646 



BELL SYSTEM TECHNICAL JOURNAL 



hand side of (46) reduces to its first term. Substitution of (47) into the 

 right hand side and selection of d.-c. components then gives: 



<P2 



'(0 



d.-c. — 



12 K 



1 - 



+ 



40 ' 2800 



- ] 



(49) 



This indicates that the rectified current decreases when the transit 

 angle d becomes appreciable. In the second part of his first electronics 

 paper/ Benham reached the conclusion that the rectified current 

 increases with frequency. To reconcile his result with (49) it is only 

 necessary to note that (49) indicates a decrease in rectified current with 

 frequency provided that the amplitude A of the first-order current 

 remains constant, whereas Benham's result was based on a constant 

 amplitude of the first-order voltage. A direct comparison therefore 

 necessitates the computation of the first-order voltage. From (41a) 

 with zero initial acceleration and velocity we have : 



{Wa-W,)x^ 



JKT' 

 12 



i-To'" 



15 



+ ^^^•^+5^0 



(50) 



Taking the amplitude of the current factor <p\"{t) to be A as in (47) 

 and the amplitude of the voltage factor {Wa — Wb)\ to be B, we find 

 from (50) that 



B'- = A' 



or 



The A- may thus be eliminated between (51) and (49) giving 



<P2 (Od.-c. — 



\2B^ 



1 + 



11 

 600 



+ 



39 



140000 



+ 



(52) 



which is in agreement with the result obtained by Benham. 



The physical explanation of the increase in rectified current which 

 occurs when the transit angle becomes appreciable follows directly 

 when it is realized that as the frequency is made higher, the funda- 

 mental component of the alternating current increases when the a.-c. 

 voltage is maintained at constant amplitude. This is because of the 

 capacitance of the diode. It is this increase in fundamental current 



