Analysis of the Effects of Space Charge on Grid Impedance

Previous theory of transit-time phenomena in high vacuum diodes is extended and augmented to provide an explanation of the high-frequency behavior of high-μ amplifiers with parallel plane electrodes. For mathematical reasons the analysis is restricted to triodes with plate at alternating-current ground and to tetrodes with screen grid at alternating-current ground. Expressions for internal input loading and capacity are derived, showing the dependence upon frequency, voltages, and tube dimensions, and it is shown how the theory in its present form can be made quantitatively applicable to many commercial tubes of cylindrical design. In agreement with both elementary theory and observation, the theory shows that at the threshold of the effect the input loading varies as the square of the frequency. For the RCA-57 there is calculated an internal input resistance of 21 megohms at one megacycle, dropping to 2100 ohms at 100 megacycles. These figures are in excellent agreement with actual measurement, and illustrate the tremendous importance of transit times in the design of tubes for ultra-high frequencies. It is likely that internal input power losses of this character, together with closely allied losses in transconductance, are primarily responsible for high-frequency failure of both amplifiers and oscillators. "Hot" input capacity exceeds the "cold" value. The magnitude and dependence upon tube parameters is given, the increase is primarily due to space charge but also depends upon τ2/τ1, the ratio of the electron transit time between control grid and plate to the transit time between cathode and control grid.