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 Ri and 

 Ri do not appear as mutual impedances. Designating the meshes in 

 which Ri and i?2 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 I^ is 



J ^ ~ -^^21 ,3s 



' A + RiR^^u, 22 + i^iAii + R2A22 ' ^ ^ 



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

 values of Ri and R2, 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, 



^2^2 



equation (3) gives 



" E 



— i?2A21 



/3 = ' '' ■ . (4) 



A + i?ii?2Aii, 22 + -^lAu + R2A22 



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

 and if the latter be denoted by a, the value of nl3 becomes 



Q _ «-^2A21 ^-x 



^'^ A + R,R2An, 22 + i?iAn + i?2A22 ^ ^ 



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 



