Presentation on theme: "Electrical Engineering 3 ELECTROMAGNETICS: Transmission Lines Dr. P. J"— Presentation transcript:
1Electrical Engineering 3 ELECTROMAGNETICS: Transmission Lines Dr. P. J Electrical Engineering 3 ELECTROMAGNETICS: Transmission Lines Dr. P.J.S. Ewen
2ELECTROMAGNETICS – TRANSMISSION LINES Arrangements are same as for Prof. Murray's part of the course:Lectures: Tuesdays – LT 2Thursdays – LT 2Fridays – LT 2Tutorials: Tuesdays – CR10
3SYLLABUSPart 1 - Introduction and BasicsLecture Topics1. General definitionPractical definitionTypes of transmission line: TE, TM, TEM modesTEM wave equation - equivalent circuit approach2. The "Telegrapher's Equations"Solution for lossless transmission lines: F(t±x/v)Simplest case of F(t±x/v)3. Direction of travel of cos/sin (ωt ± βx) wavesPhase velocity of a wave on a transmission lineGeneral transmission line: attenuation
4Part 2 - Characteristic Impedance and Reflections Lecture TopicsCurrent and voltage on a transmission line:Characteristic impedance, ZOCharacteristic impedance of lossless linesCharacteristic impedance of general linesInfinitely long transmission linesReflections on transmission linesTransmission line with change of ZO: voltagereflection coefficientVoltage reflection coefficient at an arbitrarydistance l from the load ZLImpedances of terminated linesVoltage Standing Wave Ratio (VSWR)Voltage Standing Wave measurement
5Part 3 - The Smith Chart and its Applications Lecture Topics7. Introduction to the Smith ChartPrinciple of operationConstruction of the Smith ChartKey points on the Smith Chart8. Using Smith Chart with load and line combinationsSmith Chart and general transmission linesEffect of variation in frequencySmith Chart and VSWRUsing the Smith Chart and VSWR to find ZL9. Adding components using a Smith ChartMatching with Smith Chart and series componentsAdmittance using a Smith ChartSingle Stub Matching
6Part 1 - Introduction and Basics Lecture 1 Define what is meant by a transmission lineLook at different types of lineLecture 2Equations governing the current and voltage on a transmission lineSolution to these equations for the simplest case – current and voltage propagate as wavesI or VLecture 3Properties of waves on a transmission lineGeneral transmission line - attenuationDistance, x
7Vr / Vi = r Part 2 - Characteristic Impedance and Reflections Lecture 4Characteristic impedance, ZOReflections on transmission lines− Forwardvoltage wave− Reflectedvoltage wave-x+xLecture 5Voltage reflection coefficientVr / Vi = rLecture 6Impedances of terminated linesZin ≠ Zo + ZL Zo ZL
8Transmission line (Zo) Part 3 - The Smith Chart and its ApplicationsLecture 7Introduction to the Smith ChartPrinciple of operationLecture 8Using the Smith Chart to solve various transmission line problemsLecture 9Designing matching circuits using the Smith ChartZoMatchingcircuit ornetworkForward power onlyZL ZoSourceLoadTransmission line (Zo)
9Recommended Text:J.D. Kraus and D.A. Fleisch,"Electromagnetics with Applications",McGraw-Hill.This is a comprehensive text covering most ofthe material in the Electromagnetics course. It isalso a recommended text for the 4th year courseon RF Engineering.
10Handout on Transmission Lines Lecture notes for all the lecturesLecture summariesTutorial sheets A - DLecture examplesFormula sheet (same as for exam)Tutorial solutions will be distributed at tutorials (and are available on LEARN).
11The PowerPoint "slides" are available on the web … … go to the“Electromagnetics 3:Signal Transmission”page on Learnand click on“Teaching materials –Transmission Lines”
14Under certain circumstances all these can be regarded as transmission lines:Pair of wiresCo-ax cablePCB tracksIC interconnects
15GENERAL DEFINITIONA transmission line can be defined as a device forpropagating or guiding energy from one point toanother. The propagationof energy is for one of twogeneral reasons:1. Power transfer (e.g. for lighting, heating, performing work) - examples are mains electricity, microwave guides in a microwave oven, a fibre-optic illuminator.
162. Information transfer – examples are telephone, radio, and fibre-optic links (in each case the energy propagating down the transmission line is modulated in some way).
17CE amplifier circuit Because signals cannot travel faster than the speed of light, ifthe voltage at Achanges it will takea finite time for theinformation toreach B – duringthat time thevoltages at A andB will be different.
18Example 1.1 - Voltage and phase difference along a transmission line A remote step-down transformer (B) is connected by a transmission line 600 km long to a generating station (A) supplying 50 Hz AC. At time t = 0 the generator is switched into the line and the voltage at the generator is at its maximum, Vm. What are the voltage and phase differences between the ends of the line at the instant power reaches the transformer?Generating stationTransformer600 km
20Example 1.2 - Phase difference between the ends of a cable. Determine the phase difference between the ends of:(a) a 10m length of mains cable for a 50Hz electricity supply(b) a 10m length of coaxial cable carrying a 750MHz TV signalλN.B. one wavelength corresponds to one complete cycle or wave, and hence to a phase change of 360º or 2π radians. So the phase change over a distance l is just360º l / λ (or 2π l / λ radians)
21PRACTICAL DEFINITIONWe have to treat a conducting system as a transmission line if the wavelength, , of the signal propagating down the line is less than or comparable with the length, l , of the line: lAssociated with transmission lines there may be:Propagation lossesDistortionInterference due to reflection at the loadTime delaysPhase changes
22Some different types of transmission lines: Crosssection2-wire line(dc)2-wire line(ac)Coaxial line(dc, ac, rf)Microstripline (rf)Rectangularwaveguide(rf)Opticalfibre (light)Radio linkwith antennas
23Microstrip line cross section conductors dielectric conductor
26MODES OF PROPAGATIONThe energy propagating down a transmission line propagates as an electromagnetic wave. Different patterns of E and H fields are possible for these waves. Each pattern constitutes a “mode of propagation”:
27MODES OF PROPAGATION TE – TRANSVERSE ELECTRIC TM – TRANSVERSE MAGNETIC These modes fall into two categories:TE – TRANSVERSE ELECTRICTM – TRANSVERSE MAGNETICTEM Modes: In the special casewhere E and H are both transverse(i.e. at right angles) to the directionof energy flow, the mode is termed TEM.E and H will also be at right angles to each other.TEM – TRANSVERSE ELECTROMAGNETICTE mode
28The kinds of mode that can propagate down a line depend on the geometry and materials of the line.Transmission lines can be classified into 2 groupsaccording to the type of mode that normallypropagates down them.1. LINES PROPAGATING TEM MODES:There is no E or H field in the direction of propagation.twin-wire, coaxial, stripline and (approximately) microstrip lines are in this group.2. LINES PROPAGATING TE OR TM MODES:E or H have components in the direction of energy flow.waveguides and optical fibres are in this group.
29EQUIVALENT CIRCUIT APPROACH TO TRANSMISSION LINE ANALYSIS TEM WAVE EQUATIONThe details of wave propagation on a transmission line can be deduced from Maxwell's Equations. However, TEM guided waves on a transmission line can also be analysed using alumped equivalent circuit approach.EQUIVALENT CIRCUIT APPROACH TOTRANSMISSION LINE ANALYSISReal transmission lines have associated with them:a resistance per unit length, Ra capacitance per unit length, Can inductance per unit length, Land a (leakage) conductance per unit length, G.(Note that R represents the resistance of both conductors in the line.)
30FOR PARALLEL WIRES: FOR COAXIAL CABLE: for wires in air and with d >> a:a = wire radiusd = wire spacingεo = permittivity of free spaceμo = permeability of free spaceFOR COAXIAL CABLE:a = radius of inner conductorb = inner radius of outer conductorε = permittivity of dielectric in cableμ = permeability of dielectric in cable
31EQUIVALENT CIRCUIT APPROACH TO TRANSMISSION LINE ANALYSIS TEM WAVE EQUATIONThe details of wave propagation on a transmission line can be deduced from Maxwell's Equations. However, TEM guided waves on a transmission line can also be analysed using alumped equivalent circuit approach.EQUIVALENT CIRCUIT APPROACH TOTRANSMISSION LINE ANALYSISReal transmission lines have associated with them:a resistance per unit length, Ra capacitance per unit length, Can inductance per unit length, Land a (leakage) conductance per unit length, G.(Note that R represents the resistance of both conductors in the line.)
32EQUIVALENT CIRCUIT FOR A TRANSMISSION LINE The existence of an inductance, capacitance, resistance and conductance (per unit length) allows us to represent the transmission line by an equivalent circuit in which each infinitessimal length of transmission line is represented by the same combination of 4 components:RΔxLΔxCΔxGΔxΔxTo make up the whole line, repeat the equivalent circuit a sufficient number of times.
33PRIMARY LINE CONSTANTS DxRDxLDxCDxGDxPRIMARY LINE CONSTANTSC = capacitance per unit length (F/m)L = inductance per unit length (H/m)R = resistance per unit length (W/m)G = conductance per unit length (S/m)Note:-R, C, L and G are all expressed per unit lengthR & G should be small for a good transmission line.If R = 0 and G = 0, the line is termed “lossless”.
34Example 1.3 - Impedance of an infinite lossless transmission line. Determine an expression for the impedance of an infinite, lossless transmission line.
35SummaryPRACTICAL DEFINITION - Transmission line analysis must be used when the wavelength, , of the energy propagating down the line is less than or comparable with the length, l , of the line: lDefinition of TE, TM & TEM modes − twin-wire, coaxial and strip lines only propagate TEM modes.Transmission lines have capacitance, inductance and resistances associated with them and can be represented by an equivalent circuit.
36C, L, R and G are the primary line constants and are DxRDxLDxCDxGDxC, L, R and G are the primary line constants and areall expressed PER UNIT LENGTHFor a LOSSLESS LINE, R = 0 and G = 0