Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

.TRANSMISSION THROUGH A NETWORK 447lem, when the network characteristics are expressed by means of apower series, or by means of a trigonometric series, the reader isreferred to a paper by Block. 2 )In the application of Frantz's methodit is necessary that the network response be expressed as a Fourierseries or, as was also indicated, by other series approximations. However,it is possible to obtain the amplitude and phase of the outputsignal by using point-by-point data from the network response curve;contrary to Frantz's statement, this can be accomplished without plottingthe output r.f. signal point by point as a function of time. Theadditional work of obtaining a series expression, as wellas questionsas to the proper convergence of this expression, are thus avoided.It isbelieved that the method of calculation to be described is, therefore,simpler and more straightforward, and in any event may be of interestas an alternate method of solution.To rephrase the problem: a network having a gain-versus-frequencycharacteristic given by R («)and a phase-versus-frequency characteristicgiven by 0( — v) t]+ J 2 (nif) [sin (w + 2v) t + sin (u> — 2v) t]+ ^3 ( m /) [sin (a> + 3v) t — sin (w — Sv) t~\ -\ .(2)To better visualize the action that is taking place, it is convenientto assume that the frame of reference rotates counterclockwise withan angular frequency u so that the carrier vector J (m f) remains stationary.If this is done, then the vectors with the higher angular fre-2A. Block, "Modulation theory," Jour. I.E.E. (London), Pt. Ill, vol91, pp. 31-42; March, 1944.