Datasheet

AD9838
Rev. A | Page 14 of 32
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 = 2π
f.
MAGNITUDE
PHASE
+1
0
–1
2
28
0
2π
4π
6π
2π
4π
6π
09077-025
Figure 20. 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 AD9838 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.