316 BELL SYSTEM TECHNICAL JOURS A L 



di 

 de 



(2) 



Inserting (2) into (1) and calling G the value of g at Ec we obtain 



^= j_^ gde + Gv + --v +--V -\--~v ■■- (3) 



The first term of this expression is the space current of the tube at no load, 

 that is when v = 0. On the g-e diagram, Fig. 1, it represents the area under 

 the curve from the tube cut off C to the tube bias Ec . The second term 

 represents the function of the tube as an amplifier. The third term repre- 

 sents the second-order modulation current. The latter is responsible for 

 the objectionable generation of a second harmonic in an amplifier and the 

 useful presence of the second harmonic in the frequency doubler, the direct 

 current in a rectifier and the sidebands in a modulator. 



The fourth and higher terms represent, in general, undesirable effects 

 of modulation. They are usually smaller than the first two and, since their 

 effects are additive, the first three terms of expression (3) may be studied 

 profitably disregarding the others. If necessary, the effects of the higher- 

 order terms may be added later. 



The Idealized Parabolic Pentode 



If, over a certain range of grid biases Ca to cb , the effect of the fourth and 

 higher terms of series (3) is negligible the g-e characteristic will be a straight 

 line. Herein lies one of the advantages of the method, for a straight portion 

 of a curve can be easily selected by inspection and checked with a straight 

 edge. It is thus possible to select easily such a tube and operating point 

 that third and higher-order modulation products are absent in the output. 

 There is no such simple method of verifying whether a current characteristic 

 is parabolic. That there are tubes having approximately straight portions 

 of g-e characteristics can be verified by inspection of (Fig. 1) where the 

 characteristic of the 6AG7 is given. 



Since a portion of the g-e characteristic is a straight line, the third term 



coefficient — may be replaced by the ratio -^ where Ae is an arbitrary inter- 

 ne Ae 



val of grid voltage and Ag the corresponding change in g. In many of the 

 following computations it will be advantageous to use for Ae the total excur- 

 sion of the grid voltage. 



On the basis of the simplifying assumption of a paraboUc pentode it is 

 possible to derive the simple formulae given below which cover the perform- 

 ance of the tube as an amplifier, rectifier and modulator. 



