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I know I can't amp a bad signal into existence, but confused over the 50' statement in the link.
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Great, it sounds like you understand that the preamplifier can not/ does not 'pull' signal from the antenna or air, that it only 'pushes' signal through loss connected to the output side of the amp. 50' of coax has little loss (not more than 3 dB at the upper end of the UHF band) so there's not much work for the amplifier to accomplish on a run shorter than that.
Then, consider that the amplifier makes the signal
and noise coming from the antenna stronger by the same amount. For example, a 24 dB gain amp will increase the desired signal 24 dB
and it will also increase the power level of the noise received from the antenna by 24 dB. So if this is where it ended, you would have the same relative difference between signal and noise (signal to noise ratio). However, the amplifier will generate some noise and add it to the signal. If the manufacturer of the amp provides the information, you'll see a specification for NF (noise figure) a good consumer grade preamp will have an NF of 3 dB or lower.
Now back to the 50' section of coax... If it has 3 dB of loss, it will make the desired signal 3 dB lower. But, the noise generated inside the tuner doesn't go down. that leaves you with a net noise margin at the tuner 3 dB lower than what was available at the antenna, before the 50' run of coax. (Adding an amp at the antenna overcomes the loss in the coax, but typically adds about 3 dB of noise (or what ever the NF spec really is). So an amp can actually make your net NM worse on shot runs of coax.
The 50' length of test coax is a rough estimate of how long a run is needed before there is any benefit to adding an amplifier.