The FM signal can be defined by the familiar formula found in Equation 1 (below).
| Equation
1: FM Modulation Xc(t) = Ac Cos [Wc(t) + B Sin Wm(t)] Where: Ac = Carrier Amplitude (constant) Wc(t) = 2 pi fc (carrier frequency) B = delta f/Fm (modulation index in radians) Wm(t) = 2 pi Fm (modulation frequency) |
This formula produces a frequency modulated carrier where the amplitude of the modulation determines the instantaneous carrier frequency, and the modulation frequency dictates the rate at which the carrier frequency is deviated around its nominal center frequency. Note that in FM comprised of only one carrier, the amplitude is constant, and the information necessary for detection is contained in the zero crossings.
Adding a Second Carrier
For the purpose of analyzing the effects of a second carrier, the addition of a booster signal can be treated as interference. A second interfering carrier will both amplitude and phase (frequency) modulate an existing, desired carrier. The characteristics of this apparent modulation are given by Equation 2.
| Equation 2:
Characteristics of an Interfering Signal Modulating a Desired Siqnal Fm = |fc - fi| Where: fc = main carrier frequency |
Or, in words, an FM receiver detecting two carriers (unmodulated for simplicity), decodes a modulation tone equal in frequency to the absolute value of the frequency separation between the carriers. Moreover, the modulation index (both AM and FM) is simply the ratio of the carrier amplitudes. Notice, however, that the modulation index is never more than one, as increasing the amplitude of the interfering signal over that of the original carrier simply makes the carrier the interfering signal to the booster. For FM, B is measured in radians (see Equation 1), while for AM, B is the percentage of amplitude modulation produced.
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