Communication Systems
AM Modulation Calculator
Modulation index, sideband power, total power, and transmission efficiency for standard full-carrier AM.
About this calculator
Standard (full-carrier, double-sideband) AM transmits s(t) = A_c[1 + μ·cos(ω_m t)]·cos(ω_c t): a carrier whose envelope follows the message. For a single sinusoidal tone, everything about the power budget follows from the modulation index μ — the ratio of peak envelope variation to carrier amplitude.
The power accounting is unforgiving. The carrier, which carries no information, takes P_c; the two information-bearing sidebands together take only P_c·μ²/2. Total transmitted power is P_t = P_c(1 + μ²/2), and the transmission efficiency — sideband power over total power — is η = μ²/(2 + μ²). Even at 100% modulation (μ = 1), η is just 1/3: two-thirds of a broadcast AM transmitter's output is spent on the carrier. That inefficiency is the entire motivation for DSB-SC and SSB, which strip the carrier and one sideband respectively.
Pushing μ past 1 does not help: the envelope then crosses zero, an envelope detector can no longer recover the message, and the clipped modulation splatters distortion into adjacent channels. The envelope chart makes this visible — at μ > 1 the upper and lower envelopes cross.
Enter μ directly, or the message and carrier amplitudes, plus the unmodulated carrier power, and every step of the power budget is worked in sequence.
Assumptions
- Single sinusoidal modulating tone; a complex message replaces μ²/2 by the mean-square modulation and changes the numbers.
- All spectral components (carrier and both sidebands) are delivered to the same load, so power ratios are independent of the load resistance.
- Ideal linear modulator — no harmonic distortion of the message and no carrier phase modulation.
When to use this calculator
Appropriate for
- Finding sideband and total power, and efficiency, for single-tone conventional AM at a given modulation index
- Seeing how modulation depth affects power distribution and the onset of overmodulation
- Teaching the AM power-budget relationships
Not suitable for
- Suppressed-carrier or single-sideband systems, which have different power relationships than conventional AM
- Complex or multi-tone modulating signals, where the single-tone index does not capture the spectrum
- Transmitter design or spectral-mask compliance without a fuller model and the governing regulations
What this calculator does not cover
- Single-tone results only — for program material the effective μ² is the mean-square modulation depth, and peak and average power must be budgeted separately.
- Standard full-carrier double-sideband AM only; DSB-SC, SSB, and VSB have entirely different power and bandwidth relations.
- No modulator or PA nonlinearity: real transmitters impose carrier shift and distortion near 100% modulation that this ideal model does not show.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
Why is AM transmission efficiency at most 33%?
Because the carrier — which carries no information — is always transmitted at full power P_c, while the sidebands carry at most P_c/2 combined (at μ = 1). η = μ²/(2 + μ²) therefore peaks at 1/3. Suppressing the carrier (DSB-SC) or one sideband as well (SSB) recovers that power at the cost of a more complex receiver.
What actually goes wrong above 100% modulation?
The envelope 1 + μ·cos(ω_m t) goes negative, which the physical envelope cannot do — it folds at zero. An envelope detector then recovers a clipped, distorted message, and the sharp folding generates spectral splatter into adjacent channels.
Does the load resistance matter for these results?
No — every spectral component sees the same load, so the ratios P_t/P_c, P_SB/P_c, and η are pure functions of μ. That is why the calculator asks for carrier power rather than voltage and resistance separately.
References
- Haykin, S., Communication Systems, 4th ed., Ch. 2 (amplitude modulation)
- Lathi, B. P. & Ding, Z., Modern Digital and Analog Communication Systems, 4th ed. (AM power relations)
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