HP 8901B Operation And Calibration Manual page 29

Model 8901B General Information
I
I
Figure
1-6. AM with Modulation Exceeding 100%
as Measured
by the PEAK+ Detector
Exponential Modulation
Exponential (or angular) modulation is the generic name given to modulation in which the frequency
or phase of the carrier is varied. Frequency and phase modulation are very closely related. In fact, it
is impossible to
t e l l whether the signal was produced by a frequency modulator or phase modulator by
analyzing the received signal unless specific information about the baseband signal is given.
It is certainly true to say that a signal is frequency modulated when the modulation is generated by
a frequency modulator. A varactor diode across the tank circuit of an LC
oscillator
will
produce FM
when the varactor bias is varied. It is also true that a signal is phase modulated when the modulation
is generated by a phase modulator. A varactor diode across an RF
filter will produce QM when the
varactor
bias
is varied.
(It
is assumed that the carrier is on the slope of the filter and that the filter is
driven from a well-buffered carrier source. This modulator simultaneously produces
AM.)
The signal from both modulators will show readings on the Modulation Analyzer when in both the
FM and QM measurement modes. When in FM, the quantity being measured is the peak frequency
deviation, which is the maximum frequency excursion from the average carrier frequency. When
measuring QM, the peak phase deviation is measured, which is the maximum phase excursion from
the average carrier phase. Phase and frequency have the relationship that phase is the integral of the
frequency or frequency is the derivative of the phase. In fact, the Modulation Analyzer demodulates
QM by integrating the demodulated FM.
This relationship is most easily visualized by some examples. Look at Figure 1-7. The first baseband
signal shown
is
a square wave. The three waveforms under it are the result of applying this signal to
an FM, QM, and AM modulator respectively. (The AM waveform is included only for reference.) It is
assumed that the phase modulator doesn't produce AM-only QM. The FM waveform is
as
expected.
The frequency goes up on the positive peak of the baseband signal and down on the negative peak. The
phase modulated signal, however, is peculiar. The frequency is generally constant throughout except for
a discontinuity where the baseband signal switches amplitude. The waveform of the figure was contrived
so that a 180" phase shift occurred exactly at a zero crossing of the carrier. In general, a discontinuity
will occur when the baseband signal switches amplitude, but the phase shift is not necessarily 180" and
does not need to occur at a zero crossing of the carrier. Mathematically, the derivative of a square wave
is the constant zero except for a positive spike (impulse) where the baseband signal switches positive
and a negative spike where the square wave switches negative.
Now look
at
the triangle wave. The frequency modulator produces a continually increasing frequency as
the baseband signal slopes upward and a continually decreasing frequency as the signal slopes downward.
The phase modulator produces a signal that resembles the signal from the frequency modulator for the
square wave baseband signal. This is because the derivative of a constant slope is a constant. When the
slope is positive, the phase shift is continually increasing, thus producing a uniform frequency shift
upward. When the slope is negative, the phase shift is continually decreasing and produces a downward
frequency shift. For the triangle wave baseband signal, the shift in frequency when the slope changes
is proportional to the change in slope.
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