Resistor Noise can be Deafening, and Hard to Reduce
Q. My low-noise amplifier is not low noise enough. What am I doing
wrong?
A. It may not be the amplifier causing the trouble; analyze where the
noise is actually coming from. A typical operational amplifier circuit
contains six uncorrelated noise sources (the smaller ones can usually
be disregarded1). The amplifier itself has three separate noise
sources: a voltage noise source appears differentially across the
inputs; and current noise sources appear in series with both inverting
and non-inverting inputs. Remarkably often the problem is not the
amplifier, though, but the thermal noise generated by one or more of
the three resistors that set the amplifier gain and provide bias
current compensation. Analog Devices has over sixty types of op amps
whose voltage noise is less than that of a 1 kΩ resistor .
This answer is rarely popular; it is far more satisfactory to blame an
imperfect amplifier and replace it with a better one than to admit
that there is a fundamental problem with apparently simple components
such as resistors. In fact, a remarkably common response to a
diagnosis of resistor noise is to seek a source of "good" resistors,
with "good" being defined as without thermal noise.
This is impossible. The basic physics of resistance shows2 that the
random thermal movement of charge carriers in a conductor always
produces electrical noise of value where k is Boltzmann's Constant
(1.38065 x 10-23 J/K), T is the absolute temperature, B is the
bandwidth and R the resistance. (We often express this noise in terms
of spectral density, making the voltage noise .
Such noise is known as thermal noise, or Johnson noise, after John B.
Johnson (Bell Telephone Laboratories – 1928), who was the first person
to observe it. It might more properly be named Johnson/Nyquist noise
as it was Harry Nyquist (also at Bell Laboratories) who explained the
physical basis of Johnson's observation.
So anywhere at all that there is resistance in a circuit, whether it
is carrying current or not, there is a noise generator with an output
voltage noise spectral density of . We can reduce the noise by
reducing the resistance (this may increase current and/or power
consumption), but reducing the temperature is not usually practicable
(if we cool a resistor from room temperature (298K) to liquid nitrogen
temperature (77K), its noise voltage is still more than half its room
temperature value). And, of course, we can't change Boltzmann's
Constant because Professor Boltzmann is dead3.
1 Any noise source less than 1/3 the magnitude of the largest can be
ignored for most practical purposes.
2
http://www.physics.utoronto.ca/~phy225h/experiments/thermal-noise/Thermal-Noise.pdf
3 Died 5 September 1906 at Diuno near Trieste, buried Zentralfriedhof,
Vienna.
Best Answer
It's because of something called safety extra-low voltage (SELV) -- certain regulatory standards allow voltages up to 60V under all conditions, and other ones allow up to 50V. (Unfortunately I can't find any references to standards, and even if I did, you wouldn't be able to view them for free. :-( ).
When you consider a 42V nominal automobile battery under worst-case conditions (load suddenly going away during charging), it can be higher than 42, so there's enough margin to stay below 50V and be able to pass those regulatory standards.
Above the ELV/SELV limits, you can operate but you have to use different connectors, make sure there's no exposed parts that are energized at that voltage, etc. -- so there's a quantum jump of expense and difficulty that starts at that point.