# Electromagnetic Fields, Part 2: How They Impact Propagation Speed

In my August 2013 column, I suggested that thinking in terms of what the electromagnetic field looks like around our traces might offer significant insight into how our circuits might be performing. In that column, I pointed out that the electromagnetic field had more to do with trace impedance than the specific trace dimensions did. That is, a trace can be “scaled” without changing the impedance (or the shape of the field.) But if the field distribution changes, then the impedance will change.

In this column, I am going to make similar observations about signal propagation speed. Recall that electronic signals travel at the speed of light, or 186,282 miles per second. This equates to 11.8 inches/ns (or what we sometimes round off to a foot per nanosecond.) In any other material, the speed of light slows down. It slows down by the square root of the relative dielectric coefficient, Equation 1.

Equation 1

Consider the situation shown in Figure 1. This is derived from a HyperLynx simulation. Here we have a trace in a stripline environment, surrounded by a dielectric. If we assume the relative dielectric coefficient of the dielectric is 4.0, then the propagation speed of the signal will be 11.8/2 = 5.9 in/ns (we sometimes round this off to 6”/ns.) Note the electromagnetic field in this figure. It is completely contained within the dielectric between the two planes on either side of the trace.

Editor's Note: This column originally appear

# Electromagnetic Fields, Part 2: How They Impact Propagation Speed

11-13-2014

In Part 1, Doug Brooks suggested that thinking in terms of what the electromagnetic field looks like around our traces might offer significant insight into how circuits might be performing. In this column, he makes similar observations about signal propagation speed.

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# Electromagnetic Fields, Part 3 - How They Impact Coupling

04-30-2014

In Part 1 and Part 2 of this series, Doug Brooks talked about how helpful it can be to recognize what the electromagnetic field looks like around a conductor or trace and how that field may change as the stackup or trace parameters are changed. In Part 3, he looks at how changes in the electromagnetic field relate to changes in coupling between traces or between a trace and the outside world.

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# Brooks' Bits: Electromagnetic Fields, Part 3 - How They Impact Coupling

04-30-2014

In Part 1 and Part 2 of this series, Doug Brooks talked about how helpful it can be to recognize what the electromagnetic field looks like around a conductor or trace and how that field may change as the stackup or trace parameters are changed. In Part 3, he looks at how changes in the electromagnetic field relate to changes in coupling between traces or between a trace and the outside world.

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# Brooks' Bits: Electromagnetic Fields, Part 2: How They Impact Propagation Speed

11-13-2013

In Part 1, Doug Brooks suggested that thinking in terms of what the electromagnetic field looks like around our traces might offer significant insight into how circuits might be performing. In this column, he makes similar observations about signal propagation speed.

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# How Electromagnetic Fields Determine Impedance, Part 1

10-23-2013

When a current flows down a conductor an electric field and a magnetic field radiates away from that conductor. Collectively, this is called the electromagnetic field. What is important to note is that this field always exists. Furthermore, the electromagnetic field and the current are inseparable.

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# Brooks' Bits: How Electromagnetic Fields Determine Impedance, Part 1

10-23-2013

When a current flows down a conductor an electric field and a magnetic field radiates away from that conductor. Collectively, this is called the electromagnetic field. What is important to note is that this field always exists. Furthermore, the electromagnetic field and the current are inseparable.

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# Trace Currents and Temperature, Part 4: Via Heat

05-08-2013

In this final installment of his four-part series, Doug Brooks suggests a new method for dealing with vias. Part 1 hypothesized that trace heating was a function of the i2R power dissipated in the trace, and trace cooling was a function of surface area. Can these same fundamental principles be applied to vias when looking at current-carrying capacities?

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# Trace Currents and Temperature, Part 3: Fusing Currents

05-01-2013

This is the third of a four-part series on trace currents and temperature from Douglas Brooks. Part 1 discussed the role of resistance and formulated a basic model for analysis. Part 2 explored various results empirically obtained. Part 3 explores using the melting temperature of a trace to your advantage, and Part 4 will suggest a way to deal with vias.

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# Trace Currents and Temperature, Part 1: The Basic Model

02-13-2013

This first of a four-part series on trace currents and temperature covers the role of resistance and then formulates a basic model for analysis. Subsequent parts will explore various results that have been empirically obtained, how we can use the melting temperature of a trace to our advantage, and how to deal with vias.

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# The Skinny on Skin Effect, Part 3: Crossover Frequency

07-25-2012

It is instructive to look more closely at the formula for skin depth that we discussed in Part 2 of this series. First, note that it does not depend on the dimensions of the conductor, or even the conductor's shape! Skin depth is purely a function of frequency. That leads to some conclusions that are not particularly intuitive.

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# Brooks' Bits: The Skinny on Skin Effect, Part 2

07-11-2012

In Part 1 of this series, I described how skin effect is all about current density. If we multiply current density by cross-sectional area, we get current. In this column we'll take a look at two propositions that are well accepted in electronics, and they are useful models, even if they are not exactly correct, as we shall see!

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# Brooks' Bits: The Skinny on Skin Effect, Part 1

06-20-2012

Why do we care about skin effect? First, it impacts any calculation that involves Ohm's Law. Thus, the voltage drop across a conductor and the power dissipated within the conductor (and therefore loss to the circuit) will increase with frequency. Second, skin effect can impact trace current/temperature effects. Doug Brooks has the first column in a series.

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# Crosstalk, Part 3: More On Shapes and Amplitudes

03-07-2012

In Part 2 of the series, I showed that a step-function change in the aggressor signal results in two crosstalk components, forward and backward crosstalk, neither one of which resembles the aggressor signal. In this column, Part 3 of the series, we will explore the shapes of these components and their amplitudes a little more fully.

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# Crosstalk, Part 2: What It Looks Like

02-01-2012

In Part 1 of this series, I pointed out that many people seemed to find the concept of crosstalk difficult to wrap their arms around. This column, Part 2, of the series, we will look more closely at the shapes of the two crosstalk components. In Part 3 of the series, we will look even more closely at the shape and the magnitude of the backward crosstalk component.

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# Crosstalk: Why It's Difficult to Understand, Part 1

01-04-2012

Why is crosstalk difficult to understand? Let's see: Crosstalk has two different fundamental causes, which generate two different signals. These two signals flow in opposite directions, but the signals can interact with each other. These two signals have significantly different shapes, which behave differently as a function of coupled length. And neither shape resembles the "aggressor" signal that caused the crosstalk in the first place!

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# Current Flow on Traces, Part 2: Common Mode and Mode Shift

12-07-2011

If we have a differential trace pair, and the signal on the return trace is exactly equal and opposite to the signal on the forward trace, there is no common-mode component. If they are not exactly equal and opposite, there will be a common-mode component to the currents on the trace. Let's carry that idea further.

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# Coupling's Effect on Impedance: Why is Zdiff Less Than 2*Zo?

11-09-2011

Assume we have a trace (T1) with a controlled impedance equal to Zo. Now bring a second trace (T2) near it (and parallel to it) so that the signal on T2 couples into T1. Consider this statement: The impedance of T1 (Zo) changes as a result of that coupling. Why is this true, and why do we only worry about it in the case of differential-mode or common mode-signals?

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# Current Flow on Traces, Part 1: Transmission Lines

10-12-2011

Current propagates down transmission lines by utilizing the distributed capacitance between the lines and the return path. There will always be reflections from impedance discontinuities along, and at the end of, the line. Do we care about such reflections? We may care, depending on the relationship between the propagation time down the trace and the rise time of the signal flowing on the trace. By Doug Brooks.

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# Rise Times and Harmonics: Introducing Mr. Fourier

08-31-2011

In very general terms, frequency relates to information and rise time relates to how quickly we can process that information. A circuit only needs to have a rise time fast enough (and not faster) to process the information flow. Bandwidth refers to how wide a frequency range a circuit (or PCB) needs to handle without distortion. So, how wide a bandwidth do I need to pass my signals?

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# Rise Time vs. Frequency: What's the Relationship?

06-07-2011

A circuit must have a fast enough rise time to accommodate the signal being processed. If it does not, information in the waveform or circuit timing may be lost or distorted. But here is the clincher: a circuit does NOT have to have a faster rise time than is required by the waveform. Faster is not necessarily better!

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# Propagation Speed in Microstrip: Slower Than We Think

05-11-2011

How fast is propagation speed in microstrip? First of all, we must remember, the propagation speed is not determined by how fast the current can travel down a wire; it is determined by how fast the electromagnetic field can propagate in the medium it is in. And propagation times are much more controllable in a stripline environment.

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# What Does Voltage Refer To, and Why Do We Care?

04-20-2011

If you do a search for voltage on the Web, you will find lots of definitions. For our purposes here, we can consider it to be the force that causes current to flow. Since current is the flow of electrons, and since electrons are negatively charged, we can consider voltage to be the difference in charge between two points. Remember that for the quiz!

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# A History of Signal Integrity: One Man's Perspective

12-15-2010

The stages of signal integrity can be broken down into stages, not unlike the stages of grief. But there's no denial or bargaining here. The only way to handle signal integrity issues is to be prepared. Remember, the more information you have, the better off you'll be if you find yourself at Stage 4!

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# Resistance, Reactance and Impedance, Part 3

11-17-2010

Congratulations! You've made it to Part 3. Part 1 focused on resistance. That was pretty simple; there is a single component value, it does not depend on frequency, and there is no phase shift. Part 2 covered reactance, which is much more complicated. This installment on impedance ties it all together.

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# Resistance, Reactance And Impedance, Part 2

10-20-2010

Capacitors and inductors are almost exactly opposite in their effects. Both "impede" current, but capacitance impedes current at low frequencies, inductance at high frequencies. Capacitance causes voltage to lag current by 90 degrees, while inductance causes voltage to lead current by 90 degrees.

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# Resistance, Reactance and Impedance, Part 1

09-30-2010

New columnist Doug Brooks brings us Part 1 of a three-part primer on resistance, reactance and impedance. Most of us are familiar with resistance, but few really understand reactance and its relationship to resistance. And few really understand the relationship between impedance and the other two properties. This series will tie them all together.

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