462 BELL SYSTEM TECHNICAL JOURNAL 



Q and Ring Time 



For satisfactoty measurement the ringtime must extend beyond nearby 

 echoes which would obscure the test signal. For most radars a ringtime of 

 20 to 30 microseconds (about 2 to 3 miles) has been found satisfactory al- 

 though considerably higher values have sometimes been provided. Even 

 apart from echoes, a long ringtime is desirable since this gives a lower decay 

 rate and a more sensitive measurement. 



Computation will show that an extremely high value of Q is necessary 

 to obtain the desired ringtime. For maximum ringtime the cavity coupling 

 should be such as to make the working Q (Ql) about 90 per cent of the non- 

 loaded Q. Values of working Q which have been provided in different fre- 

 quency ranges are approximately as follows: 



Frequency Q, Frequency Q^ 



1,000 mc 70,000* 10,000 mc 100,000 



3,000 40,000 24,000 200,000 



* In this case a higher Q was needed for a long range ground search system. 



The difference in performance corresponding to a given change in ring- 

 time can be determined from the decay rate which is 



d = 27.3 Z/Ql <f6/niicrosecond (9) 



For a given frequency the ringtime is directly proportional, and the decay 

 rate inversely proportional, to Q. For a given ringtime, the required Q is 

 directly proportional to frequency. 



Accurate measurement of extremely high Q's is essential in echo box work. 

 A decrement method, in which a pulsed RF oscillator and oscilloscope are 

 used to determine the loss corresponding to a known time interval, has 

 proved most satisfactory. 



Spectrui^i An.\lysis 



The frequency components of a non-repetitive rectangular d-c. pulse may 

 be determined by well known methods using Fourier integral analysis. 

 The envelope of amplitudes is of the form (sin x)/x where x = irfT. This 

 envelope is shown by the right-hand side of the curve of Fig. 15a, /o being 

 assumed to represent zero frequency. The first zero occurs at the fre- 

 quency / = 1/T. 



Similarly the envelope of the spectrum of a rectangular a-c. pulse is given 

 by the complete curve of Fig. 15a, /o in this case being the carrier frequency. 

 For a non-repetitive pulse all frequencies are present in amplitude as shown 

 by the envelope. WTien a stable carrier frequency is pulsed at uniform 

 intervals and in precise phase relation, only harmonics of the repetition 



