Calculator
Example Data Table
| Mode | Inputs | Computed Bandwidth | Notes |
|---|---|---|---|
| From f₀ and Q | f₀ = 1.00 kHz, Q = 25 | Δf = 40 Hz | Narrower bandwidth for higher Q. |
| Series RLC | R = 10 Ω, L = 10 mH | Δf ≈ 159.15 Hz | Uses Δf = R/(2πL). |
| Half‑power | f₁ = 950 Hz, f₂ = 1050 Hz | Δf = 100 Hz | f₀ = √(f₁f₂) ≈ 999.37 Hz. |
Formula Used
How to Use This Calculator
- Select a calculation mode based on available inputs.
- Enter values using the correct units for frequency, L, and C.
- Click Calculate to display results above the form.
- Use Download CSV or Download PDF from the result box.
- If you have f₁ and f₂, prefer the half‑power method for accuracy.
Technical Article
1) What resonance bandwidth represents
Resonance bandwidth (Δf) is the frequency span around the peak where the response stays within the half‑power level. A narrow Δf means strong selectivity and low losses, while a wide Δf indicates heavier damping and faster decay.
2) Bandwidth and quality factor relationship
For lightly damped resonators, the key link is Δf = f₀/Q. For example, if f₀ = 1.00 MHz and Q = 200, the bandwidth is about 5.00 kHz. If Q drops to 50, bandwidth increases to about 20.0 kHz.
3) Half‑power method for measured data
When you have sweep data, compute Δf from the half‑power points: Δf = f₂ − f₁ and f₀ = √(f₁f₂). If f₁ = 9.95 kHz and f₂ = 10.05 kHz, then Δf = 100 Hz, f₀ ≈ 10.00 kHz, and Q ≈ 100. This method naturally includes loading from probes and fixtures.
4) Series RLC bandwidth behavior
In a series RLC, losses are modeled mainly by series resistance R, giving Δf = R/(2πL). Example: R = 10 Ω and L = 10 mH yields Δf ≈ 159.15 Hz. If you also enter C, the tool can derive f₀ = 1/(2π√(LC)) and Q = ω₀L/R for consistent reporting.
5) Parallel RLC and high‑impedance resonators
For a parallel RLC, a shunt resistance sets the damping, so Δf = 1/(2πRC). Example: R = 50 kΩ and C = 1 nF gives Δf ≈ 3.18 kHz. Adding L allows f₀ and Q = R√(C/L) to be estimated for tank circuits.
6) Damping ratio for mechanical resonance
In vibration and control work, damping ratio ζ can estimate bandwidth using Δf ≈ 2ζf₀ and Q ≈ 1/(2ζ). With ζ = 0.02 at f₀ = 30 Hz, Δf ≈ 1.20 Hz and Q ≈ 25. Use this mainly when ζ comes from ring‑down identification.
7) Choosing the right input mode
Use Q mode when a datasheet provides f₀ and Q. Use RLC modes when you know the component values and the dominant loss element. Use half‑power mode when you measured f₁ and f₂. Use damping mode when ζ is the most reliable parameter you have.
8) Interpretation, units, and reporting
The calculator evaluates internally in Hz, then scales results to a readable unit. For clear documentation, record f₀, Δf, and Q together, then export to CSV or PDF so your design notes, test logs, and validation reports remain consistent.
FAQs
1) What does the 3 dB bandwidth mean?
It is the frequency span between the two points where power drops to half of the peak value. For voltage magnitude, it corresponds to about 0.707 of the peak amplitude in many resonant responses.
2) When should I prefer the half‑power method?
Prefer it when you have measured cutoff frequencies from a sweep or frequency response test. It captures real‑world effects such as loading, component tolerances, and small asymmetry around the peak.
3) Is Δf = f₀/Q always valid?
It is a good approximation for lightly damped resonators and many filters. For heavy damping, strong nonlinearity, or unusual response shapes, use measured half‑power points instead of relying only on Q.
4) Why do series and parallel RLC formulas differ?
Series RLC losses appear mainly through R in series with L and C, giving Δf = R/(2πL). Parallel RLC losses are represented by a shunt resistance, leading to Δf = 1/(2πRC).
5) Can I compute f₀ if I only enter L and C?
Yes, when both L and C are entered in the RLC modes, the calculator derives f₀ = 1/(2π√(LC)). Bandwidth still depends on R in the chosen topology, so R is required.
6) What unit should I use for best accuracy?
Use units that keep numbers in a normal range to reduce typing mistakes. The calculator converts internally, so accuracy depends on correct values, not the selected unit. Auto output picks a readable scale.
7) What if my calculated bandwidth seems too large?
Check that R, L, and C units are correct and that cutoff frequencies are entered in the same unit. Large bandwidth can also indicate low Q, strong damping, or heavy loading from measurement equipment.