COPPER OXIDE MODULATORS IN CARRIER SYSTEMS 331 

 which is maximum for 



Rq= ■ ^'' (16) 



"V/l — KaKhZpsZqs 



The maximum efficiency is then 



K "^7 7 



-t»-a ^-^ ps^^ qa 



''7max. — 



(1 + Vl - KaKj^paZ^sf 



When equation (16) is substituted in (14) it is found that 



(17) 



R,=?-= ^"^ =. (18) 



tp Vl — KaKbZpsZ qs 



In order to evaluate KaKb, open circuit impedance measurements 

 must also be made. By superposition methods like those used in 

 obtaining equations (11) and (12) it can readily be shown that 



(19) 

 (20) 



(21) 

 (22) 



^ qa 



and KaKb can be determined from any three of the open-short measure- 

 ments by using (21) and (22). It follows that 



Z 



KaKbZpsZ qa = 1 — -^— • (23) 



Upon substitution in (16) and (18) it is found that 



Rq = <Zq^q, . (24) 



and 



Rp = ^ZpoZpa (25) 



when 3-4 is terminated in i?g for maximum efficiency. 



Open and short-circuit measurements enable us to compute the 

 optimum efficiency from equation (17) only if the transfer admittance 



