Vrije Universiteit Brussel Faculteit Toegepaste Wetenschappen Departement ELEC Pleinlaan 2, B-1050 Brussels, Belgium MODEL BASED CALIBRATION OF D/A CONVERTERS Balázs Vargha Promotors: Proefschrift ingediend tot het Prof. Dr. Ir. Johan Schoukens behalen van de graad van doc- Dr. István Zoltán tor in de toegepaste weten- schappen 2002 Vrije Universiteit Brussel Faculteit Toegepaste Wetenschappen Departement ELEC Pleinlaan 2, B-1050 Brussels, Belgium MODEL BASED CALIBRATION OF D/A CONVERTERS Balázs Vargha Voorzitter: Prof. G. Maggetto (Vrije Universiteit Brussel) Vice-voorzitter: Prof. J. Vereecken (Vrije Universiteit Brussel) Promoters: Prof. J. Schoukens (Vrije Universiteit Brussel) Prof. I. Zoltán (Budapest University of Technology and Economics) Jury: Prof. A. Barel (Vrije Universiteit Brussel) B. Bell (National Institute of Standards and Technology, USA) Prof. I. Kollár (Budapest University of Technology and Economics) Prof. Y. Rolain (Vrije Universiteit Brussel) Prof. G. Vandersteen (IMEC) Table of Contents TABLE OF CONTENTS . I LIST OF FIGURES . V LIST OF TABLES . .IX GLOSSARY OF SYMBOLS. .XI PREFACE. XV CHAPTER 1: INTRODUCTION . 1 1.1 SELF-CALIBRATION AND SELF-CORRECTION . .1 1.2 D/A CONVERTERS IN GENERAL . .2 1.2.1 Digital coding schemes . .3 1.2.2 D/A architectures. .3 1.2.3 Transfer characteristics and error diagrams . .5 1.2.4 Multiplying D/A converters . .7 1.3 SHORT OVERVIEW OF ORTHOGONAL FUNCTIONS. .7 1.3.1 Rademacher functions. .8 1.3.2 Walsh functions and transformation. .8 1.3.3 Haar functions . 10 CHAPTER 2: STATIC TESTING OF D/A CONVERTERS . 13 2.1 FORMER METHODS. 13 2.1.1 Mixed-signal modeling . 15 2.1.1.1 Physical models. 15 2.1.1.2 A priori models . 16 i Table of Contents 2.1.1.3 Empirical models . 17 2.2 MODELS OF THE CONVERTER . 19 2.2.1 Linear error modeling . 20 2.2.1.1 High speed testing. 22 2.2.2 Nonlinear error modeling. 23 2.3 ANALYZING THE ERROR TERMS. 24 2.3.1 Bit errors. 24 2.3.1.1 Conclusions. 28 2.3.2 Higher-order errors . 28 2.3.3 Fourier or Walsh transformation based diagnostics. 32 2.4 DETERMINING THE ERROR TERMS . 34 2.4.1 Transformation matrix . 34 2.4.1.1 Illustrating the problem . 35 2.4.1.2 General case. 36 2.4.2 Noise analysis . 40 2.4.2.1 Mean value . 43 2.4.2.2 Covariance matrix . 44 2.4.2.3 Conclusions. 46 2.5 CUSTOM-DESIGNED TEST CIRCUIT. 46 2.5.1 D/A converters . 46 2.5.2 Support circuitry . 48 2.5.3 Static measurement set-up . 49 2.6 MEASUREMENT RESULTS. 50 2.7 CONCLUSIONS . 56 CHAPTER 3: CALIBRATION OF D/A CONVERTERS . .59 3.1 FORMER METHODS . 59 3.1.1 Fixed reference D/A calibration . 59 3.1.1.1 AD760 self-calibrating D/A converter . 59 3.1.2 Dynamic element matching . 63 3.1.3 Current source calibration . 65 3.1.4 Model inversion . 67 ii Table of Contents 3.1.4.1 Using for D/A nonlinearity compensation. 68 3.2 NONLINEAR MODEL BASED APPROACH . 69 3.2.1 Error due to the finite precision of the measuring device . 71 3.3 PROPERTIES OF THE ERROR TERMS . 73 3.3.1 First-order errors . 73 3.3.2 Second-order errors. 76 3.3.3 Measurements on different chips. 78 3.3.4 Measurement results of the calibrated converter . 80 3.4 ERRORS AFFECTING THE CALIBRATION. 83 3.5 CONCLUSIONS . 84 CHAPTER 4: NONLINEARITY OF THE ANALOG PATH . 87 4.1 DETECTION OF HARMONIC DISTORTIONS . 87 4.1.1 Special-odd multisine excitation . 89 4.2 APPLYING THE THEORY. 90 4.2.1 Measurement set-up . 90 4.2.2 Failure detection . 92 4.2.3 Identifying the failure . 95 4.2.4 Analyzing the distortions . 98 4.2.4.1 Increasing the dynamic range of the measurements . 100 4.3 CONCLUSIONS . 103 CHAPTER 5: EFFICIENT TESTING OF D/A CONVERTERS . 105 5.1 INTRODUCTION. 105 5.2 TEST TIME REDUCTION USING AN A PRIORI MODEL . 106 5.2.1 Determining the model. 109 5.2.2 Modeling error determination . 110 5.2.3 Selecting the error terms . ..