CHAP T E% Metallic Cable Transmission Media CHAPTER OUTLINE 12-1 Introduction 12-8 Wave Propagation on a Metallic Transmission Line 12.2 Metallic Tyansmission Lines 12-9 Transmission Line Losses 12-3 Transverse Electromagnetic Waves 12-10 Incident and Reflected Waves 12-4 Characteristics of Electromagnetic Waves 12-11 Standing Waves 12-5 Types of Transmission Lines 12-12 Transmission-Line Input Impedance 12-6 Metallic Transmission Lines 12-13 Time-Domain Reflectometry 12-7 Metallic Transmission Line Equivalent Circuit 12-14 Microstrip and Stripline Transmission Lines OBJECTIVES Define the general categories of transmission media Define guided and unguided transmission media Define metallic transmission lines Explain the difference between transverse and longitudinal waves Define and describe transverse electromagnetic waves Describe the following characteristics of electromagnetic waves: wave ‘velocity, frequency, and wavelength Describe balanced and unbalanced transmission lines ‘Explain baluns Describe the following paral‘2l-conductor transmission lines: open-wire, twin-lead, twisted-pair, unshielded twisted:pair, shielded twisted-pair, and coaxial transmission lines Describe plenum cable Descrits a transmission-line equivalent circuit Detine the following transmission characteristics: characteristic impedance and propagation constant Describe transmission-line propagation and velocity factor Explain what is meant by the electrical length of a transmission line 514line losses: conductor loss, dielectric heating loss, radiation loss, coupling Define and describe incident and reflected waves Explain the difference between resonant and nonresonant transmission lines Describe the term reflection coefficient Describe standing waves and standing wave ratio Analyze standing waves on open and shorted transmission lines Define transmission tine input impedance Describe how to match impedances on a transmission line Describe time-domain reflectometry Describe microstrip and stripline transmission lines 124 INTRODUCTION 124 512 ‘Transmission media can be generally categorized as either unguided or Le Guided transmission media are those with some form of conductor that provides a con iuit ee electromagnetic signals are contained. In essence, the conductor directs the signal that is propagating down it. Only devices physically connected to the medium can receive signals propagating down a guided transmission medium. Examples of guided transmission media are copper wire and optical fiber. Copper wires transport signals using electrical current, ‘whereas optical fibers transport signals by propagating electromagnetic waves through a nonconductive material. Unguided transmission media are wireless systems (Le., those without a physical conductor), Unguided signals are emitted then radiated through air or a vacuum (or sometimes water). The direction of propagation in an unguided transmission é medium depends on the direction in which the signal was emitted and any obstacles the sig- nal may encounter while propagating. Signals propagating down an unguided transmission medium are available to anyone who has a device capable of receiving them. Examples of Uunguicvd transmission media are air (Earth's atmosphere) and free space (a vacuum) A cable transmission medium is a guided transmission medium and can be any phys- ical 1acility used to propagate electromagnetic signals between two locations in a commu- nications system. A physical facility is one that occupies space and has weight (i.c., one that you can touch and feel as opposed to a wireless transmission medium, such as Earth’s at- mosphere or a vacuum). Physical transmission media include metallic cables (transmission lines) and optical cables (fibers). Metallic transmission lines include open wire, twin lead, and twisted-pair copper wire as well as coaxial cable, and optical fibers include plastic and glass-core fibers encapsulated in a wide assortment of cladding materials. Cable transmis- sion systems are the most common means of interconnecting devices in local area networks because cable wansmission systems are the only transmission medium suitable for the transmission of digital signals. Cable transmission systems are also the only acceptable tansmission media for digital carrier systems such as T carriers. 2 METALLIC TRANSMISSION LINES 7 A transmission line isa metallic conductor system used to transfer electrical energy from one point to another using electrical current flow. More specifically, a transmission line is two or more electrical conductors separated by a nonconductive insulator (dielectric), such as a pait of wires or a system of wire pairs, A transmission line Feyeles/s ~ cycle To solve for wavelength in feet or inches, Equation 12-4 can be rewritten as ° i __ 1:18 x 10? in/s _ inches a5 Feycles/s cycle . 83X 10°f/s feet aos) Feycles/s cycle Figure 12-2 shows a graph of the displacement and direction of propagation of a trans- verse electromagnetic wave as it travels along a transmission line from a source to 2 load, ‘The horizontal (X) axis represents distance and the vertical (¥) axis displacement (voltage). ‘One wavelengthis the distance covered by one cycle ofthe wave. Itcan be seen that the wave ‘moves tothe right or propagates down the line with time. If a voltmeter were placed at any stationary point on the line, the voltage measured would fluctuate from zero to maxirum positive, back to 2er0, to maximum negative, back to zero again, and then the cycle repeats. 12-5 TYPES OF TRANSMISSION LINES 514 ‘Transmission lines can be generally classified as balanced or unbalanced, 12-5-1 Bulanced Transmission Lines With two-wire balanced lines, both conductors carry current; however, one conductor car ries the signal, and the other conductor is the return path. This type of transmission is called differential, or balanced, signal transmission. The signal propagating down the wire is ‘measured as the potential difference between the two wires. Figure 12-3 shows a balanced Chapter 12Meimum + to L | tems E * ‘ 4+ n+} or I FIGURE 122 Displacement and velocity of @ transverse weve 2s ft prope: gates down a trensmssion ine [son Diteranta sana vote are + Seutonse ff * Common-made voltage (noise) exons LE FIGURE 42-3 Differential, or balanced, transmission system transmission line system. Both conductors in @ balanced line carry signal currents. The two currents are equal in magnitude with respect to electrical ground hut travel in opposite di- rections, Currents that flow in opposite directions in a balanced wire pair are called metallic circhit currents. Curreats that flow in the same direction are called longitudinal currents, A balanced wire pair has the advantage that most noise interference (sometimes called ‘common-mode interference) is induced equally in both wises, producing longitudinal cur- rents that cancel in the load. The cancellation of common mode signals is called common- ‘mode rejection. Common-mode rejection ratios of 40 dB to 70 dB are common in balanced transmission lines. Any pair of wires can operate in the balanced mode, provided that nei- ther wire is at ground potential. This includes coaxial cable that has two center conductors and a shield. The shield is generally connected to ground to prevent static interference from penetrating the center conductor. * Metallic Cable Transmission Media 515 atte516 » o 3 balanced transmission ing: FIGURE 12-4 Results of metallic and longitudinal currents on seals wokegee {6} metalic currents due to signal vokages; {b) longitudinal currents due urrents on a Wo-wire bal. i ¥ ic and longitudinal c\ Figure 12-4 shows the result of metallic and longit i yodinal cuvent (ok anced transmission line. From the figure, it can be seen that the I ten produced by static interference) cancel in the load. 125-2 Unhalanced Transmission Lines With an unbalanced transmission line, one wire is at ground potential, whereas the other wire is at signal potential. This type of transmission line is called single-ended, or unbalanced, signal transmission, With unbalanced signal transmission, the ground wire ‘may also be the reference for other signal-carrying wires. If this is the case, the ground wire must go wherever any of the signal wires go. Sometimes this creates a problem because a length of wire has resistance, inductance, and capacitance and, therefore, a small potential difference may exist between any two points on the ground wire. Consequently, the ground wite is not a perfect reference point and is capable of having noise induced into it. ‘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. The primary disadvantage of unbal: nced transmission lines is reduced im- ‘munity to common-mode signals, such as noise ar d other interference. Figure 12-5 shows two unbalanced transmission systems. The potential difference on each signal wire is measured from that wire to acommon ground reference, Balanced trans- mission lines can be connected to unbalanced lines and vice versa with special transform- rs called baluns. 125-3. Baluris Acircuit device used to connect a balanced transmission line to an unbalanced load is called a balun (balanced to unbalanced). Or more commonly, an unbalanced transmission line, such as a coaxial cable, can be connected to a balanced load, such as anantenna, using a special transformer with an unbalanced primary and a center-tapped secondary winding. ‘The outer conductor (shield) of an unbalanced coaxial transmission line is generally con- nected to ground, At relatively low frequencies, an ordinary transformer can be used to iso- Jate the ground from the load, as shown in Figure 12-6a. The balun must have an electro- static shield connected to earth ground to minimize the effects of stray capacitances. For relatively high frequencies, several different kinds of transmission-line baluns exist. The most common type is a narrowband balun, sometimes called a choke, sleeve, of bazooka balun, which is shown in Figure 12-6b. A quarter-wavelength sleeve is placed around and connected to the outer conductor of a coaxial cable. Consequently, the imped- ance seen looking back into the transmission line is formed by the sleeve, and the outer con- ductor and is equal to infinity (.., the outer conductor no longer has a zero impedance 10 Chapter 12Cirout 1 signal wire Signa! 1 votuge Circuit 2 signal wire Amplifier + Signal 2 voltage Ground reference FIGURE 12-5 Singleended, or unbalanced, transmission system Balanced diode antenns ced ine Transtormor fre ey ms balanced input _C22xa cable Balanced output Shits b+} conto: conductor Unbalanced coaxit ine ” Cy FIGURE 12-6 Baluns: (a) transformer balun; (b) bazooka balun ground), Thus, one wire of the balanced pair can be connected to the sleeve without short- circuiting the signal. The second conductor is connected to the inner conductor of the coax- ial cable. 12-6 METALLIC TRANSMISSION LINES ‘ Al data communications systems and computer networks are interconnected to some de- ‘gree'or another with cables, which are all or part ofthe transmission medium transporting signals between computers. Although there is an enormous variety of cables manufactured today, only a handful of them are commonly used for data communications circuits and ‘computer networks. Belden, which is a leading cable manufacturer, lists more than 2000 dif- ferent types of cables in its catalog. The most common metallic cables used to interconnect data communications systems and computer networks today are parallel-conductor trans- mission lines and coaxial transmission lines. Metallic Cable Transmission Media 517 Bee eee eee eee eee eee eee eee eee eee eee eee ee518 FIGURE 12-8 Twin lead twowire transmission line 12-6-1 Parallel-Conductor Transmission Lines Parallel-wire transmission lines are comprised of two or more metallic conductors (usu- ally copper) separated by a nonccaductive insulating material called a dielecir:.. Com- mon dielectric materials include air, rubber, polyethylene, paper, mica, glass, and Teflon, ‘The most common parallel-conductor transmission lines are open wire, twin lead, and ‘twisted pair {including unshielded twisted-pair (UTP) and shielded twisted-pair (STP). 12-6-1-1 Open-wire transmission line. Open-wire transmission lines are two-wire parallel conductors (see Figure 12-7). Open-wire transmission lines consist simply of two Parallel wires, closely spaced and separated by air. Nonconductive spacers are placed at pe- riodic intervals not only for support but also to keep the distance between the conductors, constant. The distance between the two conductors is generally between 2 inches and 6 inches. The dielectric is simply the air between and around the two conductors in which the TEM wave propagates. The only real advantage of this type of transmission line is its sim- ple construction, Because there is no shielding, radiation losses are high, and the cable is sus- ceptible to picking up signals through mutual induction, which produces crosstalk. Crosstalk ‘oceurs when a signal on one cable interferes with a signal on an adjacent cable. The primary use of open-wire transmission lines is in standard voice-grade telephone applications, 12-6-1-2 Twin lead. Twin lead is another form of two-wite parallel-conductor transmission line and is shown in Figure 12-8. Twin lead is essentially the same as open- wite transmission line except thatthe spacers between the two conductors are replaced with ‘8 continuous solid dielectric that ensures uniform spacing along the entire cable. Uniform spacing isa desirable characteristic for reasons that are explained later in this chapter. Twin- ‘ead transmission line is the flat, brown cable typically used to connect televisions t0 rooftop antennas. Common dielectric materials used with twin-lead cable are Teflon and polyethylene. ‘i Chapter 12FIGURE 12-9 Twistedpair twowire transmission line Four insulated ‘wisted-pair cables i Sheath _ FIGURE 12-10 Unshielded bwistedpair (UTP) cable 12-6-1-3 Twisted-pair transmission lines. A twisted-pair transmission line (shown in Figure 12-9) is formed by twisting two insulated conductors around each other. Twisted Pairs are often stranded in units, and the units are then cabled into cores containing up to 3000 pairs of wire. The cores are then covered with various types of sheaths forming cables. Neighboring pairs are sometimes twisted with different pitches (twist length) to reduce the effects of electromagnetic interference (EMI) and radio frequency interference (RFI) from external sources (usually man-made), such as rluorescent lights, power cables, motors, re~ Jays, and transformers. Twisting the wires also reduces crosstalk between cable pairs. ‘The size of twist-d-pair wire varies from 16-gauge (16 AWG [American Wire Gauge)) to 26 gauge. The higher the wire gauge, the smaller the diameter and the higher the resis- tance. Twisted-pair cable is used for both analog and digital signals and is the most com- monly used transmission medium for telephone networks and building cabling systems. ‘Twisted-pair transmission lines-are also the transmission medium of choice for most local area networks because twisted-pair cable is simple to install and relatively inexpensive ‘when compared to coaxial and optical fiber cables. ‘There are two basic types of twisted-pair transmission lines specified by the EIA/TIA. 568 Commercial Building Telecommunications Cabling Standard for local area networ 100-chm unshielded twisted pair and 150-ohm shielded twisted pair. A typical network uti- lizes a vanety of cabling technologies, depending on the network's size, its topology, and the protocol used. The 568 standard provides guidelines for interconnecting various cabling technologies by dividing network-wiring systems into six subsystems: horizontal cabling, backbone cabling, work area, telecommunications closet, equipment room, and building entrance. The six subsystems specified in the 568 standard are described in more detail in a later chapter. Unshielded twisted-pair (UTP) cable consists of two copper wires where each wire 1s separately encapsulated in PVC (polyvinyl chloride) insulation (see Figure 12-10). Be- cause a wire can act like an antenna, the wires are twisted two or more times at varying lengths to reduce crosstalk and interference. By carefully controlling the number of twists per foot and the manner in which multiple pairs are twisted around each other, manufac- turers can improve the bandwidth (ie., bit rate) of the cable pair significantly. The mini- mum number of twists for UTP cable is two per foot. Most telephone systems use UTP cable, and the majority of new buildings are prewired with UTP cable, Generally, more cable is installed than is initially needed, providing room Metallic Cable Transmission Media * 519520 Tabla 12-1 EIA/TIA S68 UTP and STP Levels and Categories Level (UTP) Suandard voice and low-speed data 2400 bps 18,000 fet Level2(UTP) Sundard voice and low-speed data MOPS santeve! 100 meter Category 3 Low-speed local area networks 16 Mops an (rst) Dales gy soOmeten Category 4 ——_Low.speed fea area networks 20 Mops and all a (UTPsTP) 3 applications 100 meters Cegory 5 Highspeed local stea networks 100 Mops crest, 100 meteor Enhanced High-speed local area networks and 350 Mbps wore category $ asynchronous transfer mode (ATM) (TPT) Proposed New Categories \o0 meer or Category 6 Very high-sped local ares networks 350 Mops eet (reste) ‘nd asynchronous wansfer mode (ATM) [Ooms or Category7 ——_Ueahigh-speed local area networks 1 Gbps 0 me Shielded snd asynchronous transfer mode (ATM) sereen twisted pair (STP) , Foiltwisted __Ultahigh-speed local area networks and >1 Gbps pair (STP) asynchronous transfer mode (ATM): designed to minimize EMI susceptibility and maximize EMI immunity > Shicledfoil _Urwchigh-speed local area networks and >I Gbps twisted pir asynchronous transfer mode (ATM): om designed to minimize EMI suseepsbilty and maximize EMI imauaity for orderly growth. This is one of the r mary reasons why UTP cable is so popular. UTPca- bles inexpensive, flexible, and easy to install. Itis the least expensive transmission medium, but itis also the most susceptible tc external electromagnetic interference. ‘To meet the operational réquirements for local area networks, the EIA/TLA 568 stan- dard classifies UTP twisted-pair cables into levels and categories that certify maximum data rates and recommended transmission distances for both UTP and STP cables (see Table 12-1). Standard UTP cable for local area networks is comprised of four pairs of 22- or 24-gauge ‘copper wire where each pair of wires is twisted around each other. ‘There are seven primary unshielded twisted-pair cables classified by the FIA/TIA 568 standard: level 1, level 2, category 3, category 4, category 5, enhanced category 5, and category 6. 1, Level 1, Level 1 cable (sometimes called category 1) is ordinary thin-copper, voice- grade telephone wire typically installed before the establishment of the 568 standard. Many ‘of these cables are insulated with paper, cord, or rubber and are, therefore, highly susceptible to interference caused by insulation breakdown, Level I cable is suitable only for voice-grade telephone signals and very low-speed data applications (typically under 2400 bps). 2. Level 2, Level 2 cable (sometimes called category 2) is only marginally better than level 1 cable but weli below the standard’s minimum level of acceptance. Level 2 cables are also typically old, leftover voice-grade telephone wires installed prior to the establish- ‘ment of the 568 standard. Level 2 cables comply with IBM's Type 3 specification GA27- 3773-1, which was developed for IEEE 802.5 Token ring local area networks operating at transmission rates of 4 Mbps. 3. Category 3. Category 3 (CAT-3) cable has more stringent requirements than level | or level 2 cables and must have atleast three turns per inch, and no two pairs within the same Chapter 12able can have the same number 6f tums pet inch, This jon provides the cable MO cable ca per inch, This specification provides local au '® crosstalk. CAT-3 cable was designed to accommodate the pe enn (CO Mbpay meres: IEEE 802.5 Token Ring (16 Mbps) and IEEE 802.3 10Base-T Eahernet Mops), In essence, CAT-3 cable is used for virtually any voice or data transmission 1bo Me MbP* and. if four wire pais are used, can accommodate transmission rates UP tO 100 Mbps. A: Category 4. Category 4 (CAT-4) cable is little more than an upgraded version of Sar Cable designed to meet tighter constraints for attenuation (loss) and crosstalk. CAT- dle trogen designed for data transmission rates up to 20 Mbps. CAT-4 cables can also han- “tagsmission rates up to 100 Mbps using cables containing four pars of Wires. i jCalet0ry 5. Category 5 (CATS) cable is manufactured with more stringent design ‘Specifications than either CAT-3 or CAT-4 cables, including cable uniformity, insulation re xi nummer Of turns per inch (12 tums per inch for CAT:5). Consequently, CAT-5 ca- ‘Atteman ent *enuation and crosstalk characteristics than the lower cable classifications. & ‘enuation an simple terms is simply the reduction of signal strength with distance, and ressalk is the coupling of signals from one pair of wires to another ‘pait. Near-enid recey Qik refers to coupling that takes place when a transmitted signal is coupled into the Teceive signal atthe same end ofthe eable CATS cable is the cable of choice for most modem-day local area networks. CAT:S Cable was designed for data transmission rates up to 100 Mbps; however, daa rates in ex- ess of 500 Mbps are sometimes achieved. CATES cable is UTP cable comprised of four Pairs of wires, although only two (pairs 2 and 3) were intended to be used for connectivity. The other two wire pairs are reserved spares. The following standard color code is speci fied by the ELA for CAT-5 cable: Pair 1: blue/white stripe and blue Pair 2: orange/white stripe and orange Pair 3: green/white stripe and green Pair 4: brown/white stripe and brown Each wire in a CAT-S cable can be a single conductor or a bundle of stranded wires re- ferred to.as Cat-5 solid or CAT-S flex, respectively. When both cable types are used inthe same application, the solid cable is used for backbones and whenever the cable passes through ‘Walls or ceilings. The stranded cable is typically used for patch cables between hubs and patch Panels and for drop cables that are connected directly between hubs and computers. 6. Enhanced category 5. Enhanced category 5 (CAT-SE) cables are intended for data ‘transmission rates up to 250 Mbps, although they often operate successfully at rates up to 350 Mbps and higher. 7. Category 6. Category 6 (CAT-6) cable is a recently proposed cable type comprised of four pairs of wire capable of operating at transmission data rates up to 550 Mbps, CAT- 6 cable is very similar to CAT-S cable except CAT-6 cable is designed and fabricated with closer tolerances and uses more advanced connectors. Shielded rwisted-pair (STP) cable is a paralJel two-wire transmission line consisting of two copper conductors separated by a solid dielectric material. The wires and dielectric are enclosed in a conductive metal sleeve called a foil. Ifthe sleeve is woven into a mesh, itis called a braid, The sleeve is connected to ground and acts as a shield, preventing sig. nals from radiating beyond their boundaries (see Figure 12-11). The sleeve also keeps elec- tromagnetic noise and radio interference produced in external sources from reaching the signal conductors, STP cable is thicker and less flexible than UTP cable, making it more difficult and expensive to install. Ia addition, STP cable requires en additional grounding connector and is more expensive to manufacture, However. STP cable offers greater secu- rity and greater immunity to interference, Metallic Cable Transmission Media 521 eee522 Two insulated twisted par ea Sheath Fol shielding FIGURE 12-11. Shielded bwisted-pair (STP) cable in Cable Table 12:2 Attenuation and Crosstalk Characteristics of Twisted-Pair Coble Attenuation (4B per 100 meters) 1 26 20 My 4 36 4 ee 16 134 82 ‘4 25 = 104 i 100 = 20 123 pd = = 214 Eedtee HEHE EeeE EP EdAze ere dE CE Near-Bnd Crosstalk (4B) 1 4 62 38 4 2 3 58 6 B “4 S04 25 = 41 415 100 = 2 385 300 = a 313 ‘There are seven primary STP cables classified by the ELA/TIA 568 standard: category 3, category 4, category 5, enhanced category 5, category 7, foil twisted pair, and shielded-foil twisted pair. 1, Category 7. Category 7 shielded-screen twisted-pair cable (SSTP) is also called IME (pairs in metal foil) cable. SSTP cable is comprised of four pairs of 22 or23 AWG cop- per wire surrounded by a common metallic foil shield followed by a braided metallic shield. 2, Foil twisted pair. Foil twisted-pair cable is comprised of four pairs of 24 AWG ‘copper wire encapsulated in a common metallic-foil shield with a PVC outer sheath. Foil twisted-pair cable has been deliberately designed to minimize EMI susceptibility while maximizing EMI immunity. 3. Shielded-foil nvisted pair. Shielded-foil twisted-pair cable is comprised of four Paits of 24 AWG copper wires surrounded by a common metallic foil shield encapsulated ina braided metalic shield. Shielded-foil twisted-pair cables offer superior EMI protection. 12-6-2 Attenuation and Crosstalk Comparison Table 12-2 shows a comparison of the attenuation and near-end crosstalk characteristics of three of the most popular types of twisted-par cable. Attenuation is given in dB of loss per 100 meters of cable with respect to freyuency. Lower dB valves indicate a higher quality cable, and the smaller the differences inthe dB value forthe various frequencies, the bet. ter the frequency response. Crosstalk is given in dB of attenuation between the transmit sig. nal and the signal returned due to crosstalk with higher dB values indicating less crosstalk Chapter 1212-63 Plenum Cable Plenum is the name given tothe area between the ceiling and the roof ina single-story build ing orbetween the ceiling and the fluor ofthe next higher level in a multistory building: Metal rectangular-shaped air duets were traditionally placed inthe plenum to control airftow in the building (both for heating ana for cooling). In more modern buildings. the cetling 1tself is used t0 control airflow because the plenum goes virtually everywhere in the building This Presents an interesting situation fa fire should occut inthe plenum because the airflow would not be contained in a fire-resistant duct system. For ease of installation, networking cables are typically distributed throughout the building in the plenum. Traditional (nonplenum) ca~ bles use standard PVC sheathing for the outside insulator; such sheathing is highly toxic when ignited. Therefore, if fire should occur, the toxic chemicals produced from the burn- ing PVC would propagate through the plenum, possibly contaminating the entire building. ‘The National Electric Code (NEC) requites plenum cable (o have special fire-resistant insulation. Plenum cables are coated with Teflon, which does not emit noxious chemicals when ignited, or special fire-resistant PVC, which is called plenum-grade PVC: Therefore, plenum cables are used to route signals throughout the building in the air ducts. Because plenum cables are considerably more expensive than nonplenum cables, traditional PVC coated cables are used everywhere else 412-6-4 Coaxial (Concentric) Transmission Lines In the recent past, parallel-conductor transmission lines were suited only for low data trans- mission rates. At higher transmission rates. their radiation and dielectric losses as well as their susceptibility to external interference were excessive. Therefore, coaxial cables were often used for high data transmission rates to reduce losses and isolate transmission paths. However, moder UTP and STP twisted-pair cables operate at bit rates in excess of 1 Gbps at much lower costs than coaxial cable. Twisted:pair cables are also cheaper. lighter, and easier to work with than coaxial cables. In addition, many extremely high-speed computer networks prefer optical fiber cables to coaxial cables. Therefore, coaxial cable 1s sec.rg less and less use in computer networks, although they are still a very popular transmission line for analog systems, such as cable television distribution networks. The basic coaxial cable consists of a center conductor surrounded + a dielectric ma- terial (insulation), then a concentric (uniform distance from the center) shielding. and fi- nally a rubber enviroamental protection outer jacket. Shielding refers to the woven or stranded mesh (or braid) that surrounds some types of coaxial cables. A coaxial cable with one layer of foil insulation and one layer of braided shielding is referred to as dual shielded. Environments that are subject to exceptionally high interference use quad shielding, which consists of two layers of foil insulation and two layers of braided metal shielding, ‘The center conductor of a coaxial cable is the signal wire and the braider outer conductor is the signal return (ground). The center conductor is separated from the shield by a solid dielectric material or insulated spacers when air is used for the dielec- trie. For relatively high bit rates, the braided outer conductor provides excellent shield- ing against external interference. However. at lower bit rates, the use of shielding is usu- ally not cost effective. : Essentially, there are two basic types of coaxial cables: rigid air filled and solid flexi- ble. Figure 12-12a shows a rigid air coaxial line. Itcan be seen that a tubular outer conductor surrounds the center conductor coaxially and that the insulating material is air. The outer con- ductors physically isolated and separated from the center conductor by space, which is gen- rally filled with Pyrex, polystyrene, or some other nonconductive material. Figure 12-12b 7 ‘shows a solid flexible coaxial cable. The outer conductor is braided, flexible, and coaxial to the center conductor. The insulating material is a solid noncondiictive polyethylene material that provides both support and electrical isolation between the inner and outer conductors. The inner conductor is a flexible copper wire that can be either solid or hollow (cellular), Metallic Cable Transmission Media 523524 ‘spacer Conter conductor Outer ‘conductor @) , Sheath Insulation (solid polyethylene) Flexibie sold copper $ canter condictor Braided shielding (outer conductor) (o) FIGURE 12-12 Cosxial or concentric transmission line: (a) rigid air- filed; (b) solid flexible Rigid air-filled coaxial cables are relatively expensive t manufacture, and to minimize losses. the air insulator must be relatively free of moisture. Solid coaxial ca- bles have lower losses than hollow cables and are easier to construct, install, and main- tain, Both types of coaxial cables are relatively immune to external radiation, radiate litte themselves, and are capable of operating at higher bit rates than their parallel-wire counterparts. For these reasons, coaxial cable is more secure than twisted-pair cable. Coaxial cables can also be used over longer distances and support more stations on a shared-media network than twisted-pair cable The prunary disadvantage of coaxial transmission lines is their poor cost-to-performance ratio. low reliability, and high maintenance. ‘The RG numbering system typically used with coaxial cables refers to cables ap- proved by the U.S. Department of Defense (DoD). The Do) numbering system is used by most cable manufacturers for generic names; however. most manufacturers have developed several variations of each cable using their own product designations. For example, the Belden product number 1426A cross-references to one of several variations of the RG 58/U solid copper-core coaxial cable manufactured by Belden ‘Table 12-3 lists several common coaxial cables and several of their parameters. Keep in mind that these values may vary slightly trom manufacturer to manufacturer and for dif- ferent variations of the same cable manufactured by the same company, 12-6-4-1 Coaxial cable connectors. There bh connectors: standard BNC connectors and 1s) sometimes referred to as “bayonet mount.” as thes cun he easily twisted on or off. N-type connectors are threaded and must be screwed on and off. Several BNC and N-type con- nectors are shown in Figure 12-13, are essentially two types of coaxial ca eN connectors. BNC connectors are Chapter 12.Teble 123 Coaval Cable Characteristics RG-BA-AU 7 046 2 RoSuAAD so 080 a 254 RG-58 foam a 0.65 20 mae, RG-S9/A-AU ey 2 ry ae RG-59 foam x 78 079 20 16.9 19 © © @ © , FIGURE 12-13 _Coatial cable connectors: (a) BNC connector; {b) BNC barrel, fc) BNC; (@) Type; and fe) TypeN barrel 12-7 METALLIC TRANSMISSION LINE EQUIVALENT CIRCUIT 12-7-1 Uniformly Distributed Transmission Lines ‘The characteristics of a transmission line are determined by its electrical properties, such as wire conductivity and insulator dielectric constant, and its physical properties, such as wire diameter and conductor spacing. These properties, in tura, determine the primary elec- trical constants: series de resistance (R), series inductance (L), shunt capacitance (C), and ‘shunt conductance (G). Resistance and inductance occur along the line, whereas capaci- tance and conductance occur between the conductors. The primary constants ":e uniformly distributed throughout the length of the ine and, therefore, are commonly called distributed parameters. To simplify analysis, disjibuted parameters are commonly given for a unit iength of cable to form an artificial electrical model of the ine. The combined parameters Metallic Cable Transmission Medie 525© = capacitance - two conductors separated by an insulator A = resistance ~ opposition to current flow = sof Inductence kage resistance of dielectric. Ry = shunt leakage resistance G= FIGURE 12-14 Twowire parallel transmission line equivalent circuit 526 | 1 Section unit tongth) ——> FIGURE 12-15 Equivalent circuit for a single sectian‘of transmission line terminated in a load equalto Z, are called lumped parameters, For example, series resistance is generally given in ohms per unit length (.., ohms per meter or ohms per foot). i Figure 12-14 shows the electrical equivalent circuit for a metallic two-wire parallel transmission line showing the relative placement of the various lumped parameters. For convenience, the conductance between the two wires is shown in reciprocal form and given as.a shunt leakage resistance (R,). 12-7-2 Transmission Characteristics ‘ ‘The transmission characteristics of a transmission line are called secondary constants and are determined from the four primary constants. The secondary constants are characteristic impedance and propagation constant. 12-7-2-1 Characteristic impedance. For maximum power transfer from the source to the load (ie., no reflected power), a transmission line must be terminited in a purely resistive load equal to the characteristic impedance of the transmission line. The characteristic impedance (2,) of a transmission line is a complex quantity that is expressed in ohms, is ideally independent of line length, and cannot be directly measured. Character- istic impedance (sometimes called surge impedance) is defined as the impedance seen look- ing into an infinitely long line or the impedance seen looking into a finite length of line that is terminated in a purely resistive load with a resistance equal to the characteristic imped- ance of the line. A transmission line stores energy in its distributed inductance and capaci- tance. If a transmission line is infinitely long, it can store energy indefinitely; energy from the source enters the line, and none of itis returned. Therefore, the line acts as a resistor that dissipates all the energy. An infinitely long line can be simulated if a finite line is termi- nated in a purely resistive load equal to Z,; all the energy that enters the line from the source is dissipated in the load (this assumes a totally lossle’s line). Figure 12-15 shows a single section of a transmission line terminated in a load 2, ‘equal to Z,. The impedance seen looking into a line of n such sections is determined from the following equation 2 BaZa + (12-7) where n is the number of sections. For an infinite number of sections, Z}/n approaches 0 if Chapter 12‘Then, zs) ‘Therefore, 2,= \(R+iebg ee (12-9) R + jwl or Zz, -10) jet (12-10) For extremely low frequencies, the resistances dominate and Equation 12-10 simplifies to R 2-2 azn) For extremely high frequencies, the inductance and capacitance dominate and Equation 12-10 simplifies to ee |e iE . aq CNG (12-12) From Equation 12-12, it can be seen that for high frequencies, the characteristic im- pedance of a transmission line approaches a constant, is independent of both frequency and length, and is determined solely by the distributed inductance and capacitance. It can also be seen that the phase angle is 0°. Therefore, Z, looks purely resistive, and all the incident energy is absorbed by the line. From a purely resistive approach, it can easily be seen that the impedance seen look- ing into a transmission line made up of an infinit: number of sections approaches the char- acteristic impedance. This is shown in Figure’ 12-16. Again, for simplicity, only the series resistance R and the shunt resistance R, are considered. The impedance seen looking into the last section of the line is simply the sum of R and R,, Mathematically, Z; is Z,=R+R,= 10+ 100 = 110 ‘Adding a second section, Z,, gives 5 Zi _ ag 4 100X 0 _ 2 Zp = Ra eee = 10+ TO erg = 10 + 5238 = 62:38 and a third section, Zy, is ye BRR = ip + 100. 62.38 : = 10 + OSE = 10 + 38.42 = 48.32 A fourth section, Za, is 100 x 48.32 2, = 10 + oo ASSS = 10 + 32.62 = 4262 100 + 48.32 Metallic Cable Transmission Medi 527FIGURE 12-16 Characteristic impedence of a transmission line of infiite sections or termi ‘nated in load equel to Z, It canbe seen that after each additional section, the total impedance seen looking into the line decreases from its previous value; however, each time the magnitude of the de- crease is less than the previous value. If the process shown above were continued, the im- pedance seen looking into the line will decrease asymptotically toward 37 2, which is the characteristic impedance of the line, ; If the transmission line shown in Figure 12-16 were terminated in a load resistance Z, = 37.9, the impedance seen looking into any number of sections would equal 37 ©, the characteristic impedance. For a single section of line, Z, is R XZ _ 100 x 37 _ 3700 _ yo BaD Rt Rg = 10+ 1995-37 ~ 10 + Tg7 = 37 Adding a second section, Za, is 1 19 4 10X37 _ 19 4 BahaR+R TZ ~ 10+ teg4 37 ~ 10+ 57 = 370 ‘Therefore, if this line were terminated into a load resistance Z, = 37 Q, Z, = 37 ‘Qno mat- ter how many sections are included. ‘The characteristic impedance of a transmission cannot be measured directly, but it .can be calculated using Ohm's law. When a source is connected to an infinitely long line and a voltage is applied, a current flows. Even though the load is open, the circuit is com- plete through the distributed constants of the line. The characteristic impedance is simply the ratio of the source voltage (E,) to the line current (J,). Mathematically, Z, is E z= (2-13) where Z, = characteristic impedance (ohms) E, = source voltage (volts) J, = transmission line current (amps) ‘The characteristic impedance of a two-wire parallel transmission line with an air dielectric can be determined from its physical dimensions (see Figure 12-17) and the formula D 76 log (12-14) where Z, = characteristic impedance (ohms) D = distance between the centers of the two conductors (inches) r= radius of the conductor (inches) i 528 Chapter 12Metallic Cable Transmission Media — © o FIGURE 12-17 Physi dimensions : Pernt Ma NS of transmission lines: (a) owoavire (b) cosxiat-cabie transmission line Example 12-1 Determine the characteristic impedance for an air dielectric two-wire parallel transmission line with 8 Dirratio of 12.22. Solution Substituting into Equation 12-14, we obtain 2, = 276 log(12.22) = 300 ohms ‘The characteristic impedance of a concentric coaxial cable can also be determined from its physical dimensions (see Figure 12-17b) and the formula 138 (|,.D 2, = BB (tog? -15) hs BE tg 2) 2.18) where Z, = characteristic impedance (ohms) D = inside diameter of the outer conductor (inches) . \ lative dielectric constant of the insulating material (unitless) Example 12-2 Determine the characteristic impedance for an RG-59A coaxial cable with the following specifica- tions: d = 0.025 inches, D = 0.15 inches, and e, = 2.23, Solution Substituting into Equation 12-15, we obtain = 138_(,,,0:15 in.) _ 2. Bh (fig) = 190 For extremely high frequencies, characteristic impedance can be determined from the indue- tance and capacitance of the cable using the following formula: Z, iE (12-16) Determine the characteristic impedance for an RG-59A coaxial cable with the following specifica- tions: L = 0.118 pH/ft and C = 21 pF/ft. Example 12-3 529530 Solution Substituting into Equation 12-16 gives us fonts x 10H weap wf EME a0 Z=N C= Vax 10 F ‘Transmission lines can be summarized thus far as follows: 1. The input impedance of an infinitely long line at radio frequencies resistive and equal toZ,. . 2. Electromagnetic waves travel down the |i called nonresonant. 3. The ratio of voltage to current at any point along the line is equal 10 2x 4. The incident voltage and current at any point along the line are in phase. 5. Line losses on a nonresonant line are minimum per unit length. 6. Any transmission line that is terminated in a purely resistive load equal to 2, acts as if it were an infinite line, ‘ a. Z=2, 1b, There are no reflected waves. ¢. Vand / are in phase. . There is maximum transfer of power from source to load. ine without reflections; such a line is 12-7-2-2Propagation constant. Propagation constant (sometimes called propagation coefficient) is used to express the attenuation (Signal loss) and the phase shift per unit length ofa transmission line. As a signal propagates down a transmission line, its amplitude de~ creases with distance traveled. The propagation constant is used to detennine the reduction in voltage or current with distance as a TEM wave propagates down a transmission line. For an infinitely long line, ll the incident power is dissipated inthe resistance of the wire asthe ‘wave propagates down the line. Therefore, with an infinitely long line ora ine that Looks in- finitely long, suchas finite lin terminated inamatched load (2, = Z,),no energy isreturned or reflected back toward the source. Mathematically, the propagation constant is yaatsB 2-17) where = propagation constant (unitless) c= attenuation coefficient (nepers per unit length) ‘ B = phase shift coefficient (radians per unit length) ‘The propagation constant is a complex quantity defined by = VRF JOLNG + J0C) (12-18) Because a phase shift of 2x rad occurs over a distance of one wavelength, (12-19) (02-20) and B= oVIC (12-21) ‘The current and voltage distribution along a transmissio. line that is terminated in a oad equal to its characteristic impedance (a matched line) are determined from the formulas rele" (12-22) ve vem (22-23) Chapter 12where J, = current at the source end of the line (armps) V, = voltage at the source end of the line (volts) ‘Y= propagation constant ; ''= distance from the source at which the current or voltage is determined For a matched load Z, = Z, and for a given length of cable /, the loss in signal volt- ‘98¢ oF current is the real part of vi, and the phase shift is the imaginary part. 28 WAVE PROPAGATION ON A MI TRANSWy ‘ IETALLIC Electromagnetic waves travel atthe speed of light when propagating through a vacuurn and nearly at the speed of light when propagating through air. However, in metallic transmis- sion lines, where the conductor is generally copper and the dielectric materials vary con- siderably with cable type, an electromagnetic wave travels much more slowly. 12-8-1 Velocity Factor. and Dielectric Constant Velocity factor (sometimes called velocity constant) is defined simply as the ratio of the ac- tual velocity of propagation of an electromagnetic wave through a given medium to the ve- locity of propagation through 2 vacuum (free space). Mathematically, yelocity factor is (12.24) where V; = velocity factor (unitless) V, = actual velocity of propagation (meters per second) ¢ = velocity of propagation through a vacuum (3 X 10® m/s) and rearranging Equation 12-24 gives Vxe=V, 2-73) The velocity at which an electromagnetic wave travels through a transmission line depends on the dielectric constant of the insulating material separating the two conductors. ‘The velocity factor is closely approximated with the formula : a aa -26) Ve (02-26) where ¢,is the dielectric constant of a given material (the permattivity of the material rela- tive to the permittivity of a vacuum — the ratio ele, where ¢ is the permittivity of the di- electric and ¢, is the permittivity of air) ‘Velocity factor is sometimes given as a percentage, which is simply the absolute ve- locity factor multiplied by 100, For example, an absolute velocity factor V, = 0.62 may be stated as 62%. Dieleciric constant is simply the relative permittivity of a material. The relative di- electric constant of air is 1.0006. However, the dielectric constant of materials commonly used in transmission lines ranges from 1.4872 to 7.5, giving velocity factors from 0.3651 to 0.82. The velocity factors and relative dielectric constants of several insulating materi- als arc listed in Table 12-4. Dielectric constant depends on the type of insulating material used, Inductors store ‘magnetic energy, and capacitors store electric energy. It takes a finite amount of time for an inductor or a capacitor to take on or give up energy. Therefore, the velocity at which an elec- tromagnetic wave propagates along a transmission line varies with the inductance and Metallic Cable Transmission Media 591532 Table 12-4 Velocity Factor and Dielactrie Constant 1.0000 1.0000 0.9997 0006, ' 0.8200 1487 0.6901 2.1000 0.46637 2.2700 0.6325 2.5000 0.6325 3 a Polyvinyl chloride 0.5505 3 Rubber osm 3.0000 Mics oar 5.0008 Glass 03651 7,500 capacitance of the cable. It can be shown that time T = VLC. Therefore, inductance, ca ppacitance, and velocity of propagation are mathematically related by the formula velocity X time = distance distance _ D (12-27) Therefore ime ‘Substituting VEC for time yields v,=-2. (12-28) VEC If distance is normalized to 1 meter, the velocity of propagation for a lossless transmission Tine is 1, _ _1_meters “oie. ~ Vee second aa where velocity of propagation (meters per second) seconds ‘L= inductance per unit length (H/m) capacitance per unit length (Fim) Example 12-4 For a given length of RG 8A/U coaxial cable with a distibuted capacitance C tributed inductance L = 241.56 nH/m, and a relative dielectric constant ¢, = locity of propagation and the velocity factor. Solution From Equation 12-16, 6.6 pm, a dis- 3, determine the ve- 1 a 7 > ese ioyaaise To | 707 * Wav From Equation 12-24, y= 207 X10! m/s 7° "3x 108 m/s 0.69 From Equaticu 12-26, 1 Masta Chapter 12of Because wavelength is directly proportionsl to velocity and the velocity of ha gre ‘TEM wave varies with dielectric constant, the wavelength of a TEM wave also varies wit ee constant. Therefore, for ‘transmission media other than free space, Equation 12-3 can beres Ao oe ee (12-30) (ff Ope, 12-8-2 Electrical Length of a Transmission Line a ‘The length of a transmission line relative tothe length of the wave propagating down itis an important consideration when analyzing wansmission-line behavior. Atlow frequencies (ong wavelengths), the voltage along the line remains relatively constant However, for high fre- quencies, several wavelengths of the signal may be present on the line atthe same time. There fore, the voltage along the ine may vary appreciably. Consequently, the length of a transmis- sion line is often given in wavelengths rather than in linear dimensions, Transmission-line Phenomena apply to long lines. Generally, a transmission line is defined as long if its length exceeds 1/16th of a wavelength; otherwise, itis considered short. A given length of transmis- sion line may appear shor at one frequency and long at another frequency. For example, a 10- ‘m length of transmission line at 1000 He is short (A = 300,000 m: 10 mis only a small frac- tion of a wavelength). However, the same line at 6 GHz is long (A = 5 cm; the line is 200 wavelengths long). It will be apparent later in this chapter, in Chapter 9, and in Appendix A thatelectrical length is used extensively for ransmission-line calculations and antenna design. 12-83 Delay Lines |In the previous section, it was shown that the velocity of propagation of an electromagnetic ‘wave depends on the media in which itis traveling. The velocity of an electromagnetic wave in free space (i.e., a vacuum) is the speed of light (3 x 10° mvs), and the velocity is slightly slower through the Earth's atmosphere (ie,, ait). The velocity of propagation through a ‘metalic ansmission line is effected by the cable's electrical constants: inductance and ca- pacitance. The velocity of propagation of a metallic transmission line is somewhat less than the velocity of propagation through either free srce or the Earth's atmosphere. Delay lines are transmission lines designed to intentionally introduce a time delay in the path of an electromagnetic wave, The amount ~, time delay is a function of the transmission line's inductance and capacitance. The inductance provides an opposition tochanges in current, as does the charge and discharge times of the capacitance, Delay time is calculated as follows: 14 LC (seconds) (12-31) where tz = time delay (seconds) L = inductance (henrys) C = capacitance (farads) If inductance and capacitance are given per unit length of transmission line (such as per foot or per meter), the time delay will also be per unit length (i.e., 1.5 ns/meter). ‘The time delay introduced by a length of coaxial cable is calculated with the follow- ing formula: w= 1016 € 42-32) where € is the dielectric constant of cable. 12-9 TRANSMISSION LINE LOSSES For analysis purposes, metallic transmission lines are often considered to be totally lossless. In reality, however. there are several ways in which signal power is lost in a ‘transmission line, They include conductor loss, radiation loss, dielectric heating loss, Metallic Cable Tranismission Media 533534 Curent Sonsity Moderate ce requ sion FIGURE 12-18 Isolated round | teaveney conductor showing magnetic lines of ade flux, current distibutons, and the positon skin effect 2 Cable manufacturers generally lump all cable losses together coupling ‘75, and corona, x unit length (e.g., dB/m, dB/ft, and so on). and specify them as attenuation loss in decibels pes 12.91 Conductor Losses Because electrical current flows through a metallic transmission line and ‘he line has a fi- nite resistance, there is an inherent and unavoidable power loss. This is sometimes called conductor loss or conductor heating loss and is simply an 7R power loss. Because resis- tance is distributed throughout a transmission line, conductor loss is directly proportional to the square of the line length. Also, because power dissipation is directly proportional to the ‘square of the current, conductor loss is inversely proportional to characteristic impedance. To reduce conductor loss, simply shorten the transmission line or use a larger-diameter wire (i:e., one with less resistance). Keep in mind, however, that changing the wire diameter also changes the characteristic impedance and, consequently, the current. Conductor loss depends somewhat on frequency because of a phenomenon called the skin effect. When current flows through an isolated round wire, the magnetic flux associ- ‘ated with it is in the form of concentric circles surrounding the wire core. This is shown in Figure 12-18. From the figure, it can be seen that the flux density near the center of the con- ductor is greater than itis near the surface. Consequently, the lines of flux near the center of the conductor encircle the current and reduce the mobility of the encircled electrons. This is a form of self-inductance and causes the inductance near the center of the conductor to be greater than at the surface. Therefore, at high frequencies, most of the current flows along the surface (outer skin) of the conduct rather than near its center. This is equivalent to reducing the cross-sectional area of the conductor and increasing the opposition to cur- rent flow ({.e., resistance). The additional opposition has a 0° phase angle and is, therefore, a resistance and not a reactance. Therefore, the ac resistance of the conductor is proportional to the square root of the frequency. The ratio of the ac resistance to the de resistance of a conductor is called the resisiance ratio. Above approximately 100 MHz, the center of a conductor can be Chapter 12completely removed and have absolutely n0 effect on the total conductor loss or EM ‘wave propagation, jon of a Conductor loss in metallic transmission lines varies from as low as a fraction 0! Aecibel per 100 meters for rigid air dicleetric coaxial cable to as high as 200 dB per 100 me- tes fora solid dielectric flexible coaxial cable. Because both [°R losses and dielectric losse~ ‘axe proportional to length, they are generally lumped together and expressed in decibels o! loss per unit length (.e., dB/ti). 12-82 Dielectric Heating Losses A difference of Potential between two conductors of a metallic transmission line causes di- electric heating. Heat is a form of energy and must be taken from the energy propagating, down the line. For ai- dielectric transmission lines, the heating loss is negligible. However, for solid-core ‘transmission lines, dielectric heating loss increases with frequency. 12-9-3 Radiation Losses Ufa separation between conductors in a metallic transmission line is an appreciable frac- tion of a wavelength, the electrostatic and electromagnetic fields that surround the conduc- tor cause the line to act as if it were an antenna and transfer energy to any nearby conduc- es material. The energy radiated is called radiation loss and depends on dielectric {Paterial conductor spacing, and length of the transmission line. Radiation losses are re~ duced by properly shielding the cable, Therefore, shielded cables (such as STP and coaxial (able) have less radiation loss than unshielded cables (such as twin lead, open wire, and UTP). Radiation loss is also directly proportional to frequency. 128-4 Coupling Losses Coupling loss occurs whenever a connection is made to or from a transmission line or when {wo sections of transmission line are-connected together. Mechanical connections are dis Conti uities, which are locations where dissimilar matenals meet. Discontinuities tend to heat up, radiate energy, and dissipate power. 12-35 Corona Corona is a luminous discharge that occurs’ between the two conductors of a trans- mission line when the difference of potential between them exceeds the breakdown Voltage of the dielectric insulator. Generally, when corona occurs, the transmission line is destroyed 12-10 INCIDENT AND REFLECTED WAVES Metallic Cable Transmission Media An ordinary transmission line is bidirectional; power can propagate equally well in both di- Fections. Voltage that propagates from the source toward the load is called incident voltage, and voltage that propagates from the load toward the source is called reflected voltage. Sim- ilarly, there are incident and reflected currents. Consequently, incident power propagates toward the load, and reflected power propagates toward the source. Incident voltage and current are always in phase for a resistive characteristic impedance. For an infinitely long line, all the incident power is stored by the line, and there is no reflected power. Also, if the ine is terminated in a purely resistive load equal to the characteristic impedance of the line, the load absorbs all the incident power (this assumes a lossless line). For a more practical definition, reflected power is the portion of the incident power that was not absorbed by the Joad, Therefore, the reflected power can never exzed tne incident power. 12-10-1. Resonant and Nonresonant Transmission Lines A transmission line with no reflected power is called a flar or nonresonant line. A trans- mission line is nonresonant if itis of infinite length or if itis terminated with a resistive 535Retiected wave FIGURE 12-19 Source, load, transmission ling, and their corresponding incident and reflected waves load equal in ohmic value to the characteristic impedance of the transmission line. On aflat lune, the voltage and current are constant throughout its length, assuming no losses, When the load is not equal to the characteristic impedance of the line, some of the incident power is reflected back toward the source. If the load is either a short or an open circuit, all the incident power is reflected back toward the source. If the source were replaced with an ‘open or a short and the line were lossless, energy present on the line would reflect back and forth (oscillate) between the source and load ends similar to the way energy is transferred back and forth between the capacitor and inductor in an LC tank circuit. This is called a resonant transmission line. In a resonant line, energy is alternately transferred between the magnetic and electric fields of the distributed inductance and capacitance of the line. Figure 12-19 shows a source, transmission line, and load with their corresponding incident and reflected waves. 1210-2 Reflection Coefficient The reflection coefficient (sometimes called the coefficient of reflection) is a vector quan- ‘ity that represents.the ratio of reflected voltage to incident voltage or reflecte. current to incident current. Mathematically, the reflection coefficient is gamma, I’, defined by Et Pa Fort (12-33) where I = reflection coefficient (unitless) E, = incident voltage (volts) E, = reflected voltage (volts) 1, = incident current (amps) 1, = reflected current (amps) From Equation 12-33 it can be seen that the maximum and worst-case value for is 1 (E, = E,), and the minimum value and ideal condition occur when T = 0 (E, = 0). 12-11 STANDING WAVES 536 When Z, = Z,, all the incident power is absorbed by the load. This is called a matched line. When Z, # Z,, some of the incident power is absorbed by the load, and some is returned (reflected) to the source. This is called an unmatched or mismatched line. With a mismatched line, there are two electromagnetic waves, traveling in opposite direc- tions, present on the line at the same time (these waves are in fact called traveling waves), The two traveling waves set up an interference pattern known as a standing wave. This is shown in Figure 12-20. As the incident and reflected ‘waves pass each other, stationary patterns of voltage and current are produced on the line. These sta- Chapter 12te FIGURE 12:20 Developing o standing weve on o trensmis- sion line: (a) incident wave; (b) reflected wave; (c) standing wave tionary waves are called standing waves because they appear to remain in a fixed posi- tion on the line, varying only in amplitude. The standing wave has minima (nodes) sep- arated by a half wavelength of the traveling waves and maxima (antinodes) also sep: rated by a half wavelength 12-11-1 Standing-Wave Ratio ‘The standing-wave ratio (SWR) is defined as the ratio of the maximum voltage to the min- imum voltage or the maximum current to the minimum current of a standing wave on a transmission line. SWR is often called the voltage standing-wave ratio (VSWR). Essen- tially, SWR is a measure of the mismatch between the load impedance and the characteris- tic impedance of the transmission line. Mathematically, SWR is V, SWR = Fr (unittess) (12-34) ‘The voltage maxima (V nq.) occur when the incident and reflected waves are in phase (ie., their maximum peaks pass the same point on the line with the same polarity), and the voltage minima (Vj) occur when the incident and reflected waves are 180° out of phase. Mathematically, Vinx 200 Vein (12-35) (12-36) ‘Therefore, Equation 12-34 can be rewritten as Vou f+ E, SWRe YEE eet From Equation 12-37, it can be seen that when the incident and reflected waves are equal in amplitude (a total mismatch), SWR = infinity. This is the worst-case condition. ‘Also, from Equation 12-37, it can be seen that when there is no reflected wave (E, = 0), SWR = EE, of 1. This condition occurs when Z, = Z;, and is the ideal situation Metallic Cable Transmission Media : 537538 ‘The standing-wave ratio can also be written in terms of I. Rearranging Equation 12-34 yields ‘earranging Equat TEE, (12.38) Substituting into Equation 12-37 gives us (12-39) Factoring out £; yields (12-40) Cross multiplying gives SwRd ~T) = 147 (12-41) SWR - SWRI (02-42) SWR =1+9T+(SWRyr (12-43) SWR-1=Ta + swe) (12-44) 8 swe +1 (12-45) Example 12-5 7 For a transmission line with incident voltage E; = 5 V and reflected voltage E, = 3 V, determine a, Reflection coefficient. b. SWR. Solution a. Substituting into Equation 12-33 yields E THE Substiuing into Equation 12-37 giver as a1 ‘When the load is purely resistive, SWR can also be expressed as a ratio of the char- acteristic impedance to the load impedance or vice versa, Mathematically, SWR is bo tn SWR = 7" or 7” (whichever gives an SWR greater than 1) (12-46) ‘The numerator and denominator for Equation 12-46 are chosen such that the SWR is always a number greater than 1 to avoid confusion and comply with the convention estab- lished in Equation 12-37. From Equation 12-46, it can be seen that a load resistance Z, = 22, gives the same SWR as a load resistance Z, = Z,/2; the degree of mismatch is the same. The disadvantages of not having a matched (flat) transmission line can be summa- rized as follows: 1, One hundred percent of the source incident power is not absorbed by the Ivad. » The dielectric separating the two conductors can break down and cause corona as a result of the high-voltage standing-wave ratio. 3. Reflections and re-teflections cause more power loss. Chapter 12 ‘4. Reflections cause ghost images. 5. Mismatches cause noise interference. Although itis highly unlikely that a transmission line will be terminated in & ee iselther an open ,ra short circuit, these conditions ae examined because they illustrate Ne ‘worst-possible cond:ions that could occur and produce standing waves that are represer tative of less severe conditions. 12-11-2 ‘Standing Waves on an Open Line ‘When incident wa¥es of voltage and current reach an open termination, none of the power is absorbed; it is all reflected back toward the source. The incident voltage wave is reflected in exactly the same manner as if it vere toccontinue down an infinitely long line. However, the incident current is reflected 180° reversed from how it would have continued if the line ‘were not open. As the incident and reflected waves pass, standing waves are produced on the line, Figure 12-20 shows the voltage and current standing waves on a transmission line that is terminated in an open circuit. Itcan be seen that the voltage standing wave has a max- imum value at the open end.and a minimum value one-quarter wavelength from the open. ‘The current standing wave has a minimum value at the open end and a maximum value one~ ‘quarter wavelength from the open. It stands to reason that maximum voltage occurs across an open and there is minimum current. The characteristics of a transmission line terminated in an open can be summarized as follows’ 1, The voltage incident wave is reflected back just as if it were to continue (i.¢., nO phase reversal), 2. The current incident wave is reflected back 180° from how it would have continued. 3. The sum of the incident and reflected current waveforms is minimum at the open. 4. The sum of the incident and reflected voltage waveforms is maximum atthe open. From Figure 12-21, it can also be seen that the voltage and current standing waves Tepeat every one-half wavelength. The impedance at the open end Z = Vinax/lmin and is ‘maximum. The impedance one-quarter wavelength from the open Z = Vin(max and is min- imum, Therefore, one-quarter wavelength from vhe open an impedance inversion occurs, and additional impedance inversions occur each one-quarter wavelength Figure 12-21 shows the development of a voltage standing wave on a transmission line that is terminated in an open circuit, Figure 12-22 shows an incident wave propagat- ing down a transmission line toward the load. The wave is traveling at approximately the speed of light; however, for illustration purposes, the wave has been frozen at eighth- wavelength intervals, In Figure 12-22a, it can be seen that the incident wave has not reached the open. Figure 12-22b shows the wave one time unit later (for this example, the wave travels one-eighth wavelength per time unit). As you can see, the wave has moved ry ' Le cotton Source | Sean end tI pen 1 1 ' ' \ 1 od $1 tb it tA et FIGURE 12-21 Voltage and current standing waves on a transmission line that. is terminated in an open circuit Metallic Cable Transmission Media 539540 ~ () Cc o ® L 1 I 1 i HRA Ah FIGURE 12-22 Incident and reflected waves on @ transmission ling terminated in an open circuit (Continued) ‘one-quarter wavelength closer to the open. Figure 12-22c shows the wave just as it arrives. at the open. Thus far, there has been no reflected wave and, consequently, no standing wave. Figure 12-22d shows the incident and reflected waves one time Unit after the inci- dent wave has reached the open; the reflected wave is propagating away from the open. Figures 12-22e, f,and g show the incident and reflected waves for the next three time units. In Figure 12-22e, itcan be seen that the incident and reflected waves are at their maximum Chapter 12