REFLEX OSCILLATORS 627 



Here V is the peak gap voltage. Expressions (al4) and (al5) are valuable 

 in making resonator calculations from exact or approximate field distribu- 

 tions. They define C, L and M in terms of electric and magnetic field. 

 The energy dissipated per cycle is 



Wj = 7rF'C/con (al6) 



Hence, we might have written Q as 



Q = 2wWJ]W (al7) 



This is one popular definition of Q. 



In (a8)-(al7) we usually assume that there is no appreciable energy 

 stored in the load or the field of the coupling loop, so that M is considered 

 as unafifected by load. The effect of "high ()" loads with considerable 

 energy storage is considered in a somewhat different manner in Sec. IXB. 



It must be emphasized that the expressions given above are valid for 

 high Q circuits only (a Q of 50 is high in this sense). Expression (al7) is 

 often used as a general definition of Q, but it is not complete without an 

 additional definition of the meaning of resonance in a low Q circuit with 

 many modes. Schelkunoff uses another definition of Q. Unforced oscilla- 

 tions in a damped circuit can be represented as a combination of several 

 terms 



F:e^" + V,^'' + • • • • (al8) 



* pi = ai+jcoi (a 19) 



Schelkunoff takes the Q of the ni\\ mode as 



Qn = w„/«n (a20) 



This is at least a consistent and complete definition. The reader can easily 

 see that it accords with the definitions given for high ()'s in connection 

 with the circuit of Fig. 116. 



Sometimes there may be a complicated circuit between the gap and a 

 coixial line or wave guide. In this case, the circuits intervening between 

 thi gap and the line can be regarded as a 4 terminal transducer (Fig. 117). 

 The constants of this transducer will vary with frequency. No further 

 consideration of this generalized treatment will be given, as it is well covered 

 in books on network theory. A particular representation of the transducer 

 will be pointed out, however. If the impedance in the line is referred to a 

 special point, one parameter can be eliminated, giving the equivalent circuit 

 shown in Fig. 118. If the gap is short-circuited, the impedance is zero 

 and the impedance at the special point to be chosen on the line is R\ the 

 special point may be chosen as the potential minimum with the gap shorted. 



