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Table of Contents

Title Page

Buildings have walls and halls.

People travel in the halls not the walls.

Circuits have traces and spaces.

Energy travels in the spaces not the traces.

Ralph Morrison

A word about the book title

Mach 1 was a barrier in flight for a long time. Aircraft that can go faster than the speed of sound are more expensive and more difficult to design. There is a barrier in digital design that occurs at clock rates around 1 GHz. One clock period is one nanosecond, and in this time an electromagnetic wave can travel about 15 cm in epoxy. This is the dimension of a typical circuit board. Circuits that can perform near or above 1 GHz present a new set of design challenges. In that sense, there is a barrier to cross. This book discusses the challenges of designing these faster and faster circuits. Many old ideas must be discarded and new ones accepted. There are no sonic booms that I know of. I hope the ride through Mach 1 is a smooth one.

Preface

The story of Digital Circuit Boards at Mach 1 GHz starts with my friend Daniel Beeker. Dan is a senior field applications engineer for Freescale Semiconductor. He was instrumental in getting me interested in circuit board design problems. He was the one that spurred me into finishing the 5th edition to my book “Grounding and Shielding,” which was published by John Wiley in 2007. I have rewritten this book five times since 1967 and when this fifth writing was finished, I really thought I was through writing books. Obviously, I was mistaken.

Dan sees the problems encountered by his customers. He recommended to his management that the users must be provided some help in the form of seminars. They agreed, and as a result Dan took on a new set of responsibilities. He was tasked to find speakers and arrange for seminars for Freescale customers. To locate speakers, Dan turned to his own personal library. The first book he took from the shelf was a copy of my “Grounding and Shielding.” He then looked into my web site and found my address. The result was that I was invited to participate in the Freescale Forum in Orlando and later to give a seminar to his customers in the Detroit area.

The seminar I gave was based on my book and was well received. For those familiar with my books, I use very simple physics to explain how interference is generated, how it enters circuits, and how the circuits can be protected. The principles are the same whether the problem is analog, digital, or rf. I had little trouble bringing transmission line theory into my discussions. I found I had to catch up on the language of circuit boards and how they are built. I had to find out what a BGA was, what prepreg meant, and what is an interposer board. I had to learn the difference between a blind and a buried via.

Fortunately, Dan followed through with additional seminars where the speakers understood the details of circuit board design and could relate more closely with the details of components and materials. I admire Dan for recognizing that the fundamentals must come first. Even though I knew little about the details of board design, I could show the users how and why layout geometry was critical if they were going to build successful boards.

Dan wanted me to get closer to the circuit board problems, so he arranged for me to attend the PCB conference in Santa Clara, given by the UP Media Group. At the conference I sat in on courses given by experts in the field. I learned a lot about how circuit boards were designed and built. The talks introduced me to the designers' problems. Many of the speakers used a combination of circuit theory and lore to explain circuit board behavior. This is just the problem I had been dealing with throughout my career. I was in a different field with a new language. I had a lot to learn. I wanted to understand the digital layout problem based on physics, not on lore.

I found that digital engineers were working in areas of nanosecond delays and picosecond rise times. This was an area where I understood the physics but not the details of board construction. I recognized that real time delays were involved, and this was not covered by circuit theory. The speakers related their real world experiences and how they resolved many difficult problems. I remember speakers saying that energy could be drawn from the ground/power plane faster than from a capacitor. This got the wheels turning. How fast is fast and how much energy is there? How fast are capacitors?

I knew the basic physics so the challenge was to learn the language and make sense out of all the material that was being presented. When I got home from the show one of the first things I examined was how energy is moved from a ground/power plane. I assumed a coaxial connection to the conducting planes. If a step load was placed on this connection, the wave that propagated outward moved in a circular pattern. The characteristic impedance of the wave depended on the radial distance from the point of coaxial connection. I recognized that there were continuous reflections as the wave propagated outward and that the energy returned to the source increased with time. Much to my surprise, I found that the power curve depended on conductor spacing and not on the dielectric constant. With a greater dielectric constant, the energy was pulled from a smaller area. With a higher dielectric constant and with multiple demands for energy there would be less cross talk.

This exercise helped me understand the problem of connecting to the ground/power plane. I recognized that vias were the accepted method of making connections between layers. Typically, a via geometry has an aspect ratio of unity, where the characteristic impedance is about 50 ohm. When I assumed that a short lead length of 50 ohm was used to connect the ground/power plane to a load, I found out a very important fact. A short section of coaxial line placed between the load and the ground/power plane increased the rise time significantly. What was happening was that a large number of wave reflections were required to move energy across this short connection.

This one fact really caught my attention. It had a far reaching impact on my thinking. How many places were there, where short sections of transmission lines were used to connect a load to a source of energy?

The first area I considered was the capacitor. The available books and all the speakers discussed the natural frequencies of capacitors. The limitations in performance were assigned to the series inductance. This was a good explanation for axial lead capacitors but what about surface mounted components? Because capacitors of any geometry have a natural frequency when tested with sine waves, the assumption that resonance is related to a simple series inductance is made. In my view, I was dealing with step functions and reflections, and these ideas of circuit theory did not exactly fit. I decided then that I needed to look at digital processes in a consistent manner. I could not mix step function discussions with sine wave terminology. I had to clean up my understanding and explain things in an unambiguous manner. Resonant frequency concepts using sine waves was not compatible with real time reflections on a transmission line.

Calling a capacitor a short transmission line was the first step. Then I realized that the symbol was misleading as it implied a midpoint connection. Then some obvious issues came to mind. How can you take energy out of a capacitor and put it back in at the same time? What kind of construction allows wave energy to enter between the conductors? If you want energy with a short time constant, how do you construct a low impedance connection to a capacitor? In working on these problems, a book was beginning to form.

I have been doing engineering and consulting while writing books for some time. I have come to the conclusion that we often use electrical symbols in a careless manner. We need the symbols, but they represent complex conductor geometries that are intended to store or dissipate field energy. This is the correct view for all electrical activity whether we describe circuit behavior in terms of step functions or sine waves. Unfortunately, the field view is cumbersome, difficult mathematically, and impractical most of the time. Circuit theory is always correct, but it requires that the simplifications that are made are applicable. For example, simple circuit theory does not allow for time delays and that eliminates transmission lines. It implies that the interconnecting leads do not affect circuit performance, as we assume zero resistance and inductance for conductors regardless of length. We can always include parasitic elements in any analysis, but when we need them they are still just approximations. A resistor at 1 MHz can be represented as having a single parasitic shunt capacitance. At 100 MHz, the lead inductance starts to play a role and a distributed parasitic capacitance is needed. At 1 GHz, the resistor becomes a part of a transmission line path and the return path geometry is critical. At 10 GHz, there is really no such thing as a resistor even if we add many correcting terms. It is a lossy conductor geometry that modifies an electromagnetic field. The problem we face is how do we represent this device? The symbols we draw are very misleading. So far, there are no suggestions on what else we might do.

In my “Grounding and Shielding book,” I recognized the need to use field theory to explain electrical activity. I kept it very nonmathematical. The ideas are important and not the exact numbers. This book is no different. The basic physics is again the starting point. In this book, the emphasis is on events that occur in picoseconds where the signals are in the volt range. In “Grounding and Shielding,” the problems were usually related to microvolt signals, where the frequencies of interest were under 1 MHz. Move the signal level and signal bandwidth up to six orders of magnitude to volts and gigahertz, and the same physics solves a different set of problems.

I treat the basics in Chapter 1. It is important for the reader to appreciate that all the answers to their problems rest somewhere in this Chapter 1. If the reader needs a more in-depth review, I suggest reading the first chapters of “Grounding and Shielding” book. Of course, there is always that textbook from school that rests on the nearby bookshelf.

This book is intended to help the reader understand the problems of laying out digital circuit boards for fast logic. It is not intended as a treatise on how circuit boards are made although this knowledge can often be very helpful. Understanding the manufacturing process helps in understanding practical design. An engineer needs to know the range of trace widths that can be accommodated or how thin a dielectric can be used or what materials will withstand soldering. He needs to understand the cost of different laminates and why they are needed. All of this comes from the experience gained in doing designs and working with a manufacturer. On top of all this knowledge, the engineer needs to know the basics of signal transmission so that the logic will function.

Learning is an ongoing process. Board manufacturers will continue to improve their art. The only constant thing will be physics. It was my intent in writing this book to stick with the basics and use the present art as an example when it seems relevant. It is interesting to note that the materials we use today are the same ones that were used 20 years ago. Change is usually a refinement in processing raw materials caused by the continuous demand to improve performance and reduce cost. I hope this book will make a few design tasks a bit easier.

Ralph Morrison

Pacifica, CA

April 2012

Chapter 1

Basics

1.1 Introduction

This book is written to provide the reader with the basic understanding that is needed to layout high speed digital circuit boards. The wiring and circuitry that interconnects components mounted on these boards has become a new field of engineering. This book treats the analog aspects of digital board design, as it relates to the hardware that is selected. The term analog applies to such topics such as rise and fall time, overshoot, transmission delay, reflections, radiation, settling time, cross talk, and energy flow. The term analog is often used to describe circuits that use a carrier signal, such as in cell phone communication. Much of the material in this book will apply to carrier signals, but the emphasis will be on digital circuit board layout. The methods described in this book work well for slower logic. These methods do not add to board cost. These methods do add to reliability and performance. Software design and selection of components that make up a logic design are not discussed.

Rather than gather a big list at the end of the book, I have placed a limited glossary at the end of each chapter. I feel that this glossary should contain the words that are most critical to an understanding of the material in the text. In an industry that is changing very rapidly, there are bound to be language problems. This is the case with the circuit board industry and digital logic. The definitions that are used must be as clear as possible or the reader will not be helped.

The reader is encouraged to read over the glossary after completing each chapter. It will serve as both a review and a test of understanding. If a phrase or expression is not found then the next step is to use the index. If I have left something out, the internet can provide some assistance.

Electrical phenomena can be explained using basic physics, but the words that are used must be carefully chosen. Some phrases have a way of changing meaning over time. The term critical length was first used by transmission line engineers in the early days of radio where the signals were sine waves. Today, the expression is applied to cross coupling between traces on a circuit board where digital logic is involved. By reapplying the term, some of the original meaning has changed.

Abbreviations are not listed or used in the glossary of terms. Only well-accepted abbreviations and acronyms are used in the text. The reader is referred to a list at the end of this book.

In describing electrical behavior, the explanations vary with frequency and with specific disciplines. At clock rates above 100 MHz, many of the concepts used in circuit analysis begin to fail. In circuit analysis, there is a time delay associated with phase shift. The steady state operation of a circuit may occur after a hundred sine wave cycles have gone by. This implies that in a circuit, there are transient effects that must totally attenuate before the steady state solution is available. In digital circuits, there is a time delay associated with signal propagation. There is no waiting for one hundred cycles while transients decay. Delays in analog circuitry must be treated quite differently than the delays caused by signals traveling on a transmission line.

In a digital circuit, every connecting trace and every component on a circuit board can be considered a transmission line. It takes time for a signal to travel the length of a transmission line, and this time is independent of clock rate. It takes time to obtain energy from a capacitor. In circuit analysis, there is no simple way to treat these delays or the propagation delay of a transmission line.

In a resonant circuit involving inductance and capacitance, the energy flows back and forth between the two components at one frequency. The analysis is called steady state when all transient effects have attenuated and the performance repeats for each cycle of the driving signal. When a wave reflects back and forth on a transmission line, there is a time of transit not found in a resonant circuit. There is a spectrum associated with every logic transmission that relates to the rise time and extends toward dc. Circuits are analyzed one frequency at a time. Logic reacts to signals that are composites of an entire spectrum of sine waves. Thus, the character of a logic signal is very different than the character of a sine wave, yet the term frequency is used for both.

Printed circuit boards (PCBs) or printed wiring boards started out as a way to avoid hand soldering the interconnection of electronic components. Early boards had traces on one or two sides of an epoxy board with few plated-through holes. As component densities and clock speeds increased, it became necessary to include conducting planes in the design. These planes are used to distribute power and ground to components and to provide a return path for signal currents. Today, many boards are manufactured with dozens of interconnected layers, with many ground and power planes using surface-mounted and embedded components. As the clock rates have risen, board designs have become more and more of an engineering problem. It is no longer an issue of simply connecting the components together. A few of the problem areas that we will discuss include traces that jump between layers, the spacing of vias, trace routing that uses stubs, energy distribution, energy dissipation, board radiation, and signal cross talk.

Today's circuit board designs require engineering, and this engineering must be based on physics. This physics controls the details of design and is the basis of this book. Effective engineering must consider price and performance, as well as topics such as radiation and susceptibility. Surprisingly, there is a lot to say.

Circuits are often thought of as a configuration of components. When the logic rise times are associated with 1 MHz clock rates, this is basically true. The leads that connect the circuit can be routed almost at random, and there will be few problems. In low signal level analog designs below 100 kHz, lead routing can make or break the product. In digital circuits operating at clock rates above 100 MHz, the routing of all leads is as important as the selection of components. This book discusses the engineering of board layout and wiring, so that logic boards can function correctly; and at the same time, the engineer can control cost and limit radiation.

N.B.
The rise and fall time of logic signals is more critical than the clock rate.

1.2 Why the Field Approach is Important

All electrical behavior from dc to light can be described in terms of the electric and magnetic fields. For many reasons, a field approach to circuit function is very impractical. This is why engineers heavily rely on circuit theory as a working tool. Our understanding of how a circuit functions is closely related to the circuit symbols we have created and to the language we use. When we use capacitors and inductors in our analysis we think of reactances and we generally ignore the fields and energy storage that are inside of these components. In a typical circuit design, the energy that is moved and stored between traces or between traces and a conducting plane is not considered. In high speed logic, this movement of energy must be considered. In fact, this energy must be controlled and dissipated so that the logic can function. The dissipation of this energy can be a serious problem as it can cause board overheating.

Every component is a conductor geometry of some sort. Fields inside the components determine their performance. In a FET (field-effect transistor), there is an electric field between the source and drain. Fields carry operating power and signals to the components over the connecting traces. Getting these fields to the components on a timely basis is handled by traces. The rou4ing of traces is a problem, and we discuss this in great detail later.

Nature does not read our circuit diagrams or symbols. She approaches a circuit as a conductor geometry that allows the flow of electromagnetic energy. Her one goal is to find a way to store less field energy. We use this one fact to get her to perform electrical tasks. A design usually starts by providing a power supply that is a source of energy. Energy leaves this power source as voltage and current. The energy actually flows in electromagnetic fields that follow in the spaces between conductor pairs. These pathways spread the energy, which leads to various losses. Consider the parallel with the flow of water. A dam stores water that we allow to flow in conduits. These conduits reach our homes to supply water for many uses. In the city, we channel water in storm drains to limit water damage during a storm. These same ideas of flow apply to our circuits. If we cooperate with nature, we can make effective use of this energy flow. Our designs must keep the energy from a storm (radiation) from entering our circuits. We want to control energy paths, so the energy required in one circuit does not interfere with another circuit.

At a sufficiently high frequency, components lose their simple circuit identity. A capacitor, for example, can be viewed as having a series resistance and inductance. The inductance implies that a magnetic field is involved in energy transport. We will see that a simple circuit theory approach may not be effective. If we turn to field theory for help, we will not get exact answers. If we want to appreciate what is actually happening in a circuit, both field theory and circuit theory must be applied to the problem. We must learn how to use the field approach so that we can make good engineering decisions.

1.3 The Role of Circuit Analysis

We are used to thinking in terms of sinusoids. The language of circuit analysis is closely related to these sine wave signals. The words impedance or reactance are defined in terms of sine waves. We are married to circuit symbols and sinusoidal measures and somehow we must stretch these meanings to fit a high speed digital world. We certainly are not going to invent a new language or use new symbols to describe our needs. The old words and symbols will have to do. Usage defines meaning and eventually usage may change. We will use the word impedance without regard to sinusoids.

In digital circuitry, the signals are usually in the form of step functions of voltage. These voltage level changes are applied to traces that carry information (energy) between components. We will refer to these traces as transmission lines. It will come as a surprise to some readers that a 1/16-in-long trace should be considered a transmission line. Also that a vias associated with a trace can modify the character of the transmission path. The reflections on sections of the energy path can result in radiation and limit performance.

Repetitive wave forms are equivalent to a group of sine waves with a harmonic relationship. For example, a square wave can be equated to a group of sine waves consisting of a fundamental and all the odd harmonics of this frequency. The amplitude of each harmonic is inversely proportional to the number of the harmonic. Digital signals are not repetitive and a harmonic wave analysis may not be directly applicable. Some of the ideas expressed by harmonic analysis can still be of value. The most important factor that we must consider is the rise and fall time of the leading edges in step functions. Sometimes, the third harmonic of the fundamental (clock frequency) can be used as a reference frequency in describing or analyzing some aspect of performance. This makes sense if the rise and fall times are 20% of the clock period.

The materials used in board manufacture have been around for a long time. Progress is the process of using these same materials in new and better configurations to serve our needs. A lot of engineering is based on past practice. Every practice has its limitations. We must question everything so that when a practice needs changing we can act accordingly. A better design will most likely be a change in how we configure these available materials. Some of the material is given to us in the form of components and some of the material is used in mounting and connecting these components. Our job is to select the right components and configure them on circuit boards so that field energy flows to perform the task at hand.

1.4 Getting Started

This book assumes that the reader is familiar with the basic physics of electricity and with basic circuit theory. There are a few ideas that need to be stressed before we discuss circuit board design. A review is a good idea and I hope that the reader will take the time to read these few paragraphs. The intent is to stress concepts. Simple equations will be presented because they are the clearest way to state relationships.

In an isolated uncharged conductor there is a balance of charge. In every atom, the inner protons carry a positive charge equal to the negative charge on the electrons. This balance is extremely precise. In a conductor, electrons can easily move between atoms. We call this motion current. The percentage of available electrons that partake in electrical circuit activity is so small that it is hard to describe it in useful terms. The ratio is like that of a teaspoon of sand to miles of beach.

The forces that exist between electrons are not easily imagined. Consider that 1% of the electrons in a human being are free to interact with the same number of electrons on a second person. The force between the charges would be enough to lift the earth out of orbit. It is obvious from this fact that the number of electrons involved in any electrical activity in our circuits is indeed very small. It is hard to realize that this immense electrical force is involved in current flow.

The protons are so well shielded inside the atom that they do not partake in normal circuit activity. In the circuits we will consider, most of the electrons move on the surface of conductors. To start, consider a group of extra electrons placed on a conductor. These electrons are free to move between atoms. The forces between these “free” electrons cause them to move apart as far as they can go. On a conductor, they assume a position that stores the least amount of potential energy. On an isolated sphere, they end up spaced uniformly on the entire outer surface.

An accumulation of added electrons is called a negative charge. A depletion of electrons from a conductor is called a positive charge. These pseudopositive charges attract electrons and move just like electrons. When a pseudopositive charge meets an electron, they are canceled. In other words, the electron is accepted by an atom to fill in its outer shell. In most of our discussions we will discuss the motion of charges and the direction of current flow. The polarity of surface charges will not be discussed.

1.5 Voltage and the Electric Field

The force field that exists around any group of charges is called the E or electric field. It is a vector field, as it has intensity and direction at all points in space. The charges (or absence of charge) we will consider are usually distributed on the surfaces of circuit conductors. This force field in the space around charged objects can be sensed by placing a very small test charge in the field. The test charge has to be small enough that it does not contribute to the field being tested. Thus, a test charge is a small accumulation of charge on a small mass.

Work must be done in moving this test charge in an electric field. The work required to move a unit charge between two points is called the potential difference (voltage) between those two points. We usually measure potential difference between conductors. In a radiated field there are no conductors to consider, yet there are potential differences.

Definition: Voltage is the work required to move a unit charge over a distance in an electric force field.

If there are voltage differences, there are electric fields. The converse is also true. If there are electric fields there must be voltage differences. If there are charges on a surface there must be an electric field. Conversely, if there are nonradiated electric fields there must be charges on conductive surfaces.

Voltage differences can exist between points in space or between conducting surfaces. Electric fields exist at all frequencies including dc. Electric fields are represented by curves that follow the direction of the field forces. In a field representation, lines of force start on a fixed amount of positive charge and terminate on the same amount of opposite charge. When the lines are close together, the forces are the greatest. In a field representation it is only necessary to use a limited number of lines to outline the shape of the field. When there is voltage, electric field lines terminate on the surface charges of a conductor. As we will see a very small electric field inside, a conductor is required for current flow. When there is no current flow there is no field inside of a conductor.

The words ground or ground plane will be used frequently. A ground is a conducting surface that is larger than the surrounding circuitry. In a facility, the earth may be called ground. In an integrated circuit die, a conducting surface can be called ground. On a circuit board, a conducting plane can be called ground. A ground has the quality that it allows charges to move freely on the surface and collect where the field line terminates. An ideal ground plane has no potential differences from point to point. In most circuits this is very nearly true. A superconductor can have current flow with zero internal electric field.

1.6 Current

shows the field pattern around a typical trace over a ground plane.