THE BIASED IDEAL RECTIFIER 



163 



To complete the evaluation of Z2, assume a relation of the following type 

 with undetermined constants Ci, C2, C3, C4: 



I (1 - 



dii 



h (1 - T/w')' V(l - «') (1 - k' w2) 



c 



'io V(l - m2)(1 -k'u^ 

 du 



u^ ^«^ + C3 y^ (J _ ^^2) ^^j _ ^^^ ^^ _ ^3^,^ 



+ C4 



z y/Cl - z^) (1 - K^ 2^) 

 1 - 1722 



(3.29) 



2 1.2 



UJ 



< 



o 



Z 1.0 



5 0.2 

 < 



-0.2 



O 



H-0.4 



< 



N. -1 



— ^\s 



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.5 IS 2.0 



RATIO OF BIAS TO LARGER FUND^MENTAL 



Fig. 15. — Fundamentals and (Ip ± q) — product from full-wave biased zero-power-law 

 rectifier with ratio of applied fundamental amplitudes equal to 0.5. Fi = larger funda- 

 mental, F2 = smaller fundamental, F3 = (2/> ± q) — product. 



Differentiate both sides with respect to z, set z = 1, and clear fractions. 

 Equating coefificients of like powers of z separately then gives four simul- 

 taneous equations in G, C2, C3, C4. Solving for C], C2, C3 and setting z = 1 

 in (3.29) gives 



r^ du 1 r 



i (1 - vuf \/(l - W) (1 -^?^) " 2(r, - 1) [^ "^ 



_j_ (2,? - 3) k" - 7,(77 - 2) jjl 



77^ 



.2 



(3.30) 



