REFLEX OSCILLATORS 505 



we can show that the admittance arising on the third transit of the gap will 

 have the form 



F: = +7o ^' Al^ [sin e, + j cos d,] (8.9) 



where /o is the effective d.c. contributing to the third transit, dt = 6 -\- Be 

 is the total transit angle made up of the drift angle in the repeller space, 6, 

 and the drift angle in the cathode space dc . As before, assume that the 

 small changes in dt caused by the changing repeller voltage over the elec- 

 tronic tuning range exercise an appreciable effect only in changing the sine 

 and cosine terms. Then we may write 



Y'e=G'e+ jB'e = y'e ^^^^ [siu Ot + j COS 9t] (8.10) 



where 



If Ad = di - dto 





Ci'e = y'e ^'^^jf^P [sin 0,0 cos ABt + cos 0,o sin A0,]. (8.11) 



C2 V 



Now 



AFr 



Ad = waT + Aw To 



Vr + V, 



Ada = AuTc (8.12) 



AVr 



Adt = CjOoT + ACOTO + AcOTc • 



Fr+ Fo 



We observe that the phase angle of the admittance arising on the third 

 transit varies more rapidly with repeller voltage (i.e., frequency) than the 

 phase angle of the second transit admittance. This is of considerable im- 

 portance in understanding some of the features of hysteresis. 



Let us consider (8.11) for some particular values of ^ccr di . We remem- 

 ber that 6 1 is greater than 6 and hence Co > Ci . Since this is so, the limit- 



. . . lAiaV) .... ^ , , ,,^,, 2/i(CiF) 



mg 1 unction — will become zero at a lower value ot l than — — . 



C2 F CiV 



We will consider two cases 6 1 — (« + 4)27r and dt — (// + f)2x. These 



