The Temperature Coefficient of Inductance, with Special Reference to the Valve Generator

This paper discusses the manner in which the inductance of a coil depends on temperature, and has been written as a contribution to the problem of the temperature coefficient of frequency of a valve generator. Preliminary consideration shows that when a coil expands without change of form, it will have a temperature coefficient of inductance equal to the coefficient of linear expansion of the metal of which it is made. Such copper coils would give a negative temperature coefficient of frequency of about eight parts in 10⁶per degree centigrade. Since valve generators are sometimes found to have a temperature coefficient much greater than eight parts in 10⁶, it is necessary to consider the effect of deforming the coil. The first type of coil examined is a concentric cable; this form is amenable to exact analysis, and the results are a valuable guide to the behavior of more common forms of coil. The temperature coefficient of "internal inductance" and of self-capacitance is calculated and found to modify the net temperature coefficient by a negligible amount; accordingly, it is argued these effects can be ignored in all forms of coil. The core is then supposed to buckle under temperature stress and this is found to make the net coefficient less than that of linear expansion. The next example is a long solenoid wound on a form which constrains one diameter, so that the cross section becomes elliptical.