# The Physical Basis of Transmission Lines

This chapter is from the book

## 7.13 Return Paths

In the beginning of this chapter, we emphasized that the second trace is not the ground but the return path. We should always remember that all current, without exception, travels in loops.

Where is the current loop in a signal propagating on a transmission line? Suppose we have a microstrip that is very long. In this first case, we’ll make it so long that the one-way time delay, TD, is 1 second. This is about the distance from the earth to the moon. To make it easier to think about for now, we will short the far end. We launch a signal into the line. This is shown in Figure 7-18. We have said in this chapter that this means we have a constant current going into the signal path, related to the voltage applied and the characteristic impedance of the line.

If current travels in loops and must return to the source, eventually we’d expect to see the current travel to the end of the line and flow back down the return path. But how long does this take? The current flow in a transmission line is very subtle. When do we see the current come out the return path? Does it take 2 seconds—1 second to go down and 1 second to come back? What would happen then if the far end were really open? If there is insulating dielectric material between the signal and return conductors, how could the current possibly get from the signal to the return conductor, except at the far end?

The best way of thinking about it is by going back to the zeroth-order model, which describes the line as a bunch of tiny capacitors. This is shown in Figure 7-19. Consider the current flow initially. As the signal launches into the line, it sees the first capacitor. As we described in Chapter 5, “The Physical Basis of Capacitance,” if the voltage across the initial capacitor is constant, there will be no current flow through this capacitor. The only way current flows through a capacitor is if the voltage across it changes. As the signal is launched into the transmission line, the voltage across the signal- and return-path conductors ramps up. It is during this transition time, as the edge passes by, that the voltage is changing and current flows through the initial capacitor. As current flows into the signal path to charge up the capacitor, exactly the same amount of current flows out of the return path, having gone through the capacitor.

In the first picosecond, the signal has not gotten very far down the line, and it has no idea how the rest of the line is configured, whether it is open, shorted, or whether it has some radically different impedance. The current flow back to the source, through the return path, depends only on the immediate environment and the region of the line where the voltage is changing—that is, where the signal edge is.

The current from the source flows into the signal conductor and, through displacement current, passes through the capacitance between the signal and return path, and back out the return path. This is the current loop. As the voltage transition edge propagates down the line, this current loop wavefront propagates down the transmission line, flowing between the signal and return path by displacement current.

We can extend the transmission line model to include the rest of the signal and return paths with all the various distributed capacitors between them. As the signal propagates down the line, there is current—the return current—flowing through the capacitance to the return-path conductor and looping back to the source. However, this displacement current loop from the signal path to the return path, flows between them only where the signal voltage is changing.

A few nsec after the signal launch, near the front end, the signal edge has passed by and the voltage is constant, and there is no current flow between the signal to the return path. There is just constant current flowing into the signal conductor and back out the return conductor. Likewise, in front of the signal edge, before the edge has gotten to that region of the line, the voltage is constant, and there is no current flow between the signal and return paths. It is only at the signal edge that current flows through the distributed capacitance.

Once the signal is launched into the line, it will propagate down the line as a wavefront, at the speed of light. Current will flow down the signal line, pass through the capacitance of the line, and travel back through the return path as a loop. The front of this current loop propagates outward coincident with the voltage edge. We see that the signal is not only the voltage wave front, but it is also the current loop wavefront, which is propagating down the line. The instantaneous impedance the signal sees is the ratio of the signal voltage to the signal current.

Anything that disturbs the current loop will disturb the signal and cause a distortion in the impedance, compromising signal integrity. To maintain good signal integrity, it is important to control both the current wave front and the voltage wave front. The most important way of doing this is to keep the impedance the signal sees constant.

When the return path is a plane, it is appropriate to ask where the return current flows? What is its distribution in the plane? The precise distribution is slightly frequency dependent and is not easy to calculate with pencil and paper. This is where a good 2D field solver comes in handy.

An example of the current distribution in a microstrip and a stripline for 10-MHz and 100-MHz sine waves of current is shown in Figure 7-20. We can see two important features. First, the signal current is only along the outer edge of the signal trace. This is due to skin depth. Second, the current distribution in the return path is concentrated in the vicinity of the signal line. The higher the sine-wave frequency, the closer to the surface this current distribution will be.

As the frequency increases, the current in the signal and return path will take the path of lowest impedance. This translates into the path of lowest loop inductance, which means the return current will move as close to the signal current as possible. The higher the frequency, the greater the tendency for the return current to flow directly under the signal current. Even at 10 MHz, the return current is highly localized.

In general, for frequencies above about 100 kHz, most of the return current flows directly under the signal trace. Even if the trace snakes around a curvy path or makes a right-angle bend, the return current in the plane follows it. By taking this path, the loop inductance of the signal and return will be kept to a minimum.

We see that the way to engineer the return path is to control the signal path. Routing the signal path around the board will also route the return current path around the board. This is a very important principle of circuit board routing.

### InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

## Overview

Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

## Collection and Use of Information

To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

### Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

### Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

### Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

### Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

### Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

### Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

## Other Collection and Use of Information

### Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

### Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

### Do Not Track

This site currently does not respond to Do Not Track signals.

## Security

Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

## Children

This site is not directed to children under the age of 13.

## Marketing

Pearson may send or direct marketing communications to users, provided that

• Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
• Such marketing is consistent with applicable law and Pearson's legal obligations.
• Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
• Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

## Correcting/Updating Personal Information

If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

## Choice/Opt-out

Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

## Sale of Personal Information

Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

## Supplemental Privacy Statement for California Residents

California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

## Sharing and Disclosure

Pearson may disclose personal information, as follows:

• As required by law.
• With the consent of the individual (or their parent, if the individual is a minor)
• In response to a subpoena, court order or legal process, to the extent permitted or required by law
• To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
• In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
• To investigate or address actual or suspected fraud or other illegal activities
• To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
• To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
• To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.