Spontaneous Resistance Fluctuations in Carbon Microphones and Other Granular Resistances

Abstract

Voltage fluctuations which occur in resistance elements of the granular type when a direct current is flowing have been measured in the granular carbon microphone, commercial grid leaks, and sputtered or evaporated metal films. The results can be experessed by the formula $\overline{V_c^2} = KV^\alpha R^\beta \log (F_2/F_1),$ where $\overline{V_c^2}$ is the mean square fluctuation voltage, V is the d.-c. voltage across the resistance R, α and β are constants having values of about 1.85 and 1.25, respectively, and F 2 and F 1 are the limits of the frequency range over which the fluctuation voltage is measured. The constant K depends, among other things on the temperature, the surrounding medium, and the dimensions and material of the resistance element; for a commonly used carbon transmitter at ordinary operating conditions its value is about 1.3 × 10−11. The spontaneous voltage fluctuations and the signal due to acoustic modulation are affected in almost an equivalent manner by the applied d.-c. voltage which suggests that the two effects arise from the same type of mechanism, namely a fluctuating resistance at the points of contact between granules. Experiment shows that although the acoustic signal produces a resistance modulation which is in phase at all contacts the spontaneous resistance fluctuations are completely random. On the assumption that a region of secondary conduction, wherein the resistance fluctuation lies, surrounds each area of primary conduction as postulated in recent contact theory a value of β consistent with experiment has been deduced. On the further assumptions that thermal energy produces the mechanical fluctuations and that the equipartition law governs the distribution of energy between oscillators the observed frequency distribution follows.