Datasheet

AD9834
Rev. C | Page 15 of 36
THEORY OF OPERATION
Sine waves are typically thought of in terms of their magnitude
form a(t) = sin (ωt). However, these 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
2p
0
2π
4π
6π
2π
4π
6π
02705-025
Figure 27. 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.
∆
Phase = ω∆t
Solving for ω,
ω = ∆Phase/∆t = 2πf
Solving for f and substituting the reference clock frequency for
the reference period (1/
f
MCLK
= ∆t),
f = ∆Phase × f
MCLK
/2π
The AD9834 builds the output based on this simple equation. A
simple DDS chip can implement this equation with three major
subcircuits: numerically controlled oscillator + phase modulator,
SIN ROM, and digital-to-analog converter (DAC). Each of these
subcircuits is discussed in the Circuit Description section.