By Richard Schreier, Gabor C. Temes
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Extra info for Understanding Delta-Sigma Data Converters
Example text
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_' • • '_ • • ' • • 1 • . ' . . , . 5: A sine wave quantized by a symmetrical 16-step quantizer. 25 2 The First-Order Delta Sigma Modulator Now consider what happens when the full-scale sine wave with frequency f I s / 8 shown in Fig. 8 is quantized by the same 16-step quantizer. The quantization error, shown in Fig. 9, is now periodic and, since it assumes only 3 values, its distribution is far from uniform. 23, or only about 70% of the expected value. The FFf shown in Fig. 10 represents an even more serious departure from our normal assumptions in that the spectrum now consists of only two spikes!
4, by contrast, y =0 occurs in the middle of a flat portion (tread) of the curve. Such devices are called mid-tread quantizers. The step size is d =2 in both cases. This common value for 6. allows the quantization levels of both quantizers to be integer values: odd integers for the mid-rise quantizer and even integers for the mid-tread quantizer. Unless otherwise noted, the quantizers considered in this text will be symmetric bipolar quantizers with 6. = 2 and a sampling period of T = 1 second.
