538 BELL SYSTEM TECHNICAL JOURNAL 



sions are not equal, then there is a distortion which may be very easily 

 exhibited by considering the case where the difference between 

 (/3io25 + /3975)/2 and jtJiooo equals 90°. The current which then results is 

 modulated by 50 cycles whereas the original wave was modulated by 

 25 cycles. Where the difference in question is intermediate in value 

 between and 90°, the detected modulating wave is complex, but has a 

 component equal to 25 cycles. This component gradually gets smaller 

 and disappears completely when 90° is reached. Now, if the circuit is 

 made still longer, the 25-cycle component in the detected modulating 

 wave again makes its appearance but has suffered a discontinuous shift 

 of 180° in passing through the extinguishing point. By the time the 

 phase difference in question has reached 180°, the received wave is 

 distortionless except for the phase shift of 180° in the envelope which 

 is not apparent, or at least is not distinguishable from a delay of one 

 half cycle. 



With this distortion in mind, it will now be apparent that the delay 

 suffered by the modulated wave we are considering is no longer a 

 definite quantity. However, it can be made definite for practical 

 purposes by confining attention to the 25-cycle component of the 

 envelope only. The distortion in question consists merely in adding 

 other components to this one but does not shift its phase (except for the 

 discontinuous change spoken of above). Consequently, for practical 

 measuring purposes, if a device is used which eliminates the various 

 harmonics of the 25-cycle current, this wave is perfectly definite for 

 delay measuring purposes excluding the exceptional case where the 

 fundamental component passes through zero. 



These two forms of envelopes have been discussed in more or less 

 detail because of the fact that they are the simplest ones for transmis- 

 sion without phase distortion. For this reason they have been used 

 as the basis of the measuring devices which will now be described. The 

 phase shift suffered by the envelope during transmission can be meas- 

 ured by comparison with a standard of the same frequency as the 

 modulating frequency. This will be, of course, a direct measure of 

 the envelope delay. 



From the preceding discussion of some of the principles involved in 

 the transmission of modulated waves, it is evident that the phase shift 

 during transmission of the simple envelope considered is equal to one 

 half the difference of the phase shifts of each of the sideband fre- 

 quencies. This phase shift of the envelope is then the difference in 

 phase shift for a definite frequency interval and is quite convenient 

 for the measurement of the envelope delay. The envelope delay so 

 measured is that for some frequency intermediate between the two 



