Author: Vigoureux J.E.P.
Title: The valve-maintained quartz oscillator
A quartz resonator connected between the grid of a valve and either of the other electrodes gives rise to oscillations in the plate circuit when the constants of that circuit satisfy certain conditions. The frequency of the oscillations depends mainly upon the natural frequency of the quartz, and is, therefore, fairly constant when the temperature is constant. In addition to temperature effects, which are not considered in the present paper, variations of frequency can be produced by (i) variations of the air-gaps of the resonator, i.e. the air-gaps between the quartz and the two electrodes of the resonator; (ii) variations of the constants of the plate circuit; and (iii) variations of the inter-electrode capacities and conductances. The object of the investigation is the study of these variations, both theoretically and experimentally. In the theoretical treatment, the quartz is replaced by a circuit made up of an inductance, a resistance and a capacity in series, the whole being in parallel with a second capacity. The validity of such a substitution has been studied experimentally by Dye. The combination of quartz resonator, valve and plate circuit is represented by a network of admittances, from which three circuit equations are obtained; to these is added the fundamental equation of the valve. These four equations yield a single linear differential equation of the fifth order, with constant coefficients. In the case under investigation, it is only required to find the frequency and the amplitude of oscillations after the latter have reached a constant amplitude. This consideration affords a means of reducing the differential equation to one of the same type, but of the second order. From the latter equation, of which the general solution is known, formul? are developed for the changes of frequency resulting from variations in the resistance and capacity of the plate circuit, in the resistance of the grid leak, in the inter-electrode capacities, and in the air-ga- p. These formul? provide useful information as to the influence of each variable on the frequency, and can with advantage be applied to the choice of the best circuits and the best valve for a quartz oscillator. As the oscillations build up after switching on, the average plate conductance of the valve alters gradually. When the amplitude of oscillation has reached its final value, the value of the average plate conductance is such as to annul the damping term, i.e. the coefficient of dy/dt in the differential equation. From this condition the average plate conductance can be determined for any values of the circuit variables. The amplitude of oscillations in the plate circuit is a function of this average plate conductance. Formul?e are developed which give the conditions for the maintenance of oscillations, and an investigation is made of the variations of amplitude with variations in (a) capacity in the plate circuit, (b) resistance in the plate circuit, and (c) grid conductance. Points of importance in the choice of circuits and valves are deduced from the formul?e and the theoretical curves. Two types of quartz oscillator are investigated, namely, the cases in which the quartz resonator is connected between (i) the grid and the plate of the valve, and (ii) the grid and the filament of the valve. A fairly complete experimental investigation is described. The admittances of the valve and of the circuits were measured, and the equivalent electrical network of the quartz was determined. The behaviour of the quartz oscillator was then investigated by altering in turn each variable in the circuits. The theoretical and experimental results are compared and discussed. The paper does not deal with circuits especially devised for obtaining large outputs from quartz crystals. Its object is the study of the influence of the circuit variables on the frequency and on the power generated as regards the simple Pierce circuits.