602 BELL SYSTEM TECHNICAL JOURNAL 



This states that the maximum j)ermitted temperature, r„, = Pm/k, shall 

 exceed the temperature Tk by the same temperature difference as that by 

 which Tr exceeds the sink temperature. From (13.4) and (13.5) it can be 

 seen that to minimize the heating and cooling times the heat capacity 

 should be small and the heat conductivity of the strut should be large. It 

 is also evident that the ratio TjJTc should be as nearly unity as possible. 

 This requires that the tuner should produce the required displacement in 

 the smallest temperature interval possible. If a given temperature diflfer- 

 ence is required to produce the necessary motion, then from a speed stand- 

 point it is desirable to make both Th and Tc large in order that their ratio 

 shall be nearly unity. The allowable temperature is usually limited by 

 constructional considerations. 



Over the normal tuning range of a reflex oscillator we have previously 

 shown that the tuning characteristic may be represented by 



X = a \/Cf + C(x) (13.7) 



where a is a constant 



Cf is a lumped fixed capacitance 



C{x) = ^ 



X 



jS isa constant. 

 Hence one can show that for small changes A.v from .Vo 



AX = -i^" (13.8) 



XoCo 



Co = C/+ C(.Vo). (13.9) 



One may also show that for the type of tuner employed and the small 

 motions involved in the 2K50 the displacement of the grids as a function 

 of the temperature diflference T — To will be 



.V = .Vo - H(T - To) (13.10) 



whence 



AX = "M^^ZlzJi.) . (13.11) 



-Tq Co 



If at time / = 0, x = .to , T = To , \ — Xn , we have for heating 



X' _ Ao = i^f^ - ToVl - e-'"'-'). (13.12) 



.To Co \k I 



If we give Pi its maximum value l\n then at / = oo the temperature of 



Pi 



the strut will be -^ = T„, ,X = X,„ 



k 



