Functional Processing of Delta-Sigma Bit-Stream by Djuro G. Zrilic

Author:Djuro G. Zrilic
Language: eng
Format: epub
ISBN: 9783030476489
Publisher: Springer International Publishing

(5.1)

(5.2)

(5.3)

Fig. 5.2A linear model of the first-order Δ-Σ divider

We see that the quantizer output dn consists of quantization error q = un – un−1 and input signal Vn−1.

Similarly, the output signal of a divider (Wn > 0) can be written as

(5.4)

Because Wn = Wn−1 = constant = W, we have

(5.5)

Taking a Z-transform of Eq. (5.5) we have

(5.6)

For a high sampling ratio, fs/fN ≫ 1, the second term in Eq. (5.6) can be neglected and the transfer function of the system is

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