chapter 11
TRANSCRIPT
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Chapter 11
Transmission Lines
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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
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Describe how standing waves are produced
Use the Smith chart to find input impedance
Use the Smith chart to match loads to lines
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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.
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Types of Transmission Lines
Two-wire open line Twisted pair Unshielded twisted pair (UTP) Shielded Pair Coaxial Lines Balanced/Unbalanced lines
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Two Wire Open Line
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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.
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FIGURE 11-2 Two-wire ribbon-type lines.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 9: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/9.jpg)
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.
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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
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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
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FIGURE 11-9 Equivalent circuit for a two-wire transmission 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.
![Page 13: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/13.jpg)
If the line is uniform along its length, the resistance and conductance are usually negligible which results in an LC network
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FIGURE 11-10 Simplified circuit terminated with its characteristic impedance.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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Twisted Pair
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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
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FIGURE 11-3 Twisted pair.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
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Unshielded Twisted Pair
(UTP)
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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
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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
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Important CAT5 UTP Parameters
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Attenuation
The amount of loss in the signal strength as it propagates throughout the conductor
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Cross Talk
Unwanted coupling caused by overlapping electric and magnetic fields
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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
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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
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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
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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
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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.
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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
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Wiring Standards for CAT5 and RJ-45 Defined by the Telecommunications
Industry Association standard TIA568B
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Shielded Pair
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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
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FIGURE 11-5 Shielded pair.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
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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
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Coaxial Cable
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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
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Types
Rigid or air coaxial line Flexible or solid coaxial line Electrical configuration of both is the
same
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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
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FIGURE 11-6 Air coaxial: cable with washer insulator.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
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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
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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
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Ten Minute Break
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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
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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.
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FIGURE 11-7 Flexible coaxial.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 55: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/55.jpg)
Characteristic Impedance of Coax
Z0 = d
Dlog
138
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Balanced/Unbalanced Lines
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Unbalanced Line—Coaxial
The electrical signal is carried by the center conductor with respect to the shield or grounded outer conductor
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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.
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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
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Baluns
Circuits that convert unbalanced to balanced lines
Typically center tapped transformers Sections of transmission line may also
be used
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DC Voltage Propagation
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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
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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
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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
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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
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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
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Velocity Constant/Factor
Velocity constant or factor is the ratio of actual velocity to velocity in free space
Vf = 1
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Wavelength
The distance traveled by a wave during a period of time or one cycle
= f
v
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Non-Resonant Line
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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
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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.
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Resonant Line
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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
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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.
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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.
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This increase in voltage must be felt by C2 and C1
Apparently there is a voltage moving back from the terminals toward the source.
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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
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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
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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
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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
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FIGURE 11-19 Development of standing waves.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 82: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/82.jpg)
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.
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Standing Wave Ratio
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Reflection Coefficient ()
=
=
i
r
E
E
0
0
ZZ
ZZ
L
L
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VSWR/SWR
Ratio of max voltage to min voltage
VSWR =
VSWR =
min
max
E
E
1
1
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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
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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
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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
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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.
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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
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Smith Chart
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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
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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
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FIGURE 11-25 Smith chart.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 95: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/95.jpg)
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
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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
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FIGURE 11-26 Smith chart for Ex. 11-8.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 98: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/98.jpg)
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
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FIGURE 11-27 Smith chart for Ex. 11-9.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 100: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/100.jpg)
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
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FIGURE 11-28 Stub tuners.
Gary M. Miller, Jeffrey S. BeasleyModern Electronic Communication, 7e
Copyright ©2002 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458
All rights reserved.
![Page 102: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/102.jpg)
Applications
![Page 103: Chapter 11](https://reader033.vdocuments.us/reader033/viewer/2022061121/546e574db4af9fba518b45a8/html5/thumbnails/103.jpg)
Discrete circuit simulations Baluns Filters Slotted lines Time domain reflectrometry
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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