Calculate the modulation index for both AM (Amplitude Modulation) and FM (Frequency Modulation) signals. Enter the message signal amplitude and carrier amplitude for AM, or the frequency deviation and message frequency for FM — and get the modulation index (μ) along with the modulation type classification.
Modulation Index (μ)
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Modulation Depth
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Modulation Status
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Carrier Amplitude (Ac)
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Message Amplitude / Freq Deviation
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The modulation index (μ) is a ratio that describes how much a carrier signal has been modulated by a message signal. For AM, it's the ratio of message amplitude to carrier amplitude. For FM, it's the ratio of frequency deviation to message frequency. A higher modulation index means more information is encoded in the carrier wave.
The AM modulation index (μa) is calculated using the formula μa = Am / Ac, where Am is the peak amplitude of the message signal and Ac is the peak amplitude of the carrier signal. For example, if Am = 50 V and Ac = 100 V, then μa = 0.5, meaning 50% modulation depth.
The FM modulation index (μf) is calculated using the formula μf = Δf / fm, where Δf is the maximum frequency deviation and fm is the frequency of the message signal. For example, if Δf = 75 kHz and fm = 15 kHz, then μf = 5.
Using the AM formula μa = Am / Ac = 20 / 100 = 0.2. This means the signal is modulated at 20%, which is considered under-modulation. The carrier is not being fully utilized for information transfer.
When μa > 1 in AM (over-modulation), distortion occurs because the carrier wave envelope is clipped, causing signal distortion and spectral splatter. Ideally, μa should be ≤ 1 (100% modulation) for a clean, undistorted AM signal.
In Amplitude Modulation (AM), the amplitude of the carrier wave varies according to the message signal, while the frequency stays constant. In Frequency Modulation (FM), the frequency of the carrier wave varies according to the message signal, while the amplitude stays constant. FM generally provides better noise immunity than AM.
For commercial FM radio broadcasting, a maximum frequency deviation of 75 kHz is allowed, and the maximum audio frequency is typically 15 kHz, giving a maximum modulation index of 5. This is considered wideband FM and provides high-quality audio reproduction.
100% modulation in AM means the modulation index μa = 1, where the message signal amplitude equals the carrier amplitude. At this point, the carrier's amplitude varies between 0 and 2×Ac. It represents the maximum modulation before distortion (over-modulation) occurs and is the most efficient use of transmitter power.