where m refers to the modulating signal and oo » oo for reasons not of 



c m 



interest here. The process of modulation results in a combination of 

 Equations [A-1] and [A- 2] into the form 



a = A cos CD t + k A cos to t cos ca t [A-31 



c cam m c 



= [a + k. A cos CD t] cos CD t 



cam m c 



where k is a proportionality factor which determines the maximum variation 



in amplitude for a given modulating signal a . The term [A + k A cos cD t] 

 '^ m camm 



is the envelope of the modulated carrier frequency in Equation [A-3]. 



A trigonometric expansion of Equation [A-3] results in the component 



separation of the modulated carrier frequency 



m A m A 



a = A cos CD t + —: — cos [ca + co ]t + — r — cos [cd - go ]t [A-4] 



cc2 cm2 cm-^ 



where m = k A /A is called the modulation index and determines the 

 a a m c 



degree or nature of the modulation as dictated by A and A . A sample 



m c 



of a modulated carrier wave given by Equation [A-3] appears in Figure 14. 

 The graph of Equation [A-4] is shown in Figure 15 as a frequency spectrum 

 of the relative amplitudes of the component waves in the modulated signal. 

 Equation [A-4] and Figure 15 show that the frequencies of the resultant 

 modulation are the carrier frequency and the sum and difference of the 

 carrier and modulating signal. 



Consider now an example where a carrier signal of 97,100 cps is 



mixed with a modulating signal of 100 cps. The resulting frequencies in 



Figure 15 will be, from left to right; 97,000 cps, 97,100 cps, and 



97,200 cps. If then a filter designed to pass only 97,000 cps receives 



the modulated signal, only that component which is the lower sideband 



31 



