Rca1948FrequencyModu.. - The New Jersey Antique Radio Club

468 FREQUENCY MODULATION, Volume Ithere be no resistive component. A complete answer to this problemis not attempted here, but a particular combination of fields has beenfound which yields a much larger reactive current than many otherusual field combinations. It also has the advantage that the loadingcan be made negligibly small.II.Lumped-Circuit TreatmentWhen free electrons are introduced into a rapidly oscillating electromagneticfield, there is in general an exchange of energy between theelectrons and the field. The electrons oscillate and induce oscillatingimage currents on the surfaces of the field boundaries. These surfacecurrents are proportional to the field amplitude and in generalare not in phase with the oscillating field. Since these currents areproportional to the field, a linear admittance function relating thecurrents to the field can be written. This electronic admittance canbe handled as a conventional circuit element in conjunction with aproper equivalent circuit to represent the over-all system. The realpart of the electronic admittance represents an energy transfer betweenthe oscillating electrons and the electromagnetic field, and the imaginarypart represents a change in the resonant frequency of the system.The first section of the paper treats the problems of estimatingthe change in admittance across a pair of parallel-plane electrodes dueto the introduction of an electron beam moving between the parallelplanes and in the direction of a constant magnetic field. From thischange in electronic admittance one can calculate the change in theresonant frequency of the oscillating system coupled to the parallelplaneelectrodes.Calculation of Electronic AdmittanceL. Malter 1 has studied certain phases of the problem, but his resultsare not readily applicable to the problem considered here.Consider a pair of parallel plates a distance d apart, infinitely longin the y direction, and of length L in the z direction, as indicated inFigure 1. In the z direction is a constant magnetic field H. Let arectangular electron beam enter the region between the plates atz = x — 0, with velocity v in the z direction. Between the plates is anoscillating electric field E x in the x direction which is constant overthe length and width of the plates. (Assume no fringe field. This1L. Malter, "Deflection and Impedance of Electron Beams at High Frequenciesin the Presence of a Magnetic Field," RCA REVIEW, vol. 5, pp.439-454; April, 1941.