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Unformatted text preview: Fundamental Noise and Fundamental Constants In this experiment a series of measurements of the Johnson noise produced by several resistors is used to derive Boltzmann’s constant, and the shot noise produced by a vacuum diode are used to derive the charge of the electron. The frequency spectra of noise and the properties of noise from amplifiers are also explored. 1 Background The typical use of the term “noise” in a physics experiment is to describe the limits of experimental sensitivity: a measurement is said to be “in the noise” when its mean value is about the same size, or less, than the standard deviation of that measurement. In other words, the measurement is not reproducible. The kinds of experimental noise may be divided into two categories: Noise due to external influences such as room vibration, outside electromagnetic fields, temperature variations, and the like, we might call interference noise. The experimenter may be able to reduce the effects of interference noise by physically isolating the apparatus, applying electromagnetic shielding, or running the experiment at night when the building is quieter. The other category of noise comes from within the apparatus itself, and we could call it inherent noise. In most experiments, electronic devices make up much of the apparatus. While it is true that the noise produced by these devices depends on their design and operation, some of the noise is a result of fundamental physical processes and quantities such as the ambient temperature, circuit resistance, and the discrete nature of electric charge. Noise of this type we may call fundamental noise. Two types of fundamental noise will be studied: thermal, or “Johnson”, noise which is present in any kind of conductor and depends only on the conductor’s resistance and temperature, and “shot” noise which is mainly evident in devices where the charge carriers overcome a potential barrier, such as a diode. In shot noise, the noise is due to fluctuations in the electric current which come from the fact that each charge crosses the barrier independently of the other charges; the variation in the current depends on the statistical variation in arrival times of the charge carriers times the charge on each carrier. Both Johnson noise and shot noise share the interesting feature that the amplitude of the energy fluctuations they produce is independent of frequency . In other words, if you were to measure the RMS power of the noise in the ranges 100 to 200 hertz, 1100 to 1200 hertz and 10,100 to 10,200 hertz, you would get the same answer in all three cases. This kind of noise is called “white”. The term comes from the analogy with light; white light is the light you get when all colors (all frequencies) are present in equal intensity. Since RMS power is proportional to the square of RMS voltage, in white noise the RMS amplitude of voltage fluctuations varies as the square root of the frequency band....
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This note was uploaded on 01/28/2012 for the course PHYSICS 431 taught by Professor Marjorieolmstead during the Winter '12 term at University of Washington.
- Winter '12