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L2340 Datasheet(PDF) 4 Page - LOGIC Devices Incorporated |
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L2340 Datasheet(HTML) 4 Page - LOGIC Devices Incorporated |
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4 / 11 page  DEVICES INCORPORATED L2340 Digital Synthesizer 4 Special Arithmetic Functions 08/16/2000–LDS.2340-E 23140 23150 23160 23170 23180 23190 23200 23140 23150 23160 23170 23180 23190 23200 X Y 23140 23150 23160 23170 23180 23190 23200 23140 23150 23160 23170 23180 23190 23200 X Y 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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