2.2 kHz, Upper Cutoff 4.7 kHz
Result: Bandwidth = 2.5 kHz
High range
Given: Lower Cutoff 44 kHz, Upper Cutoff 94 kHz
Result: Bandwidth = 50 kHz
Maximum range
Given: Lower Cutoff 0.44 MHz, Upper Cutoff 0.94 MHz
Result: Bandwidth = 0.5 MHz
Solving for each variable
Solve for Bandwidth
Lower Cutoff 11 Hz, Upper Cutoff 23.5 Hz → 12.5 Hz
Solve for Lower Cutoff
Bandwidth 5 Hz, Upper Cutoff 23.5 Hz → 18.5 Hz
Solve for Upper Cutoff
Bandwidth 5 Hz, Lower Cutoff 11 Hz → 16 Hz
How Bandwidth changes with Lower Cutoff
| Lower Cutoff (input) | Bandwidth (result) |
|---|---|
| 0.22 kHz | 4.48 kHz |
| 0.55 kHz | 4.15 kHz |
| 1.1 kHz | 3.6 kHz |
| 1.65 kHz | 3.05 kHz |
| 2.2 kHz | 2.5 kHz |
| 3.3 kHz | 1.4 kHz |
| 4.4 kHz | 0.3 kHz |
The same result in other units
| Unit | Value |
|---|---|
| Hz | 2500 |
| kHz | 2.5 |
| MHz | 0.0025 |
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<p><a href="https://vbatpower.com/formulas/bandpass-bw/">Bandpass Bandwidth</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Bandpass Bandwidth?
Use BW = f2 - f1. With Lower Cutoff 2.2 kHz, Upper Cutoff 4.7 kHz, Bandwidth works out to 2.5 kHz.
What is the formula for Bandpass Bandwidth?
The formula is BW = f2 - f1. The bandwidth of a bandpass filter is simply the difference between the upper and lower -3dB cutoff frequencies.
How do you find Lower Cutoff when you know the other values?
Rearrange for Lower Cutoff: with Bandwidth 5 Hz, Upper Cutoff 23.5 Hz, Lower Cutoff is 18.5 Hz.
How do you find Upper Cutoff when you know the other values?
Rearrange for Upper Cutoff: with Bandwidth 5 Hz, Lower Cutoff 11 Hz, Upper Cutoff is 16 Hz.
What units does Bandpass Bandwidth use?
Bandwidth is shown in Hz, kHz, MHz. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
All Filters formulas →Need more features?
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