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Sigma-delta converters are in wide use among applications that demand high precision and accuracy. A variant of the sigma-delta architecture, called the continuous-time sigma delta (CT-S?), has found homes in embedded applications such as mobile handsets for some time. Due to the high performance, efficiency, and ease of use of the CT-S? architecture, manufacturers of high-performance analog-to-digital converters (ADCs) are now bringing this converter architecture to market as a standard product.
A simplified block diagram of a CT-S? ADC consists of a sigma-delta modulator and a decimation filter (Fig. 1). Much like the discrete-time sigma-delta converters found in many high-precision applications, the continuous-time sigma-delta architecture incorporates oversampling and noise shaping to achieve high resolution.
To understand how sigma-delta converters work, it’s important to briefly introduce the oversampling theory. Consider the technique of oversampling in the frequency domain where a dc conversion has a quantization error of up to ½ LSB. A perfect N-bit ADC has a rms quantization noise of q/v12 uniformly distributed within the Nyquist band from dc to fs/2, where q is the value of an LSB and fs is the sample rate. If the sample rate increases to kfs, the rms quantization noise remains q/v12; however, the noise is now distributed over a wider bandwidth from dc to kfs/2.
The factor k is referred to as the oversampling ratio (OSR). Since the quantization noise is distributed over a wider bandwidth, the noise within a narrow band of interest is reduced by a factor of vk.
In combination with the principle of oversampling, a sigma-delta converter applies noise shaping in the modulator to further reduce the quantization noise within the band of interest. Noise shaping, as the name implies, involves attenuating the in-band quantization noise at the expense of amplifying noise in the out-of-band region. The resulting spectrum at the output has minimal quantization noise in-band and large out-of-band noise (Fig. 1, again). If a digital low-pass filter is applied to the output, the out-of-band noise can be removed.
After filtering, the out-of-band region contains no quantization noise or signal, allowing the output data rate to be reduced without corrupting the in-band signal. This process of filtering and sampling-rate reduction is commonly referred to as decimation filtering. The decimation filter removes the large out-of-band noise; the result is a high-performance, wide-dynamic-range analog-to-digital converter.