Measuring AM modulation index with an FFT

The modulation index m of an AM signal (0…1, or 0…100 %) states how far the carrier envelope swings. In the frequency domain there is an elegant shortcut: a clean AM signal shows the carrier plus two sidebands offset by the modulating frequency, and the difference in dB between carrier and sideband encodes the modulation depth exactly.

The formula

With ΔdB = (carrier level) − (one sideband level):

m = 2 x 10^(-ΔdB / 20)

Δ =  6 dB  →  m = 1.00  (100 %)
Δ = 12 dB  →  m = 0.50  (50 %)
Δ = 20 dB  →  m = 0.20  (20 %)
Δ = 26 dB  →  m = 0.10  (10 %)

Making the measurement

• On a spectrum analyzer: span a few times the modulating frequency around the carrier, RBW well below the offset, then use the delta-marker from carrier peak to either sideband
• On an oscilloscope: enable FFT math with a flat-top or Blackman window, zoom to the carrier region, and use cursors the same way
• Insert ΔdB into the formula — or keep the table above on the bench

Example: carrier −10.2 dBm, sideband −30.2 dBm → Δ = 20 dB → m = 0.20 (20 % AM)