# Thermal noise

circuit that there will be no voltage across any of the components, a resistor for
example. On average this is correct but a close look at the rms voltage would reveal that a
“noise” voltage is present. This intrinsic noise is due to thermal fluctuations and can be
calculated as may be done in your second year thermal physics course! The main goal of
this experiment is to measure and characterize this noise: Johnson noise.
In order to measure the intrinsic noise of a component one must first reduce the
extrinsic sources of noise, i.e. interference. You have probably noticed that if you touch
the input lead to an oscilloscope a large signal appears. Try this now and characterize the
signal you see. Note that you are acting as an antenna! Make sure you look at both long
time scales, say 10 ms, and shorter time scales, say 1 s. What are the likely sources of
the signals you see? You may recall seeing this before in the First Year Laboratory.
This interference is characterized by two features. First, the noise voltage is
characterized by a spectrum, i.e. the noise voltage V ( f ) n is a function of frequency.
Since noise usually has a time average of zero, the power spectrum  V 2 ( f )  n is
specified in each frequency interval df . Second, the measuring instrument is also
characterized by a spectral response or bandwidth. In our case the bandwidth of the
oscilloscope is from L f =0 (when input is DC coupled) to an upper frequency H f usually
noted on the scope (beware of bandwidth limiting switches). In this case the scope is a
`low pass’ instrument since all frequencies up to  H f are treated equally. When the
scope is AC coupled L f >0 so that it rejects signal components with frequencies less than
L f . In this case the scope is in a `band pass’ configuration where L H f  f  f is the pass
band.
In this light one obvious way to reduce noise is to limit the bandwidth of the
system. This is done in audio amplifiers which have their gain rolled off at about 20 KHz
which happens to be the upper limit of hearing. Radio receivers make use of a pass band
which just allows the signals of interest through (perhaps from one particular cell phone
channel) and not other signals or noise.
Interference can also be reduced by shielding. Compare the signal seen on a scope
with a banana plug connected vs. a coaxial cable. Wherever possible in this experiment
you should use coaxial cables to effectively shield out the interference you observed
earlier.

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