Transmission Line Fundamentals And Electromagnetic Fields, Part 1

In a recent article, I described a question that we had received from a former student regarding the traditional approach to PDS design versus one that is based on energy flow. When we deal with “abstract” aspects of electromagnetic fields and how they function, it can be easy to get lost in the weeds regarding them. This two-part article will address this topic and these concepts. The first part of this article will address an important aspect of transmission line fundamentals, namely how electromagnetic field and electromagnetic wave propagation effects a transmission line. The second portion will review the basics of electromagnetic fields. This article’s end goal is to create a core understanding of these concepts so that when it comes time to design a PDS, the proper design methodologies are followed and a properly working PDS is achieved appropriately, the first time and every time.

Overview of Transmission Line and Electromagnetic Field Theory Fundamentals

The purpose of a transmission line is to supply charge to components, acting similar to a capacitor. The components will draw current from the line while switching from 0 to 1. This is done by charging up the parasitic capacitance on the input leads of the component with respect to the nearby reference plane. In essence, this is fundamentally the whole purpose of the PDS. Trying to explain the purpose of the transmission line and the PDS by ascribing to them concepts such as “plane cavities” and decoupling capacitors that are “two-port open-ended stubs” doesn’t speak to what is occurring, only serves to confuse the design process and potentially leads to hardware which does not perform as it should. Ultimately, when it comes to designing a PDS, the factors to keep in mind as part of that effort include:

• The fundamental task of the PDS is to put a charge on the transmission lines.
• The stored energy that is put on a transmission line is extracted from the PDS.
  • The PDS supports the switching event.
• Fundamentally, there are two capacitors.
  • One is in the capacitors of the PDS and the planes that make up the PDS.
  • The other is in the transmission line.
  • A charge is always being transferred from one capacitor to another.
  • If you don’t want voltage variations (ripple) from the source of the charge, the PDS impedance has to be low and low at all of the frequencies needed by the loads.
• When energy is moving, it is in the form of an electromagnetic field.
  • This field is in motion during the charging process.
  • The electromagnetic field and charge are transferred in concert as governed by Maxwell's Equations.

What is in Motion on a Transmission Line?

As noted above, the entities that are in motion on a transmission line are the electromagnetic fields. Confusion creeps in when people attempt to describe what is happening with a signal by using the terms current flow or current loops. This reasoning falls far short of accounting for what is happening in signal behavior. The thing to keep in mind: Current flow is the consequence or symptom of the electromagnetic field’s presence, not the reverse. 

A Mechanical Analogy

A good way to envision a mechanical transmission line is through the classic Newton’s Cradle Kinetic. Balls educational toy. A depiction of this toy is provided in Figure 1.

Figure 1. A Newton’s Cradle

Here, the three variables are spring force, mass, and resistance. In electrical transmission lines, the equivalent three variables are inductance, capacitance, and resistance. When a ball at the end of Figure 1 is swung up and away from the string, it contains potential energy. When the ball collides with the transmission line’s end, its kinetic energy is transferred into the transmission line. This energy travels at the speed of sound through the transmission line as an acoustic wave and is transferred into the last ball. The balls in the middle of the transmission line don’t move; they simply compress and expand (spring force) as the acoustic wave passes through them. The last ball swings up as high as the first ball, turning the kinetic energy back into potential energy. Since there is nothing at the “receive end” of the transmission line to absorb the energy transferred into the last ball, it reverses direction, falls back, collides with the transmission line, and moves the energy back into the transmission line. In principle, this process is repeated forever. What happens is that each time the energy traverses the transmission line, a small amount of it is absorbed into the line resistance, and the swing is slowly dampened out.

The Importance of Termination for Electromagnetic Waves

Because there is nothing at either end of the transmission line to absorb the energy, it is reflected down the line. If this reflection is not wanted, something must be placed at the load end of the line to absorb the energy. In the instance of a mechanical transmission line, a hand at the end of the transmission line can serve as the absorber. In an electrical transmission line with a component that has high input impedance (i.e., low load capacitance), the absorber is provided by a parallel termination. Another approach to the foregoing is to allow the energy to reflect preceding at the load end and travel back to the source, thereby creating another absorber type. This absorber is referred to as a series termination (more about this below).

An electromagnetic transmission line behaves in the same manner as the mechanical one. When an electromagnetic wave is launched down the transmission line, and no absorber or terminator is placed at the load end of the line, the energy is reflected toward the load source or the driver. If this reflected energy is not wanted, the energy must be absorbed in the load by using a parallel termination. Suppose it is not possible to use a parallel termination. In that case, the energy will be reflected down the transmission line and then reflect off the source or driver unless that source or driver is of  such an impedance that it can absorb this energy. If the electromagnetic field “sees” an impedance of the same magnitude when it arrives back at the source, this impedance will absorb the energy, and the reflections will be stopped. As noted above, this method of absorbing the energy is done with a series termination. Allowing the energy to reflect off the open end of the transmission and then be absorbed in the driver or source is known as reflected wave switching.

If there is something in the middle of the transmission line that creates a change in the impedance, such as a connector or a lumped load, some of the energy will reflect back to the source at the location of this change and not be available to develop a signal voltage at the load, and the signal will be degraded. In order to keep this signal degradation within reasonable limits, the impedance of all the parts of the transmission line must be held within limits determined by the tolerance of the circuit in use. In electronics, there is referred to as impedance control.

The primary operations fundamentally happen with all transmission lines, whether used for RF, microwave, analog, or digital implementations. Ultimately, the concept is quite simple. The art involved in engineering transmission lines involves:

• Knowing the possible sources of signal degradation (loss, distortion, skew, etc).
• Knowing how much degradation is acceptable.
• Invoking design rules that keep degradation within limits.

Keeping these factors in mind results in transmission lines that deliver a good signal or voltage waveform. Thus, there is no magic, black or white. However, successful transmission line design requires an understanding of the behavior of electromagnetic fields, which will be discussed in Part 2 of this article.

Moving On

I’ve explained the elements and factors that comprise a mechanical transmission line in contrast with those containing an electrical transmission line. In mechanical transmission lines, the variables are spring force, mass, and resistance. In electrical lines, inductance, capacitance, and resistance are the equivalents. If you compare the differential equation for an oscillator circuit with that for a mechanical oscillator, it is quite easy to see the correspondence between these various elements.

This effort’s key goal is to address the key functions of transmission lines relative to their impact on the PDS design process, which is one of the most, if not the most, important aspect of the design and development of today’s high-speed electronic products. As noted previously, the fundamental task of the PDS is to put a charge on the transmission lines so that it can support switching events. The two capacitors in play during the process are the capacitors of the PDS and the capacitance in the transmission line. When energy is moving on a transmission line it does so in the form of an electromagnetic field. This field behaves, and its impact on an electronic product’s overall operation is the focus of this part.

The Behavior of an Electromagnetic Field

An electromagnetic field is a compound field comprised of an electric field and a magnetic field. This compound field is how energy is transmitted from one place to another. It’s not uncommon for engineers, both novice and experienced, to struggle with the concept that current flow occurs due to the presence of an electromagnetic field. The key takeaway for electrical engineering: electromagnetic fields induce current flow. Electromagnetic fields are not induced by current flow.

To better understand that current flow exists because an electromagnetic field travels on or gets close to a conductor and induces a current flow in it, we can consider the following signals. All of them are examples of electromagnetic energy traveling from one place to another, and there are no electrons in the path to creating a current flow. They include:

• Radar Waves
• AM Radio Waves
• FM Radio Waves
• Television Signals
• Pager Signals
• RFI Energy
• Light Waves
• EMI Energy
• Microwave Signals

Mastering the concept of electronic energy moving from one place to another in the form of an EMI field is crucial to understanding how high-speed signaling functions. It is also critical to understanding how EMI happens. 

As can be seen above, both EMI and RFI are on the same list as useful signals. This is because both of them are made of the very same energy, like valuable signals. That is why they are referred to as interference as both types of energy escape from a product and interfere with other products. These escape methods are the same as those used to create useful signals. For example, RF energy is coupled to a radiating surface (antenna) in both cases. That’s why we say, when confronted with an EMI problem on a PCB, that there is something on the board that is acting as an antenna. Containment of both EMI and RFI is accomplished by removing the RF energy source or ensuring that the RF energy cannot reach a radiating surface or antenna. This is why controlling EMI is neither mysterious nor subject to the various “black magic” approaches floating around the community as viable design Methodologies.

The Symbiotic Relationship Between Magnetic and Electrical Fields

Figure 1 depicts an electromagnetic field surrounding a stripline transmission line. 

Figure 3. An Electromagnetic Field Surrounding a Stripline Transmission Line

This is an end-on view of a trace traveling between two planes. As can be seen, there are two fields—a magnetic one and an electrical one. Any time energy moves from one place to another on a transmission line or in space; it does so as an electromagnetic field. It’s important to remember that both fields are always present when energy is transmitted, and they are always orthogonal to one another. The voltage difference between the transmission line trace and the surrounding planes is a measure of the electric field’s strength. The magnitude of the current loop flowing in the transmission line is a measure of the magnetic field’s strength. If we want to relate these concepts from transmission lines to PDS design, we need to also think in terms of power that is carried on the line.

Transmission Line Power

The product of these two fields is a measure of the power being carried on the transmission line by the electromagnetic field. If you want to calculate this, you can use Poynting's vector from electromagnetic theory, but EE's normally just use the relation P = I x V. In other words, in one vicinity of the line, the current in that region and the voltage between the line and its reference plane in the same region, determine the power carried on the line. One field cannot exist without the other because the two fields induce each other, again mediated by motion of charge as described by Maxwell's equations.

Beyond High-Speed PCB Design

It should be noted that electromagnetic fields are not only the province of high-speed signaling. They are present in all electronic circuits regardless of the speed at which they operate. Types of products where they exist range from flashlights to switching power supplies and, as noted above, AM and FM radios. The reason that electromagnetic fields are of concern in high-speed circuits is that they rapidly change. When looking at Maxwell's equations, one finds that the strength of one induced field is proportional to the rate of change in the other field. This is why crosstalk is more intense when high-speed signals are sent down transmission lines; the edge rate is faster, so the field reach the victim line is stronger, thus the induced signal is also stronger.

These rapidly changing fields are also affected adversely by parasitic inductance and capacitance existing in the PCB layout through which they travel. Because most engineers are first introduced to current flow and voltage drop concepts, it is not uncommon for them to conclude that current flow creates an electromagnetic field. This misunderstanding gives rise to what is happening in a transmission line due to current flows and, current loops. This idea falls far short of what occurs. As a result, many effects, such as EMI, don’t appear to behave as expected.

When the analysis or explanation is based on the behavior of electromagnetic fields present and the environment in which they operate, the resulting current flows are automatically handled. This cannot necessarily be said of the reverse. For example, in the case of a transformer, the electromagnetic field emanates from the primary winding. Further, the magnetic lines of force in this field slice through the secondary windings, thereby inducing a voltage in the secondary winding but without the flow of any energy. If a path exists for the energy to flow from the secondary, such as a load, an electromagnetic field flows through that load, and a current is induced.

Summary

Understanding the functions of transmission lines and that the energy flowing on them is in the form of electromagnetic fields are vital for creating a fully-functioning PDS for a high-speed electronic product.

The tendency to veer off track by ascribing to transmission lines the concepts of current flows and voltage drops is disastrous, erroneous, and potentially catastrophic when designing a product that will perform as predicted and as designed.

Would you like to find out more about how Altium can help you with your next PCB design? Talk to an expert at Altium. You can also discover how utilizing a PCB transmission line calculator makes the design more accessible.

References:

1. Ritchey, Lee W., and Zasio, John J., “Right The First Time, A Practical Handbook on High-Speed PCB and System Design Volume 1.