330 BELL SYSTEM TECHNICAL JOURNAL 



Zpo = impedance at p for open circuit at q\ 

 50 — q p\ 



Zp> = " " p " short " " g; 



Zq, = " " q " " " " p; 



Rq = impedance termination at frequency q; 

 Rp = impedance of modulator at frequency p with i?g at 3-4 terminals 



for frequency q; 

 Ka = transfer admittance between voltage at frequency p applied 



at the 1-2 terminals and short-circuit current at frequency q 



flowing from 3-4 terminals; 

 Kb = transfer admittance between voltage applied at 3-4 terminals 



at frequency q and short-circuit current at frequency p 



flowing from 1-2 terminals. 

 For Rq first short-circuited 



U^ = PKa, (9) 



ip, = /- • (10; 



^ JDS 



If the short circuit on Rg is removed, the following two additional 

 currents will flow due to superposition of a new voltage — iqR, 



and 



(11) 



(12) 

 (13) 



(14) 



The efficiency of the frequency translation, measured by the ratio 

 of the power delivered to i?, to the power into terminals 1-2, is 



i^r- 



i -R . . . 



"^ ipP ~ J_ _ KaKbR, ' ^ ^ 



P' 1 _1_ "^ 



7 



^ as 



