Modulation Index Calculator
Select a modulation type (AM, FM, or PM), enter your signal parameters, and get the modulation index, percentage depth, bandwidth, and power distribution instantly. The results update as you type, with step-by-step working and a breakdown chart.
Formula
Worked example
For an AM signal with Am = 3 V and Ac = 5 V: m = 3/5 = 0.6 (60% depth). If fc = 1 MHz, fm = 5 kHz, Pc = 100 W: bandwidth = 2 x 5000 = 10 kHz; total power = 100 x (1 + 0.36/2) = 118 W; each sideband = 9 W; efficiency = 18/118 = 15.3%. For FM with Df = 75 kHz and fm = 15 kHz: beta = 75/15 = 5; Carson bandwidth = 2 x (75+15) = 180 kHz.
What is modulation?
Modulation is the process of varying a property of a high-frequency carrier wave in proportion to a lower-frequency message signal so that the information can travel long distances over radio, cable, or optical links. The three fundamental analog modulation types are amplitude modulation (AM), frequency modulation (FM), and phase modulation (PM). In AM, the amplitude of the carrier rises and falls with the message. In FM, the carrier frequency shifts above and below its rest frequency. In PM, the carrier phase advances and retards. The modulation index (or modulation depth) quantifies how much the carrier property is changed relative to its unmodulated value, and it determines bandwidth, power distribution, and noise performance.
Amplitude modulation: index, depth, and power
The AM modulation index m equals the peak message amplitude Am divided by the peak carrier amplitude Ac. When measured from an oscilloscope trace of the modulated waveform, the equivalent formula is m = (Vmax - Vmin) / (Vmax + Vmin), where Vmax and Vmin are the highest and lowest envelope peaks. An index of 0 means no modulation; an index of 1 (100% depth) is the maximum that produces no distortion. Above 1.0, the carrier is cut to zero during part of each cycle, creating over-modulation and harmonic distortion. Total transmitted power equals Pc x (1 + m^2 / 2), where Pc is the carrier power. Each sideband carries Pc x m^2 / 4, so both sidebands together hold at most 50% of the carrier power at full modulation. Standard AM is power-inefficient: the carrier, which carries no information, dominates. Single-sideband (SSB) and double-sideband suppressed-carrier (DSB-SC) variants remove the carrier entirely to improve efficiency. The AM signal occupies a bandwidth of 2 x fm, where fm is the highest message frequency.
Frequency modulation: deviation ratio and Carson's rule
The FM modulation index, also called the deviation ratio or beta (b), equals the peak frequency deviation Df divided by the message frequency fm. Broadcast FM radio uses Df = 75 kHz; with a maximum audio of 15 kHz, b = 5. Narrowband FM (NBFM), used in walkie-talkies and aircraft radios, keeps b below 0.5, giving a bandwidth close to an AM signal. Wideband FM (WBFM) with b from 0.5 to 5 offers much better noise rejection because the receiver can use limiting to strip amplitude noise, and the FM improvement factor multiplies the post-detection SNR by approximately b^2. Carson's rule estimates the occupied bandwidth as BW = 2 x (Df + fm), which captures roughly 98% of total signal power. The exact spectrum consists of a carrier component and theoretically infinite sidebands at fc plus and minus integer multiples of fm, whose amplitudes are given by Bessel functions Jn(b). In practice, sidebands below about 1% of the unmodulated carrier are ignored.
Phase modulation and its relationship to FM
Phase modulation shifts the instantaneous phase of the carrier by an angle proportional to the message amplitude. The PM index mp equals kp x Am, where kp is the modulator's phase sensitivity in radians per volt. Direct phase deviation Dp may also be entered. Because differentiating a PM signal produces an FM signal with deviation Df = kp x Am x fm, PM and FM are closely related: FM signal generators are often implemented as PM modulators preceded by an integrator. The bandwidth of a PM signal can be estimated with a modified Carson's rule: BW = 2 x (mp + 1) x fm. Unlike FM, where the deviation ratio is independent of modulation frequency, the apparent frequency deviation in PM increases with message frequency, so the spectrum changes shape as the message frequency varies.
Modulation index quick reference
| Type | Index range | Classification | Typical use |
|---|---|---|---|
| AM | 0 to 0.5 | Under-modulated | Voice radio, low distortion |
| AM | 0.5 to 1.0 | Normal / optimal | Standard broadcasting |
| AM | > 1.0 | Over-modulated | Distortion - avoid |
| FM | < 0.5 | Narrowband FM (NBFM) | Two-way radios, aircraft comms |
| FM | 0.5 to 5 | Wideband FM (WBFM) | FM broadcast radio (75 kHz dev) |
| FM | > 5 | High-deviation FM | Studio-quality links |
| PM | <= 1 rad | Narrowband PM | DSPK, low-bandwidth links |
| PM | > 1 rad | Wideband PM | High-fidelity phase links |
Typical operating ranges and classification for each modulation scheme.
Frequently asked questions
What happens if the AM modulation index exceeds 1?
Over-modulation (m > 1) causes the carrier to be cut off to zero amplitude during part of each cycle. The demodulated signal has flat regions where the carrier dropped out, introducing severe harmonic distortion. Receivers using envelope detectors produce badly distorted audio. For this reason, AM transmitters include limiters that prevent the modulation index from exceeding 1. The maximum useful modulation depth is 100% (m = 1).
Why is FM more noise-resistant than AM?
Atmospheric and receiver noise mainly appears as amplitude fluctuations on the received signal. An FM receiver uses a limiter stage before the discriminator to strip all amplitude variations, so amplitude noise is removed. The FM SNR improvement over AM is approximately b^2 for wideband FM, where b is the modulation index. Broadcast FM radio with b = 5 gains about 25x (14 dB) SNR improvement over equivalent-power AM, which is why FM audio sounds much cleaner in noisy conditions.
What is Carson's rule and how accurate is it?
Carson's rule states that the bandwidth containing approximately 98% of an FM signal's power is BW = 2(Df + fm), where Df is the peak frequency deviation and fm is the highest message frequency. It is a practical engineering approximation, not an exact figure. The true spectral extent is infinite (the Bessel function sidebands continue forever), but components beyond Carson's bandwidth are negligible. For narrow-band FM (b < 1) it is very accurate; for high-index FM (b > 5) it slightly overestimates bandwidth. Carson's rule is used by the FCC and other regulators to define channel spacing.
How do I measure the modulation index from an oscilloscope?
Connect the AM transmitter output to an oscilloscope. The modulated waveform shows an "envelope" shape with a maximum amplitude Vmax and a minimum amplitude Vmin. Read these values from the screen, then compute m = (Vmax - Vmin) / (Vmax + Vmin). For example, if the envelope peaks at 8 V and dips to 2 V, m = (8 - 2) / (8 + 2) = 6/10 = 0.6, or 60% modulation depth. This calculator supports this envelope measurement method directly via the "Envelope peaks" input option.
What is the difference between FM and PM?
Both FM and PM are angle modulation schemes that change the instantaneous phase of the carrier, but they differ in how the phase changes. In FM, the instantaneous phase is the integral of the instantaneous frequency, so a constant message amplitude produces a constant frequency deviation regardless of message frequency. In PM, the instantaneous phase is directly proportional to the message amplitude, so the apparent frequency deviation increases linearly with message frequency. PM is the basis for digital phase-shift keying (PSK) and quadrature amplitude modulation (QAM) used in modern digital communications.
Why is AM power inefficient?
In standard AM, the carrier is always present and accounts for most of the transmitted power. At 100% modulation (m = 1), the total power is 1.5 times the carrier power, and only 1/3 of total power is in the two sidebands. At 50% modulation (m = 0.5), the sidebands hold just 1/9 of total power. Since the carrier carries no information, this is wasted. SSB transmission eliminates the carrier and one sideband, putting all the power in the single information-bearing sideband and achieving a 9 dB power advantage over AM at m = 1.