REFLEX OSCILLATORS 585 



established and then switching the tuner power off and measuring the inter- 

 val, Tc , until the operating frequency reaches /c . These quantities are of 

 importance in determining the "Out of Operation" time in case the frequency 

 reference of the control system is momentarily lost, so that the control starts 

 cycling in order to re-establish the reference. 



While the cycling times can be taken to give an indication of the average 

 speed of tuning, more detailed information is required to determine the 

 hunting deviation. This demands a knowledge of the instantaneous tuning 

 rates which will result at any point in the band when the power is switched 

 full on or off. These rates vary through the band since the overdrive avail- 

 able, for example, on heating will decrease as the operating frequency ap- 

 proaches the limit nearest to the maximum drive. 



In the following, an outline will be given of the factors which must be 

 considered in designing a thermally tuned reflex oscillator. The 2K45 will 

 be used as an illustration. Our first consideration concerns the time re- 

 quired for the tuner to heat and cool between given temperatures. In 

 Appendix XI expressions are derived for the cycling times th and Tc . The 

 expressions applicable to the 2K45 are: 



CT 



T, = ^^ [F,(Trn) - F,{Trc)\ (13.1) 



CT 



To = ^4 [F.iT^c) - F^{Tsk)\ (13.2) 



2KT\ 



where the symbols are defined in the appendix. The functions Fi and F2 

 are plotted in terms of the reduced temperatures, Tr and Ts in Figs. 79 and 

 80. In the analysis conduction cooHng is neglected and it is assumed that 

 the whole of the expanding element operates at the same temperature. 

 Because of these limitations the theory is largely qualitative. It will be 

 observed that the cycling time, th , is proportional to the ratio of the heat 

 energy stored in the tuner at the maximum equilibrium temperature to the 

 rate of loss of energy at this temperature. It is therefore apparent that this 

 equilibrium temperature should have the maximum possible value, and also 

 that the heat capacity of the tuner should be kept to a minimum. Assuming 

 for simplicity that the frequency of oscillation is proportional to the tem- 

 perature, so that a given temperature difference is proportional to the fre- 

 quency, one sees by examining the function Fi that it is desirable to keep 

 the reduced temperatures Trh and Trc small compared to 1. Under these 

 circumstances, the cycling time n will have its minimum value and will be 

 more or less independent of the reduced temperatures. If we examine the 

 expression for the cycling time for cooling, Tc , we observe that this is 

 proportional to the ratio of the heat stored in the tuner at the equilibrium 



