The Second-Order Sigma-Delta Modulator

  • Isacco Arnaldi


This chapter focuses on specific system-level simulations of the second-order Sigma-Delta modulator, to be referred as MOD2, formed by a second-order loop filter and a single-bit quantizer. Similarly to Chap. 2, the aim is to gain a significant appreciation of the practical aspects needed during the design process. Therefore, the operation for DC and sinewave inputs as well as the non-idealities affecting the modulator behavior will be studied by performing the practical exercises suggested in the MATLAB® and Simulink® environment. Since the chapter follows almost exactly the sequence of simulations conducted for MOD1, the reader is encouraged to make frequent comparisons between the performance of MOD1 and MOD2 in order to gain a better understanding of the concepts covered. Moreover, in Sect. 3.7 a comprehensive investigation on the theory underlying alternative architectures is presented, as well as suggestions on the simulations to conduct on those modulator structures.

Supplementary material


  1. 1.
    Oppenheim AV, Schafer RW. Discrete-time signal processing. New Jersey: Prentice-Hall Inc.; 1989.zbMATHGoogle Scholar
  2. 2.
  3. 3.
    Schreier R, Temes GC. Understanding Delta-Sigma data converters. New Jersey: Wiley; 2005.Google Scholar
  4. 4.
    Candy JC, Benjamin OJ. The structure of quantization noise from Sigma-Delta modulation. IEEE Trans Commun. 1981;29(9):1316–23.CrossRefGoogle Scholar
  5. 5.
    Friedman V. The structure of the limit cycles in Sigma Delta modulation. IEEE Trans Commun. 1988;36(8):972–9.CrossRefGoogle Scholar
  6. 6.
    De la Rosa JM, Del Rio RF. CMOS Sigma-Delta converters: practical design guide. London: Wiley; 2013.CrossRefGoogle Scholar
  7. 7.
    Norsworthy SR, Schreier R, Temes GC. Delta-Sigma data converters: theory, design and simulation: Wiley-IEEE Press; 1996.CrossRefGoogle Scholar
  8. 8.
    Candy JC, Temes GC. Oversampling Delta-Sigma data converters: theory, design and simulation. USA: Wiley-IEEE Press; 1991.CrossRefGoogle Scholar
  9. 9.
    Casier H, Steyaert M, Van Roermund AHM. Analog circuit design: robust design, Sigma Delta converters, RFID. London: Springer; 2011.CrossRefGoogle Scholar
  10. 10.
    Reiss JD. Understanding Sigma-Delta modulation: the solved and unsolved issues. JAES. 2008;56(1/2):49–64.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Isacco Arnaldi
    • 1
  1. 1.CaldognoItaly

Personalised recommendations