Capacitance: The Transducer that Converts Resistors into Electromagnetic Sensors

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Vol. 259, Issue 5, October 2022, pp. 1-11

Capacitance: The Transducer that Converts Resistors into Electromagnetic Sensors

José-Ignacio IZPURA

Dept. of Aerospace Systems, Air Transport & Airports, Universidad Politécnica de Madrid (UPM) ETS Ingeniería Aeronáutica y del Espacio (ETSIAE),
Plaza Cardenal Cisneros 3, 28040, Madrid, Spain

^* E-mail: joseignacio.izpura@upm.es

Received: 5 September 2022 /Accepted: 10 October 2022 /Published: 31 October 2022

Abstract: It is widely known since 1928 that each resistor at temperature T shows a voltage noise of spectral density 4kTR V²/Hz, where k is the Boltzmann constant. However, the way in which this voltage arises from the exchanges of energy of this device with its thermal bath remains still unclear. Leaving aside strange features ascribed to its resistance R in order to justify how this random voltage is generated, we have considered for this purpose the electrical capacitance C of each resistor of volume VQ sandwiched between its two equipotential terminals (plates). Using a new, Fluctuation-based noise model that excels the Dissipation-based model in use today, we have shown that Johnson noise is the measurable effect caused by truly impulsive charge noise that takes place in this reactive element with a mean square value of 4kT/R Coulombs²/second. Hence, capacitance is the transducer that converts thermal fluctuations of electric field within VQ into this random voltage called Johnson noise. The C²/s units that emerge from this advanced noise model for the familiar value of the Nyquist density 4kT/R A²/Hz and its partition into 2kT/R ultra wideband and 2kT/R band-limited noises, are two new results of this advanced model.

Keywords: Charge noise and fluctuations, Conduction current and dissipation, Displacement currents and shot noise, Noise out of thermal equilibrium, Two-terminal devices and complex immitances.

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