574 BELL SYSTEM TECHNICAL JOURNAL 



due to cause (a) but the introduction of new frequencies can only be 

 due to cause (b) . As is now known (Bell System Technical Journal 

 October, 1923) the response of the ear itself is non-linear so that sub- 

 jective harmonics and sum and difference tones are heard by every 

 listener. Under good conditions, therefore, the distortion produced 

 by the non-linear transmission of the amplifier will be so small com- 

 pared to that produced in the ear itself that it will not be noticed. 

 On the other hand, it may be so great as to render unrecognizable the 

 speech or music being transmitted. This condition will be familiar 

 to everyone who has been compelled by an enthusiastic friend to listen 

 to a heavily overloaded radio receiver. 



The principal parts of a vacuum tube amplifier where one might 

 expect to find the non-linear response under consideration are in the 

 magnetic circuits of the transformers and retard coils and in the 

 vacuum tubes. Generally, in the amplifiers considered in this paper, 

 the design of the transformers is such that the magnetic flux density 

 is small so that the magnetization curve is practically a straight line 

 and very little distortion is to be expected from this cause. On the 

 other hand the Ec — Ib characteristic of the vacuum tube is approxi- 

 mately straight for only a small portion of its length and has a pro- 

 nounced curvature in the usual working range. This is the case even 

 for well designed circuits where under proper operation there is no 

 possibility of the grid of the tube drawing current. It is therefore, 

 in the characteristics of the vacuum tubes that the principal source of 

 trouble of this nature is to be looked for. That this anticipation is 

 justified will be shown by the results described in this paper. 



The relationship between output and input of a vacuum tube has 

 been studied from a mathematical viewpoint and formulae have been 

 established by which the resultant output for a given input may be 

 calculated provided the tube parameters and circuit impedances are 

 precisely known. For any commercial amplifier having several stages 

 the measurement of these quantities and the necessary calculations 

 would be a slow procedure. By experimental methods it is possible 

 to determine directly and quantitatively the distortion that occurs 

 in any particular case. This has been done for a number of amplifiers 

 under various load conditions with a view to establishing convenient 

 criteria by which it is possible to determine quickly and easily how 

 much energy any amplifier will transmit without serious distortion. 

 The amplifiers dealt with were all audio-frequency amplifiers so that 

 no questions of radio frequency amplification or of intentional rectifi- 

 cation or modulation are considered and the measurements were all 

 made with single frequency inputs as this naturally forms the basis 



