90 BELL SYSTEM TECHNICAL JOURNAL 



tion, then the system represented by the diagram will oscillate when 

 the terminals between which the impedance was measured are con- 

 nected together. 



Verification of this rule, together with further extension to more 

 general cases are expected to be discussed in a subsequent paper. For 

 the present, its validity will have to be accepted on faith, but with 

 the assurance that the applications employed in this discussion are 

 readily capable of demonstration. 



Returning to consideration of the positive grid triode with complete 

 space charge on both sides of the grid, and a slightly positive plate, 

 whose R — X diagram is given in Fig. 11, we see at once that the dia- 

 gram does not encircle the origin as it stands. Of course only positive 

 values of frequency are included in the curves as they are shown. The 

 inclusion of negative frequencies (never mind their physical meaning) 

 would produce a curve which would be the image of the curve shown, 

 a reflecting mirror being regarded as a plane perpendicular to the 

 paper, and containing the i?-axis. The curve A, for instance, would 

 have its part corresponding to negative frequencies lying above the 

 i?-axis and forming an image of the part lying below. This is shown by 

 the dotted curve in Fig. 12. 



It is obvious that the curve of Fig. 12 will encircle the origin or 

 not depending on what happens at infinite frequencies. However, the 

 slightest amount of resistance in the leads to the tube will be sufficient 

 to move the curve to the right and thus exclude the origin. This 

 means that no oscillations would be obtained if an alternating-current 

 short were placed between plate and cathode. The result, although in 

 accord with experiment, is not particularly useful. The important 

 thing is to find whether the curve can be modified by the addition of a 

 simple electrical circuit in such a way that the origin of the resulting 

 R — X diagram for the combination of tube and circuit is encircled in 

 a clockwise direction. 



Suppose that a simple inductance is connected in series with the 

 plate lead, and the impedance diagram of the series combination of 

 tube and inductance is plotted. For this arrangement, the R — X 

 diagram of Fig. 12 would be modified as shown in Fig. 13. Here the 

 part of the curve corresponding to negative values of resistance has 

 been pushed upward until the origin is enclosed within a loop which 

 encircles it in a clockwise direction. It is therefore to be expected that 

 oscillations will result. As to their frequency, we can say that the 

 grid-plate transit angle must be at least as great as 27r for this particular 

 example. This follows by supposing a certain amount of resistance to 

 be added in series with the circuit. The effect of this resistance will 



