Transmission Media Key Learning Points Characteristics of Transmission Lines Transmission Line Models Characteristic Impedance and Impedance Matching Antenna Characterization Antenna Field Pattern Antenna Gain Antenna Design

Transmission Lines wire carries signal (current and voltage) cable includes wire, connectors, insulation, etc. goal: efficiently transfer signal energy from source to load over a cable high frequency issues line and load impedance termination signal reflections

Low Frequency Signals primarily a resistive circuit that depends on wire thickness thicker wires carry more current without overheating thinner wires have higher resistance Vdrop = IRwire Rwire = wire resistance, depends on thickness and length e.g. WG 22 = 16.5/1000ft Higher Frequencies require more accurate model transmission line modeled as RLC circuit depends on material, diameter, spacing, insulation L & C are negligible at low frequencies, significant at high frequencies

Z0 = characteristic impedance of line properties of Z0 characterizes wire at varying signal frequencies determines efficiency of signal energy propagation optimal value relative to source and load impedance magnitude due to voltage/current ratio looking into cable determined by L & C affect is similar to LPF affects amplitude, phase and system ground

Z = impedance  ratio of voltage to current v = Ri v = i = C V = RI V = jwLI V = I . jwC time frequency Z R jwL 1 = - j jwC wC Z = R + jX R = resistance X = reactance X > 0  inductive impedance (current lags voltage) X < 0  capacitive impedance (current leads voltage)

power transfer from source to line maximum when impedances are complex conjugate (R jX) impedance mismatch results in wasted energy G = conductance inverse of dielectric resistance between shield & conductor results from small current leakage between them R = DC resistance of wire, proportional to length & thickness C = wire’s inherent capacitance L = wire’s inherent inductance

Lumped Sum Parameter Model - Coax Cable uses discrete R,L,C,G components physically, parameters exist continuously over cable, specified in electrical units per meter C = shunt capacitance G = shunt conductance R = series resistance L = series inductance R C G L

Z0 = impedance of infinite line length Z0 = impedance of finite line terminated by resistance Z0 Z0 = often in practice DC resistance and current leakage are very low Z0 =

Impedance of Coaxial Cable in terms of physical dimensions Z0 = D = outer coax diameter d = inner conductor diameter  = dielectric constant of inner material (1.0..2.8) Other Types of Transmission Lines with Similar Models

Line and Load Impedance Matching signal source not always a physical generator signal load = receiver of the signal Tx Rx transmission line source/load electrical length =

Impedance Mismatch ZL  Z0 reflections from load end cause periodic repetition of voltage voltage & current cycles Value of Z0 cycles from inductive to capacitive - depends on where it is measured Impedance Matched: ZL = Z0 transmission line terminated with Z0 transmission line impedance is constant flat line (non-resonant) no reflected energy – all absorbed by load ZL = Load Impedance Z0 = Characteristic Impedance of Transmission Line i

impedance of components determined by dimensions & characteristics antenna cable transistor amplifiers often not practical to change impedance goal: make signal source see desired load value - even if physical value is different

Stub Matching: short piece of cable with end open or shorted shorted end preferred – radiates less energy acts like a reactance, jX, placed in parallel with transmission line varying position & length of stub  stub takes on full range of jX impedance of stub varies with position due to phase difference between current & voltage

Antennas & Propagation Antennas are designed to radiate & receive signals Design & selection impacted by - application - location - channel characteristics & signal propagation Antenna’s performance characterization - shape of the transmitted signal field - ability to reject signals to the side of main line of strength - bandwidth capabilities

Types of antennas simple antennas: dipole, long wire complex antennas: additional components to shape radiated field provide high gain for long distances or weak signal reception size  frequency of operation combinations of identical antennas - phased array electrically shape and steer antenna

Propagation & Antennas transmit antenna: radiate maximum energy into surroundings receive antenna: capture maximum energy from surrounding radiating transmission line is technically an antenna good transmission line = poor antenna antennas are transducers - convert voltage & current into electric & magnetic field - bridges transmission line & air - similar to speaker/microphone with acoustic energy EM field = electromagnetic field

Transmission Line voltage & current variations  produce EM field around conductor EM field expands & contracts at same frequency as variations EM field contractions return energy to the source (conductor) All of the energy in the transmission line remains in the system Antenna Designed to Prevent most of Energy from returning to Conductor Specific Dimensions & EM wavelengths cause field to radiate several  before the Cycle Reversal - Cycle Reversal - Field Collapses Energy returns to Conductor - Produces 3-Dimensional EM field - Electric Field  Magnetic Field - Wave Energy Propagation  Electric Field & Magnetic Field

Antenna Performance depends heavily on Channel Characteristics: obstacles, distances temperature,… Signal Frequency Antenna Dimensions transmit & receive antennas theoretically are the same (e.g. radiation fields, antenna gain) practical implementation issue: transmit antenna handles high power signal (W-MW) - large conductors high power connectors, receive antenna handles low power signal (mW-uW)

Ground or Surface wave: follow earths contour Propagation Modes Ground or Surface wave: follow earths contour affected by natural and man-made terrain salt water forms low loss path several hundred mile range 2-3 MHz signal Space Wave Line of Sight (LOS) wave Ground Diffraction allows for greater distance Approximate Maximum Distance, D in miles is (antenna height in ft) No Strict Signal Frequency Limitations hrx htx D =

reflected off ionosphere (20-250 miles high) Sky Waves reflected off ionosphere (20-250 miles high) large ranges possible with single hop or multi-hop transmit angle affects distance, coverage, refracted energy ionosphere transmitted wave reflected refracted skip distance Layer altitude (miles) Frequency Range Availability D 20-25 several MHz day only E 55-90 20MHz day, partially at night F1 90-140 30MHz 24 hours F2 200-250

Satellite Waves Designed to pass through ionosphere into space uplink (ground to space) down link (space to ground) LOS link frequencies >> critical frequency penetrates ionosphere without reflection high frequencies provide bandwidth geosynchronous orbit  23k miles (synchronized with earth’s orbit) long distances  result in high path loss EM energy disperses over distances intensely focused beam improves efficiency

Free Space Path Loss equation used to determine signal levels over distance G = antenna gain: projection of energy in specific direction can magnify transmit power increase effective signal level at receiver (dB) total loss = Gt + Gr – path loss (dB)

Antenna Characterization EM field pattern developed by antenna not always possible to model mathematically difficult to account of obstacles antennas are studied in EM isolated rooms to extract key performance characteristics relative signal intensity used relative field pattern determined by antenna design absolute value of signal intensity varies for given antenna design - at transmit antenna is related to power applied at transmitter - at receive antenna is related to power in surrounding space

Polar Plot of relative signal strength of radiated field shows how field strength is shaped generally 0o aligned with major physical axis of antenna most plots are relative scale (dB) - maximum signal strength location is 0 dB reference - closer to center represents weaker signals forward gain = 10dB backward gain = 7dB +10dB +7dB + 4dB 0o 270o 180o 90o beam width null

radiated field shaping  lens & visible light application determines required direction & focus of signal antenna characteristics - radiation field pattern - gain - lobes - beamwidth - directivity antenna field pattern = general shape of signal intensity in far-field far-field measurements measured many wavelengths away from antenna near-field measurement involves complex interactions of decaying electrical and magnetic fields - complicated details of antenna design involve near-field measurements

Measuring Antenna Field Pattern field strength meter used to measure field pattern indicates amplitude of received signal calibrated to receiving antenna relationship between meter and receive antenna known measured strength in uV/meter received power is in uW/meter directly indicates EM field strength

Determination of overall Antenna Field Pattern form Radiation Polar Plot Pattern use nominal field strength value (e.g. 100uV/m) measure points for 360o around antenna record distance & angle from antenna connect points of equal field strength practically distance between meter & antenna kept constant antenna is rotated plot of field strength versus angle is made 0o 270o 180o 90o 100 uV/m

Why Shape the Antenna Field Pattern ? transmit antennas: produce higher effective power in direction of intended receiver receive antennas: concentrate energy collecting ability in direction of transmitter - receiver only picks up intended signal avoid unwanted receivers: - security - multi-access systems locate target direction & distance – e.g. radar not always necessary to shape field pattern standard broadcast often omnidirectional - 360o

Antenna Gain Gain is Measured Specific to a Reference Antenna isotropic antenna often used - gain over isotropic - isotropic antenna – radiates power ideally in all directions - gain measured in dBi (reference to isotropic antenna) - test antenna’s field strength relative to reference isotropic antenna - at same power, distance, and angle - isotropic antenna cannot be practically realized ½ wave dipole often used as reference antenna - easy to build - simple field pattern

Antenna Gain  Amplifier Gain antenna power output = power input – transmission line loss antenna shapes radiated field pattern power measured at a point is greater/less than that using reference antenna total power output doesn’t increase power output in given direction increases/decreases relative to

lamp  isotropic antenna lens  directional antenna  lens provides a gain/loss of visible light in a specific direction  lens doesn’t change actual power radiated by lamp e.g. transmit antenna with 6dB gain in specific direction over isotropic antenna  4  transmit power in that direction receive antenna with 3dB gain is some direction receives twice as much power than reference antenna

Antenna Gain often a cost effective means to (i) increase effective transmit power (ii) effectively improve receiver sensitivity may be only technically viable means more power may not be available (batteries) front end noise determines maximum receiver sensitivity Rotational Antennas can vary direction of antenna gain Directional Antennas focus antenna gain in primary direction

Antenna Design results in Beamwidth, Lobes & Nulls Lobe: area of high signal strength - main lobe - secondary lobes Nulls: area of very low signal strength Beamwidth: total angle where relative signal power is 3dB below peak value of main lobe - can range from 1o to 360o Beamwidth & Lobes indicate sharpness of pattern focus beam width lobe null

Antenna Design – Spectral Parameters Center Frequency - optimum operating frequency Antenna Bandwidth  -3dB points of antenna performance Bandwidth Ratio: Bandwidth/Center Frequency e.g. let fc = 100MHz with 10MHz bandwidth - radiated power at 95MHz & 105MHz = ½ radiated power at fc - bandwidth ratio = (105-95)/100 = 10%

Bandwidth Issues High Bandwidth Antennas tend to have less gain than narrowband antennas Narrowband Receive Antenna - reduces interference from adjacent signals - reduces received noise power main trade-offs for Antenna Design directivity & beam width acceptable lobes maximum gain bandwidth radiation angle

55 2.14 dB                                Dipole                           360 0 dB Isotropic Beamwidth -3 dB Gain (over isotropic) Shape Name Radiation Pattern 20 30 50 200 25 14.7 dB 10.1 dB -0.86 dB 3.14 dB 7.14 dB Parabolic Dipole Helical Turnstile Full Wave Loop Yagi Biconical Horn 15 15 dB Horn 360x200 14 dB