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 dilTerent values of y, 170 

 and 770'. From the tabulated values for 7^(170') and /(?7o) given by 

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



y[_B - C - DJe-y'dy, (51) 



may be evaluated by mechanical means for several values of rjo and 

 ifjo'. 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 



g dfivo) ' 



drjo 



or Q = BXidfi-qo) /drjo) — S = function of 770' only. 



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

 values of rjo 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 7?o', should approach a constant value as 770 is 

 increased since X does assume the 0.644 value for 770 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 difTerence 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 770' and 770 may be determined 

 from the following relations: 



W = logef\ (52) 



