AD9837 datasheet(11/28 Pages) AD

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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

228

2π

4π

6π

2π

4π

6π

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/fMCLK = Δt),

f = ΔPhase × fMCLK∕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

fOUT 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 fOUT/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.

SYSTEM CLOCK

fOUT

fC – fOUT

fC + fOUT

fC – fOUT

fC + fOUT

fC – fOUT

fC + fOUT

0Hz

FIRST

IMAGE

SECOND

IMAGE

THIRD

IMAGE

FOURTH

IMAGE

FIFTH

IMAGE

SIXTH

IMAGE

FREQUENCY (Hz)

sin(x)/x ENVELOPE

x = π (

f/fC)

Figure 19. DAC Output Spectrum

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