L2340
DEVICES INCORPORATED
Digital Synthesizer
Circle Test
error will introduce noise when
performing waveform sythesis,
modulation, and demodulation.
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
When performing a coordinate
transformation, inaccuracies are
introduced by a combination of
quantization and approximation
Data values for Figure 2 and Figure
3 are shown in Table 3. By looking
errors. The accuracy of a coordinate at these values, we observe the step
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.
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.
0.00002° and could therefore prop-
erly calculate the theoretical mini-
mum angle resolution.
FIGURE 2. CIRCLE TEST RESULT NEAR 45°(16-BIT INTERNAL PROCES-
SOR)
23200
23190
23180
23170
23160
23150
23140
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.
Y
23140 23150 23160 23170 23180 23190 23200
X
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
FIGURE 3. CIRCLE TEST RESULT NEAR 45°(24-BIT INTERNAL PROCES-
SOR)
23200
23190
23180
23170
23160
23150
23140
Y
23140 23150 23160 23170 23180 23190 23200
X
Special Arithmetic Functions
08/16/2000–LDS.2340-E
4
LOGIC [ LOGIC DEVICES INCORPORATED ]
