Plenary Lecture
Stability Analysis and Limit Cycles of High Order Sigma-Delta Modulators
Professor Valeri Mladenov
Dept of Theoretical Electrical Engineering
Technical University of Sofia
Bulgaria
E-mail: valerim@tu-sofia.bg
Abstract: Sigma-Delta modulation has become in recent years an increasingly popular choice for robust and inexpensive analog-to-digital and digital-to-analog conversion. Despite the widespread use of Sigma-Delta modulators theoretical understanding of Sigma-Delta concept is still very limited. This is a consequence of the fact that these systems are nonlinear, due to the presence of a discontinuous nonlinearity - the quantizer.
A number of researchers have contributed to the development of a theory of Sigma-Delta modulation based on the principles of nonlinear dynamics. That work, has succeeded in explaining many fundamentally nonlinear features of the modulators. In the original author’s work stability (in the sense of boundness of the states) analysis approach based on decomposition of the general N-th order modulator has been developed. This decomposition is considered for all cases of poles of the transfer function of the modulator loop filter. Based on this decomposition the stability conditions of high order modulators are extracted. They are determined by the stability conditions of each of the first order modulators but shifted with respect to the origin of the quantizer function.
Limit cycles are well known phenomena that often appear in practical ÓÄ modulators. For data processing applications it is very important to predict and describe possible limit cycles. Main results concerning the limit cycles for low order Sigma-Delta modulators are discussed in many references. In his research the author uses the decomposition approach for description and validation of limit cycles in high order modulators with constant input signals. The obtained conditions for the existence and verification of limit cycles are easily to be checked and implemented.
The aim of the talk is to present the unified approach for study the stability and validation of potential limit cycles of one bit high order Sigma-Delta modulators. The approach is general because it uses the general form of a Sigma-Delta modulator. It is based on a parallel decomposition of the modulator and a direct nonlinear systems analysis. In this representation, the general N-th order modulator is transformed into a decomposition of low order, generally complex modulators, which interact only through the quantizer function. The presentation will cover several issues. First, the parallel decomposition technique for different cases of poles of the loop filter transfer function will be presented. Then the stability analysis study for first and high order modulators will be explained. Next the limit cycle analysis will be discussed and throughout the presentation several examples to show the applicability of the presented techniques will be given.
Brief Biography of the Speaker:
Valeri Mladenov graduated in Electrical Engineering (with distinction) from the Higher Institute for Mechanical and Electrical Engineering, Sofia (now Technical University of Sofia), Bulgaria in1985. He received his Ph.D. from the same institution in 1993. Since 1986 he has been a Lecturer in the Department of Theory of Electrical Engineering at the Technical University of Sofia Bulgaria, teaching courses on "Circuit Theory I & II", "Electrical Engineering", "Fuzzy Control and Neural Networks" and "Discrete Structures". In 2004 he becomes a Head of the Department of Theory of Electrical Engineering. In June 2011 he becomes a Dean of the Faculty of Automation and since December 2011 he is a Vice-Rector of the Technical University of Sofia. He is a guest lecturer at the Department of Electrical Engineering, Eindhoven University of Technology, the Netherlands, where he taught a course "Nonlinear Systems and Neural Networks". He has been invited lecturer in the Technical University of Ilmenau, Germany, National Technical University of Athens, Greece and many others.
Dr. Mladenov's research interests are in the field of nonlinear circuits and systems, neural networks, artificial intelligence, applied mathematics and signal processing. He has received many international research fellowships. He has more than 170 scientific papers in professional journals and conferences. He is a co-author of ten books and manuals for students. He have received many research grants from the Technical University of Sofia, Bulgarian Ministry of Education and Science, DAAD – Germany, NWO – Netherlands, Royal Society – UK, NATO,TEMPUS and others and also with his team he participated and now participate as a coordinator, team leader, etc. in many national and international projects (TEMPUS, DAAD, FP6, FP7).
As a member of several editorial boards Dr. Mladenov serves as a reviewer for a number of professional journals and conferences. He is a Senior Member of the Institute of Electrical and Electronics Engineering, Inc. (IEEE) http://www.ieee.org/, member of the IEEE Circuit and Systems Technical Committee on Cellular Neural Networks& Array Computing and Chair of the Bulgarian IEEE Circuit and Systems (CAS) chapter. He is also a member of the Steering Committee of the International Symposium on Theoretical Electrical Engineering (ISTET), member of the Board of Directors of the World Scientific and Engineering Academy and Society (WSEAS) http://www.wseas.org/ and editor-in-chief of the WSEAS Transactions on Circuits and Systems. He is an organizer and a chair of many International Conferences and Symposiums.