L2330 datasheet(7/14 Pages) LODEV

7 / 14 page

DEVICES INCORPORATED

Special Arithmetic Functions

L2330

Coordinate Transformer

09/27/2001–LDS.2330-E

23140

23150

23160

23170

23180

23190

23200

23140

23150

23160

23170

23180

23190

23200

23140

23150

23160

23170

23180

23190

23200

23140

23150

23160

23170

23180

23190

23200

Circle Test

When performing a polar-to-rectangu-

lar transformation, a 24-bit internal

processor proves to be significantly

more accurate than a 16-bit internal

processor.

In this study, we compare how accu-

rately 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 (maximum before

overflow),

θ is incremented using the

accumulator of the L2330 in steps of

0000 4000H until all the points of a full

circle are calculated into rectangular

coordinates.

The resulting rectangular coordinates

were plotted and graphed. A graphical

representation of the resulting vectors

for both 16-bit and 24-bit internal

processors are compared near 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 3, we see significant errors due

to the inherent properties of a digital

coordinate transformation system. In

comparison, the 24-bit internal proces-

sor proves to be significantly more

accurate than a 16-bit internal processor

due to minimization of truncation

errors. In many applications, this

margin of error is of great significance

especially when being used in applica-

tions such as medical ultrasound or

modulation techniques.

Data values for Figure 3 and Figure 4

are shown in Table 4. 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,

FIGURE 3.

CIRCLE TEST RESULT NEAR 45° (16-BIT INTERNAL PROCESSOR)

FIGURE 4.

CIRCLE TEST RESULT NEAR 45° (24-BIT INTERNAL PROCESSOR)

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 resolu-

tion that could be produced is 0.00175°

when x = 7FFFH and y = 1H. A 16-bit

internal processor can produce a

minimum angle resolution of only

0.00549° and will not be able to prop-

erly calculate the theoretical minimum

angle resolution. On the other hand, a

24-bit internal processor can produce a

minimum angle resolution of 0.00002°

and could therefore properly calculate

the theoretical minimum angle resolu-

tion.

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