Minimizing Spurious Tones in Digital Delta-Sigma Modulators
Digital Delta-Sigma Modulators (DDSMs) are widely used in frequency synthesizers and oversampled digital-to-analog converters. In fact, they are more widely used commercially that their analog counterparts. This book describes several DDSM arc
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ANALOG CIRCUITS AND SIGNAL PROCESSING Series Editors: Mohammed Ismail Mohamad Sawan
For other titles published in this series, go to http://www.springer.com/series/7381
Kaveh Hosseini · Michael Peter Kennedy
Minimizing Spurious Tones in Digital Delta-Sigma Modulators
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Kaveh Hosseini Cypress Semiconductor Cork, Ireland [email protected]
Michael Peter Kennedy University College Cork Cork, Ireland [email protected]
ISBN 978-1-4614-0093-6 e-ISBN 978-1-4614-0094-3 DOI 10.1007/978-1-4614-0094-3 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011930097 c Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
To Monireh, Mohammad Saleh, Samira (K.H.) To Rossana (M.P.K.)
Preface
Analog Delta Sigma Modulators (ADSM) have been extensively analyzed and used in the context of analog-to-digital conversion; however, less attention has been paid to Digital Delta Sigma Modulators (DDSM) which are commonly used in digitalto-analog conversion and fractional-N frequency synthesis. Motivated by this fact, combined with their widespread use in wireless transceivers, we aim to demystify an important aspect of some popular DDSM structures, namely the existence of spurious tones due to the inherent periodicity of signals in DDSMs with constant inputs. The architectures under investigation include Multi-stAge noise SHaping (MASH), Single Quantizer (SQ) and Error Feedback (EF) DDSMs. A DDSM is a finite state machine (FSM); it is implemented using finite precision arithmetic units and the number of available states is finite. A deterministic FSM has a deterministic rule for transitioning from each state to the next. If the input is constant, the most complex behavior the DDSM can exhibit is a trajectory that visits each state once before repeating; in fact, the output must always be constant or periodic. Therefore, the DDSM always produces a periodic output signal (a cycle) when the input is constant. Furthermore, the quantization error signal (commonly called the quantization noise) is also periodic in this case. When the length of the cycle is short, the average power of the quantization noise in the DDSM is spread over a small number of discrete tones. According to Parseval’s re
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