10. transmission lines

7/26/2019 10. Transmission Lines

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Transmission Lines


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Introduction

Signals can be delivered from the transmitter tothe receiver using a variety of means: Metallic cable Optical fiber Radio transmission


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Coaxial Lines Two conductors are

concentric, separated by an insulatingdielectric

Coaxial cables are

unbalanced because oftheir lack of symmetrywith regard to ground


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Parallel Lines Parallel lines are

typically balancedlines, the impedanceto ground from eachof the wires being

equal Balanced refers to thesignals being the samelevel but opposite in

polarity


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Electrical Model of aTransmission Line

The electrical characteristics of a transmission line become

increasingly critical as the frequency of transmissionincreases

Factors influencing transmission lines: Resistance Skin effect Conductance of the dielectric Impedance Capacitance Inductance

These factors are distributed rather than lumped


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Model Transmission Line


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Step and Pulse Response of Lines In a line of infinite length, a stepped input signal

will surge forever because of the capacitance ofthe line

The characteristic impedance of the line is alsoknow as the surge impedance

The impedance is a real number for a line with nolosses; for example, a 50-ohm line does not referto the resistance of the wire in the line, but thevoltage/current ratio as seen by the source


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C jG L j R Z

0

Characteristic Impedance of a Line A terminated transmission line that is matched in

its characteristic impedance is called a matchedline

The characteristic impedance depends upon theelectrical properties of the line, according to theformula:


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Characteristic Impedance The characteristic impedance for any type of

transmission line can be calculated by calculatingthe inductance and impedance per unit length For a parallel line with an air dielectric the impedance

is:

For a coaxial cable:

d D

Z r

log138

0

r

D Z log276

0


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Coaxial Cable Applications In practice, it is usually unnecessary to find the impedance

of coaxial cable since the impedance is part of the cable

specification As indicated in the table, there are standard impedances for

coaxial cableImpedance

(ohms) Application Typical type numbers

50 Radio TransmittersCommunications

Receivers

RG-8/URG-58/U

75 Cable TelevisionTV Antenna feedlines

RG-59/U

93 Computer networks RG-62/U


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Velocity Factor A signal moves down a transmission line at a finite rate,

i.e. somewhat less than the speed of light The propagation velocity of a signal, compared to the

speed of light, varies as follows: Coaxial cable with polyethylene dielectric: 66% Coaxial cable with polyethylene foam dielectric: 78%

Air-dielectric cable: 95% Rather than specify the actual velocity, manufacturers

specify the velocity factor The velocity factor for a transmission line depends

almost entirely upon the dielectric


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Reflections In a line where the termination is equal to the

impedance of the line, the reflections are zero A line that is terminated other than Z 0 is said to be

mismatched and will have reflections

The reflection coefficient is found by:

i

r

V V


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Wave Propagation on Lines If a sine wave is applied to a transmission line, the

signal moves down the line and disappears intothe load Such a signal is called a traveling wave This process also takes time

A time delay of one period causes a phase shift of360, which is indistinguishable from the original

The length of a line L that causes a delay of one period is known as a wavelength


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Traveling Waves


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Standing Waves The interaction of incident

and reflected waves in atransmission line results in

standing waves When a reflected wave is

present but has lower

amplitude than theincident, there will be no point on the line where thevoltage or current remainszero over the whole cycle


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Variation of Impedance Along a Line A matched line presents its impedance to a source

located any distance from the load An unmatched line impedance can vary greatly

with its distance from the load

At some points mismatched lines may lookinductive, other points may look capacitive, at stillother points it may look resistive


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Characteristics of Open andShorted Lines

An open or shorted line can be used as aninductive, capacitive, or even a resonant circuit

In practice, short-circuited sections are morecommon because open-circuited lines radiateenergy from the open end

The impedance of a short-circuited line is:

tan0

jZ Z


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Variation of Impedance


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Transmission Line Losses

No real transmission line is completely lossless However, approximation is often valid assuming

lossless lines


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Loss Mechanisms The most obvious loss in a transmission line is due

to the resistance of the line, called I 2

R loss The dielectric can also cause loss, with theconductance becoming higher with increasingfrequency

Open-wire systems can radiate energy Loss becomes more significant as the frequency

increases Loss becomes worse as spacing between conductors

increases


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Loss in Decibels Transmission line losses are usually given in

decibels per 100 feet or 100 meters When selecting a transmission line, attention must

be paid to the losses A 3-dB loss equates to 1/2 the power being

delivered to the antenna Losses are also important in receivers where lownoise depends upon minimizing the losses beforethe first stage of amplification


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Mismatched Lossy Lines When a transmission line is lossy, the Standing-

Wave Ratio (SWR) at the source is lower than thatat the load

The reflection coefficient and standing-wave ratio both have larger magnitudes at the load

Computer programs and Smith Charts areavailable to calculate losses and mismatches intransmission lines


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Impedance Matching Impedance mismatches are deleterious in transmission lines

Mismatches result in power being reflected back to the sourceand in higher-than-normal voltages and currents that canstress the line

Best results are obtained when the load is matched to thecharacteristic impedance of the transmission line

Impedance matching can be accomplished by matchingnetworks using: Lumped constants (inductors, capacitors, transformers) Waveguide components Transmission line sections


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Matching Using a Transformer

A transformer can be used for impedancematching provided the load impedance is real atthe point where the transformer is inserted

Transformers are also used for connecting balanced and unbalanced lines. These transformersare called balun transformers


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Series Capacitance and Inductance When the resistive part of the load is correct, the

reactive part of the load impedance can becorrected by adding a series of reactances of theopposite type

Stub Matching

Shorted transmission line stubs are often used insteadof capacitors or inductors at VHF and above In these cases, admittance is calculated for, rather than

impedance


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Transmission-Line Measurements

Specialized test equipment is available to measureand evaluate transmission lines using thesetechniques: Time-Domain Reflectometry

The Slotted Line Standing-Wave-Ratio Meters and Directional

Wattmeters

10. transmission lines

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