THEORY OF MULT I -ELECT RODE VACUUM TUBE CIRCUITS 671 



General Case 

 Let the impressed grid e.m.f. be 



«ff = Z^acos {c^ht + Kh) = RT,khe'^''»'+"'\ i = V- 1 (11) 



where the summation extends from h =^ 1 to /j = n, and the letter R 

 before an expression means its real part. Referring to Fig. 2 it may- 

 be shown that 



(12) 



where 



Z(co) 





X [Z2(fp + Z/) + r^Z/] 



- Zg'Zp'iiXgZi - ;'„)(mpZ2 - O}, (13) 



«i 



/ N ^ Zi[Z2(rp + ZpQ + rpZp'] 

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



02(0)) = 

 asCco) = 

 a4(co) = 



ZiZp'{iXpZi — Tp ) 



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



Zi{fXpZ2 -\- (j-pZp -\- Zp') 

 {Z, + Z,){Z., + ZJ) ' 



ZxZiTp + Z\ZiZp{\ — MwMp) + ZirpZp'(l + Mr;) 



(Zi + ZJ(Z2 + Z/) 



Z/(a)) = 



Zz + Zp 



Z/(co) 



Z\Zg 



Zx + Zg 



(14) 

 (15) 

 (16) 

 (17) 

 (18) 



The right-hand expressions in (13)-(18) are to be evaluated at co. 

 If we write 



Z{o:) 



Oik 



M 



Z(a,) 



e-iw("), k = 1, 2, 3, 4, 



(19) 



