THEORY OF VIBRATION OF THE LARYNX 



219 



Fig. 4a is a schematic diagram of a three-element vacuum tube 

 oscillator circuit known as the "tuned grid" circuit. This is one of 

 many kinds. The transformer coupling between the plate and grid 

 circuit is represented by an auto-transformer. Fig. 4b represents 

 the same circuit schematically but with circuit elements only. In this 

 R2 represents that part of the resistance of the coil which belongs to 

 the grid circuit and any other associated dissipation, L2 is the in- 

 ductance of the coil as seen from the grid mesh and Ko the reciprocal 

 of the combined tuning capacity across the grid and that of the grid- 

 filament. It is the electrical stiffness or elasticity of the grid mesh, 



K, 



^ 



:^2 





AAAAM- 



nmr^ 



Fig. 4—" Tuned Grid " Oscillator. 



in other words. Ri is a plate-filament resistance ("a.c") and Lj 

 that part of the coil in the plate circuit. M is the mutual inductance 

 of the transformer which is not part of the mesh impedance of either 

 plate or grid. The element K,, is the " uni-lateral mutual impedance " 

 (G. A. Campbell, 1914) between the plate and grid meshes and is 

 numerically equal to (jlK^, where ^ is the amplification constant of 

 the tube. Other internal tube impedances are as usual neglected. 

 The impedance determinant may be written directly from the circuit 

 diagram Fig. 3b. 



{p'-L, + pR,) {^M + K„) 

 pHI ip-Lo + pR, + K.2) 



D 



(32) 



The quantities on the principal diagonal of this determinant, that is 

 the first and last elements, are as usual in a circuit determinant the 

 mesh impedances while the others are the mutuals. The principal 

 features of the analogy may be seen by comparison of determinants 

 (31) and (32). Except for the thus far undefined external or trachea 

 impedance the mesh impedances are the same, from which it appears 

 that the glottis is analogous with the plate-filament path in the vac- 

 uum tube and the vocal cords with the grid-filament path. The air 



