THE BIASED IDEAL RECTIFIER 



157 



of a linear rectifier under control of two carrier frequencies and a bias. 

 The results may therefore be applied to general modulator problems based 

 on the method described by Peterson and Hussey**. We may also combine 

 the Fourier series with proper multiplying functions to analyze switching 

 between any arbitrary forms of characteristics. We give the results for 

 positive values of ^o- The corresponding coefficients for —ko can be ob- 

 tained from the relations: 



(3.1) 



-^00 ^00 



Here we have used plus and minus signs as superscripts to designate co- 

 efficients with bias +^o and — ^o respectively. We thus obtain a reduction 

 in the number of different cases to consider, since Case III consists of nega- 

 tive bias values only, and these can now be e'xpressed in terms of positive 

 bias values falling in Cases I and II. It is convenient to define an angle 6 

 by the relations: 



^ T^ ^^^-^ k,> \,h- h<\ . (Case I) \ 

 ,h + h<\,h- k,> -\ (Case 11)/ 



arc cos - 



Zero-Power Rectifier or Total-Limiter Coefficients 

 Setting y(2) = a in (1.10), 



—^ = 1 — — / arc cos (^o + ki cos y) dy. 

 2a r Je 



— = 4 f Vl - {ko + kr cos yy dy 



An ^ 2h r sin^ y dy 



a TT^ ie \/l — (^0 + ^1 cos yY 



— = — / cos Vl — (^0 + ^1 cos y)- dy \ {2>3) 

 a TT^ Je 



— = — -^ / (^0 + ki COS y) Vl - (^0 + ki cos yy dy 

 a TT^ J e 



Aw. _ 2^1 r sin^ y cos y dy 



a TT^ h Vl — (^0 + ^1 cos yy 



— - — — / (^0 + ^1 COS y) COS y Vl — (^o + ki cos y)' dy 

 a TT^ Jft J 



' E. Peterson and L. W. Hussey, Equivalent Modulator Circuits, B. S. T. J., Vol. 18, 

 pp. 32-48, Jan. 1939. 



