A few years later, we moved HBO to channel 2 (so we could sell
> HBO to hotels and motels), installed negative traps to secure
> it, .....
Whereup> What science can take away, science can put back. Those traps
did _not_ *completely* eliminate the signal getting into the
> customer premises, they just made it so weak that a
> conventional TV set couldn't amplify it enough to make a decent
> picture. A decent high-gain single-channel pre-amp, on
> the other hand, installed 'in front of' the TV receiver, could
> do a surprisingly good job of resurrecting the 'killed' signal.
>
Except that the relevant parameter is noise figure, not gain. To the extent that the preamp has a better (i.e., lower) noise figure than the TV set's own tuner (and holding all other variables constant), you'll get a decibel-for-decibel improvement.
But even a relatively low-gain preamp (say, ca 20 dB) will show similar improvement if it has a similarly lower noise figure.
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Neal McLain