PERCENT OF MODULATION. - Before we explain 100-percent modulation in an fm system, let's review the conditions for 100-percent modulation of an AM wave. Recall that 100-percent modulation for AM exists when the amplitude of the modulation envelope varies between 0 volts and twice its normal umodulated value. At 100-percent modulation there is a power increase of 50 percent. Because the modulating wave is not constant in voice signals, the degree of modulation constantly varies. In this case the vacuum tubes in an AM system cannot be operated at maximum efficiency because of varying power requirements.

In frequency modulation, 100-percent modulation has a meaning different from that of AM. The modulating signal varies only the frequency of the carrier. Therefore, tubes do not have varying power requirements and can be operated at maximum efficiency and the fm signal has a constant power output. In fm a modulation of 100 percent simply means that the carrier is deviated in frequency by the full permissible amount. For example, an 88.5-megahertz fm station operates at 100-percent modulation when the modulating signal deviation frequency band is from 75 kilohertz above to 75 kilohertz below the carrier (the maximum allowable limits). This maximum deviation frequency is set arbitrarily and will vary according to the applications of a given fm transmitter. In the case given above, 50-percent modulation would mean that the carrier was deviated 37.5 kilohertz above and below the resting frequency (50 percent of the 150-kilohertz band divided by 2). Other assignments for fm service may limit the allowable deviation to 50 kilohertz, or even 10 kilohertz. Since there is no fixed value for comparison, the term "percent of modulation" has little meaning for fm. The term MODULATION INDEX is more useful in fm modulation discussions. Modulation index is frequency deviation divided by the frequency of the modulating signal.

MODULATION INDEX. - This ratio of frequency deviation to frequency of the modulating signal is useful because it also describes the ratio of amplitude to tone for the audio signal. These factors determine the number and spacing of the side frequencies of the transmitted signal. The modulation index formula is shown below:

Views (A) and (B) of figure 2-9 show the frequency spectrum for various fm signals. In the four examples of view (A), the modulating frequency is constant; the deviation frequency is changed to show the effects of modulation indexes of 0.5, 1.0, 5.0, and 10.0. In view (B) the deviation frequency is held constant and the modulating frequency is varied to give the same modulation indexes.

Figure 2 - 9. - Frequency spectra of fm waves under various conditions.

You can determine several facts about fm signals by studying the frequency spectrum. For example, table 2-1 was developed from the information in figure 2-9. Notice in the top spectrums of both views (A) and (B) that the modulation index is 0.5. Also notice as you look at the next lower spectrums that the modulation index is 1.0. Next down is 5.0, and finally, the bottom spectrums have modulation indexes of 10.0. This information was used to develop table 2-1 by listing the modulation indexes in the left column and the number of significant sidebands in the right. SIGNIFICANT SIDEBANDS (those with significantly large amplitudes) are shown in both views of figure 2-9 as vertical lines on each side of the carrier frequency. Actually, an infinite number of sidebands are produced, but only a small portion of them are of sufficient amplitude to be important. For example, for a modulation index of 0.5 [top spectrums of both views (A) and (B)], the number of significant sidebands counted is 4. For the next spectrums down, the modulation index is 1.0 and the number of sidebands is 6, and so forth. This holds true for any combination of deviating and modulating frequencies that yield identical modulating indexes.

Table 2-1. - Modulation index table

You should be able to see by studying figure 2-9, views (A) and (B), that the modulating frequency determines the spacing of the sideband frequencies. By using a significant sidebands table (such as table 2-1), you can determine the bandwidth of a given fm signal. Figure 2-10 illustrates the use of this table. The carrier frequency shown is 500 kilohertz. The modulating frequency is 15 kilohertz and the deviation frequency is 75 kilohertz.

Figure 2-10. - Frequency deviation versus bandwidth.

From table 2-1 we see that there are 16 significant sidebands for a modulation index of 5. To determine total bandwidth for this case, we use:

The use of this math is to illustrate that the actual bandwidth of an fm transmitter (240 kHz) is greater than that suggested by its maximum deviation bandwidth (75 kHz, or 150 kHz). This is important to know when choosing operating frequencies or designing equipment.

Q.4 What characteristic of a carrier wave is varied in frequency modulation?
Q.5 How is the degree of modulation expressed in an fm system?
Q.6 What two values may be used to determine the bandwidth of an fm wave?