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The best introduction to the
AWG is to parallel the procedure
of generating a carrier with a
conventional signal generator.
With a signal generator, one
simply enters the carrier
frequency and the output ampli-
tude, such as 1000 kHz at
0 dBm. With an AWG, one
creates a sequence of points to
represent the waveform:
A sin
ω
c
t
where A is the peak amplitude
and ω
c
is the frequency. Since a
0 dBm sinusoid has a peak
amplitude of 0.316 V
(0.224 Vrms), the carrier is:
0.316 sin (2π 1000e3 t) Volts.
For a continuous sinusoid this
equation applies for all time, but
the signal can also be defined as
a single cycle sinusoid with a
period of 1 µs that repeats every
1 µs. The unique or arbitrary
part of the signal is a 1 µs series
of points defined by the above
equation. If amplitude modula-
tion is enabled on a signal
generator, one enters the tone
modulation frequency and
depth, such as 1000 Hz at 50%.
Similarly, with an AWG, one
adds the modulation to the wave-
form description:
(1+ k sin(ω
m
t)) A sin ω
c
t ,
where k is the modulation depth
between 0 and 1, and ω
m
is the
sinusoidal modulation frequency.
Thus, our example waveform
becomes:
(1+ 0.5 sin(2π 1000 t) )
x 0.316 sin (2π 1000e3 t) Volts.
This waveform description can
be entered in the AWG’s equa-
tion editor to describe our
modulated carrier (Figure 1).
The unique or arbitrary part of
the continuous waveform is now
1 ms, so one defines a time range
of 0 to 1 ms. For convenience,
define several constants, k0, k1,
and k2, so that the modulation
parameters are easily altered.
Finally, a record length of
20,000 points is selected,
keeping in mind the basic AWG
relationship:
Record length (points)
= Waveform period (seconds)
x Sample rate (points/sec).
Basic Sine Wave Amplitude Modulation (AM)
1
Figure 1. The AWG’s equation editor permits
direct entry of the mathematical representation of
the modulated carrier. Constants k0, k1, and k2
are used to simplify alterations to modulation
parameters. The user can directly specify the
record length — 20,000 points in this case.
Analog Carriers and Modulation