Chapter - 3 Transmission Lines Flashcards
It is a metallic conductor system used to transfer electrical energy from one point to another using electrical current flow and it is designed to deliver RF power from the transmitter to the antenna and maximum signal from the antenna to the receiver
Transmission Lines
Two Main Categories of Transmission Lines
- Guided
- Unguided
those with some form of conductor that provides a conduit which electromagnetic energy are contained
Guided Media (wired)
signals are emitted then radiated through air or vacuum those signals propagating down the unguided transmission media are available to anyone who has a device capable of receiving them
Unguided (Wireless)
Types of Transmission Lines
- Balanced
- Unbalanced
also known as “differential transmission line”, which is made up of two parallel conductors spaced from one another by a distance of 1/2 inch up to several inches and both conductors carry signal currents , which are equal in magnitude with respect to electrical ground but travel in opposite direction
Balanced Transmission Lines
it has an advantage that most noise interference is induce equally in both wires, producing longitudinal currents that cancel in the load
Balanced Transmission Lines
Example of Balanced Transmission Lines are
Parallel Conductor Transmission Lines
it is also known as “single ended transmission lines” or “concentric transmission lines”, which consists of a solid conductor surrounded by an insulator, wherein one wire is at ground potential and the other wire is at signal potential. its disadvantages is its reduced immunity to common mode signals
Unbalanced Transmission Lines
Example of Unbalanced Transmission Lines are
Coaxial Cable Transmission Lines
current flows in opposite directions are known as
metallic circuit currents
current flows in same directions are known as
longitudinal circuit currents
balun stands for
balanced and unbalanced
- use to connect balanced and unbalanced transmission lines
most common type of balun is
Narrowband Balun which is also known as choke , sleeve or bazooka
balun has turns ratio of
4 : 1
it is comprised of two or more metallic conductors , separarted by non conductive insulating material known as dielectric (air , rubber , polyethylene , paper ,mica , glass and teflon ).
Parallel Conductor Transmission Lines
it is also known as ladder cable , which consist of two parallel wires , closely spaced and separated by air. it has non conductive spacers which are placed at periodic intervals for support and to keep distance between conductors is generally between 2 to 6 inches. but because no shielding radiation losses are high
Open Wire Line
primary use : voice-grade telephone
it is also known as ribbon cable. and it is the same with open wire transmission lines except that the spacers between the two conductors are replaced with a continuous solid dielectric that ensures uniform spacing along the entire cable , the distance between two conductors is 5/16 inches for Television Transmission Cable. the most common dielectric is TEFLON (polytetrafluoroethylene)
Twin Lead
primary use : television to rooftop antenna
it is formed by twisting together two insulated conductors around each other; the purpose of twisting is to reduce the effects of EMI (Electromagnetic Interference) and RFI (Radio Frequency Interference)
Twisted Pair : UTP and STP
primary use : Local Area Network because it is easy to install and inexpensive
it consist of two copper wires where each wire is separately encapsulated in PVC ( polyvinyl chloride ) insulation
it is inexpensive , flexible and easy to install but it is also the most susceptible to external electromagnetic interference
UTP - Unshielded Twisted Pairs
the minimum number of twist for UTP is
Two Twist per Foot
7 types of UTP according to EIA/TIA 568 Standard:
Level 1 , 2 , Category 3 ,4 ,5 Enhanced Category 5 and Category 6
it consists of two copper conductors separated by a solid dielectric material, and its wires and dielectric are enclosed in a conductive metal sleeve known as FOIL
if sleeve is woven into a mesh it is known as BRAID
more expensive than UTP but greater security and greater immunity to interference
STP - Shielded Twisted Pair
7 typer of STP according to EIA/TIA 568 Standard:
Category 3,4,5 Enhanced Category 5 , Category 7 , Foil Twisted Pair , and Shielded Foil Twisted Pair.
is an electromagnetic interference between two conductors that occurs when current flows through one conductor, it produces a magnetic field that can interfere with the adjacent conductor.
Crosstalk
for twisted pair as category number increases
the number of twist also increases and also the information capacity
UTP Connectors are:
RJ:(registerred jack)
- 45
- 11
it consist of center conductor surrounded by a dielectric material, then a concentric shielding, and finally a rubber environmental protection outer jacket
it provide excellent shielding against external interference, it is commonly used in high frequency applications to reduce losses and to isolate transmission paths
Coaxial Cable
types of coaxial cable:
- Rigid Air-Filled Coaxial Cable
- Solid Flexible Coaxial Cable
it has a center conductor surrounded coaxially by a tubular outer conductor and the insulating material is air some are pressurized with an inert gas to prevent moisture from entering.
Rigid Air-Filled Coaxial Cable
it consists of a flexible inner conductor and a concentric outer conductor of metal braid, the two are separated by a continuous insulating material (commonly teflon which is white color).
Solid Flexible Coaxial Cable
are military standards and specifications for coaxial cables by the US Department of Defense
RG ( Radio Government )
Coaxial Cable Connectors:
- BNC ( Bayonet Neil Concealman ) Connector
- N-Type Connector
it is also known as bayonet mount as they can easily twisted on or off
BNC
it is threaded and must be screwed on and off
N-Type Connector
refers to the woven stranded mesh that surrounds some types of coaxial cables
Shielding
coax with one layer of foil and one layer of braided shielding is known
Dual Shielding
there is also Quad Shielding which is two foil and two braided shielding
the characteristics of a transmission lines are determined by its ______, such as wire conductivity and insulator dielectric constant, and its ______, such as wire diameter and conductor spacing
electrical properties and physical properties
these are uniformly distributed throughout the length of the line and are commonly known as distributed parameters ( the combined parameters are known as lumped parameters )
Primary Constants
RL // RC - lumped parameters
primary constants:
–series resistance and series inductance
ohm/length and henry/length
–shunt conductance and shunt capacitance
siemen / length and farad / length
parallel conductor transmission line
Series Inductance :
L=(u/pi) ln(2S/d)
where :
S= Separation or Distance between two Conductors
parallel conductor transmission line
Series Capacitance :
C=(pi x e/ ln(2S/d)
where:
e=permittivity of medium
d=diameter of inner diameter
Coaxial Cable Transmission Line
Series Inductance :
L= (u/2pi) ln (D/d)
where:
D=inside diameter of the outer conductor
parallel conductor transmission line
Series Capacitance :
C=2 pi e / ln (D/d)
where:
e=permittivity of medium
d=diameter of inner diameter
these are the transmission characteristics of a transmission lines:
Secondary Constant:
- Characteristic Impedance
- Propagation Constant
it is also known as “surge impedance” and it is defined as the impedance seen looking into an infinite long line or the impedance seen looking into a finite length of a line that is terminated in a purely resistive load with resistance equal to the characteristic impedance of the line
Characteristic Impedance
Characteristic Impedance Formula:
Zo = sqrt ( R + JwL / G + JwC )
Characteristic Impedance Formula for RF / High Frequencies , R = G = 0
Zo = sqrt ( L/C ) … Lucy Torres
Characteristic Impedance Formula for Audio Frequencies / Low Frequencies , wL = wC = 0
Zo = sqrt (R/G) … Richard Gomez
Characteristic Impedance Formula for Parallel Conductor Transmission Lines :
Zo = ( 276 / sqrt(er) ) log (2S/d)
er = relative permittivity
d=diamter of inner conductor
Characteristic Impedance Formula for Coaxial Cable Transmission Lines
Zo = ( 138 / Sqrt(er) ) log (D/d)
er = relative permittivity
D= inside diameter of the outer conductor
d=diamter of inner conductor
it is also known as propagatoin coefficient that is used to express the attenuation ( signal loss ) and the phase shift per unit length of the transmission lines.
Propagation Constant:
y = sqrt ( (R+JwL) (G+JwC) )
y = a + jB
Attenuation Coefficient :
a = R / Zo a(np/m) = R / (2 x Zo) a(db/100ft) = 4.343 (R / Zo)
Phase Shift Coefficient :
B = 360 / lambda = 2 pi / lambda B = w sqrt(LC) .... for High Frequency
it is also known as velocity constant, and it is defined as the ratio of the actual velocity of propagation of an electromagnetic wave through a given medium to its velocity of propagation in free space vacuum.
Velocity Factor
Velocity Factor Formula:
vf = vp / c vf = 1/sqrt (er) vf = 1/n
it is simply the relative permittivity of a material, and it depends on the type of insulating material used.
Dielectric Constantc
these are transmission lines designed to intentionally introduce a time delay in the path of the electromagnetic wave.
the amount of time delay is a function of the transmission line’s inductance and capacitance
Delay Lines
Time Delay :
td = Distance / Velocity
Time Delay For 1 Meter :
td = sqrt (LC)
Time Delay For 1 Foot
td = 1.016 sqrt(er)
the length of a transmission line relative to the length of the wave propagating down it is an important consideration when analyzing
” transmission line behavior “ :
- physical length = 10km
- length in terms of wavelength =0.25lambda
- electrical length = 120degrees
Transmission Line Losses
- Conductor Loss
- Dielectric Heating Loss
- Radiation Loss
- Coupling Loss
- Corona
it is also known as “conductor heating loss” or “I^2R los”, and it is directly proportional to the square of the length of the line and inversely proportional to the characteristic impedance.
it is the inherent and unavoidable power loss because of the finite resistance of the transmission lines, and depends somewhat on frequency because of a phenomenon known as “skin effect”
Conductor Loss
it is caused by a difference of potential between conductors in a metallic transmission line (ie., it is caused by the heating of the dielectric material between conductors, taking power from the source).
it increases for solid dielectric lines because of gradually worsening properties with “increasing frequency”
Dielectric Heating Loss
if the separation between the conductors in a transmission line is an appreciable fraction of wavelength, the electrostatic and electromagnetic that surrounds the conductor caused the line to act as an antenna ( radiation of signal occurs ).
it depends on dielectric material , conductor spacing and length of the transmission line, and it can be reduced by “properly shielding the cable”
Radiation Loss
it occurs whenever a connection is made to or from a transmission line or when two section of transmission lines are connected together.
Coupling Loss
it is a luminous discharge that occurs between the two conductors of a transmission line when the difference of potential between them exceeds the breakdown voltage of the dielectric insulator, and when this occurs , usually the transmission line is destroyed
Corona
is a phenomenon wherein the signals tend to propagate at the outer edge of the cable if the frequency of the operation is too high. this happens when frequency increases , the region of high current density becomes thinner, reducing the cross-sectional area and increasing the resistance of the conductor
Skin Effect
it is also known as Flat Line or a Matched Line, wherein there is no reflected power in the transmission line
a transmission line is a resonant line if it is a infinite length or if it is terminated with a resistive load equal to the ohmic value of the characteristic impedance of the transmission line
Non-Resonant Transmission Line:
Zo=Zl
it is also known as a mismatched line, in which if the load impedance is not equal to characteristic impedance of the line some of the incident power is reflected back to the load.
in a resonant line, the energy is alternately transferred between the magnetic and electric fields of the distributed inductance and capacitance of the line
Resonant Transmission Line: Zo not equal to Zl ZL is Shorted ZL is Open ZL = R + jX
it is also known as coefficient of reflection, wherein it is a vector quantity that represents the ratio of the reflected voltage to the incident voltage or reflected current to the incident current
Reflection Coefficient : r= Vref/Vinc r=Iref/Iinc r=sqrt(Pref/Pinc) r=ZL-Zo/Zl+Zo r= SWR-1/SWR+1 r= Vmax - Vmin / Vmax + Vmin r= Imax - Imin / Imax + Imin
it is defined as the ratio of the maximum voltage or current to the minimum voltage or current of a standing wave in a transmission line
it is a measure of mismatch between the load impedance and characteristic impedance
Standing Wave Ratio : VSWR = Vmax / Vmin ISWR = Imax / Imin SWR = ZL/Zo SWR = Zo/ZL SWR = Vinc + Vref / Vinc - Vref SWR = Iinc + Iref / Iinc - Iref SWR = 1 + r / 1 - r
Typical Value:
r < 1
SWR > 1
Ideal Value:
r = 0 SWR = 1
Worst Case Value:
r = +1 or -1 SWR = Infinite
it is an “interference pattern” setup by two travelling waves. it is the formation of which due to the interaction between the incident and reflected waves that causes what appears to the stationary pattern of waves on the line.
Standing Wave
standing wave on an open circuited line
the “voltage incident wave” is “reflected back” just as if it were to continue down the line
the “current incident wave” is “reflected 180” degrees from how it would have continued
the sum of incident and reflected current waveform is “minimum at open”
the sum of incident and reflected voltage waveform is “maximum at open”
standing wave on a short circuited line
the “voltage incident wave” is “reflected 180” degrees from how it woulds have continued
the “current incident wave” is “reflected back” just as if it were to continue down the line
the sum of incident and reflected current waveform is “maximum at short”
the sum of incident and reflected voltage waveform is “minimum at short”
Absorbed Power by the Load :
Pabs = Pinc - Pref Pabs = Pinc ( 1 - r^2 ) Pabs = Pinc ( 4SWR / ( 1 + SWR )^2 )
Return Loss And Mismatch Loss:
RL = 1 / r^2 RL(db) = -20log(r)
Mismatch Loss :
ML = 1 / 1-r ML(db) = -10log(1-r)
Transmission Line Input Impedance:
Zin = Zo ( Zl + j Zo Tan(Bl ) / Zo + jZl Tan(Bl) )
Matched Load : ZL=Zo
V ref = 0 , I ref = 0 , RL=0 , r = 0 , SWR = 0
VL = IL x ZL
IL = VL / ZL
Zin = Zo = ZL
Short Circuited Load: ZL=Zo
VL = 0 V ref = -V inc Iref = I inc = IL /2 IL = I inc + I ref IL = 2 Iinc SWR = infinite Zin = jZo Tan (Bl)
Open Circuited Load : Zl = infinite
V ref = V inc = Vl/2 I ref = -I inc VL = V inc + V ref VL = 2 V inc IL = 0 r = 1
Traveling waves that are coming from the transmitter.
Incident Waves
Traveling waves that are brought back to the transmitter due to unmatched line
Reflected Waves
For A Maximum Power Transfer from source to load
a transmission line must be terminated in a purely resistive load equal to the characteristic impedance of the transmission line.
vector quantity
reflection coefficient
scalar quantity
standing wave ratio
the behavior of transmission line depends on its:
Length And Termination
when a transmission line is terminated in either short or open circuit, there is an :
impedance inversion in every quarter-wavelength
transmission lines that are terminated by either a short or an open circuit can be used as:
REACTANCES or as either SERIES or PARALLEL RESONANTS CIRCUITS depending on their length
at UHF and Microwave Frequencies where one-half wavelenght is less than 1 foot :
transmission lines are commonly used to replace conventional LC Tuned Circuits
it is a section of a transmission line, electrically a quarter-wavelenght in the length that is used to match a transmission line to a purely resistive load whose resistance is not equal to the characteristic of the line
Quarter Wave Transformer
Impedance Of Quarter Wavelength Transformer:
Zo(lambda/4) = sqrt ( Zo x ZL )
the quarter wave transformer act as a transformer with :
1:1 turns ratio
Zo = ZL
a = 1
the quarter wave transformer acts as a step-down transformer when :
ZL > Zo
a > 1
the quarter wave transformer acts as a step-up transformer when :
ZL < Zo
a < 1
it is a short section of line, usually short-circuited at one end that is used for impedance matching, and it is placed across the primary line as close to the load as possible
it is used to remove (cancel) the reactive component of the complex impedance of the load and to match it to the transmission line
Stub
Types of Stub matching :
- Series Open Stub
- Series Short Stub
- Shunt Open Stub
- Shunt Short Stub
Shorted Stubs are preffered because Open Stubs ?
Have tendency to radiate , especially at higher frequencies
if the load is inductive
the capacitive stub is used
if the load is capacitive
the inductive stub is used
is used to match a resistive load while stub is used to match a complex or reactive load
the quarter wave transformer
is used to match a complex or reactive load
stub
it is used to measure the power being delivered to a load or an antenna through a transmission line, moreover , it allows the measurement of power moving along the line in each direction thus it is possible to measure incident and reflected power separately
Directional Coupler
it is used to measure standing waves ; TDR ( Time Domain Reflectometry) it is a technique that can be used to locate an impairement in a metallic cable
Reflectometer
in TDR,
a step input or pulse is applied to the input of a transmission line ; by examining the reflected signal , much information can be gained about such things as the length of the line , the way in which it is terminated, and the type and location of any impedance discontinuities on the line.
it is a short section of air-dielectric coaxial line, with a slot in the outer conductor through which a probe is inserted; the probe does not actually touch the inner conductor , it is CAPACITIVELY COUPLED , so as to disturb the signal on the line as little as possible
it permits convenient and accurate measurement of standing waves
SLOTTED LINE
it is the graphical calculator, created and developed by Phillip Smith , used for transmission line matching
it is a polar impedance diagram which consist of two sets of circles or arc of circles, which are so arranged that various important quantities connected with mismatched transmission line may be plotted and evaluated fairly easily
Smith Chart
at low frequencies
Standard Transmission Lines would be too long fro practical use as reactive components or tuned circuits
for high frequency applications,
special transmission lines consctructed with copper patterns on a PCB have been developed to interconnect components on PC boards.
these are two printed circuit board implementations of transmisison lines known as _____ and ______are widely used to Create Resonant Circuits and Filters
STRIPLINES , MICROSTRIP
it is a flat conductor separated from a ground plane by insulating dielectric material.
its characteristic impedance is dependent on its physical characteristics
it has advantage over stripline in being simpler construction and easier integration with semiconductor devices, tending itself well to printed circuit and thin film techniques
Microstrip
Microstrip Characteristic Impedance :
Zo = ( 87 / sqrt(er + 1.41 ) ) ln (5.98h / 0.8w + t )
it is a flat conductor sandwiched between two ground planes.
it is more difficult to manufacture than microstrip, but it is less likely to radiate; thus losses in stripline are lower than microstrip
Stripline
Stripline Characteristic Impedance :
Zo = ( 60 / sqrt(er) ) ln ( 4d / ( 0.67pi x w ) ( 0.8 + t/h ) )
