Example data table
| Example | Method | Inputs | Modulation frequency (fm) |
|---|---|---|---|
| 1 | From period | T = 2 ms | fm = 500 Hz |
| 2 | From angular frequency | ωm = 12,566.370 rad/s | fm = 2,000 Hz |
| 3 | From deviation and index | Δf = 5 kHz, β = 2.5 | fm = 2 kHz |
| 4 | From sideband spacing | fc = 1.000 MHz, fsb = 1.002 MHz | fm = 2 kHz |
Formula used
- fm = 1 / T (when period T is known)
- fm = ωm / (2π) (when angular frequency ωm is known)
- β = Δf / fm ⇒ fm = Δf / β (FM relationship)
- fm = |fsb − fc| (spacing between carrier and any sideband)
- Sidebands: f = fc ± n·fm for n = 1, 2, 3, …
How to use this calculator
- Select the method that matches your known data.
- Enter the required values and pick appropriate units.
- Optionally add a carrier frequency to list sidebands.
- Click Calculate to show results above the form.
- Use CSV or PDF buttons to export your output.
Modulation frequency guide
1) What “modulation frequency” means
Modulation frequency (fm) is the rate at which a carrier is varied by the message signal. In AM it matches the tone or baseband component; in FM/PM it is the frequency of the modulating waveform that creates frequency or phase changes.
2) Period-to-frequency conversion
If you know the modulation period T, convert with fm = 1/T. For example, T = 2 ms gives fm = 500 Hz. This method is common when you measure time spacing on an oscilloscope.
3) Using angular frequency
Some instruments report angular frequency ωm in rad/s. Convert with fm = ωm / (2π). A reading of 12,566.37 rad/s corresponds to 2,000 Hz. This avoids manual π mistakes when your data is already in radians.
4) Sideband spacing rule
For a single-tone modulation, spectral lines appear at fc ± n·fm. The spacing between adjacent sidebands is fm. If you see peaks at 1.000 MHz and 1.002 MHz, the spacing is 2 kHz, so fm = 2 kHz.
5) Deviation and modulation index
In FM, the modulation index is β = Δf / fm, where Δf is peak frequency deviation. Rearranging gives fm = Δf / β. Example: Δf = 5 kHz and β = 2.5 yields fm = 2 kHz.
Bandwidth estimates often use Carson’s rule: BW ≈ 2(Δf + fm). With Δf = 75 kHz and fm = 15 kHz, the occupied bandwidth is roughly 180 kHz, a helpful check for spectrum masks.
6) Typical real-world ranges
Audio modulation commonly spans 20 Hz to 20 kHz. Broadcast FM stereo uses baseband components up to about 15 kHz for the main audio, while telemetry and control links may use much lower fm values (sub‑Hz to hundreds of Hz) for slow sensor changes.
7) Units and “gotchas”
Most errors come from mixing ms with s, kHz with Hz, or rad/s with Hz. Always convert to base units before calculating, then convert back for display. Also note that “sideband spacing” must be measured between adjacent lines, not from carrier to a distant harmonic.
8) Why this calculator is useful
This tool cross-checks fm from time-domain, frequency-domain, and FM parameters, so you can validate measurements quickly. It also lists sidebands from a chosen carrier, helping you sanity-check spectra during alignment and troubleshooting. These checks reduce rework and speed up verification in lab and field work.
FAQs
1) Is modulation frequency the same as carrier frequency?
No. The carrier (fc) is the high-frequency signal being varied. The modulation frequency (fm) is the rate of the message waveform that causes the variation, usually much lower than fc.
2) How do I get modulation frequency from period?
Measure the modulation period T in seconds, then compute fm = 1/T. If you measure in milliseconds, convert to seconds first (divide by 1000) to avoid a 1000× error.
3) What does sideband spacing tell me?
For a single-tone modulation, adjacent spectral lines are separated by fm. Measure the frequency difference between neighboring sidebands (not between distant peaks), and that difference is the modulation frequency.
4) Can modulation frequency be higher than the carrier?
In practical analog modulation, fm is typically far lower than fc. Extremely high fm values would require wide bandwidth and can violate hardware limits, filtering, and spectral regulations.
5) When should I use the deviation and index method?
Use it for FM when you know peak deviation Δf and modulation index β. The calculator applies fm = Δf/β, which is useful when your analyzer reports deviation and your spec lists an index.
6) Why does the calculator ask for units?
Because Hz, kHz, ms, and rad/s represent different scales. Choosing units lets the tool convert safely, show readable results, and prevent common mistakes like mixing milliseconds with seconds or radians per second with hertz.
7) What sidebands does the calculator list?
If you enter a carrier, it lists fc ± n·fm for several orders. This is a quick sanity check for where tones should appear on a spectrum display under ideal, single-tone conditions.