A Handbook of Black Magic

Howard W. Johnson and Martin Graham
Prentice Hall, 1993
ISBN 0-13-395724-1
447 pages, hardback

Considered the original "bible" of high-speed design issues, High-Speed Digital Design focuses on a combination of digital and analog circuit theory. This comprehensive volume helps engineers who work with digital systems shorten their product development cycles and fix their latest high-speed design problems.

NOTE: This book is not required for the High-Speed Digital Design Seminar, but it makes a terrific companion. The seminar treats a subset of the book material, and in a different way more condusive to live explanations. The book, being 447 pages in length, obviously delves into the subject matter in greater detail. Think of the seminar as an introduction and, if you like it, get the book for on-the-job reference.

Topics Covered

  • Covers signal reflection, crosstalk, and noise problems that occur in high-speed digital machines.
  • Includes checklists that ask the questions an experienced designer would ask about a new system.
  • Offers useful formulae for inductance, capacitance, resistance, risetime, and Q.
  • Explains the trade-offs between signal crosstalk, mechanical fabrication of tolerances, and trace routing density.
  • Presents a methodology for determining how many layers will be required to route a printed circuit board.

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How This Book Is Organized

Each chapter in this book treats a specialized topic having to do with high-speed digital design.

Chapters 1–3 introduce analog circuit terminology, the high-speed properties of logic gates, and standard high-speed measurement techniques, respectively. These three chapters form the core of the book and should be included in any serious study of high-speed logic design.

The remaining chapters, 4–12, each treat specialized topics in high-speed logic design and may be studied in any order.

Chapters 4 begins with an introduction to the properties of a simple, uniform, infinite transmission line and works up to an understanding of transmission line losses, reflections, and various common cases of source and load impedances. It considers reflections from reactive loads and ends with a discussion of how a large number of loads connected to a common bus loads the bus, changing both its impedance and propagation delay.

Chapter 5 introduces the concept of returning signal current, a notion crucial to the understanding of crosstalk in high-speed digital layout. With the importance of a solid reference plane understood, the chapter presents a number of layer stack examples.

Chapter 6 looks at issues having to do with terminations, including DC biasing, power dissipation, resistor layout, series inductance, and crosstalk.

Chapter 7 gives a brief look at the mechanical properties of vias and the parasitic capacitance and inductance of vias, a subject treated much more thoroughly in the book, High-Speed Signal Propagation.

Chapter 8 explores the architecture of a power system. It looks into issues of voltage fluctuation and DC droop. The chapter presents an electrical model of a capacitor, and discusses the relation of capacitor packaging to the equivalent series inductance of a capacitor, a subject more thoroughly presented in the High-Speed Digital Design Seminar. The chapter concludes with notes concerning the properties of three popular capacitor dielectric materials.

Chapter 9 extends the idea of returning signal current to explain the mutual-inductive mode of crosstalk within connectors. It shows an example of how connectors create EMI. It then considers the parasitic capacitance of a connector its impact on the loading of a multi-drop bus. The Chapter includes notes on special measurement procedures for connector, leading to a discussion of the importance of continuity of the reference planes at the board-to-connector interface. The chapter ends with discussions of differential connectors

Chapter 10 involves the use of ribbon cables and ribbon cable connectors.

Chapter 11 opens with a definition of clock skew and moves on to present multiple methods of distributing clock with controlled skew.

Chapter 12 wraps up the book on the subject of clock oscillators, and clock jitter.

Appendix A collects highlights from each section, listing the most important ideas and concepts presented. It can be used as a checklist for system design or as an index to the text when facing a difficult problem.

Appendix B details the mathematical assumptions behind various forms of rise time measurement. This section helps relate results given in this book to other sources and standards of nomenclature.

Appendix C lists standard formulas for computing the resistance, capacitance, and inductance of physical structures.

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The reader need not have a background in electrical engineering or circuit theory to read and understand this book. No mathematics are used beyond simple algebra and 1st-order derivatives. The authors do assume a general familiarity with digital logic and the concepts of voltage and current.

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This is a book for digital designers. It highlights and explains analog circuit principles relevant to high-speed digital design. Teaching by example, the authors cover ringing, crosstalk, and radiated noise problems which commonly beset high-speed digital machines.

None of this material is new. On the contrary, it has been handed down by word of mouth and passed along through application notes for many years. This book simply collects together that wisdom. Because much of this material is not covered in standard college curricula, many practicing engineers view high-speed effects as somewhat mysterious, ominous, or daunting. For them, this subject matter has earned the name “black magic.” The authors would like to dispel the popular myth that anything unusual or unexplained happens at high speeds. It’s simply a matter of knowing which principles apply, and how.

Digital designers working at low speeds do not need this material. In low-speed designs, signals remain clean and well behaved, conforming nicely to the binary model.

At high speeds, where fast signal rise times exaggerate the influence of analog effects, engineers experience a completely different view of logic signals. To them, logic signals often appear hairy, jagged, and distorted. For their products to function, high-speed designers must know and use analog principles. This book explains what those principles are and how to apply them.

Readers without the benefit of formal training in analog circuit theory can use and apply the formulas and examples in this book. Readers who have completed a first year class in introductory linear circuit theory may comprehend this material at a deeper level.


"Dr. Howard W. Johnson and Dr. Martin Graham have blessed us with a text that in many ways addresses exactly this juxtaposition of designer and engineer in the high-speed board world....this is one of the finest efforts to come along in the field of applied high-speed digital design because of its focus on providing tools for the whole design team bringing a high-speed product to life. For all the PCB designers and circuit designers out there, buy it; read it; keep it." - Dan Baumgartner, Printed Circuit Design

"'High-Speed Digital Design'...treats the gray area between signals that are digital, and the analog aspects that are so important when you want your digital buses to behave at higher and higher speeds - not a trivial task. This book is there to help, with serious advice and good philosophy." - Bob Pease, Electronic Design

"Engineers who must make high-speed circuits work will find this book invaluable. Johnson and Graham strike what seems to me to be just the right balance between rigor and nuts-and-bolts practicality. The book should be must reading for EE students who aspire to work in digital-hardware design. It should also occupy a place in the libraries of most of the experienced practitioners of the art." - Dan Strassberg, EDN


  • Table of Contents (.pdf format).
  • Errata Page applies to all printings (.pdf format)
  • Appendix C includes all the equations from the back of the book, with examples (.pdf format)
  • MathCad modelling scripts includes Appendix C coded for MathCad v.13 in .zip format, in human-readable .pdf format, plus examples and also a simple lossless transmission-line simulator(see below)
  • Presentation showing what a simple lossless transmission-line simulator can do: shortline-presentation.pdf
  • Equations used in the preceeding presentation: shortline-equations.pdf
  • Skin Effect Calculations: Special discussion on derivation of Skin Effect Calculations
  • Resistance: Concerning the derivation on page 414 of the equation for calculating the DC resistance of power planes based on the diameters of two contact points space at X amount of distance. (newsletter v1-11)
  • Ground-bounce calculations: On page 62 of the High-Speed Digital Design Text… where does the factor of 1.52 come from? (newsletter v1-12)
  • Equiv. Circuit Source Impedance: What is the true source impedance of the equivalent circuit shown on page 13, figure 1.6? (newsletter v2-09)
  • Via Capacitance: On page 257, formula [7.6] for the capacitance of a via is a crude approximation--I've now got some better material. (newsletter v5-09)
  • Via Inductance: On page 259, formula [7.9] glosses over the location of the signal return current associated with the via. A full discussion of the issue is now available. (newsletter v6-04)

NOTE: About the use of MathCad, let me explain. Over the years I've come to appreciate a good mathematical spreadsheet. A mathematical spreadsheet lets you compose pictures, add explanatory text, and insert "live" equations in a single document. For high-speed design problems, where you must document detailed calculations pertaining to physical circuit dimensions, the benefits are obvious. Compared to regular spreadsheets, the mathematical spreadsheets have the advantage of showing your work. You can see the equations. So can your co-workers.

The mathematical spreadsheet concept is not unique. Math spreadsheet applications are available from several vendors. Popular versions include MathCad, Mathematica, and MatLab. Any of the three tools can accomplish the basic purpose of recording graphics, text and equations.

We happen to be MathCad users, and for a very good reason: the MathCad syntax looks much like ordinary equations. That makes it a great teaching tool. Other tools may be more popular, or more powerful, but we find MathCad to be very good for presentation work, so our collection of high-speed design utilities have been formatted for use with the MathCad application. You will need the MathCad application to run the spreadsheets. If you use a different spreadsheet, it's not difficult to convert the equations to your format.

The "MathCad modelling scripts" download is a .zip file. It includes everything from Appendix C encoded for MathCad, but with additional examples. The scripts are provided in both MathCad v.13 syntax and also human-readable .pdf format in case you need to port the equations to another brand of mathematical spreadsheet. Also included in the .zip file is a simple short-line transmission line simulator that incorporates the effects of source impedance, load impedance, transmission line delay, characteristic impedance, and risetime of the driving waveform. The simulator does not incorporate skin-effect or dielectric loss. If you want that, look here in the download package for the book High-Speed Signal Propagation.