Datasheet
Data Sheet AD9837
Rev. A | Page 11 of 28
THEORY OF OPERATION
Sine waves are typically thought of in terms of their magnitude
form: a(t) = sin(ωt). However, sine waves are nonlinear and not
easy to generate except through piecewise construction. On the
other hand, the angular information is linear in nature; that is,
the phase angle rotates through a fixed angle for each unit of
time. The angular rate depends on the frequency of the signal
by the traditional rate of ω = 2πf.
MAGNITUDE
PHASE
+
1
0
–1
2
28
0
2π
4π
6π
2π
4π
6π
0
9070-023
Figure 18. Sine Wave
Knowing that the phase of a sine wave is linear and given a
reference interval (clock period), the phase rotation for that
period can be determined as follows:
ΔPhase = ωΔt (1)
Solving for ω,
ω = ΔPhase/Δt = 2πf (2)
Solving for f and substituting the reference clock frequency for
the reference period (1/f
MCLK
= Δt),
f = ΔPhase × f
MCLK
∕2π (3)
The AD9837 builds the output based on this simple equation. A
simple DDS chip can implement this equation with three major
subcircuits: numerically controlled oscillator (NCO) plus phase
modulator, SIN ROM, and digital-to-analog converter (DAC).
Each subcircuit is described in the Circuit Description section.
The AD9837 provides a sampled signal with its output following
the Nyquist sampling theorem. Specifically, its output spectrum
contains the fundamental plus aliased signals (images) that occur
at multiples of the reference clock frequency and the selected
output frequency. A graphical representation of the sampled
spectrum with aliased images is shown in Figure 19.
The prominence of the aliased images depends on the ratio of
f
OUT
to MCLK. If the ratio is small, the aliased images are very
prominent and of a relatively high energy level as determined by
the sin(x)/x roll-off of the quantized DAC output. In fact, depend-
ing on the f
OUT
/reference clock ratio, the first aliased image can
be on the order of −3 dB below the fundamental.
External filtering is required if the aliased image is within the
output band of interest.
09070-040
SYSTEM CLOCK
f
OUT
f
C
–
f
OUT
f
C
+
f
OUT
2
f
C
–
f
OUT
2
f
C
+
f
OUT
3
f
C
–
f
OUT
3
f
C
+
f
OUT
f
C
0Hz FIRST
IMAGE
SECOND
IMAGE
THIRD
IMAGE
FOURTH
IMAGE
FIFTH
IMAGE
SIXTH
IMAGE
2
f
C
3
f
C
FREQUENCY (Hz)
SIGNAL AMPLITUDE
sin(x)/x ENVELOPE
x = π (
f
/
f
C
)
Figure 19. DAC Output Spectrum