Modulation Calculator

Modulation places information from a lower-frequency message signal onto a higher-frequency carrier so that the information can be transmitted efficiently. Radio, television, telemetry, wireless links, and many measurement systems use controlled changes in carrier amplitude, frequency, or phase. This modulation calculator compares the three classic analog methods and reports the dimensionless modulation index, an estimated occupied bandwidth, and useful lower and upper frequency limits. In amplitude modulation, the carrier amplitude varies with the message waveform. For a single sinusoidal tone, the AM modulation index is message amplitude divided by carrier amplitude. An index of 0.5 corresponds to 50% modulation, while an index above one indicates overmodulation and can cause envelope distortion in a conventional receiver. Ordinary double-sideband AM creates spectral components at the carrier frequency plus and minus the message frequency, so its bandwidth is twice the highest message frequency. In frequency modulation, the carrier's instantaneous frequency moves above and below its nominal value. The FM modulation index is peak frequency deviation divided by message frequency. Theoretically FM produces infinitely many sidebands, but Carson's rule estimates the bandwidth containing most signal power as twice the sum of peak deviation and highest message frequency. The calculator implements the equivalent expression using modulation index. This estimate is widely used for channel planning, although regulatory masks and actual message spectra may require additional margin. Phase modulation changes carrier phase in proportion to the message. Its modulation index is the peak phase deviation in radians. For a single-tone PM signal, the peak frequency deviation equals phase index multiplied by message frequency, so Carson's rule again gives twice the message frequency multiplied by one plus the phase index. FM and PM are closely related angle-modulation methods, but the way deviation depends on message frequency is different. Carrier and message amplitudes are shown for all modes so one form can support comparison. The amplitude values determine the AM index, while FM uses the entered frequency deviation and PM uses peak phase deviation. Frequencies are entered in kilohertz and all displayed limits remain in kilohertz. The lower and upper values are symmetric planning limits around the carrier; they are not a list of every discrete sideband. Use the results for introductory communications problems, transmitter checks, channel-spacing estimates, and signal-processing education. Real signals may contain many message frequencies, filtering, pre-emphasis, noise, and nonlinear effects. In those cases use the highest significant modulating frequency and verify the estimate with a spectrum analyzer or the applicable communications standard.