THE BIASED IDEAL RECTIFIER 

 FXJNDAMENTALS 



159 



(3.9) 



(3.10) 



(3.11) 



(3.12) 



AWaP = 1 + -^ f f(^o + ^1 COS y) Vl - {h + ^1 cos yY 



— arc cos (^o + ^i cos y)] dy 



Aoi/aP = ki-^-f [Vl - (ko + ki COS yy 

 •K^ J e 



— {ko + ^1 COS y) arc cos (^o + ^i cos y)] cos y dy 

 Sum and Difference Products — Second Order 

 ^11 = ^ / [(^0 + ki cos y) Vl - (^0 + ki cos yy 



— arc cos (^o "1" ki cos y)\ cos y dy 

 Sum and Difference Products — Third Order 



A21 = ^ I [1 — (^0 + ki cos yYf~ cos y dy 

 6t~ Je 



The above products are the ones usually of most interest. Others can 

 readily be obtained either by direct integration or by use of recurrence 

 formulas. The following set of recurrence formulas were originally derived 

 by Mr. S. O. Rice for the biased linear rectifier: 



2n Amn + ^1 (« — m — 3) Am+l,n-l 



-{- ki (m -\- n -{- 3)Am+i,n~i + 2kon .4„,+i,„ = 



2» Amn + kl (n -j- m — 3) Am-l.n+l 



+ ^1 (w — w + 3) A „,-!,„+! + 2kon Am-\.n = 



2m ki Amn -\- {m — n — 3) Am-l,n^l 



+ (m -f n + 3)A„.+i,„+i + 2^ow ^m,„+i = 

 2 m h Amn + {m -]r n — 3) Am-i.n-\ 



-\- {m — n -\- 3)Am+l,n-l + 2^oW A^.n-l = 



By means of these relations, all products can be expressed in terms of .4 00, 

 ^10, Aoi, and An. The following specific results are tabulated: 



.^20 = 3(^00 ~ 2kiAn ~ 2^0^10) 



_ 1 \ (3.14) 



A02 — -TT- (^1^1 no ~ 2^4 11 — 2^0 -4 01) ' 

 3ki ) 



(3.13) 



