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AM Modulation Index Calculator

Calculate AM modulation index: m = (Amax − Amin) / (Amax + Amin). Computes sideband amplitudes, bandwidth (2 × fm), power efficiency, and flags overmodulation (m > 1).

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Formula

m=Am/Ac;η=m2/(2+m2)m = Am / Ac; η = m²/(2 + m²)
m— Modulation index (0 to 1)
Ac— Carrier amplitude (V)
Am— Message signal amplitude (V)
BW— Bandwidth = 2·f_m (Hz)
η— Power efficiency (%)

How It Works

The AM Modulation Index Calculator computes modulation depth and sideband power for amplitude modulation — essential for broadcast transmitter design, aviation radio compliance, and RF communication analysis. Broadcast engineers, avionics technicians, and RF test engineers use this to ensure regulatory compliance and optimize transmission efficiency. Per Proakis "Digital Communications" (5th ed., Appendix A), modulation index m = Am/Ac, where Am = modulating signal amplitude and Ac = carrier amplitude. At m = 1 (100% modulation), sidebands contain 25% of total power each; carrier contains 50%. For m = 0.5 (50% modulation), only 11% of power carries information — 89% wasted in carrier. Per ITU Radio Regulations and FCC Part 73, AM broadcast stations maintain m between 0.85-0.95 for maximum efficiency without overmodulation distortion.

Worked Example

An AM broadcast transmitter operates at 1 kW carrier power with 85% modulation depth. Calculate sideband power and total power. Step 1: Modulation index m = 0.85. Step 2: Total power Pt = Pc (1 + m^2/2) = 1000 (1 + 0.85^2/2) = 1361 W. Step 3: Power in each sideband = Pc m^2/4 = 1000 0.85^2/4 = 180.6 W. Step 4: Efficiency = sideband power / total power = 361/1361 = 26.5%. Step 5: Per FCC Part 73.1560, transmitter must handle 1.4 kW peak power without distortion. This configuration matches typical 1 kW AM broadcast station per NAB Engineering Handbook specifications.

Practical Tips

  • ✓Per FCC Part 73, maintain modulation index 0.85-0.95 for maximum intelligibility without overmodulation
  • ✓Use negative peak limiter to prevent m > 1 — overmodulation causes envelope distortion and adjacent channel interference per ITU-R BS.559
  • ✓Monitor with oscilloscope trapezoidal display — parallel sides indicate clean modulation per NAB Handbook
  • ✓For SSB efficiency (100% of power carries information), suppress carrier and one sideband per ITU-R M.1173

Common Mistakes

  • ✗Allowing modulation index > 1 — causes envelope inversion, 100% THD, and illegal splatter per FCC regulations
  • ✗Neglecting asymmetric modulation — positive peaks can reach 125% legally but negative must stay below 100% per FCC Part 73
  • ✗Ignoring sideband power in link budget — only 33% of power carries information at m=1 vs. 100% for FM

Frequently Asked Questions

Per ITU-R BS.559: 0.85-0.95 for broadcast. Lower values waste power (m=0.5 puts only 11% in sidebands). Higher values risk overmodulation. Aviation AM (VHF) uses m=0.7-0.9 per ICAO Annex 10. CB radio allows up to m=1.0 per FCC Part 95. For maximum range, use highest m without distortion.
AM bandwidth = 2 * fm_max regardless of modulation index per Carson's rule. Higher m increases sideband power but not bandwidth. For 5 kHz audio: BW = 10 kHz. Per FCC Part 73, AM broadcast limited to +/-10 kHz occupied bandwidth. Unlike FM, AM bandwidth is independent of modulation depth.
No — m = |Am|/Ac is magnitude ratio, always positive per IEEE standard definitions. Negative modulation refers to negative-going peaks (toward carrier nulls) vs. positive peaks. FCC allows 125% positive modulation but only 100% negative to prevent envelope reversal.

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