146 



BELL 5VSTEM TECHNICAL JOURNAL 



in the second frequency, the two-frequency modulation coefficients are ob- 

 tained. Some early calculations carried out graphically in this way are 

 the source of the curves plotted in Figs. 18 to 21 inclusive, for which I am 

 indebted to Dr. E. Peterson. 



If reactive elements are used in the rectifier circuit, the voltage across the 

 rectifying element may depart from the input wave shape applied to the 

 complete network. The solution then loses its explicit nature since the 

 rectifier current is expressed in terms of input voltage components which in 

 turn depend on voltage drops produced in the remainder of the network 

 by the rectifier currents. Practical solutions can be worked out when 

 relatively few components are important. 



n 



In+ Ii 



BIASED RECTIFItR 

 UNIT 



E-InR 



effective: bias on 



Fig. 5. — Biased rectifier in series with RC network. 



As an example consider the familiar case of a parallel combination of 

 resistance R and capacitance C in series with the biased rectifier, Fig. 5. 

 If C has negligible impedance at all frequencies of importance in the rectifier 

 circuit except zero, we may assume that the voltage across R is constant and 

 equal to loR, where /o is the d-c. component of the rectifier current. The 

 voltage across the rectifier unit is then E — loR- The effect is a change 

 in the value of bias from b io b -\- IqR. If the d-c component in the output 

 is calculated for bias b + IqR, we obtain the value of /o in terms of 6 -f- IqR, 

 an implicit equation defining Io- If this equation can be solved for /n, the 

 bias b + !oR can then be determined and the remaining modulation products 

 calculated. 



A more imj)ortant case is that of the so-called envelope detector, in which 

 the imjjcdance of the condenser is very small at all frequencies contained in 

 the input signal, but is very large at frequencies comparable with the band 

 width of the s[)cctrum of the input signal. These are the usual conditions 

 prevailing in the detection oi audio or video signals from modulated r-f or 

 i-f waves. The sf)lution dei)en(ls on writing the input signal in the form 

 of a slowly varying positive valued envelope function multiplying a rapidly 



