Proces pomiaru w przetworniku A/C typu Sigma-Delta

Działania realizowane przez przetwornik A/C typu Sigma-Delta opisano w artykule jako proces pomiaru podzielony na trzy etapy: przetwarzanie analogowe, kwantowanie i przetwarzanie cyfrowe. Poddano analizie podstawowe źródła błędu, a następnie określono wpływ decymacji i filtracji na właściwości wypadkowego błędu wyniku pomiaru. Rozważania analityczne zilustrowano wynikami symulacji uzyskanymi przy użyciu metody Monte Carlo.

A basic scheme of a Sigma-Delta AD converter, analyzed in the paper, is shown in Fig. 1. The converter performs a quantization process, which can be described as compensation of the charge, delivered to the integrator from the source of the measured voltage Ux, with quanta of charge obtained synchronously with clock CLK when the switch P is closed. Value of a charge quantum is given by Eq. (1) and the balance state of the quantizer by Eq. (2). Basing on this equation one can obtain expression (3) describing a measurement result and Eq. (4) that describes value of a voltage quantum. All stages of the processing made by Sigma-Delta converter, i.e. analog conversion, quantization and digital processing, are shown in Fig. 3. One can distinguish three main error sources in this process - input error described by Eq. (6) and two errors connected with quantization: quantization error and standard error caused by dispersion of the quanta values (Eqs. (8), (9) and Fig. 3). Next considerations deal with analysis of decimation and averaging influence on the quantization error and the standard error. Fig. 4 shows exemplary histogram of the quantization error after averaging and Fig. 5 the error being the result of composition of both mentioned errors. Having the errors described one can calculate uncertainty of a measurement result using the procedure presented in paper [3].