Tektronix 1L40, Instruction Manual

Page: 22 / 145

Operating Instructions— Type 1L40
(evidenced by signal jitter), non-linear modulation and
overmodulation.
Spectrum of a Frequency Modulated Signal
When a CW signal (Fc) is frequency modulated at a
rate (Fm), it theoretically produces an infinite number of
sideband frequencies. These frequencies equal the carrier
frequency plus or minus the modulating frequencies (Fc ±
nFm where n = 1, 2, 3, . . .etc). Figure 2-15 illustrates various
degrees of frequency modulation.
The bandwidth of a frequency modulated signal is usually
determined by the number or width of the sidebands that
contain sufficient energy to dominate the display. A very
approximate calculation of the signal bandwidth equals
2 (AFC - f FJ, where AF
c
is the frequency deviation of the
carrier and Fm is the frequency of the modulating signal.
Frequency deviation of the carrier is primarily dependent on
the modulating signal amplitude.
This ratio of frequency deviation to modulating frequency
is known as modulation index. Bessel function and fre­
quency spectra for different modulation indices may be
found in the 4th edition of Reference Data for Radio Engi­
neers, Chapter 19.
Fig. 2 -1 6 . Formation o f a pulse m odulated signal spectrum.
The resolution requirements for the spectrum analyzer to
resolve adjacent sideband components in a frequency
modulated display is the same as the requirements to re­
solve an amplitude modulated spectrum.
Spectra of a Pulse Modulated Signal
When a CW signal is pulse modulated, the carrier is
periodically turned on and off. The on period is determined
by the modulating pulse width; the o ff time is related to
the pulse repetition time or frequency. The carrier is usually
modulated by a rectangular-shaped pulse.
A symmetrical square wave is composed of its funda­
mental frequency plus odd harmonics. If the relative am pli­
tudes and phase of the harmonics are changed, a number of
wave shapes are produced; rectangular, trapezoidal, saw­
tooth, etc. The spectrum of the rectangular wave or any
pulse shape is displayed according to its frequency compo­
nents and their amplitudes. Common pulse forms and their
spectra are also described in Reference Data for Radio
Engineers, 4th edition, Chapter 35. ITT 1956.
Fig. 2-16A illustrates a theoretical voltage spectrum of
a pulse-modulated oscillator that is modulated by a rec­
tangular pulse. The main lobe and the side lobes are
shown as groups of spectral lines extending above and
below the baseline. The number of these side lobes, for
a truly rectangular pulse, approaches infinity. Any two ad­
jacent side lobes are separated on the frequency scale by
a frequency equal to the inverse of the modulating pulse
width.
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 dis­
played and appears as illustrated in Fig. 2-16B.
Fig. 2-17 illustrates the relative effects the pulse w idth and
pulse repetition frequency have on a pulsed RF spectrum.
Since the spacing between the spectral lines of the pulsed
RF spectrum is a function of the PRF (pulse repetition fre­
quency), the spectrum analyzer resolution bandwidth should
be less than the PRF to respond to any one frequency
component. This is impractical in most instances, however
the spectrum envelope can be plotted with pulses. If the
analyzer swept frequency is slow, it w ill plot a series of
pips or lines, the locus of which represents the relative
energy distribution of the swept spectrum. The number or
density of these pips for a given PRF w ill depend on the
sweep speed, or Time/Cm selection of the plug-in oscillo­
scope.
It is possible, by sweeping very slowly, to obtain the
spectrum of a very low PRF signal. The display simulates
a pulse spectrum and contains the same information for
analysis. To resolve this spectrum the resolution bandwidth
of the analyzer need only be less than the side lobe fre­
quency width, or the reciprocal of the modulating pulse
width. Fig. 2-18 illustrates the effect of frequency modula­
tion on the pulse modulated display.
The peak amplitude of the main lobe of a pulse modula­
ted RF spectrum represents only a portion of the total energy
contained in the lobe. The main lobe is less than the am pli­
tude of an equal peak value CW signal by an amount
which is approximately 3 /2 (tp) X the resolution bandwidth,
2-16
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