The spontaneous background noise in amplifiers due to thermal agitation and shot effects

This paper discusses the spontaneous excitation of any vibrating system by random impulses, and in particular the spontaneous excitation of an electrical circuit by the chaotic movement of the free electrons within it. With the hypothesis that the average value of the electrical energy in a circuit is equal to the average energy of a molecule, it is shown that the means square value of the voltage across the condenser varies directly as the absolute temperature and inversely as the capacitance. Formulÿ are then developed for the response of a thermionic amplifier, of any given characteristic, which is used to record the thermal-agitation voltage. These formulÿ are put to searching experimental proof, and satisfactory values of Boltzmann´s constant are deduced from the measurements. The effect of temperature is also investigated. Formulÿ are then developed for the voltage due to the shot effect; that is, the shock excitation of the anode-circuit impedance by the pattering of the electrons on the anode. Experimentally-determined curves are given of the shot voltage both with and without space-charge limitation. A formula is developed for the shot voltage in working conditions. It appears from this that the signal/noise ratio can be improved by increasing the mutual conductance of valves, provided that the increase is not accompanied by an increased anode current. Finally, the interaction of a radio-frequency carrier voltage with the voltages due to thermal agitation and to the shot effect is discussed.