L2340
DEVICES INCORPORATED
Digital Synthesizer
error will introduce noise when
performing waveform sythesis,
modulation, and demodulation.
Data values for Figure 2 and Figure
3 are shown in Table 3. By looking
at these values, we observe the step
resolution on a 16-bit internal
processor is not 1 unit in the x and
y. In most cases, the minimum step
resolution is 2 units in the x and y.
On the other hand, step resolution
on a 24-bit internal processor is 1
unit in the x and y thus resulting in
greater accuracy.
The minimum theoretical angle
resolution that could be produced is
0.00175° when x = 7FFFH and y = 1H.
A 16-bit internal processor can
produce a minimum angle resolu-
tion of only 0.00549° and will not be
able to properly calculate the
theoretical minimum angle resolu-
tion. On the other hand, a 24-bit
internal processor can produce a
minimum angle resolution of
0.00002° and could therefore prop-
erly calculate the theoretical mini-
mum angle resolution.
Circle Test
When performing a coordinate
transformation, inaccuracies are
introduced by a combination of
quantization and approximation
errors. The accuracy of a coordinate
transformer is dependent on the
word length used for the input
variables, the word length used for
internal calculations, as well as the
number of iterations or steps per-
formed. Truncation errors are due
to the finite word length and ap-
proximation errors are due to the
finite number of iterations. For
example, in the case of performing a
polar-to-rectangular transformation,
the accuracy of the rotation will be
determined by how closely the input
rotation angle was approximated by
the summation of sub-rotation
angles.
In this study, we compare how
accurately a coordinate transformer
with a 16-bit internal processor
versus a 24-bit internal processor
can calculate all the coordinates of a
circle. By setting the radius to
7FFFH,
θ
is incremented using the
accumulator of the L2340 in steps of
0000 4000H until all the points of a
full circle are calculated into rectan-
gular coordinates.
The resulting rectangular coordi-
nates were plotted and graphed. A
graphical representation of the
resulting vectors for both 16-bit and
24-bit internal processors are com-
pared at 45°. Theoretically, a
perfect circle is the desired output
but when the resulting vectors from
a coordinate transformer with 16-bit
internal processor are graphed and
displayed as shown in Figure 2, we
see significant errors due to the
inherent properties of a digital
synthesizer. In comparison, the 24-
bit internal processor proves to be
significantly more accurate than a
16-bit internal processor due to
minimization of truncation errors.
In many applications, this margin of
F
IGURE
2.
SOR
)
C
IRCLE
T
EST
R
ESULT
N
EAR
45° (16-B
IT
I
NTERNAL
P
ROCES
-
23200
23190
23180
Y
23170
23160
23150
23140
23140
23150
23160
23170 23180
23190
23200
X
F
IGURE
3.
SOR
)
C
IRCLE
T
EST
R
ESULT
N
EAR
45° (24-B
IT
I
NTERNAL
P
ROCES
-
23200
23190
23180
Y
23170
23160
23150
23140
23140
23150
23160
23170 23180
23190
23200
X
Special Arithmetic Functions
4
08/16/2000–LDS.2340-E
LOGIC [ LOGIC DEVICES INCORPORATED ]
