MEASUREMENT OF PHASE DISTORTION 537 



This is the simplest form of transmitted current to which the term 

 envelope delay can be applied. This type of wave, being made up of 

 two sinusoidal components of equal magnitude, has the important 

 property that its envelope suffers no distortion regardless of the length 

 and complexity of the circuit as long as it has no non-linear element and 

 as long as the two component frequencies are transmitted with equal 

 attenuation. 



Going back now to the original case of the 1000-cycle sine wave 

 modulated by the 25-cycle sine wave where both sidebands and car- 

 rier are transmitted, the corresponding graphical expression for this 

 current is 



2(1 + cos 25 27/) sin 1000 2^ 



and the corresponding analytical expression is 



2 sin 1000 27r/ + sin 975 27r/ + sin 1025 27r/. 



Now if the three components suffer phase changes equal to ^^to, /3iooo, 

 and /3]025, the analytical expression for the wave at the receiving end is 



2 sin (1000 27r/ - iSiooo) + sin (975 27r/ - ^3975) + sin (1025 27r/ - /3io25); 



and there is no simple corresponding graphical expression. It will be 

 convenient to consider this wave as being made up of two components, 

 one being the steady component 



2 sin (1000 27t - /3iooo) 

 and the other being a variable component 



O ^^„ /oC T~~i /3i025 — ^975 \ • / i nr»n T^i ^1025 + /3975 



2 cos 25 27r/ 7: sm 1000 27r/ r 



which is the same as the total current discussed above. The outstand- 

 ing complexity in this wave is the presence of a distortion which arises 

 from the fact that the 1000-cycle carrier wave in these two components 

 is not transmitted with the same phase change. The phase change of 

 the 1000-cycle current, making up the steady component, is equal to 

 /3iooo, whereas the phase change in the variable wave is represented by 



fiilb + /3l025 



In other words, it is the average of the phase changes at 975 and 1025 

 cycles. Now, if it happens that these two expressions are equal, then 

 there is no distortion. If, however, as is the general case, these expres- 



