AN-808| Application Note

Long Transmission Lines and Data Signal Quality

Long Transmission Lines and Data Signal Quality
Overview
This application note explores another important transmission line characteristic, the reflection coefficient. This concept is combined with the material in AN-806 to present graphical and analytical methods for determining the voltages and currents at any point on a line with respect to distance and time. The effects of various source resistances and line termination methods on the transmitted signal are also discussed. This application note is a revised reprint of section four of the Fairchild Line Driver and Receiver Handbook. This application note, the third of a three part series (See AN-806 and AN-807), covers the following topics: Factors Causing Signal Wave-Shape Changes Influence of Loss Effects on Primary Line Parameters Variations in Z0, () and Propagation Velocity Signal Quality -- Terms

National Semiconductor Application Note 808 Kenneth M. True March 1992

Signal Quality Measurement -- The Eye Pattern Other Pulse Codes and Signal Quality

Introduction
Transmission lines as discussed in AN-806 and AN-807 have always been treated as ideal lossless lines. As a consequence of this simplified model, the signals passing along the lines did not change in shape, but were only delayed in time. This time delay is given as the product of per-unit-length delay and line length ( = , ). Unfortunately, real transmission lines always possess some finite resistance per unit length due to the resistance of the conductors composing the line. So, the lossless model only represents short lines where this resistance term can be neglected. In AN-806 the per-unit-length line parameters, L, R, C, G, were assumed to be both constant and independent of frequency (up to the limits mentioned, of course). But with real lines, this is not strictly correct as four effects alter the per-unit-length parameters, making some of them frequency dependent. These four effects are skin effect, proximity effect, radiation loss effect, and dielectric loss effect. These effects and how they influen
ce the intrinsic line parameters are discussed later in this application note. Since these effects make simple ac analysis virtually impossible, operational (Laplace) calculus is usually applied to various simplified line models to provide somewhat constrained analytical solutions to line voltages and currents. These analytical solutions are difficult to derive, perhaps even more difficult ot evaluate, and their accuracy of prediction depends greatly on line model accuracy. Analytical solutions for various lines (primarily coaxial cables) appear in the references, so only the salient results are examined here. Engineers designing data transmission circuits are not usually interested in the esoterica of lossy transmission line theory. Instead, they are concerned with the following question: given a line length of x feet and a data rate of n bps, does the system work -- and if so -- what amount of transition jitter is expected? To answer this question using analytical methods is quite difficult because evaluat
ion of the expressions representing the line voltage or current as a function of position and time is an involved process. The
Teflon is a registered trademark of E.I. DuPont de Nemours Company

references at the end of this application note provide a starting point to generate and evalute analytical expressions for a given cable. The effects on the LRCG line parameters, the variations in Z0, (), and propagation velocity as a function of applied frequency are discussed later in this application note. Using an empirical approach to answer the "how far -- how fast" question involves only easily made laboratory measurements on that selected cable. This empirical approach, using the binary eye pattern as the primary measurement tool, enables the construction of a graph showing the line length/ data rate/signal quality trade-offs for a particular cable. The terms describing signal quality are discussed later in this application note. The technique of using actual measurements from cables rather than theoretical predictions is not as subject to error as the analytical approach. The only difficulties in the empirical method are the requirements for a high quality, real time (or random sampling) oscilloscop
e and, of course, the requisite amount of transmission line to be tested. Also discussed in this application note are commonly used pulse codes.

Factors Causing Signal Wave Shape Changes
In AN-806 and AN-807, it was assumed that the transmission lines were ideal so the step functions propagated along the lines without any change in wave shape. Because a single pulse is actually composed of a continuous (Fourier) spectrum, the phase velocity independence on an applied frequency, and the absence of attenuation (R = 0, G = 0) of the ideal line always allows the linear addition of these frequency components to reconstruct the original signal without alteration. For real lines, unfortunately, the series resistance is not quite zero, and the phase velocity is slightly dependent on the applied frequency. The latter results in dispersion; i.e., the propagation velocity will differ for the various frequencies, while the former results in signal attenuation (reduction in amplitude). This attenuation may also be a function of frequency. Attenuation and dispersion cause the frequency components of a signal, at some point down the line, to be quite different from the frequency components of the signal ap
plied to the input of the line. Thus, at some point down the line, the frequency components add together to produce a wave shape that may differ significantly from the input signal wave shape. In many ways, then, a real transmission line may be thought of as a distributed lowpass filter with loss. The fast rise and fall times of the signals become progressively "rounded" due to attenuation and dispersion of the high frequency signal components. It should be noted that there is a theoretical condition where attenuation is independent of frequency and dispersion is zero. This results in a line causing signal amplitude reduction, but no change in signal wave shape. This condition was first discussed by Heavyside and is called the distortionless line. To make a line distortionless, the primary line parameters must satisfy the relation (R/L) = (G/C). Because for real lines (R/L) > (G/C), the distortionless line is only of historical

AN-808

2002 National Semiconductor Corporation

AN011338

www.national.com