Modulation Calculator

Calculate the modulation index, bandwidth, and sideband power for AM and FM modulation schemes used in radio communications.

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What Is Modulation?

Modulation is the process of encoding information (audio, data) onto a carrier wave for radio transmission. The carrier is a high-frequency sinusoidal wave whose amplitude, frequency, or phase is varied according to the information signal. Amplitude Modulation (AM) varies the carrier's amplitude, while Frequency Modulation (FM) varies its instantaneous frequency. Understanding modulation parameters is essential for radio system design, spectrum management, and signal processing.

The modulation index is the key parameter determining signal quality and bandwidth. For AM, it ranges from 0 (no modulation) to 1 (100% modulation). Exceeding m=1 causes overmodulation and distortion. For FM, the modulation index can be any positive value and determines whether the signal is narrowband (m << 1) or wideband (m >> 1).

Modulation Formulas

AM: BW = 2fm  |  Ptotal = Pc(1 + m²/2)
FM: m = Δf/fm  |  BW ≈ 2(Δf + fm) (Carson's rule)

AM vs FM Comparison

ParameterAMFM
Bandwidth2fm (narrow)2(Δf + fm) (wide)
Noise immunityPoorExcellent
Power efficiencyLow (carrier carries no info)High (all power is useful)
Typical useAM radio, aviationFM radio, TV audio

Frequently Asked Questions

Why is FM better quality than AM?

FM is inherently resistant to amplitude noise because information is in the frequency, not amplitude. An FM receiver can clip amplitude variations (limiters) without losing information. FM also uses wider bandwidth, which by the noise-bandwidth tradeoff provides better signal-to-noise ratio. Commercial FM broadcasts use 200 kHz bandwidth vs 10 kHz for AM.

What is overmodulation in AM?

When m exceeds 1, the carrier envelope drops to zero and then inverts, causing severe distortion. The demodulated signal is clipped and harmonics appear. AM transmitters include modulation limiters to prevent this. At exactly m=1, the carrier amplitude varies between 0 and 2x its unmodulated value.

What is Carson's rule?

Carson's rule approximates the bandwidth of an FM signal as BW = 2(Δf + f_m), where Δf is the peak frequency deviation and f_m is the maximum modulating frequency. This captures about 98% of the signal power. For commercial FM radio: BW = 2(75 + 15) = 180 kHz, plus guard bands giving 200 kHz channel spacing.