Pulse Modulated Signal Spectrum
When a CW signal is pulse modulated, the carrier is per-
iodically turned on and off. The on period is determined by
the modulating pulse width, the off periods is related to the
pulse repetition rate or frequency. The carrier is usually
modulated with rectangular shaped pulses.
A square wave is composed of its fundamental frequency
plus the odd harmonics. If the relative amplitudes and phase
of the harmonics are changed, a number of waves hapes are
produced; rectangular, trapezoidal, sawtooth, etc. The spec-
trum of the square wave or any pulse shape is displayed
according to its frequency components and their amplitudes.
Common pulse forms and their spectrum are described in
Reference Data for Radio Engineers, 4th edition, Chapter 35,
ITT 1956.
square-pulse, pulse-modulated oscillator. The main lobe and
the side lobes are shown as groups of spectral lines extend-
ing above and below the baseline, The number of these side
lobes for a truly rectangular pulse, approaches infinity, since
the number of harmonics in a square pulse approaches an
infinite quantity. Any two adjacent side lobes are separated
an the frequency scale by a distance equal to the inverse of
the modulating pulse width. See Fig. 2-20A.
Fourier theory shows that adjacent lobes are "180 out of
phase; however, since the spectrum analyzer is insensitive
to phase, only the absolute value of the spectrum is displayed
and appears as illustrated in Fig. 2-20B.
and pulse repetition frequency have on a pulsed RF spectrum.
Fig. 2-20. Formation of a pulse modulated signal spectrum.
Since the spacing between the spectral lines of the pulsed
Frequency Modulated Signal Spectrum
RF spectrum is a function of the PRF, the spectrum analyzer
resolution bandwidth should be less than the PRF to respond
When a CW signal FC is frequency modulated at a rate
to one frequency component at a time. In mast instances this
( Fm), it will theoretically produce an infinite number of side-
is impractical; for example, a short pulse at a PRF of 100 hertz,
band frequencies. These frequencies are equal to (F C
would require an effective r e s o l u t i o n o f 1 0 0 h e r t z . T h i s
nF
where
n
=
1,
2,
3,
etc.
m
would produce an extremely fine grain display, and would
be impractical for analysis.
Frequency modulated signal bandwidth is usually deter-
mined by the width of the sidebands containing sufficient
energy to dominate the display. Signal bandwidth is approx-
The spectrum envelope, however, is plotted with pulses
is t h e f r e q u e n c y
imately equal to
+ Fm ) where
instead of lines. If the analyzer is swept slowly, it will plot
deviation of the carrier and F m is the frequency of the mod-
a series of pips or lines, the focus of which repre-
ulating signal. Frequency deviation of the carrier is pri-
sents the relative energy distribution of the swept spec-
marily dependent on the modulating signal amplitude.
trum. The number or density of these pips for a given PRF
will depend on the sweep speed, or TIME/DIV selection, on
This ratio of frequency deviation to modulating frequency
the analyzer. It is possible, by sweeping very slowly, to obtain
is known as modulation index. Bessel function and frequency
the spectrum of a very low PRF signal. This display closely
spectrum for different modulation indices may be found in
simulates a pulsed spectrum and contains the same informa-
the 4th edition of Reference Data for Radio Engineers, Chap-
tion for analysis. This spectrum may now be resolved, since
ter 19.
the resolution bandwidth of the analyzer need only be less
than the side lobe frequency width, or the reciprocal of the
To resolve adjacent sideband components in a frequency
modulating pulse width. Fig. 2-22 illustrates the effects the
modulated display, the spectrum analyzer resolution band-
pulse shape will have an the RF spectrum. Notice the reduc-
width should be less than the lowest modulating frequency
tion of side lobes when the pulse is no longer rectangular;
in the spectrum which is the same as the requirements for an
amplitude modulated spectrum.
2-18
