Figure 211 A baseband modulating signal s effect on a carrier after frequency modulation
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Figure 212 A time-domain view of frequency
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frequency (exaggerated here for clarity) These rapid FM frequency fluctuations are evidenced by the shortening and lengthening of the carrier s wavelength on the scope s screen, creating a blurring of the signal And since wavelength equals the speed of light divided by the frequency, we can readily see that any shift in wavelength corresponds to a change in frequency The total FM transmitter power will always stay constant during baseband modulation, so the combined power or voltage in an FM signal will not vary whether it is modulated or unmodulated However, any sidebands formed by the modulation must gain their power from the carrier itself This carrier must then sacrifice some of its own power in the creation of the FM sidebands For instance, let us assume that an FM transmitter is sending out an unmodulated carrier at 100 watts When the RF carrier is modulated by the baseband signal it must give some or even all of its power to these sidebands Thus, the carrier and its significant sidebands must all total up to the original 100 watts that was present in the unmodulated carrier Indeed, at certain modulation indexes (see below), the carrier itself will actually vanish, while the sidebands will now contain all of the power An infinite number of sidebands will be created during the modulation process, since the carrier is sent through an infinite number of frequency or phase values by the continuously changing baseband frequencies This action produces an infinite amount of sideband frequencies; even a single test-tone, changing in a sinusoidal manner, has an infinite number of discrete amplitudes within a single cycle Because of the difficulties inherent in infinite, the concept of the significant sideband was created Significant sidebands are any sidebands with an amplitude that is 1 percent or more of the amplitude of the unmodulated carrier When a sideband is below this level it can be ignored, while the higher the amplitude of the baseband modulation, the higher the number of these significant sideband frequencies that will be produced
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However, unlike amplitude modulation, more than one pair of sidebands will be created for each single-tone modulation (Fig 213) The sidebands are also separated on each side of the carrier and from each other by an amount that is equal to the frequency of the single-tone baseband signal The ratio between the FM carrier s instantaneous frequency deviation (fDEV) divided by the instantaneous frequency of the modulation (fMOD) is an important FM specification, and is referred to as the modulation index We can find the number and amplitudes of all significant sidebands generated during FM modulation from the modulation index by simply reading the chart of Table 21 To use this table, first calculate the FM signal s modulation index by fDEV /fMOD; take this number and find its value under the Modulation index column; now read across The relative amplitude of the carrier, and each sideband with its number of significant sidebands, will be shown We can also find the bandwidth of the modulated RF signal by multiplying the number of significant sidebands by two, then multiplying by the maximum modulating frequency, or BW 2N fmod(max) The following is a basic example of the modulation index and its effect on what we might see in the frequency domain With a modulation index of zero, we would be generating no sidebands at all (Fig 214), since this would be just a simple continuous-wave (CW) carrier with no baseband modulation But as the modulation index increases to 15, we see in Fig 215 that the sidebands will start to consume more bandwidth This is a good example of why the frequency of the baseband modulation, and its amplitude, must be controlled so that we may lower FM bandwidth demands and adjacent channel interference (ACI) The two-way, narrowband FM radio modulation index is normally maintained at 2 or less, since the maximum allowed frequency deviation would be approximately 5 kHz with a maximum baseband audio frequency of about 25 kHz Thus, a bandwidth of between 12 and 20 kHz is customarily considered