THEORY OF MULTI-ELECTRODE VACUUM TUBES 49 



It may also be written in the following form which will be found 

 useful later: 



^ _ Rp-R M _ Rp-R ^^ ,.^. 



^"~ R, + R' R,~ Rp + R'^'- ^^^^ 



It should be emphasized, perhaps, that the electrical parameters of 

 multi-electrode tubes and the output current, as defined by the 

 foregoing equations, are subject to the condition that the voltages 

 applied to all of the electrodes other than the plate and control grid 

 are maintained constant. The satisfactory operation of multi- 

 electrode tubes in circuits also usually requires that this condition be 

 fulfilled. It requires that the impedance to alternating current com- 

 ponents in each of these circuit branches be very low. This is ac- 

 complished in practice by connecting these electrodes to ground, so far 

 as alternating currents are concerned, through reasonably large 

 capacitances. 



From the foregoing analysis it is apparent that, with proper inter- 

 pretation, the definitions of plate resistance, transconductance, and 

 amplification factor applicable to triodes are also applicable to multi- 

 electrode tubes; in addition, the same expressions for output current 

 and voltage amplification are applicable. This follows from the fact 

 that these quantities are expressed in terms of the differential coeffi- 

 cients of the static characteristics, that is, they depend only upon the 

 slopes of these characteristics at the given operating voltages and not 

 upon their form. However, as will appear later, the difference in the 

 shape of the static characteristics of multi-electrode tubes from those of 

 triodes is very important in determining great differences not only in 

 the magnitude of the electrical parameters, but also in the character 

 and amount of distortion resulting when the tubes are operated under 

 conditions such that large portions of the characteristics are traversed. 



In multi-electrode tubes, as well as in triodes, the total space current 

 drawn from the cathode is determined by the extent to which the 

 resultant field, due to the electrodes, overcomes the opposing field 

 produced by space charge. While space charge extends throughout the 

 interelectrode space, it is relatively so much more dense in regions of 

 very low electron velocity that, as a first approximation, its effect 

 usually may be neglected in other regions. Except in space-charge- 

 grid tubes and a few other special tubes, the only important space- 

 charge region is confined to a relatively thin sheath near the cathode 

 surface. Consequently, in such structures the total space current is 

 determined largely by the extent to which the resultant positive field 

 due to the electrodes neutralizes the negative field near the cathode 



