The Bell System Technical Journal 



January, 1931 



The Detection of Two Modulated Waves Which Differ 

 Slightly in Carrier Frequency * 



By CHARLES B. AIKEN 



The present paper coiUains an analysis ol the detection of two waves 

 modulated with the same, or with different, audio frequencies and differing 

 in carrier frequency by several cycles or more. Both parabolic and straight 

 line detectors are treated and there are derived the expressions for all of the 

 important audio frequencies present in the output of these detectors when 

 such waves are impressed. There are discussed the types of interference 

 which result when one station is considerably weaker than the other and 

 simple attenuation formulae are employed in estimating the character and 

 extent of the interference areas around the two transmitters. Beyond the 

 use of such formulae no attention is given to phenomena which may occur in 

 the space medium such as fading, diurnal variations in field intensity, etc. 



WHENEVER one of two stations operating on the same wave- 

 length assignment wanders from its proper frequency, waves 

 are Hkely to be received which differ in carrier frequency by several 

 cycles or more. Ihider such conditions the two signals may be thought 

 of as made up of entirely distinct frequencies and phase relations 

 lietween analogous components of the two waves need not be con- 

 sidered. In the important case in which the carriers are of identical 

 frequency this is no longer true and phase and its dependence on 

 position and transmission phenomena must be taken into account. 

 This case will be reserved for future study, the present work being 

 limited to a consideration of the phenomena connected with the 

 detection of distinct frequencies. 



The most important undesired frequency which is present in 

 the output of the detector is the beat note between the two carriers. 

 It is sometimes carelessly assumed that if the frequency of this beat 

 note is reduced below the audible range the only remaining interference 

 will be due to the speech from the undesired station. Such is not the 

 case and it will be shown later on that when the beat frequency is 

 reduced below the audible range, but not to zero, there remains a group 

 of spurious frequencies which will introduce an interfering background. 

 When the undesired carrier is of relatively small intensity this back- 

 ground is a great deal stronger than the interfering speech. It is 

 therefore desirable to obtain quantitative data on the interfering spec- 



* Proc, I. R. E., Jan., 1931. 



1 



