Theory Of Operation; Circuit Description - Analog Devices AD9833 Manual

AD9833
TERMINOLOGY
Integral Nonlinearity
This is the maximum deviation of any code from a straight line
passing through the endpoints of the transfer function. The end-
points of the transfer function are zero scale, a point 0.5 LSB
below the first code transition (000 . . . 00 to 000 . . . 01),
and full scale, a point 0.5 LSB above the last code transition
(111 . . . 10 to 111 . . . 11). The error is expressed in LSBs.
Differential Nonlinearity
This is the difference between the measured and ideal 1 LSB
change between two adjacent codes in the DAC. A specified differ-
ential nonlinearity of ±1 LSB maximum ensures monotonicity.
Output Compliance
The output compliance refers to the maximum voltage that can be
generated at the output of the DAC to meet the specifications.
When voltages greater than that specified for the output compli-
ance are generated, the AD9833 may not meet the specifications
listed in the data sheet.
Spurious-Free Dynamic Range
Along with the frequency of interest, harmonics of the fundamental
frequency and images of these frequencies are present at the output
of a DDS device. The spurious-free dynamic range (SFDR) refers
to the largest spur or harmonic present in the band of interest.
The wideband SFDR gives the magnitude of the largest harmonic
or spur relative to the magnitude of the fundamental frequency
in the 0 to Nyquist bandwidth. The narrow-band SFDR gives the
attenuation of the largest spur or harmonic in a bandwidth of
±200 kHz about the fundamental frequency.
Total Harmonic Distortion
Total harmonic distortion (THD) is the ratio of the rms sum of
harmonics to the rms value of the fundamental. For the AD9833,
THD is defined as
V
2
THD = 20 log
where V is the rms amplitude of the fundamental and V , V ,
1
V , V , and V are the rms amplitudes of the second through
4 5 6
sixth harmonics.
Signal-to-Noise Ratio (SNR)
SNR is the ratio of the rms value of the measured output signal
to the rms sum of all other spectral components below the Nyquist
frequency. The value for SNR is expressed in decibels.
Clock Feedthrough
There will be feedthrough from the MCLK input to the analog
output. Clock feedthrough refers to the magnitude of the MCLK
signal relative to the fundamental frequency in the AD9833's
output spectrum.
2 2 2 2 2
+ V + V + V + V
3 4 5 6
V
1

THEORY OF OPERATION

Sine waves are typically thought of in terms of their magnitude
form a(t) = sin(t). 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  = 2f.
+1
0
–1
2p
0
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.
Solving for 
Solving for f and substituting the reference clock frequency for
the reference period
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 + phase modulator,
SIN ROM, and digital-to-analog converter.
Each of these subcircuits is discussed in the following section.
2 3

CIRCUIT DESCRIPTION

The AD9833 is a fully integrated direct digital synthesis (DDS)
chip. The chip requires one reference clock, one low precision
resistor, and decoupling capacitors to provide digitally created
sine waves up to 12.5 MHz. In addition to the generation of this
RF signal, the chip is fully capable of a broad range of simple
and complex modulation schemes. These modulation schemes
are fully implemented in the digital domain, allowing accurate
and simple realization of complex modulation algorithms
using DSP techniques.
The internal circuitry of the AD9833 consists of the following
main sections: a numerically controlled oscillator (NCO),
frequency and phase modulators, SIN ROM, a digital-to-analog
converter, and a regulator.
–8–
MAGNITUDE
2 4
2 PHASE 4
Figure 4. Sine Wave
DPhase = wDt
w = DPhase/Dt = 2pf
( )
1/ f t
= D
MCLK
f = DPhase ¥ f / 2p
MCLK
6
6
REV. A