# Performance Regions

This chapter is from the book

## 3.12 Scaling Copper Transmission Media

Lengthening a transmission line increases its delay while reducing its bandwidth. These two properties are inextricably interrelated. Longer almost always means slower.

Let me pause here to explain that I am writing to you about the optimal use of transmission lines—specifically, the use of properly terminated transmission lines with drivers that put out clean, fast, full-sized signals and receivers that do not excessively load the far-end terminus of the line. In that case the behavior of the transmission line is governed by its propagation coefficient [3.13]. This coefficient prescribes the attenuation at each frequency in units of dB per meter (or nepers per meter). The overall attenuation of such a physical link scales linearly with distance.

For example, suppose you have one transmission line that has an attenuation of 3 dB at 100 MHz. A second line of twice the length (but otherwise the same) would have precisely 6 dB of attenuation at 100 MHz. Doubling the length doubles the attenuation.

Any exaggeration of the attenuation (by lengthening or any other method) must necessarily lower the 3-dB point. This happens because the attenuation function for real-world transmission lines is always monotonic and decreasing. Increasing the length always reduces the bandwidth.

For robust performance on unequalized receivers with binary data, one normally requires that the 3-dB bandwidth of the transmission media exceed 70% of the bit rate; in this case, increasing the length reduces not only the bandwidth but also the maximum rate of digital transmission that can occur over that transmission system.

If you know the slope of the attenuation function, you can predict the precise relation between the maximum communication rate and distance. Here nature helps us in a profound way: Almost all practical transmission lines have about the same shape to their attenuation function. Most transmission lines used for high-speed digital work display a smooth, rounded knee in their attenuation function, with a profile something like this:

Equation 3.149

 where a is the attenuation in decibels, the constant of proportionality depends on the materials and geometry of the cabling, ω is the frequency of operation, rad/s, η is a slowly varying constant between 1/2 and 1, and l is the length of the transmission line, m.

A value of η = 1/2 is typical for transmission lines that are limited primarily by the skin effect. Good examples of skin-effect-limited media would include any of the transmission lines in Figure 3.1 taken over the frequency range from 10 to 1000 MHz.

In the skin-effect-limited range the ω1/2 dependence creates an interesting property of scaling: Doubling the length but cutting the frequency by 1/4 produces precisely the same attenuation. In the time domain,

for skin-effect-limited media, doubling the length while slowing down to 1/4 the bit rate produces the same eye pattern.

Horrible, isn’t it! The penalty for doubling the line length is a reduction in bandwidth by a factor of four.

Turn that around the other way and you see the other side: Cutting the length in half speeds up the system by a factor of four. This is what made 10BASE-T Ethernet so popular. At one time, prevailing wisdom suggested that telephone-style unshielded twisted-pair cabling had an inherent bandwidth of only 3KHz to 4 KHz. This reasoning was based on an assumption of length, namely, that every system had to be able to operate at distances sufficient to reach the nearest telephone central office, which could be as much as 5000 meters distant. Once people in the LAN business recognized that interoffice LAN communications needed only to go 100 meters, the bandwidth assumption could be boosted by a factor of (5000/100)2, resulting in easily sufficient bandwidth to operate at 10 Mbps.

For many high-speed systems the skin effect is the most significant bandwidth-limiting factor. At extremes of frequency, however, the skin effect is superceded by dielectric loss. In the dielectric-loss-limited region the constant η asymptotically approaches a value of 1. In the dielectric-limited region the relation between speed and distance becomes merely inverse, not inverse-squared.

For dielectric-effect limited media, doubling the length while slowing down to 1/2 the bit rate produces the same eye pattern.

Fortunately for high-speed digital designers, the bandwidth of a typical pcb trace is pretty incredible. Figure 3.42 illustrates the performance of a 152-μm (6-mil) stripline trace implemented on Getek. The trace is 0.3-m long. The 3-dB attenuation point for this trace occurs at 5 GHz.

Figure 3.42. Either doubling the line length or halving the line width cuts bandwidth by a big factor.

If this sort of performance is not enough for your application, let me explain how to get even higher bandwidth. These ideas build on a simple approximation for transmission-line attenuation:

Equation 3.150

 where a is the attenuation in decibels, ω is the frequency of operation, rad/s, l is the length of the transmission line in meters, ω0 is the frequency at which AC line parameters are specified, rad/s, R0 is the AC resistance of the line at frequency ω0, Z0 is the characteristic impedance of the line at frequency ω0, v0 is the velocity of propagation at frequency ω0, m/s, and tan θ0 is loss tangent of the dielectric material at frequency ω0.

This expression contains many terms; there should therefore exist many ways to reduce the attenuation, thus increasing the 3-dB bandwidth.

1. Use more copper. If you want higher bandwidth, try using wider traces (for cables, use bigger signal conductors). At the same time you make the trace wider, also raise it up further away from the nearest solid plane. This change results in a new geometry with the same impedance as the original, but less resistance R0. The resistance R0 varies inversely with trace width.

NOTE: Above 1 GHz the dielectric losses become rapidly more significant than skin-effect losses. Monkeying around with skin-effect loss in a system that is dominated by dielectric problems makes progressively less and less sense as you go to frequencies far above ωθ.

2. Don’t go as far. In the skin-effect zone the bandwidth varies inversely with the square length; in the dielectric zone it’s an inverse relationship. Either way, longer traces have less bandwidth. If you must go a long way, consider using repeaters.

3. Use a higher-impedance trace. Moving your signal conductor farther from its nearest return path (without increasing its trace width, or diameter) increases the Z0 while leaving R0 mostly unchanged. This adjustment lowers the ratio R0 / Z0, lowering the skin-effect attenuation, thus raising the bandwidth. Unfortunately, this method has the side effect of rendering the trace more susceptible (percentage-wise) to lumped capacitive loads.

4. Do something so the attenuation doesn’t matter. Fixed equalization can extend the operating distance by at least 50%. This approach is used in the popular 10BASE-T Ethernet standard at 10 Mb/s over category-3 unshielded twisted-pair wiring (see Section 8.2, “UTP Transmission Example: 10BASE-T”). Fixed equalization may be incorporated into the driver, the receiver, or a combination of both. Adaptive equalization is a more powerful technique, although more difficult to design. It can in some cases more than double the operating distance. An adaptive equalization approach is used in many 100BASE-X Ethernet chips at 100 Mb/s over category-5 unshielded twisted-pair wiring. In systems with very low levels of background noise, and where the complexity of the receiver is not an objection, multilevel coding can provide even greater benefits. The 1000 Mb/s Ethernet standard for category-5 unshielded twisted-pair wiring (1000BASE-T) combines adaptive digital equalization, multilevel coding, and adaptive digital cancellation of near-end crosstalk to obtain a signaling rate of 250 Mb/s per pair on 100-m lengths of category-5 unshielded twisted-pair cabling.

5. Use a better dielectric material. The lower the loss tangent of the material, the less dielectric loss your signals will endure. Less dielectric loss translates to higher bandwidth. A lower dielectric constant, even with the same loss tangent, also helps because that increases the propagation velocity v0, lowering dielectric losses.

As technology advances, more options become available. You can look at recent LAN standards to get a glimpse of what may someday become commonplace in ordinary digital logic families. For example, fixed equalization (10BaseT), adaptive equalization (100BaseTX), and multilevel coding with digital adaptive filtering and near-end crosstalk cancellation (1000BaseT) are fast becoming mass-market realities.

Many designs have not yet reached the point at which trace bandwidth becomes a serious limitation, but just you wait. When typical trace widths go down to 0.002 in. and typical clocks reach 1 GHz, you’ll be there.

• Five ways to improve the performance of a copper transmission channel: use more copper, don’t go as far, use a higher characteristic impedance, add equalization, or use a better dielectric material.

### 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.