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Rev. 2.8;Page 1 ©1996-2005, R.Levine

Transmission Line Fundamentals

Southern Methodist University

EETS8320

Fall 2005

Session 5

Slides only. (No notes.)

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Rev. 2.8;Page 2 ©1996-2005, R.Levine

Major Transmission Facts 1 Electromagnetic waves flow via the non-

conductive space in or around wire/cableconductors, and not via the metal conductor itself. ± Some of this electromagnetic power may be coupled

to/from other nearby wires, producing ³crosstalk´

± Transpositions, twisted pairs, or use of co-axial cable(having minimum external EM fields) minimize crosstalk

Electromagnetic waves are guided byconductors (in twisted pair, co-axial cable, or wave guides).

Power loss is due to: ± A. Longitudinal metallic resistance of wire/cable

± B. Radiation losses (particularly for twisted pairs)

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Rev. 2.8;Page 4 ©1996-2005, R.Levine

Structure and EM Fields in Co-ax

See footnote on previous page.

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Rev. 2.8;Page 6 ©1996-2005, R.Levine

Major Transmission Facts 3

R typically increases proportional to frequencybecause the ³skin´ depth of EM wave penetration intothe metallic conductors is inversely proportional tofrequency.

Aside from power loss, typical wire/cable transmissionmedium has slightly different wave speeds for differentsine wave frequency components of a complicatedwaveform, thus producing an altered waveform after passing through many km of wire/cable ± Attenuation is a problem for voice and modem signals both.

± Waveform changes are a problem primarily for modems.

When two transmission wires/cables having differentZ0 are ³spliced,´ EM wave power is partially reflectedand partially transmitted. This produces ³echo.´

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Rev. 2.8;Page 7 ©1996-2005, R.Levine

Most metal objects have ³linear´ resistance properties. Ohm¶s ³lawápplies: v= Ri , where i is current (amps), R is resistance (ohms), andv is voltage (volts)

Longitudinal electric resistance of a wire is determined by:

± R = V length/area ± where V is the material resistivity* (unit: ohmmeter), with a high value for

some materials (e.g. platinum) and low for others (e.g. silver). The unitohmcentimeter is also used historically.

± area is Tr 2 for circular wire of radius r (but note later about ³skinéffect)

Power ³lost´ due to electrical resistance R carrying current i , is i 2 R (also equivalent to v 2 /R or vi )

± This formula describes dc (constant current) power loss accurately.Current density is uniform throughout the area for unvarying or ³directćurrent.

*Material resistivity of copper can be increased by repeatedly bending and flexing the wire to modify theatomic level crystal structure. Newly manufactured ³soft drawn´ copper wire has slightly lower resistivitythan ³hard drawn´ wire that was repeatedly flexed via roller machines before selling. Hard drawn wire ismechanically stronger and can be pulled with less breakage.

Electrical Resistance

length

area

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Rev. 2.8;Page 8 ©1996-2005, R.Levine

Power Loss

Power really flows via an electromagnetic wave in the spacesurrounding the wires (only a little electric field in the copper)

± Wave speed is affected by the insulation material (e.g.,plastics, paper pulp,silk or other woven fibers, etc.)

± Only a surface portion of the copper carries alternating current, so-called³skin effect,́ -- to form a ³boundary´ for EM wave

± depth of the current ³skin´ is inversely proportional to square root ( of frequency -- therefore effective resistance is higher at higher frequency due

to smaller effective current-carrying area Resistance of the wire causes i 2 R loss, the conversion of electric

power into heat

± Silver would be slightly better, but too costly (silver coating/plating sometimes used)

± Aluminum¶s low resistivity is close to Cu -- also lighter in weight!... but its surface oxideis a poor conductor*

Some EM Field power Radiates into Space

± Particularly for non-shielded wire, curved wires, etc.

± Even with super-conducting wires (zero resistance) there would be someradiation losses

*Resistive surface aluminum oxide led to heating and home fires in 1960s through 1980s. Consequently

Aluminum power wiring was banned, or installed only with special coating or terminal fittings.

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Rev. 2.8;Page 9 ©1996-2005, R.Levine

Wire ³Gauge´ In North America, wire diameter is described by peculiar ³gauge´ (ga or AWG) number

± Based on the number of times the wire is drawn through smaller and smaller conical diamond forming dies during manufacture.Larger ga or AWG number implies smaller diameter

Most other countries list actual diameter (in mm)[dc resistance stated in table]

Abbreviations: AWG=American Wire Gauge, B&S=Brown & Sharpe (manufacturer of measuring equipment), ; = Ohms

B&S or

AWG Copper

Wire Gauge

Diameter

(inches)

Diameter

(mm); per km (at dc, 0 Hz)

[loop ; is twice the resistance of

one wire]

12 0.08 2.053 10.42

14 0.064 1.628 16.56

19 0.036 0.91 51.6

22 0.025 0.644 103.8

24 0.020 0.511 164.4

Electric power uses

Electric power uses

Telephone history interest

Telephone use today

Telephone use today

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Rev. 2.8;Page 10 ©1996-2005, R.Levine

Transmission Lines

Electromagnetic waves propagate or flow in a directionparallel to the wire¶s axis, but power flow is mostly inthe electromagnetic field outside the metallic wires

± The wires act as a waveguide, although the name

³waveguide´sometimes describes a hollow tube The most accurate, but complicated, method of

analysis is to examine the electromagnetic wavepattern in space

± Is the propagation completely parallel to the wires, or do wavesbounce around on diagonal reflected paths as in a hollowwaveguide or a multi-mode optical fiber?

A sufficiently accurate method for many applications isto describe the transmission line properties byapproximate ³lumped´ electrical parameters

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Rev. 2.8;Page 11 ©1996-2005, R.Levine

Free-wave Coupling

Why don¶t the EM waves just flow out into space awayfrom the wires?

± With certain geometrical arrangements, they do just that:

» Parallel wires separated far more than their diameters

» Wires bent to right angles from parallel (so-called dipoleantenna) like the lines above...

» A bend in the two parallel wires (over large distancecompared to the wavelength)

EM waves from other sources may induce voltage or current on wires

± One cause of ³cross talk,´ particularly at audio frequencies ± Called a ³radio receiving antenna´ when intentional

± Electromagnetic waves may cause primarily magnetic or primarily electrostatic coupling or induction, depending ongeometrical arrangement

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Rev. 2.8;Page 12 ©1996-2005, R.Levine

Transmission Line Properties Approximate ³lumped´ section model of wave transmission Resistance per unit (loop) length, R

± unit: ohm/meter

Inductance per unit (loop) length, L

± unit: henry/meter (where henry=voltsec/amp)

Leakage Conductance per unit length, G ± unit: mho/meter or 1/(ohmmeter) of conductance per unit length (³leakage´

from one wire to another)

± Conductance is 1/resistance (informal unit ³mho´ is ohm spelledbackwards -- official name ³siemens´)*

± plastic insulation is very good so very little ³mhos´

Capacitance per unit length, C ± unit: farad/meter (where farad= ampsec/volt)

Following two ³thought experiments´ require relatively short section of wire, so EM waves travel to far end in a very short time.

* Backward spelling is also used informally: 1/henry=yrneh (³ernie´), 1/farad=daraf

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Rev. 2.8;Page 13 ©1996-2005, R.Levine

Inductance/unit length

Isolate a unit length of transmission wire pair,³short circuit´ the two wires at the far end ± Theoretically, it is desirable to chill the material to a low

(super-conducting??) temperature, so the electricalresistance does not complicate the measurement!

± This is what scientists call a ³thought experiment´

Apply a constant voltage V a-b for T seconds.The current i will increase ³slowly´ and themagnetic field increases proportional to i .

Compute V T / i at the end of the time. This is

the inductance L. (Blue ³area´ is V T .)

b

a

t

0 T

t

0 T

V

I

ampsvolts a-b

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Rev. 2.8;Page 14 ©1996-2005, R.Levine

Capacitance/unit length

Isolate a unit length of transmission wire pair Apply a constant current I for T seconds. The

voltage V a-b will increase ³slowly´ as theelectric field increases. Positive electriccharge is drawn away from the lower wire and

pumped up to the upper wire. The totalamount of charge transferred in T seconds isI T (ampsec or coulomb)

Compute I T / V at the end of the time. This isthe capacitance C. (Green ³area´ is I T .)

b

a

t

0 T

t

0 T

I

Vamps volts a-b

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Rev. 2.8;Page 15 ©1996-2005, R.Levine

Resistance, Conductance, etc. The loop resistance per unit length is measured in an

experiment similar to measuring inductance. We find dc loopresistance from the ratio V / I using constant current I .

The conductance between the two wires is measured in anexperiment similar to measuring capacitance, except wemeasure the ³leakage´ current I that flows from one wire to

another due to imperfect insulation. All of these measurements can be made in a more practical wayusing sine wave test current or voltage at different frequencies.The effects of inductance and series resistance can bemathematically calculated using the measured ratio of voltageto loop current. Similarly, the effect of capacitance andconductance can be mathematically calculated.

We find that each of these four parameter measurements giveslightly different results at different frequencies. For example,skin effect produces higher measured effective seriesresistance (ESR) at higher frequencies.

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Rev. 2.8;Page 16 ©1996-2005, R.Levine

Illustration of Skin Effect

Cr oss-section

of wir e carrying

curr ent into

paper.

B or H fieldcir culates

In clockwise

dir ection.

Intensity of

H field (amp/m)

Diametr ical distance

Inside wir e (mm)0 1 2

f=0 kHz (DC)

f=1 kHzf=2 kHz

Exter nal H field falls off

asymptotically inver sely

pr opor tional to distance

f r om wir e center.

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Rev. 2.8;Page 17 ©1996-2005, R.Levine

Lumped Element Model for

Transmission Line This represents a 1 km loop of 19 ga copper wire, with

typical plastic insulation.

Leakage conductance between wires is more oftendescribed as 0.14 µmho or µsiemens of conductance,

instead of 7.14 M;of resistance

Note: These parameters are all dc values for 20º C temperature.

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Rev. 2.8;Page 18 ©1996-2005, R.Levine

Common (Longitudinal) Mode Electrical ³Balance´ is important in telephone transmission lines

± Electrical characteristics such as capacitance or leakage conductance fromeither wire to ground should be the same (symmetrical).

Telephone lines run parallel to electric power wires for miles, ontelephone poles or in underground conduits

± Power wires are furthest from the street level for safety of telephone repair crews

Longitudinal voltage can be magnetically coupled to bothtelephone wires

± ³Common Mode´ voltage appears on both wires with respect to ground/earth

± A device that senses the ³differential mode´ (voltage difference between thetwo wires) will not respond to a common mode voltage. Example: telephone

set

Longitudinal voltage produces significant ac power frequency³hum´ if telephone line is ³unbalanced´

± Example: unbalance occurs when one wire has lower resistance than other wire vis-à-vis ³ground/earth,´ due to damaged or wet insulation.

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Rev. 2.8;Page 19 ©1996-2005, R.Levine

Unbalanced Model Real transmission lines must have well

balanced electrical characteristics to preventlongitudinal or common mode inducedvoltages from appearing at the ends

However, for many theoretical purposes, an

³unbalanced´ model with the same tot al loopparameter values is simpler for analysis

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Rev. 2.8;Page 20©1996-2005, R.Levine

dc or Resistive Model

A model which ignores L and C is only useful for thesingle special purpose of computing dc loop current

Omitting inductance and capacitance theoreticallyremoves time delay and waveform distortions. Power

loss still occurs. ± Note for dc that L becomes a zero ohm resistance or a short

circuit, while C becomes an open circuit

or

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Rev. 2.8;Page 21©1996-2005, R.Levine

Wire Resistance R Depends On...

Material resistivity (copper, aluminum, etc.)

Resistivity partly depends on metallic atomic arrangement

± Hard drawn (³work hardened´) copper has small irregular metalcrystals, higher resistance, but it is less damaged by handling or installation.

± Soft drawn copper has large regular crystals of metal, lower resistance

Temperature: resistance of metal increases about 1% for each higher degree Celsius

± Standard room temperature is 20º C (=68º F)

Wire Diameter (more generally, current carrying crosssectional area). Larger diameter implies lower resistance.

Signal frequency: due to frequency-dependent skin effect

± Higher equivalent resistance for higher frequency

± Because current-carrying area is smaller at high frequency

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Rev. 2.8;Page 22©1996-2005, R.Levine

Inductance L Depends On... Inductance is the ratio of the total ³flux linkage´ to the

current. Flux linkaage is measured in voltsec, and isfound by integrating the magnetic field intensity over asuitable surface between the two conductors

In general, L depends on geometric shape and

separation of conductors. Major types are: ± Parallel round/cylinder wires (usually ³twisted pair´)

± Co-axial cable (outer and inner cylindrical conductors)

Use of magnetic materials

± Magnetic materials in the field region can affect L, but usuallynon-magnetic materials (µ/µo=1) are used

± Some older cables were made with a magnetic alloy(e.g.,³permalloy´) built in between the current carrying wires.

L is very slightly dependent on frequency, indirectlydue to skin effect

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Rev. 2.8;Page 23©1996-2005, R.Levine

Conductance G Depends on...

³Leakage´ conductance is ratio of wire-to-wire leakagecurrent, divided by voltage. It is determined by«.

Intrinsic resistance of insulation material

Thickness of the insulation. Thicker insulation gives

lower G value.

Conductive impurities such as water (particularly withdissolved ions) which can permeate through theplastic under some conditions

± Much more serious problem with older porous pulp or fiber (cotton or silk) insulation

³Wet´ cable can be dried out by use of dry nitrogen(N2) gas under continuous pressure from anevaporating tank of liquid nitrogen

Slightly temperature dependent

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Rev. 2.8;Page 24©1996-2005, R.Levine

Capacitance C Depends On...

Capacitance is the ratio of the electric charge (on the surfaceof one conductor) to the voltage between the two conductors

In general, C depends on geometric shape and separationdistance of conductors

Dielectric permittivity ³epsilon´ r of the insulation. Mostplastic insulation materials have relative r =I /Io)(³dielectricconstant´) value in range 3 to 8, compared to air.

S ig nificant ly depends on temperature.

Slight increase if water molecules permeate the insulation

Frequency dependence due to skin effect and materialproperties. See F ey nman Lec t u r es on P hy sic s, Vol.II, chapters10, 11 and 32, for a more fundamental physical description of why dielectric properties depend on frequency.

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Rev. 2.8;Page 25©1996-2005, R.Levine

Wave Speed cm= 1/(LC) The wave speed depends on electrical parameters of the insulationfor most practical wires and cables

Regardless of shape, for a transverse electromagnetic wave(propagation parallel to the wires) in a lossless (non-resistive,perfectly insulated) line,

The wave speed described here is the ³phase velocity´ of a test sine

wave -- not the velocity of a general waveform ± If the phase velocity is the same for all frequency components, then the

velocity of any arbitrary waveform is the same. If the phase velocity of different frequencies is different, then the waveform of a traveling wavewill be modified after traveling different distances!

For lossy lines, or lines with other components insertedperiodically*, the phase velocity varies greatly at different test

frequencies ± Therefore, a non-sinusoidal waveform can have its different frequency

components arrive with different delays, thus changing the receivedwaveform. (an effect called ³dispersion´)

* For example, when loading coils (inductors) are connected in series in the wires atintervals of 6000 ft, the wave speed is lower than for non-loaded wires.

IQ/1!mc

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Rev. 2.8;Page 26©1996-2005, R.Levine

Data Transmission ³Speed´ The wave speed or time delay depends on physical

parameters of the transmission system

The data rate (data bits per second) affects the time requiredto transmit a fixed amount of data. A channel which cantransmit more bits/second can transmit the same data file in ashorter time. We l oosely call this higher ³data speed´ although

the term ³data rate´ or ³bit rate´ is more accurate andappropriate

The bit rate capacity of a channel is sometimes called its³bandwidth´ although the term ³bit rate´ is more accurate andappropriate

When all other factors (type of modulation, etc.) areunchanged, a higher data rate does correspond to a waveformwith a higher bandwidth. However, by changing the type of modulation (e.g., from two level to 4 level coding) one canchange the bandwidth of a signalw i t hou t changing its digitalbit rate.

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Rev. 2.8;Page 27©1996-2005, R.Levine

Lossy Distortionless Line

A transmission line having the following ratio of parameters:R/L=G/C , has the same loss and wave speed (phase shift or timedelay) at all frequencies. It is therefore distortionless (no change inwaveform shape), since all frequency components are reducedproportionately in amplitude and have the same time delay. They stayin phase with each other. The signal is reduced in amplitude as ittravels along the wires, but the waveform is otherwise unchanged.

G/C is normally a much, much smaller ratio than R/L. The simplestmodification to achieve the same ratio with R/L is to use lowresistance insulation between the wires (to increase G ), but then theoverall power loss is too much to be economically interesting, evenwith amplifiers.

A more practical method to improve transmission line loss is toartificially increase L by installing ³loading coils´ described later.

More practical method to combat dispersion, for modems and other waveform sensitive devices, has been to use adaptive equalizers.Equalizers combine various internally delayed copies of the receivedwaveform to compensate for dispersion.

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Rev. 2.8;Page 28©1996-2005, R.Levine

Characteristic Impedance Zo=(L/C) Zo is ratio of V / I in a traveling wave. V is transverse voltage (wire-to-

wire), I is longitudinal current. In contrast, ohmic series (loop)resistance R is ratio of longitudinal voltage drop to longitudinal current

Zo depends on geometry ± When two conductors are far separated in comparison to their diameter or

width, Zo is larger

For a transverse electromagnetic wave (propagation parallel to thewires) in a lossless (non-resistive, perfectly insulated) ³square´ parallel

plate transmission line, Zo= (µ/) = 377; approximately ± That is an approximation assuming all significant electric and magnetic field is

almost completely confined in the space between the two parallel plates

Geometry with increased distance between conductors has higher Zo

value.

For lossy lines, or lines with material µ or properties dependent onfrequency or temperature, the Zo will be different if these parameters

change

When two line sections with differ ent Zo values (due to change in wirediameter, insulation type, etc.) connect, some of the wave power willbe reflected and some will continue into the next section of transmissionline

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Rev. 2.8;Page 29©1996-2005, R.Levine

Nominal Zo for Subscriber Loop In the early days of the telephone, the two telephone

wires of a loop were installed far apart on a ³cross-arm´ of a telephone pole. Wire centers were separatedby 20 or more times the diameter of the wires.

Via theoretical calculations of surge impedance, wesee that wires with centers separated i n ai r by about 5times the wire radius will have approx Zo=600 ; surge

impedance ± The measured surge impedance varies slightly with frequencydue to changes in skin depth with frequency, etc.

± Despite many variations when comparing different types of wireand cable, Zo=600; purely resistive (current and voltage in-phase) is often used as the nominal surge impedance intechnical specification documents, etc.

In modern telephone cables, wires are typically

separated by about 3 wire diameters, and each wire iscoated with plastic insulation. Theoretical surgeimpedance of this pair is about 300 ;.

Resistor-capacitor circuit model often used to better represent an average length subscriber loopterminated in a central office subscriber card.

900; 1.2µF

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Rev. 2.8;Page 30©1996-2005, R.Levine

Transpositions and Helices

A second wire pair installed on the same cross arms produced strongmagnetic field coupling (cross-talk) due to the magnetic field fromboth loops sharing the space in between the wires.

Coupling can be neutralized by ³transposing´ the second pair of wires at the midpoint of installed length

Third pair of wires can be transposed in four sections. Similarly moretranspositions can be used for the 4th, 5th, and succeeding pairs (4th,

5th not shown). Twisting each individual pair in a cable into a helix with different pitch

(length of one turn of the helix) helps minimize induction cross talk. ± Twisted pairs also hold the two wires comprising the same loop in close

proximity, thus reducing the area susceptible to magnetic induction. Also,allows the installation technician to separate individual subscriber looppairs more easily for installation purposes.

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Rev. 2.8;Page 31©1996-2005, R.Levine

Wave Reflections When two transmission lines having different values of Zo are

joined, and an electromagnetic wave arrives at the joint fromone side ± Part of the power will travel through the joint into the second transmission

line

± Part of the power will be reflected back towards the source

If the reflected wave occurs in a purely unidirectional wire pair,

this may not be a problem ± Example: one unidirectional pair of a two-pair (4 wire) system

If the reflected wave occurs in a bi-directional wire pair, or canget into the ³return´ unidirectional wire pair via a 2-to-4 wireconversion point (a ³hybrid´ or directional coupler), theparticipants may perceive an echo.

We try to prevent echo, but when it occurs the best presentremedy is an echo canceller. ± The echo canceller determines the time delay, amplitude and polarity (+ or

-) of the echo waveforms, and generates a canceling signal by means of digital signal processing (DSP).

± In dialed call service, the echo canceller must adaptively re-adjust itsparameters (time delay, etc.) for each new telephone call.

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Rev. 2.8;Page 32©1996-2005, R.Levine

Proportional Decrease In Power

Wire to wire (transverse) voltage decreases exponentially*with distance. There is a uniform per cent age power lossper unit length.

For a 1 kHz test signal, 19 ga wire looses approx 20% of section input power (leaving 79.4% output) for each 1 mi(1.6 km) section (this corresponds to ~1 dB/mi)

3 mi of wire delivers 0.794y0.794y0.794 = 0.50056, or about1/2 of original power

Engineers don¶t like to do tedious repeated multiplication,so they use logarithms: loss of 1 dB per mi, added 3 timesfor 3 miles, yields a total loss of 3 dB (corresponding to

about 1/2 of original input power)*The wor d ³exponentially´ is a jar gon ter m implying a change of a

fixed per centage for each km of wir e. It does not mer ely mean³lar ge change.´

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Rev. 2.8;Page 33©1996-2005, R.Levine

Transmission Loss

³Loss´ is usually expressed in dB for convenience in addingtotal logarithmic loss for a chain of devices

± simpler than multiplying the numerical input/output ratios for a chain of sections

For a length of wire or cable, transmission* ³gain´ in dB is:

10log10

(output power/input power)

With output lower than input power, this ³gain´ will be anegative number (that is, a ³loss´ of power)

For 1 mi of 19 ga wire loop using 1 kHz test signal, input tooutput pow er ratio is 1.26/1 = 1/0.794)

Corresponds to -1 dB/mi (-0.6 dB/km) gain (+1 dB/mi loss)

Also corresponds to input-outputv ol t age ratio 1.122/1 (or

1/0.89) for a mile of 19 ga wire* Be careful about often careless and confusing usage of minus sign. Strictly speaking,

negative loss is ³gain´ or amplification. Transmission gai n could also theoretically beproduced by wire with negative resistance!

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Rev. 2.8;Page 34 ©1996-2005, R.Levine

Transmission Loss Also Depends On...

Wire diameter (gauge). At 1 kHz:

Frequency (due primarily to skin effect R) 19 ga

Temperature (due primarily to increased R)

± Loss per mi (or per km) is greater at higher temperature

Frequency (k Hz) 1 10 100

Loss (dB/mi) 1 3.2 6.1

AWG gauge 19 22 24

Loss (dB/mi) 1 1.79 2.2

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Rev. 2.8;Page 35 ©1996-2005, R.Levine

³Insertion´ Loss

Conceptually think of ³breaking´ the chain of equipment and inserting another device of interest(more wire, an amplifier, etc.)

Addi t i onal loss due to this insertion of another device

is the so-called i nser t i on l oss Insertion loss and transmission loss are the same in a

chain of devices with the same surge impedance ± thatis, the same ratio of V / I at all connection points

± That is, uniform ³characteristic impedanceór ³surgeimpedance´ at all points in the transmission chain

± Not accurate throughout the audio frequency range, buttelephone systems often approximate the surge impedance Zo of wire pair by using 600 ; (resistive) as a nominal approximatevalue for certain test purposes

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Rev. 2.8;Page 36 ©1996-2005, R.Levine

Exponential Losses in Transmission Line

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4

P( )x

x

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Rev. 2.8;Page 37 ©1996-2005, R.Levine

Linear Loss Described Using Logarithmic dB

5

4

3

2

1

0

1

0 1 2 3 4

T( )x

x

T(x)=10log(P(x))

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Rev. 2.8;Page 38 ©1996-2005, R.Levine

Loop Length S ubsc r iber Loo p length is usually limited by dc loop current

(so-called ³resistance limit´)

± At least 5 to 10 mA needed to properly operate microphone and tone dialin a telephone set. 20 mA or more is desirable.

In contrast, t r u nk length is usually limited by signal loss

± This can be corrected by amplification, so there is no theoreticalphysical limit from this cause (of course, signal power falls to near noisepower level, etc.)

± Longer trunks require more amplifiers

» Trunk wire with high loss requires amplifiers (one type of repeater)with higher gain and/or closer spacing

± When dc current is used in t r u nk s to power repeaters, the overall design

of the equipment is normally done so that dc current is not the limitingfactor.

± In some cases, the signal delay is limited due to call processing signalrequirements (even while speech delay is not yet a problem) to 1.5 or 2milliseconds for some switching devices such as remote line modules or concentrators used with telecom switches.

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Rev. 2.8;Page 39 ©1996-2005, R.Levine

Conflicting Objectives

Amplifiers are used in anal og transmission systems tocompensate for power loss in transmission wire, cable

± In digital transmission systems, dispersion and other waveform changesmust also be compensated by repeaters. The example here considersonly amplification.

One very high gain amplifier could, in theory, compensate for

the loss of any length of line But if the signal gets too small before further amplification,

the effects of thermal ³noise´ and interference will be severe

If the signal is amplified too high before transmission, thevoltage will be huge (and possibly even dangerous!)

The cost of a v er y high gain amplifier is also muc h greater than a low gain amplifier

The optimum engineering-economic arrangement is to use anumber of amplifiers of moderate gain, inserted at equaldistances into the transmission wires

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Rev. 2.8;Page 40 ©1996-2005, R.Levine

Optimum Number of Amplifiers is Set by

Economics, as well as Technology A definite cost model is required

± changing technology may change the cost model

Usual practice is to place amplifiers (repeaters)

periodically at fixed distance intervals so: ± Required amplifier gain is moderate, so unit cost is moderate

± Input signal is never too low compared to noise & interference

± If the first or last section of line is not the standard intervallength, a Line Build-Out (LBO) network is connected into theend. LBO can be made using inductors, resistors and

capacitors, or sometimes by merely using a spool of wire or cable of the correct length.

± An example showing economic optimization of repeater spacingwill be given on the practice quiz

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Rev. 2.8;Page 41 ©1996-2005, R.Levine

Approximate Loss Formula For (G/C)<<(R/L), which is the typical transmission line case,

dB loss per km is approximately proportional to

[( R/2) ( C/L)] + [( G/2) ( L/C)] + other smaller terms.

The first term is biggest. If we could increase L (or decreaseC or R ), loss would decrease. Increasing L is the mostpractical alternative.

Both Pupin and Campbell (and others) recognized this about1900, and added lumped inductive ³loading coils´ in serieswith the telephone wires, thus decreasing the first loss term( R/2)( C/L).

Loading Coils are passive, reliable devices, used widely untilthe 1960s. Loading coils have mostly been removed sincethen, but are still occasionally found in place on old outsideplant wiring.

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Rev. 2.8;Page 42 ©1996-2005, R.Levine

Pupin Loading Coils

Practical approximation to increased L uses ³lumped´series inductors

± Most widely used spacing interval is 6000 feet (1.848 km)

» European systems use 2 km spacing

±

Most widely used inductor is 88 mH, toroidal shape» There is some added resistance due to thin wire in the

loading coil, but overall transmission loss is improved

Used historically for baseband transmission on bothsubscriber loops and trunks

The 6000 ft spacing of loading coils led directly to the

same spacing later for T-1 digital carrier repeater units,since access and enclosures were already available atthese locations.

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Rev. 2.8;Page 43 ©1996-2005, R.Levine

Loading Coils Have Mainly Historical Significance Today

Due to use of lumped inductors, loaded line has better loss only at lowfrequencies, and has muc h w or se loss at high frequencies (above 4 kHz)

± Acts like a type of ³low pass filter´

± Designed to pass up to 3.5 kHz audio for desired speech quality

Loading coil toroidal cores are also used to wind transformers for radioand other applications

±

Available at low cost on the used equipment market. Used by radio ³hamsánd experimenters

In some cases where two pairs split off from one pair (a ³bridged tap´), acoil is wired in series with each pair to increase the Zo and reducereflected power

± This is called a ³bridge lifter´

Loading coils and bridge liftersmu s

t be removed to install anytransmission system which utilizes frequencies above about 4 kHz, such

as:

± All types of digital systems (T-1, ISDN, etc.)

± Data above voice (several proprietary systems)

± ADSL, HDSL, etc.

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