random variations in potential, current, or voltage in electric circuits and communications lines. They are produced by the random movement of charge carriers, caused by thermal agitation, and by other physical processes in matter that stem from the discrete nature of electricity, as well as by the random variations and instability inherent in a circuit. Fluctuations may occur in passive circuit elements (metallic and nonmetallic conductors), in active elements (electronic, ion, and semiconductor devices), and in the atmosphere through which radio waves are propagated.
Thermal fluctuations (thermal noise) are caused by the random movement of thermally excited charge carriers in a conductor, which results in a fluctuating difference in potential between the conductor’s terminals. Because of the large concentration of conduction electrons in metals and the shortness of the mean free path, the velocities of thermally excited electrons are many times greater than the velocity of the directed motion in an electric field. Consequently, the electrical fluctuations in metals vary with temperature, but they are not a function of the applied voltage (the Nyquist formula). At room temperature the intensity of thermal electrical fluctuations remains constant up to frequencies of approximately 1012 hertz. Although thermal electrical fluctuations only occur in resistances, the presence of reactive elements (capacities and inductances) can alter the frequency spectrum of the fluctuations. In nonmetallic conductors, electrical fluctuations at low frequencies exceed the thermal electrical fluctuations by several orders of magnitude. Such noise is explained by the slow, random rearrangement of the conductor’s structure under the influence of the current.
Electrical fluctuations in electron-tube and ion devices are associated chiefly with the random nature of electron emission from a cathode (seeSHOT NOISE). The intensity of such fluctuations is practically constant for frequencies ≤108 hertz and depends on the presence of residual ions and the amount of space charge (seeSHOT EFFECT). Additional sources of electrical fluctuations in these devices are secondary electron emission from the plate and grid of electron tubes and the dynodes of photomultipliers, as well as the random redistribution of current among the electrodes. Also observed in electron-tube and ion devices are slow electrical fluctuations associated with various processes in the cathode. In low-pressure gas-discharge devices, electrical fluctuations result from the random motion of thermally excited electrons.
Electrical fluctuations in semiconductor devices are due to the random nature of the generation and recombination processes for electrons and holes (generation-recombination noise) and for the diffusion of the charge carriers. These processes contribute to both thermal and shot noise in semiconductor devices. The frequency spectrum of these electrical fluctuations depends on the mean life and the drift of the carriers. Also observed in semiconductor devices are electrical fluctuations caused by the trapping of electrons and holes by defects in the crystal structure (seeDEFECTS, CRYSTAL and SEMICONDUCTOR).
Devices that operate on the principle of stimulated emission, such as masers, may generate spontaneous emission noise, which is due to the quantum nature of the electromagnetic emission.
Certain electrical fluctuations are associated with temperature changes and aging in circuits, the instability of power supplies, interference from industrial equipment, vibration and shock, and the degradation of electrical contacts.
Electrical fluctuations in oscillators produce amplitude and frequency modulations of the oscillations (seeMODULATION OF OSCILLATIONS). This may impart a continuous frequency spectrum to the oscillations, or it may broaden the spectral line for the oscillations by a value from 10–7to 10–12 times the value of the carrier frequency.
Electrical fluctuations result in the appearance of spurious signals, or noise, at the output of signal amplifiers, limiting sensitivity and noise immunity. They also reduce stability in oscillators and lower the reliability of automatic control systems.
REFERENCESVlasov, V. F. Elektronnye i ionnye pribory, 3rd ed. Moscow, 1960. Chapter 13.
Bonch-Bruevich, A. M. Radioelektronika v eksperimental’noi fizike. Moscow, 1966.
Levin, M. L., and S. M. Rytov. Teoriia ravnovesnykh teplovykh fluktuatsii v elektrodinamike. Moscow, 1967.
Malakhov, A. N. Fluktuatsii v avtokolebatel’nykh sistemakh. Moscow, 1968.
Van Der Ziel, A. Shum. Moscow, 1973. (Translated from English.)
I. T. TROFIMENKO