Quality Factor (Bandwidth)
Q = f₀ / BW
Quick answer
This calculator solves Q = f₀ / BW for Q Factor. With Resonant Frequency 100 kHz, Bandwidth 1 kHz, the result is 100. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The quality factor Q is a dimensionless measure of how selective or sharp a resonant circuit's frequency response is. It is defined as the ratio of the center (resonant) frequency to the -3dB bandwidth. A high Q circuit has a narrow passband and rejects frequencies outside its resonant peak very effectively, while a low Q circuit has a broad response. Q also represents the ratio of energy stored to energy dissipated per cycle, multiplied by 2π. In practical terms, a Q of 10 means the bandwidth is one-tenth of the center frequency.
Variables
- Q — Quality factor (dimensionless)
- f₀ — Resonant (center) frequency in hertz (Hz)
- BW — Bandwidth at -3dB points in hertz (Hz)
Practical Notes
Typical Q values: simple LC circuits 10-100, crystal oscillators 10,000-100,000, optical cavities over 10^9. Higher Q means better frequency selectivity but also slower transient response and tighter component tolerances required.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Q | Q Factor | — | — |
| f0 | Resonant Frequency | kHz | Hz, kHz, MHz, GHz |
| BW | Bandwidth | Hz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Resonant Frequency 100 kHz, Bandwidth 1 kHz
- 2. The relation: Q = f₀ / BW
- 3. Substitute: f0 = 100 kHz, BW = 1 kHz
- 4. Result: Q Factor = 100
Worked examples
Minimum range
Given: Resonant Frequency 100 Hz, Bandwidth 5 Hz
Result: Q Factor = 20
Low range
Given: Resonant Frequency 1 kHz, Bandwidth 50 Hz
Result: Q Factor = 20
Typical
Given: Resonant Frequency 100 kHz, Bandwidth 1 kHz
Result: Q Factor = 100
High range
Given: Resonant Frequency 0.5 MHz, Bandwidth 20 kHz
Result: Q Factor = 25
Maximum range
Given: Resonant Frequency 5 MHz, Bandwidth 0.2 MHz
Result: Q Factor = 25
Solving for each variable
Solve for Q Factor
Resonant Frequency 100 Hz, Bandwidth 5 Hz → 20
Solve for Resonant Frequency
Q Factor 0.025, Bandwidth 5 Hz → 0.125 Hz
Solve for Bandwidth
Q Factor 0.025, Resonant Frequency 100 Hz → 4 kHz
How Q Factor changes with Resonant Frequency
| Resonant Frequency (input) | Q Factor (result) |
|---|---|
| 10 kHz | 10 |
| 25 kHz | 25 |
| 50 kHz | 50 |
| 75 kHz | 75 |
| 100 kHz | 100 |
| 150 kHz | 150 |
| 0.2 MHz | 200 |
| 0.4 MHz | 400 |
| 0.7 MHz | 700 |
| 1 MHz | 1000 |
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<p><a href="https://vbatpower.com/formulas/quality-factor-bw/">Quality Factor (Bandwidth)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Quality Factor (Bandwidth)?
Use Q = f₀ / BW. With Resonant Frequency 100 kHz, Bandwidth 1 kHz, Q Factor works out to 100.
What is the formula for Quality Factor (Bandwidth)?
The formula is Q = f₀ / BW. The quality factor Q is a dimensionless measure of how selective or sharp a resonant circuit's frequency response is.
How do you find Resonant Frequency when you know the other values?
Rearrange for Resonant Frequency: with Q Factor 0.025, Bandwidth 5 Hz, Resonant Frequency is 0.125 Hz.
How do you find Bandwidth when you know the other values?
Rearrange for Bandwidth: with Q Factor 0.025, Resonant Frequency 100 Hz, Bandwidth is 4 kHz.
Related Concepts
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