This is the waveform of a 1 MHz carrier modulated with a 1 kHz sine wave at the 100 percent modulation level. Note that the carrier disappears for an infinitesimal period of time at the negative modulation peaks. Also, notice that the modulation waveform appears distortionless.
This is the waveform of a 1 MHz carrier modulated with a 1 kHz sine wave at the 125 percent modulation level when an attempt is made to simply add more modulation sidebands. Notice that the envelope is distorted so that an envelope detector will produce significant distortion while, in fact, the signal is distortionless as can be proved from the mathematics used to generate this signal.
This is the waveform of a 1 MHz carrier modulated with a 1 kHz sine wave at the 150 percent modulation level when an attempt is made to simply add more modulation sidebands. The distortion that would be obtained from an envelope detector should be obvious. However, a distortionless signal could still be recovered by other means.
Here is the general equation for creating an Amplitude Modulation waveform. In this instance, y(t) represents each sample at any instantaneous interval in time t. For conventional Amplitude Modulation, A is set to 1. If it were 0, we would produce a double-sideband suppressed-carrier signal (DSSC) such as a stereophonic sub channel. The value of A sets the amount of carrier component. The peak modulation component normally adds to, or subtracts from, this component. Therefore, the modulation occurs by multiplying the instantaneous carrier component by 1 plus the instantaneous modulation component.
One can produce a graphical representation of this function by plotting a number of points. At one time, this was tedious; however, it now becomes quite simple using software. In the attached software, I plot this function using 10 thousand points or “samples.” Each of these samples represents the instantaneous signal amplitude at a particular time. This is the method used to digitize a continuously varying signal so the result is the same. The output of the included ‘C’ program is a number of files, each containing ten-thousand sets of two numbers, the first number in the set being the abscissa and the second being the ordinate of a plot. Here is an example of the first ten lines of an output file:
Many plotting programs can use these data to produce a graphical presentation. Here, I used PRESTO.
This is a double sideband, suppressed carrier envelope (DSSC) using the same carrier and modulating frequencies and amplitudes. Note that envelope detection will not recover the modulation, and the frequency of any recovered information will be twice the modulation frequency.
C source code
You can download the ‘C’ source-code that generated the data for these waveforms by clicking here to obtain Amod.c. The graphics can be generated using many of the free plotting programs available on the web. The graphics used here are generated by PRESTO.
This is the result of an attempt to detect an over-modulated AM signal of the described type using a conventional envelope detector. In the image, most of carrier signal has been filtered out. However, considerable carrier remains which, in an inexpensive receiver, is simply rejected by the audio-frequency stages.
With conventional amplitude modulation transmitters, both vacuum tube and solid-state, the carrier is generated separately and the carrier level is modulated with an audio-frequency waveform by instantaneously varying the power, (voltage, current, or both), being fed to the modulated stage. With such a topology, it is not obvious that a multiplication has occurred in the generation of the AM output signal. Nevertheless, the result is identical to the technique described above until one attempts to modulate in excess of 100 percent. With conventional implementations, the power into the modulated stage cannot be less than zero. Therefore, during the entire time that the negative peaks would exceed 100 percent modulation, the carrier is cut off, which can cause excessive spurious emissions called splatter, unless some processing steps are taken to prevent this from occurring. Such audio processing is beyond the scope of this note. However, if negative peaks are simply clipped off, the spurious emission result (splatter) may be similar to that caused by over-modulation of the final amplifier stage.
Observe the envelope-detected output from the 100 percent modulated signal initially shown. This signal is detected as conventional envelope detection, except it is full-wave rectified to reduce the amount of carrier to filter. All of the signal generation mechanisms as well as the detection and filtering are included in the ‘C’ source code provided.
This text and all references are placed in the public domain, Richard B. Johnson, author.
1. Author’s website
2. Wikipedia article