Enhancing Signal Integrity Design Methodologies Utilizing Discrete Frequency Domain Techniques A DISSERTATION SUBMITTED TO THE FACULTY OF THE UNIVERSITY OF MINNESOTA BY Paul Eric Dahlen IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Hal H. Ottesen, Adviser April 2014 © Paul Eric Dahlen 2014 Acknowledgements I would like to acknowledge the efforts of my Ph.D. advisor, Hal H. Ottesen, of the University of Minnesota - Rochester, and also retired from IBM, for his patience, assistance, and mentorship on this project. Our technical discussions and advising sessions have enabled these results. Similarly, I would like to acknowledge my previous academic advisors, Ronald D. Moe at the University of North Dakota, and Keith S. Champlin at the University of Minnesota - Twin Cities, without whose encouragement I would have not have pursued further graduate degrees in electrical engineering. I also gratefully acknowledge the support of my employer, the IBM Corporation, which has generously funded this project through the IBM Degree Work Study Program and evaluation of intellectual property items related to this project for patenting or publication. I would like to particularly thank my electrical packaging technical mentors, IBM Distinguished Engineers Gerald K. Bartley and John M. Ryba, as well as all of my direct first-line IBM managers over my career, namely, Lowell Avery, Dennis Foster, Wayne Vlasak, Scott Bancroft, Linda Van Grinsven, Michael Gruver, and Jim Barnhart. Finally, I must thank the following individuals, my IBM electronic packaging and signal integrity engineering colleagues, for their input and peer review of the dissertation. Gerald K. Bartley, Distinguished Engineer, IBM Rochester Mark O. Maxson, Senior Technical Staff Member, IBM Rochester Darryl J. Becker, Senior Electronic Packaging Engineer, IBM Rochester Gregory R. Edlund, Senior Signal Integrity Engineer, IBM Rochester Trevor J. Timpane, Senior Signal Integrity Engineer, IBM Rochester Matthew S. Doyle, Advisory Signal Integrity Engineer, IBM Rochester Benjamin A. Fox, Advisory Signal Integrity Engineer, IBM Rochester Wesley D. Martin, Advisory Signal Integrity Engineer, IBM Rochester Thomas W. Liang, Advisory Signal Integrity Engineer, IBM Rochester Jesse M. Hefner, Staff Signal Integrity Engineer, IBM Rochester George R. Zettles, Staff Signal Integrity Engineer, IBM Rochester Layne A. Berge, Signal Integrity Engineer, IBM Rochester i Dedication This dissertation is dedicated to my immediate family. My parents, Howard and Gloria, have always encouraged, but never pressured, me. My wife, Jane, and my sons Peter, Philip, and Andrew, are my greatest supporters and cheerleaders. They are my most priceless treasures. ii Abstract Signal integrity engineering involves the use of electrical models and time- domain simulation to predict signal waveform degradation as the signal propagates across interconnects. It is employed most prevalently in the design of large digital systems, such as computers. Typically, the analysis and design techniques are concentrated in the continuous time domain, with the evaluation of time-domain waveform signal attributes being the primary tool for quantification of the degradation effects. Consistent with this continuous time-domain approach, the system models are often identified and expressed in the analog frequency domain, since this is the most natural domain for model identification, either by electromagnetic field simulation or empirical measurement. This research investigation focuses on the use of digital signal processing techniques in the discrete time domain and associated discrete frequency domains to augment typical signal integrity engineering techniques. Specifically, it explores in detail the use of Laplace-domain (s-domain) to z-domain transform methods to convert system interconnect models identified in the analog frequency domains to models in the discrete frequency domains. The models are first converted from the analog frequency domain, using known vector fitting algorithms, to form a rational function approximation for the system in the s-domain. They are then converted from the s-domain to the z-domain using methods generally applied in the fields of control theory and digital filter design, but which are less familiar in the field of signal integrity engineering. Two new s- to z- domain transformation techniques are developed that are particularly well-suited for signal integrity applications. The z-domain models are then assessed thoroughly in the z-plane using a variety of pole-zero analysis techniques to gain further insight into the nature of the system, and a new enhanced graphical method is introduced for the efficient assessment of such models in the z-plane. The overall results of this project are targeted toward enhancing signal integrity design methodologies in an industrial setting. iii Table of Contents Acknowledgements .............................................................................................................. i Dedication ........................................................................................................................... ii Abstract .............................................................................................................................. iii List of Tables .................................................................................................................... xii List of Figures .................................................................................................................. xiii List of Acronyms ............................................................................................................. xxi List of Symbols and Notation ........................................................................................ xxiv Chapter 1: Introduction and Thesis Organization ............................................................... 1 1.1 Introduction .............................................................................................................. 1 1.2 Thesis Organization .................................................................................................. 2 Chapter 2: Background ....................................................................................................... 5 2.1 Introduction .............................................................................................................. 5 2.2 System Description ................................................................................................... 6 2.2.1 System Block Diagram ...................................................................................... 7 2.2.2 Physical Representation of an Interconnect Structure ....................................... 8 2.2.3 Electrical Representation in Electrical Schematic Form in SPICE ................... 9 2.2.4 Electrical Representation as Two-Port Networks ............................................ 10 2.3 Use of Simulation Techniques in Signal Integrity Engineering ............................. 11 2.3.1 Model Extraction ............................................................................................. 11 2.3.2 Simulation Using SPICE Engines to Calculate the Transient Response ......... 13 2.3.3 Simulation Using Statistical Simulation Analysis Engines to Calculate the Transient Response ................................................................................................... 14 2.3.4 Assessment of Transient Response Waveforms .............................................. 15 iv 2.3.5 Using Simulation to Calculate the Frequency Response ................................. 16 2.4 Signal Integrity Engineering in an Industrial Setting ............................................. 17 2.4.1 Block Diagram of a Signal Integrity Engineering Design Flow ...................... 17 2.4.2 Problems and Challenges ................................................................................. 18 2.5 Conclusion ............................................................................................................ 23 Chapter 3: Theoretical Foundations .................................................................................. 25 3.1 Introduction ............................................................................................................ 25 3.2 Continuous-Time and Analog-Frequency Domains ............................................... 26 3.3 Discrete-Time and Discrete-Frequency Domains ................................................... 28 3.3.1 Discrete-Time Domain Relation to Continuous-Time Domain ....................... 29 3.3.2 Discrete-Frequency Domain Relation to Analog-Frequency Domain ............. 29 3.3.3 DTFT, DFT, FFT, and CTFT Relationships .................................................... 29 3.4 Complex Frequency Domain .................................................................................. 31 3.4.1 Laplace Transform Domain, or s-Domain ....................................................... 31 3.4.2 z-Transform Domain, or z-Domain ................................................................. 34 3.4.3 Ha(s) to Hd(z) Transformation Methods .......................................................... 37 3.4.4 Time-Frequency Uncertainty Principle for Quantities Related by the Fourier Transform .................................................................................................................. 42 3.5 Circuit Theory ........................................................................................................