How this instrument works
Modulation index measures how far an amplitude-modulated carrier's envelope swings away from steady, expressed as a plain ratio between 0 and 1. Trace the envelope on an oscilloscope and it rises to a maximum voltage on the loudest peaks of the audio and sinks to a minimum on the quietest troughs; the index is simply how much of that swing there is relative to how big the carrier itself is.
The formula is shaped the way it is because of where the two peaks come from. Write the envelope as a steady carrier Vc plus a wobble of amplitude Vm: the top of the swing is Vc + Vm and the bottom is Vc − Vm. Subtract the two and the carrier cancels, leaving 2Vm; add the two and the wobble cancels, leaving 2Vc. Divide one by the other and both twos fall away, leaving m = Vm ⁄ Vc exactly — the ratio of audio amplitude to carrier amplitude, recovered from nothing but two peak readings off a scope.
At m = 1 the trough touches zero volts — full modulation, the most audio power an AM transmitter can carry without distortion. Push the audio drive any harder and the envelope tries to swing below zero, which a real carrier cannot do; instead the trough flattens and clips, an overmodulated signal that splatters energy into neighbouring channels. A modulation index above 1 is therefore a symptom of a badly adjusted transmitter, not a number this instrument will ever return from real voltage readings.
- Enter the envelope's highest voltage in Maximum envelope voltage — the peak reached on the loudest part of the audio.
- Enter its lowest voltage in Minimum envelope voltage — the trough on the quietest part; it cannot go below zero.
- Read Modulation index (0-1) — the dimensionless ratio, 0 for a bare carrier and 1 at full modulation.
- Read Modulation depth, % — the same ratio scaled by 100, the figure most datasheets and license conditions quote.
Worked example — an envelope reading of 10 V and 2 V
A technician checking an AM transmitter's output on an oscilloscope reads the envelope's peak at 10 V and its trough at 2 V. The modulation index is m = (10 − 2) ⁄ (10 + 2) = 8 ⁄ 12 = 0.666666666667 — the fraction 8/12 reduces to exactly two thirds, a repeating decimal the instrument carries out to full precision rather than rounding early.
Multiplied by 100, that index reads out as 66.6666666667% modulation depth. That is comfortably below the 100% ceiling, so the carrier still has headroom: pushing the audio drive further would lower the trough toward 0 V and raise the depth toward 100%, but shove it past that point and the envelope cannot follow, clipping the trough and distorting the transmitted audio.
Questions
What voltage should I actually read off an oscilloscope for these fields?
Read peak values, not peak-to-peak or RMS. Maximum envelope voltage is the highest point the trace reaches above the oscilloscope's zero line, and Minimum envelope voltage is the lowest point the trough dips to, also measured from zero. Using peak-to-peak or an RMS-scaled reading for either field will produce a modulation index that is wrong by a fixed but non-obvious factor.
What does 100% modulation actually mean?
It means the envelope's trough has dropped to exactly 0 V — Vmin = 0 — so m = Vmax ⁄ Vmax = 1. That is the deepest modulation an AM signal can carry cleanly: it delivers the maximum audio power the scheme allows, and any further increase in audio drive cannot lower the trough any further without clipping.
Can the modulation index be higher than 1, or the depth higher than 100%?
Not from a real, undistorted envelope — the formula only returns values from 0 up to 1, because Vmin cannot physically fall below 0 V. Over-driving a transmitter instead produces clipping: the trough flattens at zero rather than swinging negative, giving a distorted, overmodulated signal that spreads energy into adjacent channels rather than a mathematically valid index above 1.
Is this the same modulation index used for FM signals?
No, it is a different quantity entirely. This ratio, sometimes called the AM modulation factor, compares two voltages on an envelope. FM's modulation index (often written β) compares a frequency deviation to a modulating frequency and has nothing to do with amplitude at all — the two share a name by convention, not by formula.
Why use Vmax and Vmin instead of measuring the carrier directly?
Because the carrier's own steady amplitude, Vc, is not something an oscilloscope shows directly once it is modulated — only the swinging envelope is visible. Adding the two peak readings and halving them recovers Vc exactly, since Vmax + Vmin = 2Vc; the formula extracts both the swing and the carrier from the same two numbers on the screen.