584 BELL SYSTEMJTECHNICAL JOURNAL 



ductors of heat. In the case of conduction the cooHng rate will depend on 

 the ratio of the length times the heat capacity divided by the cross-section. 

 For radiation cooling the rate depends on the heat capacity divided by the 

 radiating area and is independent of the length except as the heat capacity 

 depends upon this factor. Radiation cooling has the advantage that it per- 

 mits more freedom of structural shape and the material may be chosen on 

 the basis of strength. In the operating range of the 2K45 the heat radiated 

 is approximately four times that conducted away. 



The automatic frequency control circuits which have been used with 

 thermally tuned beating oscillators in radar receivers have been of a full 

 on or off type so that they do not continuously hold the frequency at a fixed 

 reference difference from the transmitter frequency. The reason for this 

 in part is that a pulse transmitter gives the required reference information 

 only during the pulse. Thus with an on-off control circuit if at a given 

 pulse a correction of frequency is demanded the power into the tuner is 

 turned full on or off, depending on the direction of the correction, and left in 

 this condition until the occurrence of the next pulse which again determines 

 the direction of the control. The result is that the frequency of the beating 

 oscillator continually hunts about the transmitter frequency. The control 

 system must be designed to hold the hunting deviation within tolerable 

 limits. It is of course possible to work within narrow-er limits than full 

 on or off tuner power. One advantage of full on or off control is that it 

 results in the minimum tuning time between required frequencies since the 

 tuning rate is at all times held to the maximum possible value. 



Under certain conditions the performance of a thermal tuner may be 

 completely described by a time constant. In general, however, this is not 

 the case and the information required in designing a control system is con- 

 cerned first with initiation of operation and second with the factors deter- 

 mining the magnitude of the hunting deviation. For initiation of operation, 

 one is concerned with the time required for the oscillator to reach the operat- 

 ing frequency. The quantities known as the cycling times give upper limits 

 for this quantity. The cycling times are to a certain extent arbitrarily 

 defined as indicated in the following. There are two band limit frequencies, 

 fc , the limit requiring the lesser power input, Pc , and corresponding to a 

 tuner temperature, Tc , and fh , the limit for which the power input will be 

 Ph , and the temperature, Th . The cycling time for heating, n, , is defined 

 and measured in the following manner. The power input to the tuner is 

 set to Pc and held at this value until equilibrium is established. The power 

 input is then switched to the maximum allowed value, Pm and the time 

 interval, n , between the instant of switching and the instant at which the 

 frequency of operation has reached fh is measured. Correspondingly, the 

 cycling time Tc for cooling is measured by setting to Pn until equilibrium is 



