# Sigma-delta A/D conversion

## Abstract

In this chapter noise-shaping techniques applied to analog-to-digital converter systems will be described. Noise-shaping is very useful when speed can be exchanged with accuracy. In reference [95] an overview of theoretical and practical aspects of oversampling converters is given. The quantization errors in a noise-shaping system are removed from the signal band of interest. Furthermore, in an analog-to-digital converter system the input noise is filtered out by the input noise-shaping function. As a result, a reduced bandwidth can be used compared to, for example, successive approximation conversion methods. Again, the removed quantization errors appear with larger amplitudes as out-of-band noise in the system. With a digital filter these errors are removed. An increased dynamic range of the system is obtained. An example of such an operation is sigma-delta analog-to-digital conversion using single bit word-lengths [92, 97, 96]. The advantage of a 1-bit converter is the extreme linearity of such a device. A very good differential linearity is obtained with these converters. The most important design criteria will be given. The dynamic range performance is related to the noise-shaping coders described in Chapter 8. At the moment the dynamic range of a system must be enlarged, but the maximum clock rate of the system cannot be increased because of technology limitations, then a multi-bit digital-to-analog converter can be used in the feedback loop. At that moment, however, the linearity of the digital-to-analog converter determines the linearity and the distortion in the system. To overcome this problem *Dynamic Element Matching* or *Continuous Current Calibration* techniques can be used to obtain the extreme linearity of the D/A converter without needing extra trimming steps. Examples of this method will be described. In the stability analysis of the sigma-delta converters the root-locus method can be applied. However, for small signal stability the root locus method of 1-bit converters must be extended using the phase uncertainty criterion. With multi-bit systems, the phase uncertainty will be reduced, while furthermore the gain of the A/D and D/A converter loop can better be determined The root locus method shows in these cases a better result. In most cases an idle pattern close to half the sampling frequency gives the best result. However, idle patterns at other frequencies, depending on the input signal randomly generated, are also allowed. In this case the quantization errors are randomized and appear as noise. Different architectures to implement higher-order sigma-delta converters will be introduced. These converters use special system architectures to avoid stability problems. The MASH structure uses a cascade of second or first order stages to avoid stability problems. A higher order noise-shaping is obtained. A special system that uses a signal-level-dependent filtering order introduces a feed-forward like filter coupling. At low signal levels the highest filter order is used, while with increasing signals the filter order is reduced. The reduced filter order results in a stable system with reduced dynamic range. Usually this reduction in dynamic range at large input signals is not a problem. A large dynamic signal range can be covered. A good optimum between filter order and stable system operation is found. Bandpass noise-shaping filters can be used to convert carrier signals into a stream of digital data. The filter structures can be of the switched capacitor form or continuous time form. The advantage of continuous time is that the sampling frequency can be varied without changing the tuning frequency of the system. However, the tuning frequency of the continuous time filter depends on the absolute accuracy of the elements used. In an IC technology a variation in the order of 10% to 20% must be expected. This requires an adjustment of the tuning frequency of the filter. Different examples of bandpass modulators will be discussed. At the end of this chapter a first-order implementation to be used in a 5-digit digital voltmeter with automatic offset compensation will be given.

## Keywords

Input Signal Loop Filter Root Locus Noise Transfer Function Signal Transfer Function## Preview

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