How Delta Sigma Works

One-bit, first-order delta-sigma modulatorNot only are delta-sigma techniques at the root of many of today’s analog-to-digital converters (ADC) and digital-to-analog converters (DAC), what they reveal about the relationship between sample rate, bandwidth, and resolution lies near the heart of the multirate techniques popular in modern digital signal processing (DSP) systems.

This multi-part series of tutorials will work its way from the basics of delta-sigma data converters to more advanced techniques, with an approach that values intuition as much as math. The series is a work in progress, so please subscribe via Atom or RSS or check back regularly for future installments.

5 thoughts on “How Delta Sigma Works”

  1. Hi,
    at first i wanted to thank you for this article.

    But there is one little question to be left.
    Is it really necessary to put an anti aliasing filter in front of the DS-Modulator?
    Isn’t it possible to filter out all not wanted signal parts with the integrator?


    1. Hi, Andy.

      It took me a while to reply because I wanted to think the answer through. In an ADC with a continuous-time loop filter (integrator), yes, you can build a delta-sigma modulator without an additional anti-aliasing filter. However, nearly all delta-sigma ADCs use switched-capacitor techniques for their loop filters. If your ADC uses switched capacitors, you will still need an anti-aliasing filter.

      Even with a continuous-time loop filter, using the loop filter for anti-aliasing constrains the design of the ADC. Depending on what kind of digital filter follows the modulator, you may need anti-aliasing for the ADC’s output sample rate, which is quite a bit lower than the modulator’s sample rate. Doing some of the filtering in an anti-aliasing filter may permit using a simpler digital filter.


  2. Dear sir,
    Please give me an outline or lecture about 1.8-V digital audio sigma delta modulator in 0.8 m cmos
    With pictures. Thanks

    1. Hello, sir.

      Unfortunately, I do not have such notes or lectures to share. I’d suggest doing some searches on Google Scholar or the IEEE web site for published papers on delta-sigma in 0.8 ㎛. I’ve never worked on one, but I have no doubt you will find relevant papers in JSSC.


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