100 BELL SYSTEM TECHNICAL JOURNAL 



lent impedances so that the ordinary circuit analysis can be employed 

 has been demonstrated. It is possible to tell something about the 

 form of the tube impedance from (8). Thus, the first term, namely 

 A I, is a real quantity and contributes a part of the total effective re- 

 sistance of the tube. All of the remaining terms are, in general, com- 

 plex, depending upon the phases of the diflerent harmonic currents. 

 Thus, the conclusion is reached that a nonlinear resistance may be 

 reduced to an equivalent linear impedance, but that this impedance 

 has a reactive as well as a resistive component in the general case. 

 There is at least one important instance where the equivalent linear 

 impedance is resistive only. This occurs when the impedance in the 

 circuit external to the vacuum tube contains resistance, only, to all of 

 the harmonic currents. 



With the general conception of the impedance of the vacuum tube, 

 described above, the fundamental component of (1) becomes 



E = 



R + ic^L + -Ay, -\- r + iX 



I (9) 



where the tube impedance is represented by r -j- iX. 



When the driving voltage, E, is zero, as in the case of oscillators, 

 then for a finite current to exist the oscillation conditions are: 



R-\- r = 

 oiL --^+X = 



(10) 



In the treatment of oscillator networks employed in the foregoing 

 paper the quantities, Tp and fg, are used in the sense of the resistance, r, 

 in (9) and (10) of this appendix. The reactive component, A^, of the 

 tube impedance has been neglected in the paper, for the reason that all 

 of the circuits discussed are of such character that the reactance of the 

 external circuit to the harmonic currents may be made quite low, and 

 the nonlinearity of the vacuum tube characteristics is not such as to 

 cause excessive production of harmonics. 



In the case of the dynatron type of oscillator, where the harmonic 

 currents are especially strong, it has been found by experiment that the 

 reactive component of the tube impedance cannot be neglected, but 

 that it is, in fact, altogether responsible for the variation in frequency 

 with battery voltages which is characteristic of the dynatron oscillator. 



