A resonant circuit responds strongly only near its centre frequency. The higher its quality factor Q, the narrower the band – radio receivers use high-Q circuits to pick out one station.
How to use the Frequency Bandwidth Calculator
- Centre frequency f₀
- Quality factor Q
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the centre (resonant) frequency and the quality factor.
Inputs explained
| Field | What to enter |
|---|---|
| Centre frequency f₀ | Units: MHz, kHz, GHz, Hz |
| Quality factor Q | A number |
What each result means
- Bandwidth = [Centre frequency f₀]÷[Quality factor Q]
- Lower cutoff frequency = [Centre frequency f₀]×(sqrt(1 + 1÷(4×[Quality factor Q]^2)) – 1÷(2×[Quality factor Q]))
- Upper cutoff frequency = [Centre frequency f₀]×(sqrt(1 + 1÷(4×[Quality factor Q]^2)) + 1÷(2×[Quality factor Q]))
Example values
How the main result changes when Centre frequency f₀ changes and everything else stays at the example values above:
| Centre frequency f₀ (MHz) | Bandwidth (kHz) |
|---|---|
| 5.35 | 107 |
| 8.02 | 160.5 |
| 10.7 | 214 |
| 13.38 | 267.5 |
| 16.05 | 321 |
| 21.4 | 428 |
Formula
BW = f₀/Q, f₁,₂ = f₀·(√(1 + 1/(4Q²)) ∓ 1/(2Q))
Worked example
Inputs — Centre frequency f₀: 10.7 MHz; Quality factor Q: 50.
Results — Bandwidth = 214 kHz; Lower cutoff frequency = 10.593535 MHz; Upper cutoff frequency = 10.807535 MHz.
Key terms
- Quality factor
- f₀ divided by bandwidth.
Frequently asked questions
What does Q measure?
How sharply a circuit resonates – centre frequency divided by bandwidth.
Are the cutoffs symmetric?
Geometrically: f₁·f₂ = f₀².
What is a typical Q?
10–100 for LC circuits, thousands for quartz crystals.
What does −3 dB mean?
Half-power points.