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.

Random Note:
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.

Steve

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	RMS Voltage
50	.0266 uV
75	.0326 uV
100	.0376 uV
150	.046 uV
200	.053 uV
250	.059 uV
300	.065 uV