THE BIASED IDEAL RECTIFIER 



153 



or 



Po = 



(i+|^)p. 



(2.12) 



where 



E = 



3i?a(l - X)2/'i 



4\/2 

 = ?^ 



/ ^ 1 -*X \ 



P 1 1> "ij ^' 2 / 



(2.13) 



V2P[2(1 - ife' + )fe')£ - (2 - yfe')(l - k')K]. 



1.4 



1.2 



15 20 25 



Pq in volts 



Fig. 8. — Performance of 3/2 — power-law rectifier as an envelope detector with impedance 

 of signal generator low except in signal band. 



By combining the curves of Fig. 7 giving V in terms of P with the above 

 equations giving the relation between P and Pq, we obtain the curves of 

 Figs. 8, 9, 10, giving F as a function of Pq. The curves approach linearity 

 as Ra is made large. On the assumption that the curves are actually linear, 

 we define the conversion loss D of the detector in db in terms of the ratio 

 of maximum power available from the source to the power delivered to the 

 load: 



D = 10 log! 



Po/8ro 



vyR 



= 10 logi 



m 



R^ 



Sro 



(2.14) 



Curves of D vs r^/R are given in Figs. 11 and 12. The optimum relation 

 between r^ and R when the forward resistance of the rectifier vanishes has 

 long been known to be r^/R. — .5. The curves show a minimum in this 



