36 BELL SYSTEM TECHNICAL JOURNAL 



curve. The variation with time of a large carrier voltage and a small 

 signal voltage are also indicated. Now if we consider the carrier to 

 provide a varying bias, then at any typical point /o we can consider 

 the signal voltage to sweep over a small segment (a, b) of the modulator 

 characteristic. The resistance is practically constant over this seg- 

 ment and of magnitude 



^ = s' (') 



the derivative being evaluated at the carrier voltage under considera- 

 tion. In general this resistance varies from point to point of the 

 carrier cycle. Thus the carrier enters the signal-sideband relation 

 only through the variation of a resistance facing the signal and modu- 

 lation products. 



If the current-voltage characteristic is a smooth curve the resistance 

 varies smoothly over the carrier cycle. If the characteristic is made 

 up of two straight lines the resistance switches between two constant 

 values. This latter is approximated by most rectifiers, such as diode 

 and copper-oxide rectifiers with suitably large carrier amplitudes; 

 it is called by analogy a commutator modulator. 



As a simple example of a variable resistance consider the char- 

 acteristic 



i = av -\- bv^, (2) 



from which 



llR = ~ = a-\- 2bv. (3) 



av 



If the impressed carrier potential, v, is P cos pt, the conductance is 



G = -1 = a + 2bPcos pt. (4) 



K 



More generally, the resistance or conductance for a given char- 

 acteristic can be expressed as a series 



CO 



R = ro -\- Y^lvn COS npl, (5a) 



1 



or 



oo 



G = g<i-\- Y^lgn COS npi. (56) 



Here the coefficients depend only on the modulator characteristic and 

 the carrier amplitude. In special cases some of the coefficients vanish. 



