Tutorial on the Theory, Design and Characterization of Delta-Sigma Analog to Digital Converters

In this episode Shahriar explores the world of Delta-Sigma modulators with emphasis on a Delta-Sigma Analog to Digital Converter (ADC). The basic concepts of analog to digital conversion is presented, particularly with respect to quantization noise spectral shape and power density. Next, oversampling ADCs are presented to demonstrate the possibility of increasing SQNR (ENOB) through manipulation of quantization noise spectrum.

Due to the practical limitations of high oversampling ratios, delta-sigma modulations is explored. The principle operation behind delta-sigma ADCs is presented with detailed explanation on noise shaping, filtering and decimation. The signal and noise transfer functions for a 1st order and 2nd order delta-sigma ADC are derived. Finally, as a practical example, a 2nd order delta-sigma ADC based on a 1-bit quantizer is presented. The ADC uses two Miller integrator op-amps, one comparator and a D-Type flip-flop. The complete measurement of this delta-sigma ADC is presented. The impact of over sampling ration, op-amp linearity and input signal bandwidth is presented. The slides for this video can be downloaded here.


  1. goh says:

    When can i download the slides?

  2. deepti says:

    awesum video..have been studying these converters..but never was it so clear as it is now….excellent..was looking some of ur more videos..cudnt find…. would appreciate if u post something on digital filters..how do they reduce the sampling rate

  3. Matt says:

    Hello, I have tried to duplcate this circuit in LTspice (Linear Tech) but I seem to be failing badly. Does anyone know if its possible with this program?

  4. Bill says:

    Just found this site yesterday and got to say I’m hooked!

    Really appreciate the practical along with the theory. It makes learning so much more intuitive. Would love to see more videos of this nature.

  5. kees says:


    Nice video.

    I have plan to play with class D amps, however what is the best to do for modulation, delta sigma, pwm, or self oscilator version, sound quality is important, I like if there are only even harmonics, a full bridge looks best, however death time is a great rule in harmonics, but needed.



  6. Antonio Castillo says:

    Hi Shahriar. I’ve been studying the sigma-delta converter many months and there are a lot of great books about this topic, but I think your tutorial is valuable to get insight about this ADC. I really appreciate your effort to share this knowledge through “The signal path”, congratulation for this amazing project.

  7. Nico says:

    Thanks for the upload! My guesses at your posed questions:
    1. Using different signal generators to prevent your sampling signal and input signal from being phase locked. This allows you to sample the input signal at maximum different phases/random phases.
    2. For the 2 spectral components: the one would be at fs-fin, and the other fs+fin. This is due to the nature of the FFT. As you said, anything beyond fs/2 can be ignored and this is due to the fact that it is a repetition of the first half (or as in literature, the “negative” frequencies) of the FFT. The second peak is a lot smaller than our first fin peak since the convolved sinc function approaches zero close to fs thereby reducing the amplitude. Hope I’m close.

  8. Mohammad says:

    Hi shahriar,
    Awesome video. You answered most of the questions that I had. I have two questions. First, would you please provide the name of the OpAmps that you have used? Second, could you please make a video for digital filters? Because the most complicated part of the sigma-delta modulators is the digital filter part.
    I will appreciate it if you would kindly answer them.

  9. Tristan says:

    Very good video, better than most college class.

  10. Jan says:

    Hey, thanks for your interesting video! unfortunately, the link seems to be dead?

  11. Homayoun says:

    Great Job!

  12. panfilero says:

    The link to the slides appears to be broken, awesome video though, definitely helpful, although it may take more than one viewing for me. Thanks!

  13. pd4z says:

    The link for slides doesnt work. It gives a 404.

  14. tasweet says:

    as always Shahriar, great video. as you guessed a little dense with inforimation. i will watch it 2 or 3 more times.
    thank you so much

  15. andy says:

    Fantastic video, as always. Thanks for putting in such effort to explain these concepts. BTW, I tried to leave a thumbs up and comment on Youtube, but Chrome and/or some Javascript error prevented me from doing so.

Leave a Reply

Your email address will not be published. Required fields are marked *

  • Social Media

  • Administrator

  • Archives