1338 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



^2 = 0. This is the condition in Fig. 41. When the amphfier is operating \ 

 as a perfect Umiter, c = 1 and Si = S2 = 0.5. Thus, in this case, the side- 1 

 band *Si is down 6 db from its value when the amplifier is operating in 

 the linear region. 



When there is conversion of AM-to-PM in the amplifier, the situation 

 becomes somewhat more complex. Suppose an AM signal is fed into the 

 amplifier and that its voltage is given by 



V = Vi{l -\- a sin wj) sin Uct 



where coc and oom are the carrier and modulating radian frequencies and 

 V\ and a are constants. The outputs will be given by 



V = KVi[l + «(1 — c) sin oo,nt] sin {coct + kpa sin co^O (5) 



Here K is the amplification, c is the compression factor and kp is a factor 

 which is a measure of the AM-to-PM conversion. It is seen that kp is 

 the output phase change for a given fractional input change a. Thus 



rCp — 



A^ 



a 



(6) 



where AO is the phase change in radians caused by a fractional input 

 change a. Later on it will be desired to express kp in terms of degrees 

 phase shift per db change in input amplitude. To express a in db we 



i(i-c) ^ 



AM 

 VECTORS 



4^ 



PM 

 VECTORS 



(a) 



(4) ' 



Fig. 42 



(a) After passing through an amplifier in compression tlie AM sidebands are 

 reduced in amplitude but the PM sidebands are unaffected. The lower two side- 

 bands which represent a signal at frequency fi — Af no longer cancel and so there 

 is a net signal at that frequency. 



(b) The locus of the resultant signal now assumes an elliptical shape. 



