REFLEX OSCILLATORS 625 



by the inductances U , Li , U and the capacitances Ci , C2 , C3 . These 

 resonant circuits are coupled to the terminals by mutual inductances Wi , 

 W2 , W3 . In series with these appears the inductance measured at very low 

 frequencies Lq , the self inductance of the couphng loop. The circuit in 

 Fig. 1 14 may be regarded as a symbolic representation to be used in evaluat- 

 ing Z, just as a mathematical expression may be a symbolic representation 

 of the value of an impedance. 



In practical cases, the resonances are usually considerably separated in 

 frequency, and near a desired resonance the efifect of others may be neglected. 

 In addition, if the Q is high we may add a conductance Gr across the capaci- 

 tance to represent resonator losses (Fig. 115). It would be equally legiti- 

 mate to add a resistance in series with L. In Fig. 115 a load impedance 

 Zt has been added. Fig. 115 is a very accurate representation of a slightly 

 lossy resonator, a low loss coupling loop, and a load impedance. The 



Fig. 115. — Etjuivalent circuit showing connection between the oscillator gap regarded 

 as one pair of terminals and the oscillator load for an oscillator resonator having only one 

 resonant frequency near the frequency of operation. 



meaning of L and C will be made clearer a little later. We will now clarify 

 the meaning of m. Suppose no current flows in the coupling loop (Z = co ). 

 Let the peak gap voltage be V . The peak voltage across m will be 



F„, = mV/L (a4) 



In a resonator, if a peak voltage V across the gap produces a peak flux \p,n 

 linking the coupling loop when no current flows in the coupling loop, then 



F„, - d^p^Jdt = tnV/L (a5) 



This defines m in terms of magnetic field, and L. 



Figure 115 is also a quite accurate representation of Fig. 113. In this 

 case the "terminals" are taken as located at the end of the wave guide. 

 Le is the inductance of the iris, which will vary with frequency. 



When we are interested in the impedance at the gap as a function of fre- 

 quency, we may equally well use the equivalent circuit of Fig. 116. Here 

 G i^ represents conductance due to load; Gr represents conductance due to 

 resonator loss. The total conductance, called Gc, is 



Gc = Gu-\r Gl (a6) 



