Transmission Media (CH12 Tomasi)

MAPUA INSTITUTE OF TECHNOLOGY - LAGUNA

ECE143 : TRANSMISSION LINES AND ANTENNA SYSTEMS Electronic Communications Systems 5th Edition Wayne Tomasi

ENGR. MARI A CRISTINA FELI Z L. ODESTE Course Coordinator 3T | 2012 - 2013

METALLIC CABLE TRANSMISSION MEDI A Electronic Communications Systems 5th Ed. Wayne Tomasi

INTRODUCTION The transmission line has a single purpose for both the transmitter and the antenna. This purpose is to transfer the energy output of the transmitter to the antenna with the least possible power loss. How well this is done depends on the special physical and electrical characteristics of the transmission line. The Navy uses many different types of transmission mediums in its electronic applications. Each medium has a certain characteristic impedance value, current-carrying capacity, and physical shape and is designed to meet a particular requirement. TRANSMISSION LINE TYPES The five general types of transmission mediums include parallel-line, twisted pair, shielded pair, coaxial line, and waveguides. The use of a particular line depends on the applied frequency, the power-handling capabilities, and the type of installation. Transmission lines are generally categorized as either unguided or guided.  Guided transmission media are those with some form of conductor that provides a conduit in which EM signals are contained. Physical transmission media include metallic cables and optical cables. 

Unguided signals are emitted then radiated through air or vacuum. The direction of propagation in an unguided transmission medium depends on the direction in which the signal was emitted and any obstacles that the signal may encounter while propagating.

Metallic transmission lines include open wire, twin lead and twisted pair copper wire as well as coaxial cable. Optical fibers include pastic and glass core fibers encapsulated in a wide assortment of cladding materials. A transmission line is a metallic conductor system used to transfer electrical energy from one point to another using electri cal current flow. More specifically, a transmission line is two or more electrical conductors separated by a non-conductive insulator (dielectric). There are two basic kinds of waves: longitudinal and transverse.  With longitudinal waves, the displacement is in the direction of propagation.  With transverse waves, the direction of displacement is perpendicular to the direction of propagation.

Guided transmission lines can be generally classified as balanced and unbalanced.  With two-wire balanced line, both conductors carry current, one conductor carries the signal and the other conductor is the return path. This type of TL is called differential or balanced signal transmission. The two currents are equal in magnitude with respect to ground but travel in opposite directions. A balanced wire pair has the advantage that most noise interference is induced equally on both wires, producing longitudinal currents that cancel in the load. 

With unbalanced transmission line, one signal is at ground potential, whereas the other signal is at signal potential. This type of TL is also called sindle-ended signal transmission. Unbalanced transmission lines have the advantage of requiring only one wire for each signal and only one ground line is required no matter how many signals are grouped into one conductor. 2

ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

METALLIC TR ANSMISSION LINES

I.

Parallel-wire TL are comprised of two or more metallic conductors (usually copper) separated by a nonconductive insulating material called a dielectric. Common dielectric materials include air, rubber, polyethylene, paper, mica, glass and Teflon. The most common parallel-conductor TL are open-wire, twin lead and twisted pair (UTP and STP).

1.

Open-wire transmission line consists simply of two parallel wires, closely spaced and separated by air. Nonconductive spacers are place at periodic intervals not only for support but also to keep the distance between the two conductors constant. The distance between the conductors are generally 2 and 6 inches. The only ad vantage of this type of TL is its simple construction. Because there is no shielding, radiation losses are high and the cable is susceptible to crosstalk.

2.

Twin lead is essentially the same as open-wire TL except that the spacers between the conductors are replaced by a a continuous solid dielectric that ensures uniform spacing along the entire cable.

3.

A twisted-pair TL is formed by twisting two insulated conductors around each other. Twisted pairs are often stranded in units, and the units are cabled into cores containing up to 3000 wire pairs. The size of twisted-pairs varies from 16 AWG to 26 AW G. The higher the gauge wire number, the smaller the diameter and the higher the resistance.

NOTE

Twisted-pair cable is used for both analog and digital signals and is the most commonly used transmission medium for telephone networks, building cabling system and local area networks because it is simple to install and relatively inexpensive when compared to coaxial and optical fibers.

There are two basic types of twisted-pair TL specified by the EIA/TIA 568 Commercial Building Telecommunications Cabling Standard for local area networks: 100 Ω UTP and the 150 Ω STP.. Unshielded twisted-pair (UTP) cable consists of two copper wires where each wire is separately encapsulated in PVC (polyvinyl chloride) insulation. The wires are twisted two or more times at varying lengths to reduce crosstalk and interference. The minimum number of twists for UTP cable is two per foot. Pair 1: blue/white strips and blue Pair 2: orange/white strips and orange Pair 3: green/white strips and green Pair 4: brown/white strips and brown

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

EIA/TIA 568 UTP and STP Categories  Cat 1 is suitable only for voice-grade telephone signals and very low speed data applications.  Cat 2 is only marginally better than cat 1. Cat 2 cables were developed for IEEE 802.5 Token ring LAN operating at 4 Mbps.  Cat 3 must have at least three turns per inch and no two pairs within the same cable can have the same number of turns per inch. Cat 3 cable was designed to accomodate the requirements for IEEE 802.5 Token Ring (16 Mbps) and IEEE 802.3 10Base-T Ethernet (10 Mbps)  Cat 4 cable was designed for data trasmission rates up to 20 Mbps and can handle transmission rates of up to 100 Mbps containing four pairs of wires.  Cat 5 cable has better attenuation and crosstalk characteristics than the lower cable classification (12 turns per inch). NEXT refers to coupling that takes place when a transmitted signal is coupled into the receive signal at the same end of the cable. Cat 5 is the cable for most modern day LAN. This cable was designed for data rates of up to 100 Mbps.  Enhanced Cat 5 are intended for data transmission rates of up to 250 Mbps and can operate successfully at rates of up to 350 Mbps and higher. 

Shielded Twisted-pair cable is a TL consisting of two copper conductors separated by a solid dielectric material. The wires and dielectric are enclosed in a conductive metal sleeve called foil. If the sleeve is woven into a mesh it is called a braid. STP cable is thicker and less flexible than UTP cable, making it more difficult and expensive to install. However, STP cable offers greater security and greater immunity to interference. Cat 7 shielded screen twisted pair cable (SSTP) is comprised of four pairs of 22 or 23 AWG copper wire surrounded by a metallic foil followed by a braided metallic shield. Foil twisted-pair cable is comprised of four pairs of 24 AWG copper wire encapsulated in a common metallic foil shield with PVC outer shield. Shielded foil twisted pair cable is comprised of four pairs of 24 AWG copper wires surrounded by a common metallic foil encapsulated in a braided metallic shield. This cable type offers superior EMI protection.

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NOTE

II.

Plenum is given to the area between the ceiling and the roof of a single story building or between the ceiling and the floor of the next higher level in a multistory building. The NEC requires plenum cable to have special fire resistant insulation. Plenum cables are coated with Teflon, which does not emit noxious chemicals when ignited.

The basic coaxial cable consists of a center conductor surrounded by a dielectric material, then a concentric shielding and finally an outer jacket. Shielding refers to the woven or stranded mesh that surrounds some types of coaxial cables. There are two basic types of coaxial cables: rigid air filled and solid flexible. The RG numbering system typically used with coaxial cables refers to cables approved by the US DoD.

There are essentially two types of coaxial cable connectors BNC connectors and type-N connectors.  BNC connectors are sometimes referred to an “bayonet mount” as they can be easily twisted on or off.  N-type connectors are threaded and must be screwed on or off.

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

WAVEGUIDES Parallel wire transmission lines cannot effectively propagate EM energy above approximately 20 GHz, because of attenuation caused by skin effect and radiation losses. A waveguide is a hollow conductive tube, usually rectangular in crosssection but sometimes circular or elliptical. In a waveguide, conduction of energy occurs not in the walls but rather through the dielectric within the waveguide which is usually dehydrated air or inert gas. The cross-sectional area of a waveguide must be of the same order as the wavelength of the signal it is propagating. Therefore, a waveguide are generally restricted to frequencies above 1 GHz. The cut-off frequency is the minimum frequency of operation of a waveguide. It is an absolute limiting frequency; frequencies below the cut-off frequency will not be propagated by the waveguide. The cut-off wavelength is defined as the largest free space wavelength that is just unable to propagate in the waveguide. In other words, only frequencies with wavelengths less than the cut-off wavelength can propagate down the waveguide. Dimension a determines the cut-off frequency of the waveguide according to the following mathematical relationship:

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Phase velocity is the apparent velocity of the particular phase of the wave. It is the velocity with which a wave changes phase in a direction parallel to the walls of the waveguide. Phase velocity can be determined by measuring the wavelength of a particular frequency wave.

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Group velocity is the velocity at which information signals are propagated. Group velocity can be measured by determining the time it takes for a pulse to propagate a given length of waveguide.

NOTE

The phase velocity is always equal to or greater than the group velocity, and their product is equal to the square of the free space propagation velocity. Phase velocity may exceed the speed of light. The principle that no form of energy can travel at a greater velocity than light is not violated because it is the group velocity, not the phase velocity, that represents the propagation of energy.

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

The mathematical relationship between guide wavelength and cut-off frequency is

TRANSMISSION LINE EQUIVALENT CIRCUIT The figure below shows the equivalent cicuit of a single section of a transmission line terminated in a load equal to Zo.

PHYSIC AL DIMENSIONS OF A TRANSMISSION LINE

parallel balanced line

concentric coaxial cable

WAVE PROPAGATION ON A TR ANSMISSION L INE

NOTE Velocity factor is defined simply as the ratio of the actual velocity of propagation of an EM wa ve through a given medium to the velocity of propagation through a vacuum. Dielectric constant is simply the relative permittivity of a material. Dielectric constant depends on the type of insulating material used.

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

TRANSMISSION LINE LOSSES Because electrical current flows through a metallic transmission line and the line has a finite resistance, there is an inherent and unavoidable power loss. This is sometimes called conductor loss, or conductor heating loss and is simply I²R loss. Conductor loss depends somewhat on frequency because of the phenomenon called the skin effect. At high frequencies, most of the current flows along the surface of the conductor rather than near its center. 1. 2.

The difference of potential between two conductors of a metallic transmission line causes dielectric heating. Coupling loss occurs whenever a connection is made to or from a transmission line or when two sections of transmission lines are connected together. Discontinuities tend to heat up, radiate energy and dissipate power. Corona is a luminous discharge that occurs between two conductors of a transmission line when the difference of potential between them exceeds the breakdown voltage of the insulator. The energy radiated from the conductors is called radiation loss and depends on the dielectric material, conductor spacing and length of transmission line. Radiation losses are reduced by properly shielding the cable and is directly proportional to frequency.

3. 4.

INCIDENT AND REFLECTED WAVES An ordinary transmission line is bidirectional; power can propagate equally well in both directions. Voltage that propagates from the source toward the load is called incident voltage, and voltage that propagate from the load toward the source is called reflected voltage.

The two EM wa ves that travel in opposite directions that are present on the line at the same time set up an interference pattern known as standing waves. The reflection coefficient is a vector quantity that represents the ratio of the reflected voltage to incident voltage or the incident current to reflected current. When Zo = ZL all the incident power is absorbed by the load. This is called a matched line. When Zo ≠ Z L some of the incident power is absorbed by the load and some is returned to the source. This is called an unmatched line. NOTE From the given equations, it can be seen that the maximum worst case value for Γ is 1 (Er = Ei) and the minimum value and ideal condition occurs when Γ is 0. If the incident and reflected voltage are equal in amplitude, SWR = infinity. This is the worst case condition.

Standing WaveRatio (SWR) is defined as the ratio of the maximum voltage to the minimum voltage or the maximum current to the minimum current of a standing wave of a transmission line.

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

TRANSMISSION LINE INPUT IMPED ANCE. Transmission line is terminated in either a short or an open circuit and there is an impedance inversion every quarter wavelength. In a more practical situation where power losses occur, the amplitude of the reflected wave is always less than that of the incident wave except at the termination. The input impedance for a lossless line seen looking into a transmission line that is terminated in a short or open can be resistive, inductive or capacitive, depending on the distance form the termination.

TRANSMISSION LINE IMPED ANCE MATCHING Power is transferred most efficiently to a load when there are no reflected waves , that is, when the load is purely resistive and equal to Zo. Whenever the characteristic impedance of a transmission line and its load are not matched, standing waves are present on the line, and maximum power is not transferred to the load. Standing waves causes power loss, dielectric breakdown, noise, radiation and ghost signals. Therefore whenever possible, a transmission line should be matched to its load. 

Quarter-wavelength transformer matching is used to match transmission lines to purely resistive loads whose resistance is not equal to the characteristic impedanc eof the line. It is not a broadband impedance -matching device and works only at a single frequency. RL = Z o  the line acts as a transformer with 1:1 ratio RL > Z o  the line acts as a step-down transformer RL < Z o  the line acts as a step-up transformer

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Stub matching. When a load is purely inductive or purely capacitive, it absorbs no energy. The reflection coefficient is 1 ans the SWR is infinity. When the load is a complex impedance, it is necessary to remove the reactive component to match the transmission line to the load. Transmission line stubs are commonly used for this purpose. A transmission line stub is simply a piece of additional transmission line that is placed across the primary line as close to the load as possible. The susceptance of the stub is used to tune out the susceptance of the load. With stub matching, either a short or an open stub can be used, however, shorted stubs are preferred because open stubs have a tendency to radiate especially at higher frequencies.

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE

TIME-DOMAIN REFELCTOMETR Y A technique that can be used to locate an impairment in a metallic cable is called time domain reflectometry (TDR). A discontinuity on the cable causes a portion of the transmiited signal to be reflected rather than continuing down the cable. If no energy is returned, the line is either infinitely long or terminated in a resistive load with an impedance equal t o the characteristic impedance of the line. TDR operates in a fashion sense similar to radar. The exact distance between the impairment and the source can be determined by the following mathematical relationship:

REVIEW QUESTIONS: 1.

Define transmission line.

2.

Describe a transverse electromagnetic wave.

3.

Describe balanced and unbalanced transmission line.

4.

Define velocity factor for a transmission line.

5.

Define reflection coefficient.

6.

List and describe the five types of transmission line losses.

7.

Define input impedance and characteristic impedance for a transmission line.

8.

Describe time-domain reflectomerty.

9.

Describe the behavior of an open and shorted transmission line as a circuit element.

10. Describe how stub matching and quarter wavelength transformer matching is accomplished. SHORT PROBLEMS: 1.

Determine the SWR for a 75 Ω transmission line that is terminated in a load resistance Z L = 50 Ω.

2.

For a transmission line with E i = 0.4 V and Er = 0.002 V, determine the standing wave ratio.

3.

Determine the characteristic impedance for an air-filled concentric transmission line with a D/d ratio of 6.

4.

Using a TDR, a transmission line impairment is located 2500 m from the source. If the elapsed tie from the beginning of the pulse to the reception of the echo is 833 ns, determine the velocity factor.

5.

For a given length of coaxial cable with distributed capacitance C = 48.3 pF/m and distributed inductance L = 241.56 nH/m, determine the velocity factor and velocity of propagation.

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ECE143 – TRANSMISSION LINES AND ANTENNA SYSTEMS | 3T 2012 - 2013 ENGR. MARIA CRISTINA FELIZ L. ODESTE