Tube FM Modulation Exciters and Transmitters -------------------------------------------------- The following are 9 ways that commercial tube type FM exciters and transmitters generated FM modulation. Armstrong Method - Armstrong "Rider & Uslan" pg 86, 102, 168 Direct FM - Reactance Tube across Oscillator LC RCA bte-10b (in btf-10d) - Varactor Diode across Oscillator LC RCA bte-10c - Diode Tube across Oscillator LC Westinghouse fm-3 Indirect FM - Phasitron GE bt-1-b - Cascade Phase Shift Raytheon rf-250 - Serrasoid Phase Shift Gates fm-1b - Crystal Osc Buffer Phase Modulator Link ufs - Split RF Path Phase Modulator Hallicrafters ht-22 FM Notes Recall that commercial FM broadcasting uses a 75 usec "pre-emphasis", i.e. for audio frequencies above about 2.1 kHz the frequency deviation of the RF carrier depends on both the amplitude and the frequency of the audio signal that is modulating the RF carrier. For true FM modulation, the peak deviation of the RF signal caused by a modulating audio sine wave, is proportional to the amplitude of the modulating audio signal and is independent of the frequency of the audio signal. Deviation Ratio (DR) is the peak frequency deviation of the RF carrier divided by the frequency of the modulating audio frequency, i.e. dev F_rf (Hz) DR = --------------- F_audio (Hz) The Deviation Ratio is sometimes called the Modulation Index. Note that for a given modulating audio frequency, as you increase its amplitude going into the FM transmitter, the Deviation Ratio of the RF signal coming out of the transmitter increases proportionally. Note also that the Deviation Ratio is inversely proportional to the frequency of the modulating audio signal. The sidebands of an FM signal are symmetrically located at integer multiples (1x, 2x, 3x, ...) of the modulating audio frequency both above and below the RF carrier frequency. The amplitude of a the sidebands is given by Bessel functions of the first kind. The amplitude of the Nth sideband is given by the "N" order Bessel function of the Deviation Ratio. For a small Deviation Ratio only the first and second order Bessel functions have significant amplitude. Note that for Deviation Ratio values that are "zeros" of the zero order Bessel function that the amplitude of the RF carrier is zero. Note that for a given modulating audio frequency, as you increase its amplitude going into the FM transmitter, the overall structure of the sidebands changes (they do not just grow in amplitude). The approximate bandwidth of an FM signal is given by "Carson's rule". Carson's bandwidth rule is expressed by the relation CBW = 2(Fdev + Fm) where CBW is the bandwidth requirement, Fdev is the peak frequency deviation of the RF carrier, and Fm is the frequency in the modulating audio signal. For example, an FM signal with 5 kHz peak deviation, and a maximum modulating audio frequency of 4 kHz, will require an approximate bandwidth of 2(5+4) = 18 kHz. Carson's rule does not apply when the modulating signal contains discontinuities, e.g. square waves. Carson's rule is from a 1922 paper: J.R. Carson, "Notes on the theory of modulation", Proc. IRE, vol. 10, no. 1 (Feb. 1922), pp. 57-64. Because of the infinite orders of the Bessel function a theoretical FM signal will have an infinite number of sidebands. But the amplitude of the higher order sidebands falls off quickly so that for most normal modulating audio signals all of the significant sideband energy (98% or more) is contained within the Carson's rule bandwidth. In the vacuum tube era Serrasoid modulation was one of the popular methods of generating an FM signal. Serrasoid modulation is really a Phase modulation system so the audio input signal must be distorted by a 1/f gain filter before it goes into the modulator in order to generate an FM output signal. Serrasoid modulation was designed by James R. Day of REL (Radio Engineering Laboratories) which was Edwin Armstrong's research lab/company). It was first described by Day in the October 1948 Issue of Electronics magazine on pages 72-76.