of Microprocessors

VOLTAGE-CONTROL METHODS 97
Perhaps a concrete example will help to clarify these terms. Figure
3-7A shows an unmodulated signal at 1,000 Hz and its spectrum, which, of
course, consists ofa single line, at 1 kHz. In Fig. 3-7B, a modulating signal
of 100 Hz has been imposed, and its amplitude is such that the original
unmodulated signal now swings between 800 Hz and 1,200 Hz for a deviation
of 200 Hz. Now, one would probably expect the spectrum to spread outand
fill the area between 800 Hz and 1,200 Hz, but as the spectral plot
shows, such is not the case. Instead, individual sine wave component lines
have been added, some of which are even outside of the 800-Hz to 1,200-Hz
range. These added frequencies are often called sideband frequencies, a term
borrowed from radio transmission jargon. Actually, a close look at the modulated
signal's waveform reveals that its shape repeats exactly 100 times/sec.
So according to Fourier's theorem, component frequencies of this waveform
can only exist at multiples of 100 Hz as the spectral plot indeed shows. To
the ear, the result is a 100-Hz tone with a rather thin, horn-like timbre.
In the situation just described, the modulating frequency is 100 Hz,
the deviation is 200 Hz, and the modulation index, therefore, is 200 Hz/lOa
Hz = 2. Figure 3-7C shows the result of increasing the amplitude of the
modulating signal such that the modulation index increases to 4. Additional
spectrum lines are visible, and those that were present with the lower index
have changed somewhat in amplitude. The audible pitch is still 100 Hz due
to the continued harmonic spacing of 100 Hz, but the timbre is thicker, due
to more low-frequency content, and less horn-like due to greater spreading of
the spectrum.
A continued increase in the modulation index causes the formation of
an even wider spectrum to the point that the lower sideband frequencies try
to go negative. What actually happens, though, is that they are reflected
back into the positive frequency domain where they mix with other sideband
frequencies already present. The resulting amplitude of a mixed sideband
frequency (also a harmonic in this case) is dependent on the exact phase
between the modulating frequency and the modulated frequency.
Effect of Deep Frequency Modulation
If the modulating frequency is increased to 200 Hz and its amplitude is
adjusted so that the modulation index is equal to 2, then the waveform and
spectrum ofFig. 3-7D results. Note that the relative amplitudes of all of the
spectral components are the same as they were in Fig. 3-7B except that they
are spread out to 200 Hz spacing. The ear now interprets this as a 200-Hz
tone. Thus·, it seems that the apparenr pitch of the frequency-modulated tone
is equal to the modulating frequency. Before jumping to this conclusion,
however, consider what happens if the modulating frequency is not a submultipIe
of the modulated frequency, such as 171Hz. The result in Fig. 3-7E
shows the expected 171-Hz spacing between the sideband components, but
these frequencies are not harmonics of a common fundamental unless 1 Hz is