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Re: [Phys-L] decibels



On 4/29/19 4:20 PM, Anthony Lapinski wrote:

Is there a lower limit?

Thermodynamics imposes a power limit of
P = ½ kT B
where B is the bandwidth (in cycles/s, not radians/s).
Reference: Back-to-back Phys Rev Letters by Johnson
(elegant experiment) and Nyquist (elegant theory).
Both Bell Labs guys. Hence the name "Johnson noise"
aka "Nyquist noise".

That's as quiet as you can get using just absorbers.
To go below that requires active measures such as
refrigerators or squeezed states.

That's the thermal limit. At low-enough temperatures
there is also a quantum limit, but at audio frequencies
it would have to get reeeeally cold before you need to
worry about that. Roughly 0.1 microkelvin.

Planck's constant in the appropriate units is
h = 21 gigahertz per kelvin

==========

BTW that gives another answer to the previous question.
When you buy a fancy laboratory-grade preamp, you might
see the /noise figure/ specified in dB. That's relative
to the thermal noise floor at some temperature (typically
290 K).

An amplifier must add some noise; otherwise it would
violate the second law of thermodynamics (and also the
Heisenberg uncertainty principle, which is essentially
the same thing). The noise figure tells you how well
the amplifier does relative to the best it could possibly
do (assuming no squeezing).

The notion of "thermal" reference level becomes inconsistent
and inconvenient if you have cryogenic preamps (which you
actually do on radio telescopes for astronomy and/or for
communication with spacecraft).