Calculate AM, FM, and PM modulation index, bandwidth (Carson's rule), sideband frequencies, carrier power, and efficiency for radio signals.
Modulation is the process of encoding information onto a carrier wave by varying its amplitude, frequency, or phase. This calculator handles three fundamental types: Amplitude Modulation (AM), Frequency Modulation (FM), and Phase Modulation (PM).
For AM signals, enter carrier and message amplitudes to find the modulation index m = Am/Ac, total power, sideband power, and efficiency. The calculator warns you when over-modulation occurs (m > 1), which causes signal distortion and spectral splatter.
For FM and PM, enter the frequency deviation to compute the modulation index β = Δf/fm and the bandwidth using Carson's rule: BW = 2(Δf + fm). The tool also shows significant sideband counts and carrier frequency allocations for common radio bands from AM broadcast through 5G millimeter wave.
Whether you are designing a radio transmitter, studying for a communications exam, or debugging a modulator circuit, this calculator gives you every key parameter in one place. Preset buttons load typical values for AM broadcast, FM radio, SSB shortwave, and VHF communications.
Understanding modulation parameters is essential for radio communication system design. This calculator eliminates manual computation of modulation index, bandwidth, and power for AM, FM, and PM signals.
It is especially useful for students, RF engineers, and amateur radio operators who need to verify modulator designs, estimate channel bandwidth, or compare modulation schemes.
AM: m = Am/Ac, BW = 2·fm, Pt = Pc(1 + m²/2), η = (m²/2)/(1 + m²/2) × 100. FM/PM: β = Δf/fm, BW = 2(Δf + fm) (Carson's rule), Pc = Ac²/(2R). Sidebands: USB = fc + fm, LSB = fc − fm.
Result: m = 0.50, BW = 10 kHz, Pt = 56.25 W, η = 11.11%
Modulation index m = 5/10 = 0.50. Bandwidth = 2 × 5 kHz = 10 kHz. Carrier power = 50 W. Total power = 50(1 + 0.25/2) = 56.25 W. Efficiency = 6.25/56.25 = 11.1%.
Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.
Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes
Use this for repeatability, keep assumptions explicit. ## Practical Notes
Track units and conversion paths before applying the result. ## Practical Notes
Use this note as a quick practical validation checkpoint. ## Practical Notes
Keep this guidance aligned to the calculator’s expected inputs. ## Practical Notes
Use as a sanity check against edge-case outputs. ## Practical Notes
Capture likely mistakes before publishing this value. ## Practical Notes
Document expected ranges when sharing results.
Over-modulation causes envelope distortion and spectral splatter into adjacent channels. The signal can no longer be demodulated correctly with a simple envelope detector.
FM trades bandwidth for noise immunity. Carson's rule gives BW = 2(Δf + fm), which is wider than AM's 2·fm, but FM provides much better SNR because information is in frequency variations rather than amplitude.
Carson's rule estimates FM bandwidth as BW = 2(Δf + fm), where Δf is the peak frequency deviation and fm is the highest modulating frequency. It captures about 98% of the signal power.
In PM, the instantaneous phase is proportional to the message signal; in FM, the instantaneous frequency is proportional. Mathematically, PM of a sinusoid produces the same spectrum as FM, but the modulation index scales differently with modulating frequency.
For AM, only the sidebands carry information. Efficiency η = m²/(2 + m²) × 100. At 100% modulation (m = 1), efficiency is only 33.3%, meaning two-thirds of the power is wasted in the carrier.
AM allows multiple stations to transmit on the same frequency and be heard simultaneously (the "party line" effect), which is critical for aviation safety. FM exhibits the capture effect, where only the strongest signal is heard.