DESIGN FACTORS OF THE 1553 TRIODE 521 



question. The "effective values" of the actual admittance are given by 

 equations (3) of the text, as follows: 



Gp = Gx (wo) 



Cp = i {B'x + 5./a;o) (Al-4) 



1 , , 



T" = 2 ('•^c' Bx — COo Bx) 



Let the complete admittances across nodal pairs 1-1' and 2-2' be called 

 Fie and Yte as in Fig. Al-2c, which is an abbreviation of Fig. Al-2b from 

 the point of view of the active transducer. 



1 



Yu = Gi 4- Gpi + Gil + iwCpi + ywCu + . , 



JwL,p\ 



1 



= Gie + ]wCu + : 



Y2e = Gi -\- Gp2 + G22 + i<^Gp2 + 7C0C22 + 



jojLu (Al-5) 



1 



j(j}Lp2 

 — G-ie + j(j:C2e + 



jwL^, 



where Gi and G2 are the line admittances as seen from the active trans- 

 ducer: 



Gi = G,/N\;G2 = Go/iVL 



The Q's of the circuit are defined as 



Qu = Cc'O Cie/Gie (Al-6) 



Qle = CCo C^JGle 



The insertion voltage gain (2) may be written as follows to emphasize 

 the manner in which it depends upon frequency: 



_ 2F21 / GieGze /.. ^x 



YuY-i. r (1 + Mi)(l + M2) ^ ^ 



Here /x == o'(coo) is the matching factor at band center. Frequently the 

 circuits are matched (mi = M2 = 1) to avoid standing waves in system 

 applications, and we shall discuss this case; but in any case mi and ^2 

 are constants with respect to frequency. For our standard circuits, Gie 

 and G^e are independent of frequency; also ordinarily the transadmittance 

 F21 may be considered constant for bandwidths commonly encountered. 

 There results then the fact that^the voltage gain (and phase) depends on 

 frequency Jn the sameway as (Fi^ F2e)~^ 



