VLTRA-HIGH-FREQUENCY VACUUM TUBES 633 



frequencies and derives expressions for the complex values taken by the 

 amplification factor and plate impedance. While these expressions 

 represent the general trend of the variations, they are based on certain 

 a priori assumptions, as was emphasized in the paper, and hence 

 partake of the telescopic viewpoint of the low-frequency vacuum tube 

 analysis rather than the microscopic viewpoint which is now necessary. 



It was with the aim of overcoming" this limitation that the work 

 described in the present paper was undertaken. Its successful outcome 

 was made possible by a very simple generalization of the methods 

 described in the references, but one which has such far-reaching 

 consequences that it appears worthwhile to start the analysis at the 

 very beginning, and abbreviate only to the extent that intermediate 

 algebraic steps are omitted because of their unwieldy length. 



For convenience, the paper is divided into four parts. In Part I the 

 mathematical analysis is outlined in its fundamental form and general 

 working formulas are developed. In a way similar to low-frequency 

 analysis these formulas may be divided into constant or d.-c. relations, 

 first-order relations, second-order relations, and so on; where the first- 

 order relations apply to a.-c. effects for small amplitudes only, the 

 second-order relations contain rectification and distortion terms; and 

 so on, in exact correspondence with the well known low-frequency 

 relations. Part II contains the solution of the first-order relations 

 expressed in appropriate form for later computations, while Part III 

 does the same thing for second-order relations. Also in Part III, by 

 way of illustration, the effect of frequency on the rectifying properties 

 of parallel plane diodes is discussed. Part IV applies the general 

 first-order and d.-c. solutions to the negative grid triode and shows how 

 its various properties depend on frequency. A discussion of the 

 important effect of active grid loss is included. 



In certain cases the same formulas are expressed in several different 

 ways. This is done because of the difficulty of determining the most 

 useful method of expression before a large number of applications shall 

 have been made. In most cases the general equations have been 

 arranged to conform as far as possible with the most widely used modes 

 of expression of the corresponding low-frequency equations. Where a 

 choice of modes of expression is available, both modes have usually 

 been given, it being left to future experience to determine the more 

 useful one. While this procedure results in some repetition, the two 

 modes of expression of the same equation are found in many instances 

 to have their individual advantages, the one being more suitable 

 for one type of application while the other is more particularly adapted 

 to a different application. 



