Modulation Index And Transmitter Power Relationship In Multiple Channel FM Systems (1972)

By By Dr. Joseph J. Vogelman, Chief Operating Officer, & Malcolm Reader, Director of Engineering, Laser Link Corp.

In a recent paper titled "Understanding Laser Link's FDM/FM Airlink System", appearing in this month's issue of Cable News (copies available on request from Laser Link Corp.), the authors reviewed the operation of frequency division multiplexed FM systems. A point was made of the fact that the FM system superposes the various subcarriers and behaves as each one existed alone in its part of the output spectrum. This corresponds to the experience of many engineers who have tested a visual carrier for SNR and an aural carrier for SNR on a single TV channel FM microwave system and have observed that the signal to noise ratios of the individual carriers are independent of the presence of absence of the other subcarriers. By the same process of superposition, it is possible to determine the effective spread of energy from the carrier to the sidebands when many television channels are combined by frequency division multiplex (see figures 1 and 2) and then impressed as a modulation drive on an FM system. In all FM systems, the concept of energy left in the carrier as opposed to energy in the sidebands must be dealt with using one precaution. Recalling that an AM system, under conditions of increasing modulation, shows increasing energy delivered to the sidebands, until 100% of modulation is reached, the communications engineer is careful to avoid further drive because this will result in overmodulation and distortion of information. 100% modulation in AM corresponds to 50% of energy in the carrier, and 50% of energy in the sidebands. If one sideband is fully suppressed, 66% of the energy is left in the carrier, and 33% is in the unsuppressed sideband. As a practical matter, suppressed sideband television with average picture content, and with the FCC standard for 0.75 mhz of the suppressed sideband still carried on the air 46% (sideband energy)- 54% (carrier energy) relationship is typical. With FM, there is no corresponding physical limitation on the depth of modulation, other than the quality of the FM equipment, and the limitations of spectrums spread imposed by legal use of bandwidth. Thus with FM systems, equal effective use of power as compared with a 100% modulated AM carrier corresponds to a modulation index of approximately 1.00 (see references 1 and 2). However, the FM system can be driven harder and harder into modulation, and at modulation index of 2.403, 100% of the energy is then in the sidebands. Further drive is quite practical with a linear FM system, producing well known the condition of improvements of signal to noise ratio with greater modulation indexes. Under these conditions, the ratio of energy in sidebands to energy in carrier grows poorer, that is to say the carrier then shows an increasing percentage of power at the expense of energy in the sidebands, while signal to noise ratio is increasing. Therefore to use the analogy of energy in sidebands as an indicator of useful distribution of energy, one must confine the area of interest to values of modulation index below 2.403. Above that value of modulation index, the analogy can be extended by using the effective power in sidebands, and referring to them as more than 100%. Thus with a modulation index 2.93 one can refer to the energy in the sidebands as being effectively 150%.

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