Modulation in Vacuum Tubes Used as Amplifiers 



By EUGENE PETERSON and HERBERT P. EVANS 



Synopsis: Recent developments in amplifier design tending toward more 

 rigorous quality requirements have shown that the solutions of Van der 

 BijI and Carson are inadequate for certain purposes since they are based 

 upon a convenient assumption which is not satisfied in fact. In particular, 

 a detailed investigation of carrier current repeaters used for the simultaneous 

 transmission of several channels, and upon which in consequence the 

 modulation or crosstalk requirements are particularly severe, showed the 

 modulation currents measured to be quite different from those specified by 

 the theory, as was the law of variation of these currents with the circuit 

 constants. 



The cause of the discrepancy was found to reside in the neglect of the 

 variation of the amplification factor (/x) with both plate and grid potentials. 

 When the actual state of affairs was taken into account in the analysis by 

 the application of a general method involving no assumptions, theory and 

 experiment were found to be in good accord. The new expressions have 

 been developed in terms of the amplification factor (fi), the internal output 

 resistance of the tube (Ro), and their differential parameters, which are 

 involved in the representation of the characteristic tube equation by a 

 double power series. Expressions for the current components are developed 

 in terms of the coefficients of the series, and modifications of Miller's method 

 for greater convenience and precision in determinations of tube charac- 

 teristics are described from which the series coefficients may be evaluated. 



Conclusions are drawn from the solutions as to desirable tube charac- 

 teristics by which, for example, a single tube may take the place of two 

 tubes in push-pull connection. Finally, certain properties of different 

 types of tubes under conditions of maximum output power are compared 

 on the basis of n constant and m variable. 



THE amount of modulation produced in vacuum tube amplifiers is 

 in many cases a controlling factor in their application and it 

 becomes of importance to determine how modulation products arise, 

 so that the possibility of reducing them by tube and by circuit design 

 may be studied. 



In restricting discussion to amplifiers, and particularly to those used 

 in communications, we are treating cases most amenable to analysis; 

 in which, normally, the applied potential variation maintains the grid 

 always negative so that conductive grid current does not flow, but in 

 which, on the other hand, the greatest negative potential does not 

 exceed the negative end of the plate current grid potential charac- 

 teristic. In applying these two detailed restrictions we are incidentally 

 insuring against prohibitive quantities of modulation; we know that, 

 for example, the flow of conductive grid current may, under special 

 conditions, produce an exceptionally efficient modulator of great 

 service as such, but highly undesirable as an amplifier. 



The necessity for suppressing modulation proceeds from the dis- 

 turbing effects attendant on it, by which there may result reduction 



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