STABILIZED FEEDBACK OSCILLATORS 



461 



impedances. In writing down the equations for the mesh currents, let 

 it be assumed that the circuit contains n meshes including the terminal 

 meshes and that the meshes are so chosen that the resistances R\ and 

 i^2 do not appear as mutual impedances. Designating the meshes in 

 which Ri and R2 appear as the first and second respectively, the mesh 

 current equations take the form 



E 

 

 







(2) 



The subscripts of the Z's denote self and mutual impedances in ac- 

 cordance with the usual conventions, the latter being subject to the 

 reciprocal relationships characteristic of linear systems. 



The solution of the above equations for the current I2. is 



h = 



- E^2l 



A + RlR■,^n, 22 + i?iAn + i?2A22 ' 



(3) 



where A is the determinant of the coefificients of equations (2) for zero 

 values of Ri and i?2, and the other determinants are the minors of A 

 obtained by crossing out the columns and rows indicated by the nu- 

 merical subscripts. Thus A21 is obtained by crossing out the second 

 column and the first row of A and An, 22 is obtained by crossing out the 

 first two columns and the first two rows. 

 Since, by definition, 



^-~E'' 

 equation (3) gives 



— i?2A21 



^ = 



A -f i?li?2A„. 22 + Rl^U + R2A2i 



(4) 



The factor ^ is the negative of the amplification constant of the tube 

 and if the latter be denoted by a, the value of /i/3 becomes 



i"/3 = 



ai?2A2i 



A + RiR^Au, 22 + RiAn + i?2A22 



(5) 



The determinants appearing in equations (4) and (5) can be ex- 

 panded by the ordinary processes to give expressions in terms of the 

 mesh impedances in any particular case. However, as they stand, they 



