Relations of Carrier and Side-Bands in Radio 

 Transmission 1 



By R. V. L. HARTLEY 



Synopsis: This paper discusses generally the characteristics of carrier 

 transmission as applied in radio and in carrier current communication o\er 

 wires and analyses the factors which affect the faithfulness with which such 

 systems reproduce the signals imparted to them. Modulation is shown to 

 generate two side bands which, with respect to frequency, lie just above and 

 just below the carrier frequency, the frequency width of each side band 

 being the same as the frequency width of the original signals. Upon detec- 

 tion, currents of frequencies corresponding to the difference frequencies 

 between all the possible pairs of component frequencies of the side bands and 

 carrier are produced and, in general, are all found in the received message. 

 It is therefore impossible to transmit messages, either telephone or tele- 

 graph, by carrier which will be absolutely free of distortion, but since the 

 amplitude of any particular difference frequency is proportional to the 

 product of the amplitudes of its two generating frequencies the distortion 

 can be reduced below a troublesome value by maintaining the amplitude 

 of the original carrier sufficiently large with respect to the amplitudes of the 

 signal components. The distortion which arises from phase shifts between 

 the component frequencies of the transmitted message and carrier is also 

 considered. 



The paper discusses single side-band transmission and carrier suppression 

 with homodyne detection and their various merits are pointed out. Single 

 side band transmission reduces the width of frequency band required for 

 each message. Carrier suppression results in a saving of power, or a more 

 economical expenditure of power, it having been determined that for proper 

 freedom from distortion the power of the carrier component alone, when 

 transmitted, should be rather larger than the peak power in a carrier sup- 

 pression system. The use of local carrier in homodyne radio telephony 

 assists in frequency selection in the sane way as does the heterodyne wave 

 in radio telegraph reception. The same applies also to static interference 

 and, as the object of high power stations is to make the signals large com- 

 pared with static, there is a gain in concentrating the power in side bands 

 rather than in carrier. 



Consideration of distortion arising from phase shifts shows that in homo- 

 dyne telegraphy distortion can most readily be avoided by transmitting 

 both side-bands, while in telephony these factors favor the transmission of 

 only one side-band. The power of the reproduced signals is twice as 

 great with two side-bands as with one, but there is no choice between one 

 and two side-bands on the basis of the ratio of signals to interference. 



The result of using a local detecting frequency which is not exactly 

 equal to the original carrier frequency is discussed, and a balanced detector 

 is described by means of which the distorting effect of the received carrier 

 may be very much reduced. Considering a local carrier which is out of 

 synchronism with the original carrier, it is again found that single side- 

 band transmission is most favorable in telephony, and the transmission 

 of both side-bands is best in telegraphy. Editor. 



AS indicated by the title, this paper will discuss some of the 

 phenomena associated with radio transmission in terms of the 

 carrier currents and side-bands into which a modulated wave may 



1 Presented before The Institute of Radio Engineers, New York, December 13, 

 1022. Printed in the Proceedings for February, 1923, and reprinted here by per- 

 mission of the Institute. 



90 



