Noise And Sensitivity Page
One of the things we do when we restore a receiver is perform a sensitivity
test. There is great rivalry among receiver nuts about which is the most
sensitive. Presumably that has something to do with pulling the weakest
signals out of the ether.
John Bertrand Johnson (who is known by the Eponym "Johnson Noise") described
thermal noise as follows:
"This is a fluctuating voltage generated by an electric
current flowing through a resistance in the
input circuit of an amplifier, not in the amplifier itself.
The motion of charge is a spontaneous and random flow of the
electric charge in the conductor in response to the heat
motion of its molecules. The voltage between the
ends of the conductor varies and is impressed upon the
input to the amplifier as a fluctuating noise." From "Electronic
Noise: The First Two Decades," IEEE Spectrum,
Volume 8, pp42-46, Feb. 1971. Johnson first reported quantitative
observations of this noise in the 1927-28 time frame (See his article
in Physics Review, V29 (1929), p367, and V32 (1928) p97
The point is that if your receiver front-end is not operating at
a temperature of absolute zero, the electrons bouncing around in the
wires, coils, resistors, and capacitors produce a noise voltage. Nyquist
in a companion paper (Physics Review, V29 (1929), p614) derived
a formula to calculate this noise voltage as follows:
V = sqrt(kTRB)
where V is the RMS voltage, T is the temperature in Kelvin (273 plus
temperature in Centigrade), k is Boltzman's constant (1.38e-23), R is
the equivalent resistance in ohms and B is the bandwidth in Hertz. For
receiver design, we generally use the normal communications receiver
bandwidth of 3500 Hertz.
I received the nicest couple of emails from one Steve Johnson. They are reproduced
here with permission:
I was surfing the net looking for information about the Johnson noises... and
I read your article. I thought you might be interested in the "rest of the story"
John Bertrand Johnson was a cousin of my father, Dr. John A. Johnson. Bert was
born to my grandfathers sister, who never married in Sweden. Bert had no
schooling in Sweden and lived in extreme poverty. My grandfather sent for
him as a teenager and he ended up on their farm in far northwestern North Dakota.
My grandfather sent Bert to school and he finally graduated from high school
and went on get his PhD in Physics from Princeton.
I was told that he worked with Einstein when he was at Princeton and went on
to be director of Bell Labs. I have contacted them to try to find more information.
Andy, I met Bert several times, but I was fairly young and most
of the family history is lost..I am in the process of trying to
piece together more details. Please feel free to put this information
on the web. Maybe one of your readers can help fill in the blanks.
How about it, folks? Anybody know more of the story? If so, please send
me an email (see contact page) and I will forward it to Steve.
Now, on with noise voltage:
You can calculate this and make a cute little table from it.
The point of this is that many of the measurements you see people talk about are
physically impossible. If we take the input impedance of a receiver to be 100 ohms
(see below for the "real" story), then there is already a .0376 microvolt potential
at the input. For a signal to be 10 dB greater than that, it would have to be .119
microvolts (10 dB is a factor of about 3.16).
Thus, any claim of receiver sensitivity that is lower than .12 microvolts
is bogus. It has to be. Any plausible sensitivity rating would have to be several
times larger than this theoretical lower bound. So, when someone tells you that their
receiver has a .5 microvolt input sensitivity, that is nothing to sneeze at (if it
was measured properly). If they tell you it has a .06 microvolt sensitivity, they
are giving you a value that violates fundamental laws of physics. Sorry.
R in Ohms