508 BELL SYSTEM TECHNICAL JOURNAL 



accounting for the relative independence of the output on the repe'.Ier 

 voltage. 



In what has been given so far we have arrived qualitatively at an explana- 

 tion for the variation of the amplitude. There remains the explanal i' ,-, 

 for the behavior of the frequency. In this case we plot susceptance as a 

 function of am])litude and, as in the case of the conductance, there will be 

 several contributions. The primary electronic susceptance will be given by 



Be = ye ^-^-^ sin e. (8.15) 



Hence, as we vary the parameter M by changing the repeller voltage the 

 susceptance curve swells as the conductance curve shrinks. The circuit 

 condition for stable oscillation is that 



Be + 2iAcoC = 0. (8.16) 



A second source of susceptance will arise from the continuing drift in the 

 cathode space. Referring to equation (8.10) we see that this will have the 

 form 



Be = ye—p^-j^— c^&Qt (8.1/) 



C2 V 



and corresponding to equation (8.11) we write 



B'e = y'e ' ^ ' ^ [cos 0,0 cos ^^ i - sin dt^ sin ^^t\. (8.18) 



C2 V 



Consider the functions given by (8.18) for values oi 6 1 — (n + l)2r and 

 (« + f)27r as functions of V. These are the extreme values which we 

 considered in the case of the conductance. The ordinates of these curves 

 give the frequency shift as a function of the amplitude. 

 In case 1 we have 



Be = —ye ' T/ ^^" ^^' (.^-l^) 



C2 y 



and case 2 



„/ /2/i(C2F) . /o lr»\ 



Be = ye ' „ sm Adt . (8.20) 



C2 V 



The total susceptance will be the sum of the susceptance appearing across 

 the gap as a result of the drift in the repeller space and the susceptance 

 which appears across the gap as a result of the cascaded drift action in the 

 repeller region and the cathode region. If sin Adt and sin Ad varied in 

 the same way with the repeller voltage, the total susceptance would expand 



