MODULATION IN VACUUM TUBES 447 



Solutions for the Plate Circuit Components 

 We now pass on to a consideration of the operation of the tube 

 working into a plate resistance. The more general case of a load 

 impedance which is a function of frequency may be treated by appli- 

 cation of the equations derived above, but it will serve our purpose 

 here to deal with the case of a pure resistance load since the experi- 

 mental work was done for that particular case which is of considerable 

 practical importance. 



If / is the alternating component of the plate current, we have 



from (3) 



/ = /. - /(£,„ £,,) 



and /, it is seen, is a function of the two variables v and e. The 

 fjuantity v depends on e of course, so that / may evidently be expressed 

 as a function of e alone or 



/ = 'zGe^ (4) 



A solution of the problem therefore consists in determining the C's in 

 terms of the circuit and tube parameters. 



The change in plate potential v may further be expressed as 



v= - RJ = - RJZCeK (5) 



k=l 



The C's are then determined by putting (4) and (5) in (3) and identi- 

 fying coefficients of similar powers of the variable. We have then 



in which powers higher than the third are neglected for this, the 

 first approximation. Carrying through the substitutions we obtain 

 the solutions 



Ci = &oi/(l + b,,R), 



C2 = (boo + b,oR'Ci' - bnRCO/C^ + byoR), .^. 



_ b,, - RC^bn + ig-Ci^&2i - R'Ci'bs, - RC2bn + 2R?C,CJ}2^ 



1 + b,oR 



The first equation, which leads to the first approximation to the 

 fundamental current, is identical with that obtained on the basis of n 

 constant, but the higher orders are distinctly changed. When e is a 



