AM modulation index 2026-10-14
In the single-sinusoid AM voltage model, is the peak fractional excursion of the signed multiplying factor from its mean value . At there is only the carrier wave; at its multiplying factor ranges from to ; at it just touches zero. For , the wave envelope extrema areThe last equality follows by adding and subtracting the first two. An oscilloscope estimate uses local carrier peaks near the message extrema and needs enough carrier cycles to approximate those bounds. Consistent local peak-to-peak amplitude readings give the same ratio because their common factor of two cancels. Mixing a peak reading with a peak-to-peak reading does not.
For and , the wave envelope ranges from to , giving . These are model values. At , the signed factor has minimum , but the nonnegative wave envelope reaches zero at its sign changes; the extrema formula would misleadingly report . It cannot measure the true depth of overmodulation from the folded envelope alone.
Amplitude modulation laboratory 2026-10-14
Rice University's ELEC 332: In the Lab makes the model experimentally testable. Preparation resets the spectrum analyzer and observes an unmodulated generator output on it and an oscilloscope. A Wavetek function generator supplies external modulation. The specified carrier and message separate three peaks. Marker readouts give frequency and level; narrowing resolution bandwidth shows how the instrument broadens a line.[ref]
ELEC 332: In the Lab, Rice University. ELEC 332: In the Lab, Part 1, “Initial Configuration”, “Initializing”, “Observing a signal”, “Changing the bandwidth”, “Using the marker” and “Resolving signals”
Part 3 uses an SA602 analog multiplier module. The message generator also triggers the oscilloscope; multiplier output feeds both displays. A no-offset module supplies a suppressed-carrier control. Replacing it with the offset-adding module restores the carrier; varying levels tests signal distortion. Finally a radio receives the conventional AM transmission, and varying message frequency checks that the heard tone belongs to this source. These are prescribed observations, not reported measurements.[ref]
ELEC 332: In the Lab, Rice University. ELEC 332: In the Lab, Part 3, module descriptions and “Connect the components” through “AM transmitter”: input/output connections, offset control, level sweep and receiver check
Calibration matters: verify generator voltage at the connected input, distinguish peak from peak-to-peak amplitude and root mean square, and check analyser units and loading before comparing heights with or power with . The unmodulated carrier is a reference control. Limited resolution can merge sidebands; generator harmonics can add peaks. Rice explicitly demonstrates both limitations in Part 1.[ref]
ELEC 332: In the Lab, Rice University. ELEC 332: In the Lab, Part 1, “Resolving signals”: message-generator harmonic distortion and unresolved sidebands when the message frequency is reduced
A complementary University of Kansas procedure, A.2 - Amplitude Modulation, calibrates the added carrier and the suppressed-carrier product separately to peak-to-peak before recombining them. It holds the carrier fixed, varies modulation depth, reads envelope extrema and carrier-to-sideband power differences, then connects the demodulator and adjusts its tunable low-pass filter for recovery, comparing the output with the message. These are setup targets and comparison instructions, not measured results.[ref]
The inference combines time and frequency spectrum readouts: correct sideband spacing tests frequency translation, relative heights test modulation depth, and the recovered message tests the detector. Hardware clipping, receiver filtering and noise can spoil recovery even at . Conversely failure of an envelope detector at does not demonstrate failure of a synchronized multiplier receiver. The two diagrams above illustrate the stipulated linear model only.