Home > Articles

This chapter is from the book

7.5 The Speed of a Signal in a Transmission Line

If the speed of the electrons isn’t what determines the speed of the signal, what does?

Figure 7-6 illustrates the simplest way to think of a signal propagating down a transmission line. The signal, after all, is a propagating voltage difference between the signal path and the return path. As the signal propagates, a voltage difference must be created between the two conductors. Accompanying the voltage difference is an electric field between the conductors.

Figure 7-6

Figure 7-6 The electric field building up in a transmission line as the signal propagates down the line. The speed of the signal depends on how fast the changing electric and magnetic fields can build up and propagate in the materials surrounding the signal- and return-path conductors.

In addition to the voltage, a current must be flowing in the signal conductor and in the return conductor to provide the charge that charges up the conductors that generates the voltage difference that creates the electric field. This current loop moving through the conductors will produce a magnetic field.

A signal can be launched into a transmission line simply by touching the leads of a battery to the signal and return paths. The sudden voltage change creates a sudden electric and magnetic-field change. This kink of field will propagate through the dielectric material surrounding the transmission line at the speed of a changing electric and magnetic field, which is the speed of light in the material.

We usually think of light as the electromagnetic radiation we can see. However, all changing electromagnetic fields are exactly the same and are described by exactly the same set of equations, Maxwell’s Equations. The only difference is the frequency of the waves. For visible light, the frequency is about 1,000,000 GHz. For the signals typically found in high-speed digital products, the frequency is about 1–10 GHz.

How quickly the electric and magnetic fields can build up is what really determines the speed of the signal. The propagation and interaction of these fields is described by Maxwell’s Equations, which say that if the electric and magnetic fields ever change, the kink they make will propagate outward at a speed that depends on some constants and material properties.

The speed of the change, or the kink, v, is given by:


ε0 = permittivity of free space = 8.89 × 10−12 F/m

εr = relative dielectric constant of the material

μ0 = permeability of free space = 4π × 10–7 H/m

μr = relative permeability of the material

Putting in the numbers, we find:

For virtually all interconnect materials, the magnetic permeability of the dielectrics, μr, is 1. All polymers that do not contain a ferromagnetic material have a magnetic permeability of 1. Therefore, this term can be ignored.

In comparison, the relative dielectric constant of materials, εr, is never less than or equal to 1, except in the case of air. In all real interconnect materials, the dielectric constant is greater than 1. This means the speed of light in interconnects will always be less than 12 inches/nsec. The speed is:

For brevity, we usually refer to the relative dielectric constant as just the “dielectric constant.” This number characterizes some of the electrical properties of an insulator. It is an important electrical property. For most polymers, it is roughly 4. For glass, it is about 6, and for ceramics, it is about 10.

It is possible in some materials for the dielectric constant to vary with frequency. In other words, the speed of light in a material may be frequency dependent. We call this property dispersion, a frequency dependence to the speed of light in the material. In general, dielectric constant decreases with higher frequency. This makes the speed of light in the material increase as we go toward higher frequency. In most applications, dispersion is very small and can be ignored.

In most common materials, such as FR4, the dielectric constant varies very little from 500 MHz to 10 GHz. Depending on the ratio of epoxy resin to fiberglass, the dielectric constant of FR4 can be from 3.5 to 4.5. Most interconnect laminate materials have a dielectric constant of about 4. This suggests a simple, easy-to-remember generalization.

As pointed out in Chapter 5, “The Physical Basis of Capacitance,” when the field lines see a combination of dielectric materials, as in a microstrip where there are some field lines in the bulk material and some in the air above, the effective dielectric constant that affects the signal speed is a combination of the different materials. The only way to predict the effective dielectric constant when the materials are inhomogeneous throughout the cross section is with a 2D field solver. In the case of stripline, for example, all the fields see the same material, and the effective dielectric constant is the bulk dielectric constant.

The time delay, TD, and length of an interconnect are related by:


TD = time delay, in nsec

Len = interconnect length, in inches

v = speed of the signal, in inches/nsec

This means that to travel down a 6-inch length of interconnect in FR4, for example, the time delay is about 6 inches/6 inches/nsec, or about 1 nsec. To travel 12 inches takes about 2 nsec.

The wiring delay, the number of psec of delay per inch of interconnect, is also a useful metric. It is just the inverse of the velocity: 1/v. For FR4, the wiring delay is about 1/6 inches/nsec = 0.166 nsec/inch, or 170 psec/inch. This is the delay per inch of a signal propagating down a transmission line in FR4. Every inch of interconnect has a propagation delay of 170 psec. The total delay through the 0.5 inch of a BGA lead is 170 psec/inch × 0.5 inches = 85 psec.

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.


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.


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.

Cookies and Related Technologies

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.


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


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


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.


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.

Requests and Contact

Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice

We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020