Theory of the Diode Voltmeter

Abstract

The current-voltage characteristic of a diode can be expressed at low currents by an equation of the form i = Gε <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">kE</sup> . An analysis based on this relation shows that the rectification efficiency and input resistance of the usual form of gridleak-condenser diode circuit can be conveniently expressed entirely in terms of the grid-leak resistance R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> , the amplitude of the impressed alternating voltage E, a single parameter k of the tube, and an adjustable constant b. k is determined by the cathode temperature, and is constant, for a given tube, as long as the heater voltage is unchanged. b is equal to k times the voltage which exists across R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> in the absence of an impressed alternating voltage, and can be adjusted to any value within a wide range by the use of a suitable bias battery. It is shown that large values of b give higher efficiencies of rectification, but that, if b is of the order of 100 or more, the effciency is practically as high as can be obtained, and is nearly independent of b. The various components of alternating current flowing through the diode are given by A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> = 2A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> (kE), in which A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> is the amplitude of the nth harmonic of the impressed frequency and A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is the direct current through the diode, which last can be separately computed. f <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> = I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> (kE)/I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> (kE). I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> (x) is the nth order Bessel's function of a pure imaginary argument.