528 



BELL SYSTEM TECHNICAL JOURNAL 



e.m.f. is impressed in the plate circuit and that the impressed e.m.f. 

 in the grid circuit is given by ^ 



K cos Oilit -\- S cos C02^. 



(14) 



We now find the instantaneous value of tiCi -\- Vi by solving the mesh 

 equations for the equivalent circuit of Fig. 2, The result is: 



ixei + Vi, = Ro 



where 



FM 



ZM 



F{o:) = 



K cos (coi/ — ^(«i)) 

 F{w^ 



+ 



6* cos {(Jilt — (p{u2)) 



Z(C02) 



Zi(juZ2 + iJ'Zp + Z/) 

 (Z, + Zi)(Z/ + Z2) ' 



Z/(i?o + fiZ/) 



(15) 



Z(co) = i?o + Z/ + 

 ZsZp 



7 ' = 



FM = 

 Zic) 



Zz + Zp 



7 ' = 



Z2 + Z/ 



Z\Zn 



(16) 



Zi + Z„ 



Z(co) 



g-v(")i(i = V- 1). 



In equations (16) we note that Zi, Z2, Z3, Z^ and Zp all are complex 

 impedances. The driving e.m.f. for the second approximation is 



RoPiiliei -h v^f. Letting 



M = Ro'P2, 



we get from (15) 

 RoP2(.tJ^ei + ViY 

 = M 



(17) 



FM 



Z(coi) 



i^2 + 



i^(w2) 



Z(C02) 



52 



+ 

 + 

 + 

 + 



FM 



Z(coi) 

 ^(0)2) 



Z(C02) 



F(o}i)F(o)2) 



Z(coi)Z(aj2) 



7^(cOl)F(c02) 



Z(coi)Z(aj2) 



X2 COS (2co,t - 2<p(coi)) 

 S^ cos (2co2^ — 2^(0)2)) 



^"6" COS ((cOi — CO2)/ — ^(cOi) + <P(^2)) 



(18) 



i^5 COS ((coi + 002)^ — v'(wi) ~ ^(''^2)) 



^ The extension to any number of sinusoidal e.m.f.'s of arbitrary phases in both 

 plate and grid circuit is obvious. 



