448 BELL SYSTEM TECHNICAL JOURNAL 



pure sine wave C<i contributes to the constant term which represents 

 the change in direct current, Cx and d contribute to the fundamental 

 component of the plate current, C^ gives rise to the second harmonic and 

 C3 gives rise to the third harmonic current. When g is a complex wave 

 the subscripts indicate the order of modulation ^ to which each 

 coefficient applies. 



The h coefficients may be readily converted into quantities de- 

 pendent on M, ^0, and their derivatives; we have 



^ dIb/dE„, bio 



and 



l/Ro = dhjdE,,, = ^10, 



so that 



JJlIRo = ^01- 



Succeeding coefficients are obtained by differentiating with respect to 

 Ep and to Ec- For example, 



1 dRo 



020 = 



2Ro~ dEp^ 



_ 1 djJL jx_ djx__ M" dRo 



'' IRodE.., ' 2RodE,, IRo'dEp, 



The b coefficients may be obtained directly from the family of 

 characteristic curves either graphically or analytically, when the 

 operating point is specified. If we obtain our coefficients from the 

 fx and Ro curves, however, derivatives of a lower order are required 

 than we need in dealing directly with the static characteristics. A 

 family of /x-curves is shown in Fig. 2, and a family of Rq curves is 

 shown in Fig. 2a. 



Results applying to the four element tube which are obtained by 

 methods analogous to the above may be stated briefly. If we express 

 the change in plate current by 



/ = Cio€ + Coye + Cooe- + Ciiee + Co^e^ • • • , 



where e and e represent the alternating potentials on the two grids, 

 3 The new frequencies produced by modulation are given by the expression 



F = 1 m/i ± n/2 ± ■ • • 1 , 



where /i, f^ are impressed frequencies and m, n are integers or zero; the order is 

 simply the sum oi m, n, • • • . 



