L2340G datasheet(4/11 Pages) LODEV

Part #	L2340G

Description	Digital Synthesizer

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Manufacturer	LODEV [LOGIC Devices Incorporated]

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DEVICES INCORPORATED

L2340

Digital Synthesizer

4

Special Arithmetic Functions

08/16/2000–LDS.2340-E

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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

FIGURE 2.

CIRCLE TEST RESULT NEAR 45° (16-BIT INTERNAL PROCES-

SOR

)

FIGURE 3.

CIRCLE TEST RESULT NEAR 45° (24-BIT INTERNAL PROCES-

SOR

)

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.

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