Abridgment of the relation between frequency and spark-over: Voltage in a spheregap voltmeter

The standard instrument for measuring crest values of high alternating voltages at 60 cycles is the spheregap voltmeter, which measures a voltage by the distance which it will flash between spheres. In much of the high-voltage research, however, very high frequencies are used. For measuring the voltages used in these high-frequency tests, the spheregap voltmeter is used, the assumption being made that its calibration at high frequency is but little, if any, different from that at 60 cycles. In the endeavor to make the spheregap a standard for measuring peak values of voltage at high frequencies, as it is at present a standard at commercial frequencies, experimental data were obtained from which calibration curves for the spheregap voltmeter were plotted for frequencies ranging from 28,000 to 425,000 cycles per sec. for standard conditions of temperature and pressure. These curves cover a voltage range from about 10,000 to 50,000 volts, the source of the high-frequency voltage being a Poulsen arc with variable inductance and capacity in its a-c. circuit. The results show no appreciable change in voltage required to flash across a given gap as the frequency increases until a frequency of about 20,000 cycles is reached, then a gradual decrease in required voltage us the frequency increases from 20,000 to 60,000 cycles, after which a single curve holds for all frequencies at least up to 425,000 cycles per sec., the highest frequency tested. The theory shows that this curve should hold up to a frequency of about 6,000,000 cycles for a one-cm. gap, after which a further decrease should be found. At and above 60,000 cycles per sec., the voltage required to flash across a one-in. gap is 13 per cent lower than the voltage required at 60 cycles, provided only the ions occurring naturally in the atmosphere are available to start the ionization which produces the flashover. In the course of the investigation it was noted that flooding the spheres with ultraviolet light decreas- d the voltage required to flash across a given gap at high frequency by about 3.5 per cent, whereas no such effect is found at commercial frequencies. Therefore a complete set of calibration curves for the frequency range covered was also obtained for the spheres flooded with ultraviolet light. The results are explained by showing that at high frequency a space charge of positive ions will accumulate between the spheres, this space charge distorting the potential gradient sufficiently to allow a spark to pass, even though the average gradient between spheres is considerably lower than is necessary at 60 cycles. The space charge depends on the rate at which ions are added to the field by ionization and the rate at which they are lost by diffusion and mutual repulsion, the terminal condition reached when the rate of gain equals the rate of loss determining the voltage at which flashover will take place at any given frequency.