Datasheet

Data Sheet AD9833
Rev. G | Page 11 of 21
THEORY OF OPERATION
Sine waves are typically thought of in terms of their magnitude
form: a(t) = sin(ωt). However, these 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
2p
0
2π 4π
6π
2π
4π
6π
0
2704-023
Figure 23. 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.
ΔPhase = ωΔt
Solving for ω,
ω = ΔPhase/Δt = 2πf
Solving for f and substituting the reference clock frequency for
the reference period (1/f
MCLK
= Δt)
f = ΔPhase × f
MCLK
∕2π
The AD9833 builds the output based on this simple equation. A
simple DDS chip can implement this equation with three major
subcircuits: numerically controlled oscillator (NCO) and phase
modulator, SIN ROM, and digital-to-analog converter (DAC).
Each subcircuit is described in the Circuit Description section.