L2330QC20 查看數據表（PDF） - LOGIC Devices Incorporated

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L2330QC20

Coordinate Transformer

LOGIC Devices Incorporated 

DEVICES INCORPORATED

L2330

Coordinate Transformer

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.

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.

FIGURE 3. CIRCLE TEST RESULT NEAR 45° (16-BIT INTERNAL PROCESSOR)

23200

23190

23180

Y 23170

23160

23150

23140

23140 23150 23160 23170 23180 23190 23200

X

FIGURE 4. CIRCLE TEST RESULT NEAR 45° (24-BIT INTERNAL PROCESSOR)

23200

23190

23180

Y 23170

23160

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,

23150

23140

23140 23150 23160 23170 23180 23190 23200

X

Special Arithmetic Functions

7

09/27/2001–LDS.2330-E

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