608 BELL SYSTEM TECHNICAL JOURNAL 



It is possible to obtain a good approximation for the effective diode 

 temperature for any operating condition by the following method. 

 The values of "C" and "Z)" in (47) may be found without too much 

 difficulty by graphical integration for several different values of y, rjo 

 and rjo'. From the tabulated values for F(rjo') and /(rjo) given by 

 Langmuir, and from the values found for C and D, the integral, 



S = I ylB - C - Dje~^'dy, 

 Jo 



(5i: 



may be evaluated by mechanical means for several values of t^o and 

 rio'. This gives the first integral in (46). 



It was found practically impossible to calculate directly the contri- 

 bution to X from the last two integrals in (46). However, a rough 

 approximation to them may be found indirectly by the following 

 method : If the sum of the two integrals is denoted by Q, then (46) may 

 be written 



^ dfivo) ' 

 drio 



or Q — B\(df(rio)/dr]o) — S = function of rjo' only. 



For a fixed value of rjo', the solution of the above equation for several 

 values of r]o should give a constant value for Q. Unfortunately, only 

 the limiting values of X are known. However, if the limiting value of 

 0.644 is substituted for X in this equation, the calculated value of Q, 

 for a fixed value of r/o', should approach a constant value as t/o is 

 increased since X does assume the 0.644 value for t/o sufficiently large. 

 The limiting value of Q calculated in this manner is the desired 

 contribution to X from the last two integrals in (46). This method of 

 evaluating Q cannot be very accurate since it involves the difference of 

 two quantities of the same magnitude. However, since Q is small 

 compared to the contribution from the first integral in (46), a large 

 error in Q will introduce a much smaller error in the value of X. 



The values of the effective diode plate resistance temperature 

 calculated in this manner for several different operating conditions are 

 shown in Fig. 2. These curves indicate that the effective diode 

 temperature is 0.644 times the cathode temperature for all practical 

 operating conditions. The values of 170' and 770 may be determined 

 from the following relations: 



Tjo' = logey^, (52) 



