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“Static [i.e. radio receiver noise], like the poor, will always be with us.” John Carson

The great mathematician, John Carson, was wrong when he made this statement, because he was arguing against Armstrong’s claim that receiver noise is suppressed in an FM system. However, the statement applies perfectly to Part 15 AM.

The good signal obtained inside the house, even with a short piece of wire as an antenna, is not representative of Part 15 AM performance. This signal is produced by the near field, which is strong near the antenna, but it diminishes rapidly as the distance from the antenna increases. The near field does not propagate. For transmitting to other houses, one must depend on the far field, which is very weak.

In a recent thread, it was pointed out that the radiated power of a good Part 15 AM installation may be around 22 uW. This is a system efficiency of only .022%. With such a low radiated power, the signal is likely to have noticeable noise even across the street. The listener must have some special motivation to stay tuned to a Part 15 AM signal. His reason for listening will not be because the station sounds good. Perhaps the station is providing some service to the neigborhood. Or, maybe the pastor from the listener’s church is on the air. It would be interesting to learn how various operators keep their audiences.

So, who was John Carson?

He was not a late-night talk show host. Probably, his greatest achievement was introducing the Laplace transform to electrical engineering. The Laplace transform significantly simpifies electrical calculations by allowing differential equations to be solved using only algebra, and not calculus.

The Laplace transform was originally known as “Heaviside’s operational calculus.” The trouble with Heaviside was that he was not merely a genius, but a savant. A genius thinks a lot like an ordinary person, except he is faster and better. A savant can’t explain how he always comes up with the correct answer. He just knows the answer, but doesn’t know why. As a result, some prominent mathematicaticians thought that operational calculus had no mathematical basis. Carson showed that operational calculus can be explained by the use of an integral equation studied by the famous mathematician, Laplace. By attributing Heaviside’s method to Laplace, Carson managed to get operation calculus generally accepted in electrical engineering.

Unfortunately, almost nobody knows about Carson’s role in developing the Laplace transform. He is best known for being wrong while giving Armstrong a hard time. Carson used his mathematical expertise studying FM, and he concluded that it has practically no advantages over AM. It looks like he studied narrowband FM, and he was not able to understand Armstrong’s wideband FM. Carson’s legacy became defined by his famous mistake, and practically all of his positive achievements have been forgotten.