1

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

2

• wire carries signal (current and voltage)• cable includes wire, connectors, insulation, etc.

Transmission Lines

goal: efficiently transfer signal energy from source to load over a cable

high frequency issues• line and load impedance• termination• signal reflections

3

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

4

magnitude due to voltage/current ratio looking into cable• determined by L & C• affect is similar to LPF • affects amplitude, phase and system ground

properties of Z0

• characterizes wire at varying signal frequencies • determines efficiency of signal energy propagation• optimal value relative to source and load impedance

Z0 = characteristic impedance of line

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Z = impedance ratio of voltage to current

v = Ri

v = dt

diL

i = C dt

dv

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)

6

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

power transfer from source to line • maximum when impedances are complex conjugate (R jX)• impedance mismatch results in wasted energy

7

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 capacitanceG = shunt conductanceR = series resistanceL = series inductance

R

C G

L R

C G

L R

C G

L

8

Z0 = impedance of infinite line lengthZ0 = impedance of finite line terminated by resistance Z0

Z0 = jwCG

jwLR

often in practice DC resistance and current leakage are very low

Z0 = C

L

jwC

jwL

9

Impedance of Coaxial Cable in terms of physical dimensions

Z0 =

d

Dlog

138

D = outer coax diameterd = inner conductor diameter = dielectric constant of inner material (1.0..2.8)

Other Types of Transmission Lines with Similar Models

10

Line and Load Impedance Matching

• signal source not always a physical generator• signal load = receiver of the signal

electrical length = signal

length wire

ii f/c

length wire

Tx Rxtransmission line

source/load source/load

11

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 ImpedanceZ0 = Characteristic Impedance of Transmission Line i

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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

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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

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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

15

Types of antennas

• simple antennas: dipole, long wire

• complex antennas: additional components to shape radiated fieldprovide high gain for long distances or weak signal receptionsize frequency of operation

• combinations of identical antennas - phased array electrically shape and steer antenna

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Propagation & Antennas

transmit antenna: radiate maximum energy into surroundingsreceive 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

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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

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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)

Antenna Performance depends heavily on • Channel Characteristics: obstacles, distances temperature,…• Signal Frequency• Antenna Dimensions

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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

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

rxtx hh 22 D =

hrxhtx

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Sky Waves

ionospheretransmitted

wavereflected

wave

refracted wave

skip distance

• reflected off ionosphere (20-250 miles high)• large ranges possible with single hop or multi-hop• transmit angle affects distance, coverage, refracted energy

Layer altitude (miles)

Frequency

Range

Availability

D 20-25 several MHz day onlyE 55-90 20MHz day, partially at nightF1 90-140 30MHz 24 hoursF2 200-250 30MHz 24 hours

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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

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total loss = Gt + Gr – path loss (dB)

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

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c

fd

P

P

r

t

c

fd4log20 10 (dB)

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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

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

relative signal intensity used relative field pattern determined by antenna design

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forward gain = 10dBbackward gain = 7dB

+10dB+7dB

+ 4dB

0o

270o

180o

90o

beamwidth

null

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

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radiated field shaping lens & visible light• application determines required direction & focus of signal • antenna characteristics

- radiation field pattern- gain- lobes- beamwidth- directivity

• 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

antenna field pattern = general shape of signal intensity in far-field

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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/meterreceived power is in uW/meter

• directly indicates EM field strength

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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

0o

270o

180o

90o

100 uV/m

practically • distance between meter & antenna kept constant• antenna is rotated • plot of field strength versus angle is made

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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

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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

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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 reference antenna

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• 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 twiceas much power than reference antenna

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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

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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

null

beamwidth lobe

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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%

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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

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552.14 dB

                              Dipole

                         

3600 dB

                              Isotropic                          

Beamwidth -3 dB

Gain (over isotropic)

ShapeName 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

1515 dBHorn                          

                         360x20014 dB