THEORY OF THREE-ELECTRODE VACUUM TUBE CIRCUITS 529 



The driving e.m.f. given by (18) thus consists of a number of 

 sinusoidal components including one of zero frequency. By means 

 of the superposition theorem and the mesh equations we obtain the 

 current and voltage distribution for our equivalent circuit in Fig. 3. 

 Let us for instance calculate the instantaneous current flowing through 

 the impedance consisting of Zp and Zz in parallel and indicated by C in 

 Fig. 3. The result is 



C= M 



F(coi) 

 Z(coi) 



K^ + 



F(C02) 



Z{wi) 



S^ 



Z(0) 



+ • 



+ 



F(a:{) 



ZiccO 



K^ 



\Z(2co,) 

 FM 



•COS (2coi^ — 2<p(o}i) — \p{2coi)) 



Zicoi) 



S' 



-f 



+ 



|Z(2C02)| 

 F(cOi)F(c02) 



•COS (2co2^ — 2^(aj2) — ^(2^2)) 



(19) 



Z(cOi)Z(c02) 



KS 



|Z(coi — 0)2) 



F(0}i)F(c02) 



COS ((oji — coo)^ — ip(coi) 



+ ^(0)2) — i/'(wi — CO2)) 



Z(coi)Z(a;2) 



KS 



|Z(coi + CO2) 



COS ((wi + 0}2)t — (p{o}i) 



— <p{(^2) — ^(oOl + W2)) 



where \p(co) is defined by 



Z(co) = |Z(co)!e^^(")(^ = V^T). 



(20) 



Let us now consider the peak value of the current of lower side-band 

 frequency. This value is from (19) 



MKS 



F(i,}i)F{ojo) 



If we write 



|Z(co)| 



i?fl 



Z(coi)Z(aj2)Z(coi — 0:2) 



1 + 



Ro + fxZ, 



- A- 7 ' 



Z2 + Z/ 



F(co)|= (m+1) 



1 + 



Z2 + ZJ 



Zi 



(z, + Zi)(z; + Z2) 



M + 1 



Z2 + Zp 



(21) 

 (22) 



(23) 



