Introduction to Microwave Systems (14)System Aspects of Antennas

In far fields:

or simply,

Time-average Poynting vector:

In summary, for finite source, in far fields,1. Spherical TEM waves.

2. Wave impedance equal the intrinsic impedance .

3. Real power flow.

Far field condition phase difference between plane wave and spherical wave

at the edge of the antenna

Additionally:

• : .

• : .

To sum up:1. At fixed frequency, .

2. At fixed antenna size,

3. At various frequency and antenna size scaled,

Examlpe 14.1 FAR-FIELD DISTANCE OF AN ANTENNAAntenna: parabolic reflectorSize: 18 inch.Frequency: 12.4 Ghz.

Radiation intensity (power/solid angle):

Then, total radiated power:

Pattern Characteristics1. Main lobe (major lobe, main beam)2. Side lobe (minor lobe)

3. Maximum side lobe level:

4. Half-power beamwidth: 5. Pattern types: Broadside, Intermediate, Endfire.6. Omnidirectional v.s. pencil beam.

Directivity:

Isotropic antenna:

Example 14.2 PATTERN CHARACTERISTICS OF A DIPOLEANTENNA

Ideal dipole:

Half-wave dipole: Mono-pole:

Power Gain (Gain):

or

Radiation efficiency:

Realized Gain:

Referenced Gain:

dBi: referenced to isotropic antenna.dBd: referenced to dipole antenna.

Aperture efficiency and Effective AreaLet be the effective area of an aperture or planar antennadefined by

where is the power received by the antenna, is powerdensity of the incident wave at the antenna. Then, in general,

Similarly,

where is the maximum effective aperture which does not takeinto the account of loss.

Let be the aperture size of an aperture antenna, then define

Aperture efficiency:

Note:

Also,

In general,

Aperture efficiency: , where is the physical aperture

size.

Background and Brightness Temperature

Noise power source received by an antenna:1. Lossy components in the antenna2. Environment

Noise power:

where is the absolute temperature, is the Boltzmann’sconstant.Note: not a function of R, but T.

Background noise temperature • Sky (toward zenith) 3–5 K, cosmic background radiation.• Sky (toward horizon) 50–100 K• Ground 290–300 K

Fig. 14.6 Background noisetemperature of sky versusfrequency. Is elevation anglemeasured from the horizon. Dataare for sea level, with surfacetemperature of and surfacewater vapor desity of 7.5 gm/m3.

• Two absorption peaks at 22 and 60 GHz due to H2O and O2oscillation.

• Toward horizon, approaching ambient temperature. • Toward zenith, approaching cosmic background. • Departure from white noise due to interaction with

atmosphere molecules. Brightness temperature of antenna Tb: the average temperatureseen by an antenna.

Note: not including the effect of loss in antenna since directivity isused in the calculation.

Antenna noise temperature: external brightness temperature +antenna thermal noise temperature.

T T TA rad b rad p 1where Tp is the antenna’s temperature.

Consider mismatch Γ and transmission line loss L, total systemnoise temperature at receiver input:

T L T T LL L TS rad b rad p p

11 1 1

2 2| | | |

G/T ratio: a figure of merit to evaluate an receiving antenna.

G T dB GT

dB KA

/ ( ) log / 10

• SNR is proportional to G/T ratio.

Wireless Communications

Friis radio link formula (assume the best scenario: no all kinds ofmismatches):

Power delivered to the load : polarization mismatch factor, : impedance mismatch factor,

In dB form or

where dBm is power in decibels above a milliwatt.

EIRP: effective (equivalent) isotropically radiated powerERP: effective radiated power by a half-dipole

Link Budget and Link Margin

Link Budget (factors related to the final received power):• Pt: transmit power• -Lt: transmit antenna line loss• Gt: transmit antenna gain• -L0: path loss (free space)• -LA: atmospheric loss• Gr: receive antenna gain• -Lr: receive antenna line loss

P dBm P L G L L G Lr t t t A r r( ) 0

L dB R0 20 4( ) log

If impedance mismatch, the resulting loss is

L dBimp ( ) log | | 10 1 2Link margin:

LM dB P Pr r( ) (min) 0Link margin that is used to account for fading effects is calledfade margin. Satellite links operating above 10 GHz often requirefade margin larger than 20 dB to account for attenuation due toheavy rain.

Example: Direct Broadcast Satellite ReceptionReceiving disk antenna: size 0.46 m in diameter,

Radio Receiver Architechtures

Functions of a radio receiver• High gain (~100 dB). Single stage: 50~60 dB. Need LNA.• Selectivity of channels. Rejection of image frequencies or

interference. Using filters.• Dow-conversion from RF to IF to ease processing and lower

cost.• Detection of analog or digital signals.• Isolation from transmitter. Avoid saturation due to transmit

power.

Tuned Radio Frequency (TRF) Receiver

• All processingbefore demodulation is at RF frequency.• Earliest types.• Suitable for low frequency.

Direct Conversion Receiver

• Down-convert to baseband from RF directly by mixing withLO which oscillate at the same carrier frequency.

• Also called homodyne receiver because fLO=fRF.• Benefit compared with TRF:

selectivity provided by low-pass filter. amplification at baseband stage. No image frequency. For AM, no demodulation needed.

• LO needs high precision and stability.

Superheterodyne Receiver

• Down-convert to IF instead of baseband.• Most common nowadays.• Higher selectivity by IF sharper cutoff BPF.• Higher gain by IF AMP. • Tuning can be achieved by voltage controlled oscillator

(VCO) to keep IF fixed.• More IF stages is possible to avoid large fLO to improve LO

stability and precision.

Wireless Communications Systems

• Cellular telephone and data systems Developed in 1970s. Solve the problem of limited number of channels by

cellular structure. Divide area into non-overlapping cells. Each cell has its

own transmitter and receiver (base station). Frequency bands can be reuse in nonadjacent cells.

• Satellite systems for wireless voice and data Large coverage area by few satellites In principle, three geosynchronous (GS) satellites can

cover whole earth. However, low signal power and high

latency. LEO (low earth orbit) satellites can provide high signal

power and low latency but need more satellites to coverwhole earth.

LEO example: Iridium system. 66 satellites. GS example: INMARSAT systems.

• Global Positioning System 24 satellites in orbits 20,200 km above. Use triangulation to determine co-ordinates. 1 cm accuracy achieved by differential GPS. Minimum 4 satellites are required to determined

coordinate. Three if height is already known. Two frequency bands: L1 1575.42 MHz, L2 1227.60

MHZ. L1 for commercial use, accuracy 100 feet. L2 for military use, higher accuracy.

• Wireless local area networks Band: 2.4 or 5 GHz. Standards

# IEEE 802.11a: 5 GHz, 54 Mbps.# IEEE 802.11b: 2.4 GHz, 11 Mbps.# IEEE 802.11g: 2.4 GHz, 54 Mbps.# IEEE 802.11n: 2.4/5 GHz, 600 Mbps.# IEEE 802.11ac: 5 GHz, 1 Gbps.

Bluetooth: 2.4 GHz, low power (1~100mW), shortranges (1~100m), low date rates (1~24 Mbps).

Future: 60 GHz.• Direct broadcast satellites (DBS)

Frequency: 10~12 GHz. Data rate: 40 Mbps. Receiving antenna: 18 inch diameter disk. Two satellites at geostationary orbit at 101.2" and

100.8" longitude. Pt =150 W. 16 Channels.

• Point to point radio systems

Provide dedicated connection between fixed points. High antenna gains. Frequency bands: 18, 24, 38 GHz. Cheaper than fiber or cable, but lower data rate. Can be used as the back bone of base station or long

distance link between cities.

Radar (Radio Detection and Ranging) Systems

• Determine the distance of the target by the time required fora pulsed signal to gravel to the target and reflected backed.

• Fast development in WWII by British and USA.• Breakthrough due to the invention of magnetron tube to

provide stable and high-power source.

Civilian application:• Airport surveillance• Marine navigation• Weather radar• Altimetry• Aircraft landing• Security alarms• Speed measurement (police radar)• Geographic mapping

Military applications• Air and marine navigation• Detection and tracking of aircraftk missiles, and spacecraft.• Missile guidance• Fire control for missiles and artillery• Weapon fuses• Reconnaissance

Scientific applications• Astronomy• Mapping and imaging• Precision distance measurement• Remote sensing of the environment

The Radar EquationFig. 14.20: (a) monostatic radar.(b) bistatic radar.

Radar cross section σ: the total scattered power to the incidentpower density in a given direction.

PS

s

i

where is the incident power density at the target, S PGRi

t4 2

Ps

is total scattered power. Then, the reflected power density at theradar is

S PG

Rr

t

4 2 2

Assume the scatter is an isotropic scatter. The received powerbecomes

(Radar equation) P PG

Rr

t2 2

2 24 4

Example 14.7 APPLICATION OF THE RADAR RANGEEQUATION

, , , , Find the maximum range.

Pulse Radar

• Determine target range by measuring round-trip time of apulsed signal.

• Typical pulse duration 100 ms to 50 ns.• Shorter pulse gives better range resolution.• Longer pulse gives better SNR.• Pulse repetition rate 100 Hz to 100 kHz.• Higher pulse repetition rate, better SNR.

• Lower pulse repetition rate avoids range ambiguities.

Doppler Radar

Detect target velocity by Doppler frequency. The change offrequency is

where + is for approaching target, - for leaving target.Can help to remove clutter from ground. A necessity for look-down radar.

Radiometer Systems• Passive radar.• Measure the blackbody radiation (noise power) at

microwave frequency.• Need sensitive receivers.• Used in remote sensing.Emissivity:

where is power radiated by nonideal body, is the powerthat emitted by a perfect black body.Brightness temperature:

where is physical temperature.

• Use at certain frequency or various frequencies toanalyze or identify the target.

• Need image or signal processing technique.• Less theoretical than experimental.

! Environmental applications" Measurement of soil moisture" Flood mapping" Snow cover/ice cover mapping" Ocean surface wind speed" Atmospheric temperature profile" Atmospheric humidity profile

! Military applications" Target detection" Target recognition" Surveillance" Mapping

! Astronomy applications" Planetary mapping" Solar emission mapping" Mapping of galactic objects" Measurement of cosmological background radiation.

Total Power Radiometer

• Superheterodyne front end: RF amplifier, mixer, localoscillator, IF stage.

• Detector: square-law device, output proportional to inputpower.

• Integrator: low-pass filter, smooth out short-term variation.Target noise power received by antenna: Receiver generated noise power: Output voltage: where is the system gain.Two unknows: and , need two calibration.Errors in measured in a radiometer:• noise fluctuations: need integrator to smooth out.

• gain fluctuations: caused active devices such as mixers,amplifiers, oscillators. Series than noise fluctuations

Example: , , , , ,. The results: ,

The Dicke Radiometer

• System gain variation time > 1 s. Built in calibration circuitoperated at period < 1 s, or typical frequency from 10 to1000 MHz.

• Synchronous demodulator: a comparator. Difference ofoutput voltage of and are fed to a feedback circuitto automatically match and .

Microwave Propagation

Atmospheric Effects• Dielectric constant of air:

P: barometric pressure in millibarsT: temperature in kelvinsV: water vapor pressure in millibars

• Decrease (approaching 1) as altitude increases sincepressure and humidity decrease with height faster thantemperature.

• Cause waves to bend toward earth.

• Line of sight distance: R: radius of earchh: antenna height

• Refraction effect can be accounted for by , where, typically which is about 15% increase in range.

• varies with weather conditions.• Refraction effect contributes to errors of radiometers when

targets are close to the horizon.• Ducting effect: when local temperature inversion causes air

permittivity to increase with height, creating waveguideeffect. Radio wave can propagate long distances on Earth’ssurface.

• Attenuation effect due to absorption of water or oxyenmolecular resonance very low below 10 GHz. water vapor resonance: 22.2 and 183.3 GHz. oxygen resonance: 60 and 120 GHz. low attenuation transmission windows: 35, 94, 135

GHz. atmospheric remote sensing uses high attenuation at

20 or 55 GHz. satellite to satellite communication uses 60 GHz to

avoid interference, jamming ro eavesdropping fromEarth.

high speed short range multimedia wirelesscommunication use 60 GHz to avoid interference.

Ground Effects

• Fading: signal degradation caused by interference ofreflected wave from Earch, buildings or other objects. vary with frequencies, polarizations, physical locations. divisity-system: reduce fading by combining outputs of

two or more channels.• Diffraction: energy scattered in the vicinity of the line-of-sight

boundary at horizon. Usually small in microwave frequency.

Plasma Effects• Plasma: gas consisting of free-moving ionized particles.• Ionosphere consists of spherical layers of atmosphere with

particles that have been ionized by solar radiation.• Dense plasma formed on a spacecraft at it enters the

atmosphere in high speed.

• Effective permittivity: ,

: plasma frequency: number of ionized particles per unit volume: charge of electron: mass of electron

• , , propagating mode.• , , no energy propagates.• On average, (short wave radio).• Waves can propagate globally by bouncing back and forth

from ionosphere and Earth.• When aircrafts reentering atmosphere will lose

communication due to the surrounding plasma.

Microwave Heating

• Invented by Percy Lebaron Spencer (1894-1970) in 1945.• Discovered by accident when Spencer was standing in front

of an active radar set when he noticed the candy bar he hadin his pocket had melted.

• Heating food by water or fat molecule oscillation in food.• Heating directly inside of food, unlike conventional oven,

heating of food from surface.• Usually at 2.45 GHz or 915 MHZ unlicensed band.

Biological Effects and Safety• Proven danger: thermal effects.

Most dangerous to: brain, eye, genitals, stomach. Excessive exposure can leads to cataracts, sterility or

cancer.• IEEE safety standard for power density (W/m2): Figure

14.32. Two standards: one for occupational workers, one for

general population. Frequency range: 100 MHZ ~ 100 GHz. For occupational workers: higher power, measured

over 6-minute period. At high frequency, 100 W/m2. Atlow frequency, 10 W/m2.

For general population: lower power, measured over30-minute period. At high frequency, 10 W/m2. At lowfrequency, 2 W/m2.

Lower allowable power at lower frequency due todeeper penetration. At higher frequency, skins absorbmost of power.

• FCC standard of SAR (specific absorption rate) for mobiledevice. A measure of power dissipated in a unit of tissuemass.

: conductivity, : density of tissue.Limit: 1.6 W/kg averaged over 1 g of tissue.

• European Union SAR limit: 2 W/kg averaged over 10 g oftissue.

• US microwave SAR limit: 1 mW/cm2 at 5 cm from the oven.

Example 14.8 POWER DENSITY IN THE VICINITY OF AMICROWAVE RADIO LINK

, , .

At main beam, 20 m from the antenna: .At side lobe, 20 m from the antenna: .