Transmission Lines PDF

WELFREDO B. VELEZ JR. TRANSMISSION LINES DEE – EcE UMTC – VISAYAN CAMPUS TRANSMISSION LINES is a metallic conductor system that is used to transfer electrical energy from one point to another. More specifically, a transmission line is two or more conductors separated by an i...

WELFREDO B. VELEZ JR. TRANSMISSION LINES DEE – EcE UMTC – VISAYAN CAMPUS TRANSMISSION LINES is a metallic conductor system that is used to transfer electrical energy from one point to another. More specifically, a transmission line is two or more conductors separated by an insulator, such as a pair of wires or a system of wire pairs. A transmission line can be as short as a few inches or it can span several thousand miles. Transmission lines can be used to propagate dc or low-frequency ac (such as 60 cycle power and audio signals); they can also be used to propagate very high frequencies (such as intermediate and radio- frequency signals). TRANSMISSION LINES The two primary requirements of a transmission line are that 1. the line introduce minimum attenuation to the signal 2. the line not radiate any of the signal as radio energy. All transmission lines and connectors are designed with these requirements in mind. TRANSMISSION LINES When propagating low-frequency signals, transmission-line behavior is rather simple and quite predictable. However, when propagating high- frequency signals, the characteristics of transmission lines become more involved and their behavior somewhat peculiar to a student of lumped constant circuits and systems. TRANSVERSE ELECTROMAGNETIC WAVES Propagation of electrical power along a transmission line occurs in the form of transverse electromagnetic (TEM) waves. A wave is an oscillatory motion. The vibration of a particle excites similar vibrations in nearby particles. A TEM wave propagates primarily in the nonconductor (dielectric) that separates the two conductors of a transmission line. Therefore, a wave travels or propagates itself through a medium. A transverse wave is a wave in which the direction of displacement is perpendicular to the direction of propagation. TRANSVERSE ELECTROMAGNETIC WAVES A surface wave of water is a transverse wave. A wave in which the displacement is in the direction of propagation is called a longitudinal wave. Sound waves are longitudinal. An electromagnetic (EM) wave is a wave produced by the acceleration of an electric charge. In a conductor, current and voltage are always accompanied by an electric (E) and a magnetic (H) field in the adjoining region of space. TRANSVERSE ELECTROMAGNETIC WAVES TRANSVERSE ELECTROMAGNETIC WAVES It can be seen that the E and H fields are perpendicular to each other (at 90° angles) at all points. This is referred to as space quadrature. Electromagnetic waves that travel along a transmission line from the source toward the load are called incident waves, and those that travel from the load back toward the source are called reflected waves. CHARACTERISTICS OF ELECTROMAGNETIC WAVES Wave velocity Waves travel at various speeds, depending on the type of wave and the characteristics of the propagation medium. Sound waves travel at approximately 1100 f/s in the normal atmosphere. In free space (a vacuum), TEM waves travel at the speed of light, c = 186,283 statute mi/s or 299,793,800 m/s, rounded off to 186,000 mi/s and 3 x 108 m/s. CHARACTERISTICS OF ELECTROMAGNETIC WAVES Frequency and wavelength The oscillations of an electromagnetic wave are periodic and repetitious. Therefore, they are characterized by a frequency. The rate at which the periodic wave repeats is its frequency. The distance of one cycle occurring in space is called the wavelength and is determined from the following fundamental equation distance = velocity * time EXAMPLE For an operating frequency of 450 MHz, what length of a pair of conductors is considered to be a transmission line? (A pair of conductors does not act as a transmission line unless it is at least 0.1 λ long.) and Calculate the physical length of the transmission line in with a 3 ⁄ 8 λ long. TYPES OF TRANSMISSION LINES Transmission lines can be generally classified as balanced or unbalanced. With a balanced transmission line, both conductors carry current and the current in each wire is 180° out of phase with the current in the other wire. With an unbalanced line, one wire is at ground potential, while the other wire carries all of the current. Both conductors in a balanced line carry current and the signal currents are equal magnitude with respect to electrical ground but travel in opposite directions. TYPES OF TRANSMISSION LINES Currents that flow in opposite directions in a balanced wire pair are called metallic circuit currents. Currents that flow in the same direction are called longitudinal currents. A balanced pair has the advantage that most noise interference is induced equally in both wires, producing longitudinal currents that cancel in the load. BALANCED LINE is one in which neither wire is connected to ground. Instead, the signal on each wire is referenced to ground. The same current flows in each wire with respect to ground, although the direction of current in one wire is 180° out of phase with the current in the other wire. UNBALANCED LINE In an unbalanced line, one conductor is connected to ground. The twisted-pair line may be used in a balanced or an unbalanced arrangement, although the balanced form is more common. PARALLEL-CONDUCTOR TRANSMISSION LINES Open-wire transmission line is a two-wire parallel conductor. It consists simply of two parallel wires, closely spaced and separated by air. Nonconductive spacers are placed at periodic intervals for support and to keep the distance between the conductors constant. The distance between the two conductors is generally between 2 and 6 in. PARALLEL-CONDUCTOR TRANSMISSION LINES Twin-lead Twin-lead is another form of two-wire parallel conductor transmission line and it is often called ribbon cable. essentially the same as an open-wire transmission line except that the spacers between the two conductors are replaced with a continuous solid dielectric. Typically, the distance between the two conductors is 5/16 in. Common dielectric materials are Teflon and polyethylene. PARALLEL-CONDUCTOR TRANSMISSION LINES Twisted-pair cable is formed by twisting together two insulated conductors and are often stranded in units, and the units are then cabled into cores. The cores are covered with various types of sheaths, depending on their intended use. Neighboring pairs are twisted with different pitch (twist length) to reduce interference between pairs due to mutual induction. PARALLEL-CONDUCTOR TRANSMISSION LINES Shielded cable pair To reduce radiation losses and interference, parallel two wire transmission lines are often enclosed in a conductive metal braid. The braid is connected to ground and acts like a shield. The braid also prevents signals from radiating beyond its boundaries and keeps electromagnetic interference from reaching the signal conductors. Consists of two parallel wire conductors separated by a solid dielectric material. The entire structure is enclosed in a braided conductive tube, then covered with a protective plastic coating. CONCENTRIC OR COAXIAL TRANSMISSION LINES Parallel-conductor transmission lines are suitable for low-frequency applications. However, at high frequencies, their radiation and dielectric losses, as well as their susceptibility to external interference, are excessive. Therefore, coaxial conductors are used extensively for high-frequency applications, to reduce losses and to isolate transmission paths. The basic coaxial cable consists of a center conductor surrounded by a concentric (uniform distance from the center) outer conductor. At relatively high operating frequencies, the coaxial outer conductor provides excellent shielding against external interference. However, at lower frequencies, the shielding is ineffective. Also, a coaxial cable's outer conductor is generally grounded, which limits its use to unbalanced applications. CONCENTRIC OR COAXIAL TRANSMISSION LINES Two types of coaxial cables 1. Rigid air filled 2. Solid flexible lines RIGID AIR FILLED the center conductor is surrounded coaxially by a tubular outer conductor and the insulating material is air. The outer conductor is physically isolated and separated from the center conductor by a spacer, which is generally made of Pyrex, polystyrene, or some other nonconductive material. Rigid air-filled coaxial cables are relatively expensive to manufacture, and to minimize losses, the air insulator must be relatively free of moisture. SOLID FLEXIBLE LINES The outer conductor is braided, flexible, and coaxial to the center conductor. The insulating material is a solid nonconductive 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 either be solid or hollow. Solid coaxial cables have lower losses, are easier to construct, and are easier to install and maintain. Both types of coaxial cables are relatively immune to external radiation, radiate little them selves, and can operate at higher frequencies than can their parallel-wire counterparts. COAXIALCABLEAPPLICATIONS CONNECTOR Most transmission lines terminate in some kind of connector, a device that connects the cable to a piece of equipment or to another cable. An ordinary ac power plug and outlet are basic types of connectors. Special connectors are used with parallel lines and coaxial cable. Connectors, ubiquitous in communication equipment, are often taken for granted. This is unfortunate, because they are a common failure point in many applications. COAXIAL CABLE CONNECTORS requires special connectors that will maintain the characteristics of the cable. Although the inner conductor and shield braid could theoretically be secured with screws as parallel lines, the result would be a drastic change in electrical attributes, resulting in signal attenuation, distortion, and other problems. Thus coaxial connectors are designed not only to provide a convenient way to attach and disconnect equipment and cables but also to maintain the physical integrity and electrical properties of the cable. COAXIAL CABLE CONNECTORS The choice of a coaxial connector depends on the type and size of cable, the frequency of operation, and the application. The most common types are the PL-259 or UHF, BNC, F, SMA, and N-type connectors. The PL-259, which is also referred to as a UHF connector, can be used up to low UHF values (less than 500 MHz), although it is more widely used at HF and VHF. It can accommodate both large (up to 0.5-in) and small (0.25-in) coaxial cable. BNC connectors are widely used on 0.25-in coaxial cables for attaching test instruments, such as oscilloscopes, frequency counters, and spectrum analyzers, to the equipment being tested. BNC connectors are also widely used on 0.25-in coaxial cables in LANs and some UHF radios. PL-259 MALE CONNECTOR BNC CONNECTORS CONNECTOR The SMA connector is characterized by the hexagonal shape of the body of the male connector. Like the BNC connector, it is used with smaller coaxial cable. CONNECTOR The least expensive coaxial cable connector is the F-type connector, which is widely used for TV sets, VCRs, DVD players, and cable TV. The shield of the coaxial cable is crimped to the connector, and the solid wire center conductor of the cable, rather than a separate pin, is used as the connection. A hex-shaped outer ring is threaded to attach the plug to the mating jack. CONNECTOR Another inexpensive coaxial connector is the well-known RCA phonograph connector, which is used primarily in audio equipment. Originally designed over 60 years ago to connect phonograph pick-up arms from turntables to amplifiers, these versatile and low-cost devices can be used at radio frequencies and have been used for TV set connections in the low VHF range. CONNECTOR The best-performing coaxial connector is the N-type connector, which is used mainly on large coaxial cable at the higher frequencies, both UHF and microwave. N-type connectors are complex and expensive, but do a better job than other connectors in maintaining the electrical characteristics of the cable through the interconnections. TRANSMISSION-LINE EQUIVALENT CIRCUIT 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 turn, determine the primary electrical constants: series dc resistance (R), series inductance (L), shunt capacitance (C), and shunt conductance (G). Resistance and inductance occur along the line, whereas capacitance and conductance occur between the two conductors. The primary constants are uniformly distributed throughout the length of the line and are therefore commonly called distributed parameters. TRANSMISSION-LINE EQUIVALENT CIRCUIT When the length of a transmission line is longer than several wavelengths at the signal frequency, the two parallel conductors of the transmission line appear as a complex impedance. The wires exhibit considerable series inductance whose reactance is significant at high frequencies. In series with this inductance is the resistance of the wire or braid making up the conductors, which includes inherent ohmic resistance plus any resistance due to skin effect. Furthermore, the parallel conductors form a distributed capacitance with the insulation, which acts as the dielectric. TRANSMISSION-LINE EQUIVALENT CIRCUIT In addition, there is a shunt or leakage resistance or conductance (G) across the cable as the result of imperfections in the insulation between the conductors. The result is that to a high-frequency signal, the transmission line appears as a distributed low-pass filter consisting of series inductors and resistors and shunt capacitors and resistors This is called a lumped model of a distributed line. TRANSMISSION-LINE EQUIVALENT CIRCUIT In the simplified equivalent circuit, the inductance, resistance, and capacitance have been combined into larger equivalent lumps. The shunt leakage resistance is very high and has negligible effect, so it is ignored. In short segments of the line, the series resistance of the conductors can sometimes be ignored because it is so low as to be insignificant. TRANSMISSION-LINE EQUIVALENT CIRCUIT To simplify analysis, distributed parameters are commonly lumped together per a given unit length to form an artificial electrical model of the line. For example, series resistance is generally given in ohms per mile or kilometer. TRANSMISSION-LINE EQUIVALENT CIRCUIT An RF generator connected to such a transmission line sees an impedance that is a function of the inductance, resistance, and capacitance in the circuit the characteristic or surge impedance Zo. If we assume that the length of the line is infinite, this impedance is resistive. The characteristic impedance is also purely resistive for a finite length of line if a resistive load equal to the characteristic impedance is connected to the end of the line. TRANSMISSION-LINE EQUIVALENT CIRCUIT For an infinitely long transmission line, the characteristic impedance Zo is given by the formula Zo = (L/C)^1/2 The formula is valid even for finite lengths if the transmission line is terminated with a load resistor equal to the characteristic impedance. This is the normal connection for a transmission line in any application. In equation form, TRANSMISSION-LINE EQUIVALENT CIRCUIT If the line, load, and generator impedances are made equal, as is the case with matched generator and load resistances, the criterion for maximum power transfer is met. An impedance meter or bridge can be used to measure the inductance and capacitance of a section of parallel line or coaxial cable to obtain the values needed to calculate the impedance. In practice, it is unnecessary to make these calculations because cable manufacturers always specify impedance. CHARACTERISTIC IMPEDANCE For maximum power transfer from the source to the load (i.e., no reflected energy), a transmission line must be terminated in a purely resistive load equal to the characteristic impedance of the line. The characteristic impedance (Zo) of a transmission line is a complex ac quantity which is expressed in ohms, is totally independent of both length and frequency, and cannot be measured directly. Characteristic impedance (which is sometimes called surge impedance) is defined as the impedance seen looking into an infinitely long line or the impedance seen looking into a finite length of line which is terminated in a purely resistive load equal to the characteristic impedance of the line. CHARACTERISTIC IMPEDANCE A transmission line stores energy in its distributed inductance and capacitance. If the line is infinitely long, it can store energy indefinitely; energy from the source is entering the line and none is returned. Therefore, the line acts like a resistor that dissipates all of the energy. An infinite line can be simulated if a finite line is terminated in a purely resistive load equal to Zo; all of the energy that enters the line from the source is dissipated in the load (this assumes a totally lossless line). CHARACTERISTIC IMPEDANCE The impedance seen looking into a line of n such sections is determined from the following expression: If CHARACTERISTIC IMPEDANCE For extremely low frequencies, the resistances dominate For extremely high frequencies, the inductance and capacitance dominate EXAMPLE Find the Zo CHARACTERISTIC IMPEDANCE The characteristic impedance of a two-wire parallel transmission line with an air dielectric can be determined from its physical dimensions EXAMPLE Determine the characteristic impedance for an air dielectric two- wire parallel transmission line with a D/r ratio = 12.22. CHARACTERISTIC IMPEDANCE The characteristic impedance of a concentric coaxial cable can also be determined from its physical dimensions EXAMPLE Determine the characteristic impedance for a RG-59A coaxial cable with the following specifications: L = 0.118 uH/ft, C = 21 pF/ft, d = 0.25 in., D = 0.87 in., and € = 1. TRANSMISSION LINES The input impedance of an infinitely long line at radio frequencies is resistive and equal to Zo. Electromagnetic waves travel down the line without reflections; such a line is called non-resonant. The ratio of voltage to current at any point along the line is equal to Zo. The incident voltage and current at any point along the line are in phase. TRANSMISSION LINES Line losses on a non-resonant line are minimum per unit length. Any transmission line that is terminated in a purely resistive load equal to Z acts like an infinite line. ✓Zi = Zo ✓There are no reflected waves. ✓V and I are in phase. ✓There is maximum transfer of power from source to load. PROPAGATION CONSTANT sometimes called propagation coefficient, is used to express the attenuation (signal loss) and the phase shift per unit length of a transmission line. used to determine the reduction in voltage or current with distance as a TEM wave propagates down a transmission line. For an infinitely long line, all of the incident power is dissipated in the resistance of the wire as the wave propagates down the line. With an infinitely long line or a line that looks infinitely long, such as a finite line terminated in a matched load (Za = ZL), no energy is returned or reflected back toward the source. PROPAGATION CONSTANT Mathematically, the propagation constant is since the propagation constant is a complex quantity, PROPAGATION CONSTANT The current and voltage distribution along a transmission line that is terminated in a load equal to its characteristic impedance (i.e., a matched line) are determined from the formula TRANSMISSION-LINE WAVE PROPAGATION Electromagnetic waves travel at the speed of light when propagating through a vacuum, and nearly at the speed of light when propagating through air. Metallic transmission lines where the conductor is generally copper and the dielectric materials vary considerably with cable type, an electromagnetic wave travels much more slowly. VELOCITY FACTOR sometimes called velocity constant is defined simply as the ratio of the actual velocity of propagation through a given medium to the velocity of propagation through free space. Mathematically, the velocity factor is VELOCITY FACTOR The velocity at which an electromagnetic wave travels through a transmission line is dependent on the dielectric constant of the insulating material separating the two conductors. The velocity factor is closely approximated with the formula VELOCITY FACTOR Dielectric constant is simply the permittivity of a material. The relative dielectric constant of air is 1.0006. However, the relative dielectric constant of materials commonly used in transmission lines range from 1.2 to 2.8, giving velocity factors from 0.6 to 0.9. The velocity factors for several common transmission-line configurations are given VELOCITY FACTOR The dielectric constant of a material is dependent on the primary constants inductance and capacitance. 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 off energy. Therefore, the velocity at which an electromagnetic wave propagates along a transmission line varies with the inductance and capacitance of the cable. It can be shown that time T = (LC)^0.5. VELOCITY FACTOR Therefore, inductance, capacitance, and velocity of propagation are mathematically related by the formula velocity x time = distance If distance is normalized to 1 m, the velocity of propagation for a lossless line is ELECTRICAL LENGTH The length of a transmission line relative to the length of the wave propagating down the line. EXAMPLE For a given length of RG8A/U coaxial cable with a distributed capacitance C = 96.6 pF/m, a distributed inductance L = 241.56 nH/m, and a relative dielectric constant €r = 2.3; determine the velocity of propagation and the velocity factor. TABLE OF COMMON TRANSMISSION LINE CHARACTERISTICS EXAMPLE A 165-ft section of RG-58A/U at 100 MHz is being used to connect a transmitter to an antenna. Its attenuation for 100 ft at 100 MHz is 5.3 dB. Its input power from a transmitter is 100 W. What are the total attenuation and the output power to the antenna? VELOCITY FACTOR Because wavelength is directly proportional to velocity and the velocity of propagation of a TEM wave varies with dielectric constant, the wavelength of a TEM wave also varies with dielectric constant. Therefore, for transmission media other than free space, can be rewritten as TRANSMISSION-LINE LOSSES For analysis purposes, transmission lines are often considered totally lossless. In reality, there are several ways in which power is lost in a transmission line. They are 1. conductor loss 2. radiation loss 3. dielectric heating loss 4. coupling loss 5. corona CONDUCTOR LOSS Current flows through a transmission line and the transmission line has a finite resistance, there is an inherent and unavoidable power loss. This is sometimes called conductor or conductor heating loss and is simply an (I^2)R loss. Resistance is distributed throughout a transmission line; conductor loss is directly proportional to line length. Power dissipation is directly proportional to current, conductor loss is inversely proportional to characteristic impedance. To reduce conductor loss, simply shorten the transmission line or use a larger- diameter wire (keep in mind that changing the wire diameter also changes the characteristic impedance and consequently the current). CONDUCTOR LOSS Conductor loss is somewhat dependent on frequency. This is because of an action called the skin effect. When current flows through an isolated round wire, the magnetic flux associated with it is in the form of concentric circles. CONDUCTOR LOSS the ac resistance of the conductor is directly proportional to frequency. The ratio of the ac resistance to the dc resistance of a conductor is called the resistance ratio. Above approximately 100 MHz, the center of a conductor can be completely removed and have absolutely no effect on the total conductor loss or EM wave propagation. Conductor loss in transmission lines varies from as low as a fraction of a decibel per 100 m for rigid air dielectric coaxial cable to as high as 200 dB per 100 m for solid dielectric flexible line. RADIATION LOSS If the separation between conductors in a transmission line is an appreciable fraction of a wavelength, the electrostatic and electromagnetic fields that surround the conductor cause the line to act like an antenna and transfer energy to nearby conductors. The amount of energy radiated depends on the dielectric material, the conductor spacing, and the length of the line. Radiation losses are reduced by properly shielding the cable. Therefore, coaxial cables have less radiation loss than do two-wire parallel lines. Radiation loss is also directly proportional to frequency. DIELECTRIC HEATING LOSS A difference of potential between the two conductors of a transmission line causes dielectric heating. Heat is a form of energy and must be taken from the energy propagating down the line. For air dielectric lines, the heating loss is negligible. However, for solid lines, dielectric heating loss increases with frequency. COUPLING LOSS Coupling loss occurs whenever a connection is made to or from a transmission line or when two separate pieces of transmission line are connected together. Mechanical connections are discontinuities (places where dissimilar materials meet). Discontinuities tend to heat up, radiate energy, and dissipate power. CORONA Corona is arcing 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. Generally, once corona has occurred, the transmission line is destroyed. 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 propagates from the load toward the source is called reflected voltage. Similarly, there are incident and reflected currents. Consequently, incident power is power that propagates toward the load, and reflected power is power that propagates toward the source. Incident voltage and current are always in phase. INCIDENT AND REFLECTED WAVES For an infinitely long line, all of the incident power is absorbed by the line and there is no reflected power. Also, if the line is terminated in a purely resistive load equal to the characteristic impedance of the line, the load absorbs all of 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 load. Therefore, the reflected power can never exceed the incident power. RESONANT AND NONRESONANT LINES A line with no reflected power is called a flat or nonresonant line. On a flat line, the voltage and current are constant throughout its length, assuming no losses. When the load is either a short or an open circuit, all of 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 load and source ends similar to the power in a tank circuit. RESONANT AND NONRESONANT LINES In a resonant line, the energy is alternately transferred between the magnetic and electric fields of the distributed inductance and capacitance. REFLECTION COEFFICIENT The reflection coefficient (sometimes called the coefficient of reflection) is a vector quantity that represents the ratio of incident voltage to reflected voltage or incident current to reflected current. Mathematically, the reflection coefficient is STANDING WAVES When Zo = ZL, all of the incident power is absorbed by the load. This is called a matched line. When Zo not equal ZL, 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 directions, 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. STANDING WAVES As the incident and reflected waves pass each other, a stationary voltage and current are produced on the line. These stationary waves are called standing waves because they appear to remain in a fixed position on the line, varying only in amplitude. The standing wave has minima (nodes) and maxima (antinodes), which are separated by half of a wavelength of the traveling waves. STANDING-WAVE RATIO The standing-wave ratio (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 on a transmission line. SWR is often called the voltage standing-wave ratio (VSWR). SWR is a measure of the mismatch between the load impedance and the characteristic impedance of the transmission line. Mathematically, SWR is STANDING-WAVE RATIO EXAMPLE For a transmission line with incident voltage E l = 5 Vp and reflected voltage Er= 3Vp, Determine: (a) The reflection coefficient. (b) The SWR. TRANSMISSION LINE PARAMETERS Return Loss (RL) The ratio of the power in the reflected wave to that in the incident wave TRANSMISSION LINE PARAMETERS Transmission Loss (TL) EXERCISES A coaxial TL with a Z0 of 50-Ω is connected to the 50-Ω output of a signal generator, and also to a 20-Ω load impedance. Calculate the mismatch loss. TRANSMISSION LINE PARAMETERS Transmitted Power (PT) The portion of the incident power consumed by the load or radiated by an antenna. TRANSMISSION LINE PARAMETERS Input Impedance (Zin) The impedance seen at the input of a lossless transmission line. EXAMPLE Calculate the effective inductance seen at the input of an open circuit TL of length 0.12 m at 3 GHz. Assume Z0=75Ω, velocity factor of 0.65 TRANSMISSION LINE WAVE PROPAGATION Infinite Transmission Line Condition If the transmission is uniform and infinite, the wave in the +z (forward) direction will continue indefinitely and never return in the –z (reverse) direction. TRANSMISSION LINE WAVE PROPAGATION Matched Impedance Condition (ZO=RLOAD) If the uniform transmission line is truncated and connected instead to a lumped resistive load RL = ZO, the entire +z wave(forward traveling wave) is dissipated in the load, which has the same effect as if an infinite line of characteristic impedance ZO were attached at the same point. This matched impedance condition is a unique situation in which all the power of the +z wave is delivered to the load just as if it were an infinite transmission line, with no reflected waves generated in the -z direction. TRANSMISSION LINE WAVE PROPAGATION The disadvantages of not having a matched (flat) transmission line can be summarized as follows: 1. One hundred percent of the source incident power does not reach the load. 2. 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-reflections cause more power loss. 4. Reflections cause ghost images. 5. Mismatches cause noise interference. TRANSMISSION LINE WAVE PROPAGATION Short-Circuit Load Condition (ZLOAD=0) For a shorted-load condition once the surge energy reaches the shorted end, the total voltage was compelled to be zero while the current can have any value, as determined by other constraints on the system. STANDING WAVES ON A SHORTED LINE The characteristics of a transmission line terminated in a short can be summarized as follows: 1. The voltage standing wave is reflected back 180° reversed from how it would have continued. 2. The current standing wave is reflected back the same as if it had continued. 3. The sum of the incident and reflected current waveforms is maximum at the short. 4. The sum of the incident and reflected voltage waveforms is zero at the short. TRANSMISSION LINE WAVE PROPAGATION Open-Circuit Load Condition (ZLOAD=∞) For an open load condition, the incoming surge of energy cannot simply disappear, because there is nothing capable of dissipating the energy at this point. What happen is that the energy reflects from the open end of the line back to the load. STANDING WAVES ON AN OPEN LINE The characteristics of a transmission line terminated in an open can be summarized as follows: 1. The voltage standing wave is reflected back just as if it were to continue (i.e., no phase reversal). 2. The current standing 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 at the open. COMPARISON BETWEEN MATCHED, OPEN, & SHORTED TL TRANSMISSION LINE APPLICATIONS Transmission line sections can be used to simulate inductance, capacitance, and LC resonance. A shorted quarter wavelength section looks like a parallel LC circuit or ideally, therefore, like an open circuit. A shorted section less than /4 looks like a pure inductance, and a section greater than /4 looks like a pure capacitance. These effects can be verified on a Smith chart by plotting ZL of 0 for a short-circuited line at the left center of the chart. TRANSMISSION LINE APPLICATIONS While open-circuit sections would seem to provide similar effects, they are seldom used. The open-circuited line tends to radiate a fair amount of energy off the end of the line so that total reflection does not take place. This causes the simulated circuit element to take on a resistive term, which greatly reduces its quality. These losses do not occur with shorted sections, and the simulated circuit has better quality than is possible using discrete inductors and/or capacitors. TRANSMISSION LINE APPLICATIONS Short-circuited /4 sections offer Qs of about 10,000 as compared to a maximum of about 1000 using a very high-grade inductor and capacitor. STUB MATCHING When a load is purely inductive or purely capacitive, it absorbs no energy. The reflection coefficient is 1 and the SWR is infinity. When the load is a complex impedance (which is usually the case), 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 shorted or an open stub can be used. THE SMITH CHART The mathematics required to design and analyze transmission lines is complex, whether the line is a physical cable connecting a transceiver to an antenna or is being used as a filter or impedance- matching network. In the 1930s, one clever engineer decided to do something to reduce the chance of error in transmission line calculations. The engineer’s name was Philip H. Smith, and in January 1939 he published the Smith chart, a sophisticated graph that permits visual solutions to transmission line calculations. REFERENCES Sharma, Sanjay (2019). Analog and Digital Communication. New Delhi: Katson Books. Spezia, Stefano (2021) Digital Communication Systems. Arcler Press. Frenzel, Louis (2017). Principles of Electronic Communication Systems. New York: McGrawHill Michael J. Roberts (2018), Signals and systems : analysis using transform methods and MATLAB, New York : McGraw-Hill Education. THANK YOU AND GOD BLESS!!!