472 BELL SYSTEM TECHNICAL JOURNAL 



suitably biased to avoid drawing grid current during operation and the 

 coupling reactance should be small in comparison with the plate re- 

 sistance of the first tube. Preferably the first tube should be of the 

 screen-grid type having a mutual conductance which is independent of 

 the connected output impedance. The two tubes by themselves have a 

 total phase shift of 360 degrees or zero, but the shunt coupling reactance 

 in combination with the internal resistance of the first tube provides a 

 further phase shift of 90 degrees which represents the total effective 

 phase shift of the amplifier. 



With a phase shift of 90 degrees in the amplifier, the oscillation fre- 

 quency will be that for which the feedback path has a phase shift of 90 

 degrees in the reverse direction. The conditions for frequency stabili- 

 zation follow readily from the principles already developed. 



For a purely reactive feedback network, the expression for /x/3 may 

 be obtained from equation (8) by substituting ± ja for the amplifica- 

 tion factor. This gives 



^'^ {R,Du + R2D22) +j{D - R.R^Du, 22) ' ^ ^ 



from which is obtained 



and 



tan ^ = ± r- , (38) 



Lf — KiKiUii, 22 



''^'='^D-R,R2Dn,22- ^^^^ 



From equation (39) giving the phase angle of /u/3, it is evident that 

 the phase angle can be zero independently of the magnitudes of the 

 tube resistances only if Dn and D22 have zero values at a common 

 frequency. This then is the criterion for stability of the oscillation 

 frequency. 



In terms of the image parameters of the coupling networks, the value 

 of ju/3 becomes 



o ^ :^jaR2^KiK2 ^.^. 



^^ {KxKi + R1R2) sinh e + {R1K2 + R2KO cosh 6 ' ^ ^ 



If it be assumed that the network is dissipative, the transfer constant 

 has an attenuation component and may be represented by 



e = A +71/' 



