Chapter 11

Chapter 11

Transmission Lines

Objectives

List the types of transmission lines Calculate the impedance of

transmission lines Calculate velocity of propagation and

delay factor Analyze wave propagation and

reflection for various line configuration

Describe how standing waves are produced

Use the Smith chart to find input impedance

Use the Smith chart to match loads to lines

Definition

A transmission line is the conductive connection between system elements that carry signal power

This “conductor” may at first appear to be a short circuit, but in fact will react differently when high frequencies are propagated along the line.

Types of Transmission Lines

Two-wire open line Twisted pair Unshielded twisted pair (UTP) Shielded Pair Coaxial Lines Balanced/Unbalanced lines

Two Wire Open Line

FIGURE 11-1 Parallel two-wire line.

Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e

Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.

FIGURE 11-2 Two-wire ribbon-type lines.




Two Wire Open

Also called twin lead or two wire ribbon cable Usually spaced from ¼ to 6 inches apart Used as the transmission line from antenna to

receiver or antenna to transmitter The end connected to the source is called the

generator or input end The end connected to the load is the load or

output end.

Electrical Characteristics

Depend on the construction Essentially a long capacitor where the

capacitance is inversely proportional to the spacing between the wires and directly proportional to the length of the line

Capacitive reactance is inversely proportional to the capacitance and frequency

Thus the line will have a total impedance resulting from: – Pure resistance caused by the wire itself– Capacitive reactance– Conductance which passes through the

dielectric medium– Inductive reactance caused by the

magnetic fields which are produced by the passing of current through the wires

FIGURE 11-9 Equivalent circuit for a two-wire transmission line.




If the line is uniform along its length, the resistance and conductance are usually negligible which results in an LC network

FIGURE 11-10 Simplified circuit terminated with its characteristic impedance.




Characteristic Impedance

Z0 symbolizes the characteristic impedance.

This impedance can be determined by using Ohm’s Law: applied voltage divided by the current flowing through the wire.

If the inductance and capacitance is known, the impedance is given by taking the square root of (L/C)– A line with 4H/m and 1.5 pF/m will exhibit a

characteristic impedance of 51.6

If the spacing between the wires and the diameter of one of the conductors and type of dielectric is known, the impedance can be found by:– Z0 =

– A D/d ratio of 3 and air dielectric will result in an impedance of 215

d

D2log

276

Line Losses

When calculating impedance of lines, losses are often ignored, but in real life these losses cannot be ignored.

Major losses– Copper– Dielectric– Radiation or induction

I2R losses

Resistance of any conductor is never zero. So when current is passed through the wire,

energy is lost in the form of heat Since R = l/A These losses can be reduced by reducing the

resistance of the wire by– Reducing the length– Increasing the cross sectional area of the wire– Using a wire with a lower resistivity

Skin Effect

At high frequencies, the I2R losses are generally due to skin effect.– When DC is applied the distribution of electron

movement is fairly uniform– When AC is applied, the flux density at the center

of the wire is greater than at the outer edge thus the the reactance is is also greater. The more reactance the lower the current.

– If other words, when AC is applied the current will flow faster on the outer edge of the conductor than through the center

Skin Effect

Since inductive reactance is directly proportional to the frequency, the skin effect increases with frequency as well.

Since the current is forced to the outside edge, the resistance cross section is also reduced thus increasing the resistance.

At sufficiently high frequencies, current will cease to flow in two wire lines

Dielectric Losses

These losses are directly proportional to the voltage across the dielectric

These losses also increase with frequency

Losses are lowest in air dielectrics

Radiation or Induction Losses

These are caused by the electrostatic and electromagnetic fields surrounding the conductors.

The electrostatic fields charge nearby objects The magnetic fields induce an EMF in nearby

conductors. These losses can be minimized by

terminating the line with a resistive load equal to the line’s characteristic impedance

Twisted Pair

What is Twisted Pair?

Two insulated wires twisted to form a flexible line without the use of spacers.

It is not used for high frequencies because of the high losses that occur in the insulation

Wet lines increase losses dramatically

FIGURE 11-3 Twisted pair.




Unshielded Twisted Pair

(UTP)

CAT5

Category 5 computer networking cable capable of handling a 100MHz bandwidth

Most often used in LANs Transmit data at rated up to 100Mbps for a

length of 100m CAT5 cable consists of four color-coded pairs

of 22 or 24 gauge wires terminated with an RJ-45 connector

CAT5

The precision in twisting along the length and at the terminations provide a significant increase in signal transmission performance

Balanced operation of the wire pairs helps to maintain the required level of performance in terms of cross talk and noise rejection

Important CAT5 UTP Parameters

Attenuation

The amount of loss in the signal strength as it propagates throughout the conductor

Cross Talk

Unwanted coupling caused by overlapping electric and magnetic fields

Near End Cross Talk (NEXT)

A measure of the level of cross talk or signal coupling within the cable

A high NEXT dB level is desired

Attenuation to Cross Talk (ACR)

Combined measure of attenuation and cross talk.

The larger the bandwidth the higher the ACR

The larger the bandwidth the greater the data capacity

Delay Skew

Measure of the difference in time for the fastest to the slowest wire pair in a UTP cable

Proposed for new specifications in CAT6 and CAT7 lines

Power Sum NEXT

Measures the total cross talk of all cable pairs ensuring that the cable can carry data traffic on all four pairs at the same time with minimal interference

Return Loss

A measure of the ratio of power transmitted into a cable to the amount of power returned or reflected.

Signal reflection is due to impedance changes in the cable link and the impedance changes related to cable loss.

CAT5, CAT6 and CAT7 cables must have low return loss specs.

Categories

CAT 3 Class C Telephone lines CAT5 Class D Computer networks CAT5e Computer networks CAT6 Class E up to 250MHz CAT7 Class F up to 600MHz

Wiring Standards for CAT5 and RJ-45 Defined by the Telecommunications

Industry Association standard TIA568B

Shielded Pair

What is Shielded Pair?

Consists of parallel conductors separated from each other and surrounded by a solid dielectric.

Conductors are contained within a copper braid tubing that acts like a shield

Assembly is covered by a rubber coating for protection from elements and mechanical damage

FIGURE 11-5 Shielded pair.




Shielded Pair

Principal advantage is the the conductors are balanced to ground– The capacitance between the cables is

uniform through out the line– Copper braid shield isolates the conductors

from external noise and prevents the signal on the shielded pair cable from radiating to and interfering with other systems

Coaxial Cable

What is Coaxial Cable (coax)?

Coaxial cable consists of two concentric conductors separated by a dielectric.

The outer conductor may be a copper or aluminum tube or wire braid and the inner conductor may be a wire or small tube, depending on the type of coax.

The dielectric may be air, plastic or ceramic

Types

Rigid or air coaxial line Flexible or solid coaxial line Electrical configuration of both is the

same

Rigid Coaxial Cable

Consists of a wire mounted inside of and coaxially with a rigid tubular outer conductor. (wire within a tube)

The inner conductor is insulated from the outer conductor by insulating spacers or beads, at regular intervals.

The spacers are made of Pyrex or polystyrene, located at regular intervals

FIGURE 11-6 Air coaxial: cable with washer insulator.




Advantages

Chief advantage of this line is its ability to minimize the radiation losses

The electric and magnetic fields do not extend outward from the outer conductor

The fields are confined to the space between the two conductors

Noise pick up is also prevented

Disadvantages

Expensive to construct Must be kept dry to prevent excessive

leakage between the two conductors, although leakage can be reduced by backfilling the cable with inert gas

Excessive high frequency losses limit the length of line used

Ten Minute Break

Flexible Coaxial Cable

The inner conductor consists of flexible wire insulated from the outer conductor by a solid continuous insulating material

Flexibility may be gained if the outer conductor is made of braided wire

Flexible Coaxial Cable

Polyethylene plastic as well as Teflon, is used to separate the two conductors.

The use of the plastic for insulation results in greater losses than for the air dielectric but cuts down on losses due to moisture

These losses are much less than for other dielectrics.

FIGURE 11-7 Flexible coaxial.




Characteristic Impedance of Coax

Z0 = d

Dlog

138

Balanced/Unbalanced Lines

Unbalanced Line—Coaxial

The electrical signal is carried by the center conductor with respect to the shield or grounded outer conductor

Balanced Line—two wire

The same current flows in each wire but 1800 out of phase with that flowing in the center conductor

Another way to look at it: the currents in the two wires of a balanced line are equal, but flowing in opposite directions.

Common Mode Rejection (CMR)

Measures the ability of a balanced line to reject signals flowing in the same direction in both conductors.

Any noise or unwanted signal picked up by the balanced line is picked up by both conductors, thus the noise is effectively canceled out

Practical CMMRs are from 40 to 70dB

Baluns

Circuits that convert unbalanced to balanced lines

Typically center tapped transformers Sections of transmission line may also

be used

DC Voltage Propagation

What is happening?

Assume an I2R loss of zero

When S1 is closed:– VL1 is very high

preventing any current to flow to C1

– Thus VC1 is zero, making the voltage across the remaining portion of the line also 0

When VL1 decays to 0:

– Current will flow to C1, increasing the voltage across C1 to Ebb (source value)

– At this point VL2 will increase to oppose VC1, preventing C2 from charging until VL2 decays

– Now C2 will charge through L2 and L1

This action will continue until all the capacitors are charged.

Since the line is infinite, there will be infinite capacitors to charge taking an infinite amount of time.

Remember that current is flowing in a finite amount

Velocity of Propagation

The electric and magnetic fields associated with the current are said to propagate down the line

The speed at which an electrical signal moves through a conductor is called the velocity of propagation

Vp = LC

d

Delay Line

A length of a transmission line designed to delay a signal from reaching a point by a specific amount of time

t = LC

Velocity Constant/Factor

Velocity constant or factor is the ratio of actual velocity to velocity in free space

Vf = 1

Wavelength

The distance traveled by a wave during a period of time or one cycle

= f

v

Non-Resonant Line

Traveling DC Waves

Nonresonant line is one of infinite length or that is terminated with a resistive load equal in ohmic value to its characteristic impedance

All of the energy is transferred down the line and absorbed by the load.

The voltage and current waves are called traveling waves and move in phase with one another from source to load.

The length is not critical

Traveling AC Waves

The charging of the line when AC is applied is very similar to when DC is applied.

All instantaneous voltages produced by the generator travel down the line in the order in which they were produed.

If the voltage waveform is plotted at any point along the line, the resulting waveform will be a duplicate of the generator waveform

Since the line is terminated with its characteristic impedance, all the energy produced by the source will be absorbed by the load.

Resonant Line

Resonant Line

A transmission line terminated with an impedance that is not equal to the characteristic impedance

May be terminated with a short or open Length of line is critical

DC—Open Terminations

Assume the characteristic impedance of the line is equal to that of the source

Thus the applied voltage will be divided equally between the source and the line.

Each capacitor will charge to the voltage of the one before it.

No current will flow through inductor L3 and its field will collapse attempting to keep current flowing in the same direction.

The additional current must attempt to flow through C3 doubling the voltage across C3.

This increase in voltage must be felt by C2 and C1

Apparently there is a voltage moving back from the terminals toward the source.

Reflection

The abrupt reversal in direction of voltage and current

The polarity and amplitude of the reflected wave voltage is the same as that of the incident wave

The current is reflected back with an opposite polarity because when the field collapsed, the current dropped to zero.

Reflected waves are undesirable

DC—to Shorted Lines

The voltage reflection is out of phase with the incident voltage wave

The current reflection is in phase with the incident current wave

The resultant load voltage is always zero

Standing Waves: Open Line

Waveforms that apparently seem to remain in one position, varying only in amplitude

At the end:– Current is zero – Voltage is maximum– Voltage and current are out of phase by

900

Standing Waves: Shorted Line

At the end of a shorted termination:– Current is maximum– Voltage is zero– Current and voltage are out of phase by

900

FIGURE 11-19 Development of standing waves.




Maximums and Minimums

Maxs and Mins occur all along the transmission line

These are predictable if the applied frequency and type of line termination is known.

Standing Wave Ratio

Reflection Coefficient ()

=

=

i

r

E

E

0

0

ZZ

ZZ

L

L

VSWR/SWR

Ratio of max voltage to min voltage

VSWR =

VSWR =

min

max

E

E

1

1

Effect of Mismatch

Full generator power does not reach the load Cable dielectric may break down as a result

of high value standing waves of voltage Existence of reflections increases the power

loss in form of I2R losses Noise problems Ghost signals can be created

Quarter Length Transformer

Used to match a line to a resistive load Example

– To match a resistive load RL to line with impedance Z0

– Use a length of line of impedance Z01 equal

to ¼ wavelength of signal

– Z01 = LRZ 0

The main idea is to reflect two signals equal in amplitude but separated by ¼ wavelength

They effectively cancel each other out. The reflected signals still exist but the

source is fooled into thinking otherwise

Electrical Length

The length of a line in wavelengths as opposed to physical length

Voltage maximums occur at /2 intervals

If the line is less than /2 , the reflections still occur but the line is so short that there is no voltage variation along the conductor.

Example

For a 300Hz signal in air – Velocity is 3 x 108 m/s = 3 x 108 m/s / 300 = 1x106 m or 621mi

For a 10GHz signal in air = 3 x 108 m/s / 10GHz =3cm or 1.2 in

Smith Chart

Transmission Line Impedance

Zs =

s = distance from the load to the point where it is desired to know the line impedance (electrical degrees)

Complexity is deterrent

sjZZ

sjZZZ

L

L

tan

tan

0

00

Smith Chart

Impedance chart developed by P.H. Smith used to analyze transmission lines

Two sets of lines– Circular lines tangent to each other at the right

hand side of the chart represent resistance– Arcs tangent to each other at the right hand side of

the chart represent constant reactance

FIGURE 11-25 Smith chart.




Using the Smith Chart

1) normalize the impedance– Divide all impedances by the lines characteristic impedance– For a 50 line, this means dividing both resistance and

reactance by 50 2) plot the resulting point on the chart 3) draw the corresponding VSWR circle 4) extend the radius through zLto intersect with the

outer scale 5) subtract this number from 0.5 6) divide the length of the transmission line by /2

retaining the remainder

7) subtract value found in step 5 from that found in step 6

8) locate this value on outer circle on top half of chart 9) draw a line from the center to this point 10) the point at which this line intersects the VSWR

circle represents zin—the normalized input impedance

Multiply zin by Z0 to get the input impedance

FIGURE 11-26 Smith chart for Ex. 11-8.




Matching Impedances with Chart

1) normalize load impedance 2) plot zL and draw the VSWR circle

3) move from zL clockwise until line is resistive (crosses horizontal line)

4) this is the point at which the matching /4 line will be inserted

5) find the normalized and actual resistance of the matching section

FIGURE 11-27 Smith chart for Ex. 11-9.




Stub Tuners

Single Stub Tuner: the stub’s distance from the load and the location of its short circuit are adjustable to allow a match between line and load

Double Stub Tuner: has fixed stub locations but the position of the short circuits is adjustable to allow a match between line and load

FIGURE 11-28 Stub tuners.




Applications

Discrete circuit simulations Baluns Filters Slotted lines Time domain reflectrometry

Summary

Quiz Review Types of transmission lines Calculate the impedance of transmission lines Calculate velocity of propagation and delay factor Describe how standing waves are produced Use the Smith chart to find input impedance Use the Smith chart to match loads to lines

Chapter 11

Documents

Transcript of Chapter 11