ELECTRON TUBE PERFORMANCE 327 



modulation; that is, we would get a third harmonic, a transconductance 

 increment, a finite detector discrimination, and so on, only their values 

 would be somewhat dififerent. Moreover, a more elaborate analysis reveals 

 that the computations as made above would be in error by relatively small 

 amounts and, what is more important, they would always be on the safe 

 side. The only important error would be the absence of the fifth harmonic, 

 which cannot be produced by third-order modulation. 



Experience with computations checked by measurement reveals that the 

 equations apply in a great majority of practical cases. The computations 

 may be used, therefore, as a guide in the selection of tubes, operating parame- 

 ters, and in experiments, even though we must realize that they may not be 

 fully justified theoretically and are not quite accurate. 



Conclusion 



The analysis of the transconductance characteristics of tubes could be 

 pushed further to fifth, sixth and higher orders of modulation, but it is hardly 

 worth it. The mathematical treatment becomes burdensome, the results 

 are uninteresting and the applications are rare except in a qualitative way. 

 Thus, having completed the discussion of the fourth-order modulation, we 

 find an extension of the treatment to higher orders of modulation un- 

 profitable. 



The material presented in this article has consisted chiefly of a Ust of 

 formulas which may be applied to practical computations of the transmission 

 and quality of transmission of electron tubes. They will be found to be 

 useful in design of electron tube circuits. The second objective of the 

 analysis is to give the user a mental picture of the tube performance in terms 

 of its conductance characteristic. 



Thus in general the quality of transmission of an amplifier, its discrimina- 

 tion against interfering voltages, amplitude distortion, and second harmonic 

 content are measured by the bias cut-off interval. The capacity of the tube 

 to deliver large currents at small distortion is measured by the area under 

 the characteristic. The gain is measured by the transconductance and, in 

 some cases, by the steepness of the characteristic. Freedom from third- 

 and fourth-harmonic distortion and input-output linearity are measured by 

 the linearity of the characteristic. 



In a modulator the current capacity of the tube is measured by the area 

 between the characteristic and the lines defining the voltage and the trans- 

 conductance range used. The conversion transconductance is measured by 

 the transconductance range available. The linearity of the characteristic 

 will measure the discrimination against third-order products. In the case 

 of a rectifier the criteria will be the same as in the case of the modulator. 



A tube with a small slope and large transconductance will deliver with 



