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SCWIS: In reality there was no increase in range from a mathematical perspective because the uV/m was exactly the same with or without the compressor.
This is true only for the field produced by the a-m carrier, alone. But within certain limits, the peak and average r-f power in the a-m sidebands still can be practically and usefully increased by using a suitable audio processor.
The r-f/i-f AGC circuits in an a-m receiver are driven mostly by the value of the received carrier, and very little by its sidebands. But increasing sideband power means that field strengths of the sidebands have increased relative to that carrier, and therefore the detected audio S/N ratio will increase for a given carrier level and AGC value. This permits a somewhat better coverage radius for a given audio S/N ratio at the receiver output (other things equal).
Positive peak limits for amplitude modulation are set by legislation in some cases, and/or by tx and processor equipment performance capabilities. Maximum negative-going peak limits for a-m are set by physics and equipment capabilities, but in no case can exceed 100% without creating high audio distortion and r-f interference to other users of the radio spectrum above and below the normal r-f bandwidth of that AM station.
Many commercial AM broadcast stations use elaborate modulation processors to produce maximum perceived loudness at the receiver without violating the limits of the previous paragraph. Quite often this results in a modulation envelope whose average value rarely falls below ~100% on their modulation meters.
For a given set of positive/negative peak modulation limits, it is the average value of the modulation that determines its perceived loudness to a radio listener. However the actions of the audio processor in generating a high average modulation value also introduce various audio distortions into the signal — so as with many things, “tradeoffs” are necessary.