Fundamental Antenna Parameters 1. Radiation Pattern An antenna radiation pattern is defined as “a graphical representation of the radiation properties of the antenna as a function of space coordinates. In most cases, the radiation pattern is determined in the far-field region. Radiation properties include radiation intensity, field strength, phase or polarization.
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Fundamental Antenna Parameters
1. Radiation PatternAn antenna radiation pattern is defined as “a graphicalrepresentation of the radiation properties of the antennaas a function of space coordinates. In most cases, theradiation pattern is determined in the far-field region.Radiation properties include radiation intensity, fieldstrength, phase or polarization.
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Radiation Intensity
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Radiation Intensity
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Radiation IntensityExamples
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1. Isotropic radiator
2. Hertzian Dipole
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DirectivityExamples
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1. Isotropic radiator
2. Hertzian Dipole
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Antenna Gain
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POWER DENSITY IN A CERTAIN DIRECTION
DIVIDED BY THE TOTAL POWER RADIATED
POWER DENSITY IN A CERTAIN DIRECTION
DIVIDED BY THE TOTAL INPUT POWER
TO THE ANTENNA TERMINALS (FEED POINTS)
IF ANTENNA HAS OHMIC LOSS…THEN, GAIN < DIRECTIVITY
DIRECTIVITY
GAIN
Antenna Gain
Sources of Antenna System Loss
1. losses due to impedance mismatches
2. losses due to the transmission line
3. conductive and dielectric losses in the antenna
4. losses due to polarization mismatches
According to IEEE standards the antenna gain does not include losses due toimpedance or polarization mismatches. Therefore the antenna gain only accounts for dielectric and conductive losses found in the antenna itself. HoweverBalanis and others have included impedance mismatch as part of the antenna gain.
The antenna gain relates to the directivity through a coefficient called theradiation efficiency (et)
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conduction losses dielectric losses
1te
impedance mismatch
Overall Antenna Efficiency
The overall antenna efficiency is a coefficient that accounts for all the differentlosses present in an antenna system.
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Reflection Efficiency
The reflection efficiency through a reflection coefficient () at the input (or feed)to the antenna.
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Radiation Resistance
The radiation resistance is one of the few parameters that is relativelystraight forward to calculate.
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Example: Hertzian Dipole
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Radiation Resistance
Example: Hertzian Dipole (continued)
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Antenna Radiation Efficiency
radcd
radcd RR
Re
Conduction and dielectric losses of an antenna are very difficult to separate andare usually lumped together to form the ecd efficiency. Let Rcd represent the actuallosses due to conduction and dielectric heating. Then the efficiency is given as
For wire antennas (without insulation) there is no dielectric losses only conductorlosses from the metal antenna. For those cases we can approximate Rcd by:
22o
cd b
lR
where b is the radius of the wire, is the angular frequency, is the conductivityof the metal and l is the antenna length
Example Problem:
A half-wavelength dipole antenna, with an input impedance of 73 is to beconnected to a generator and transmission line with an output impedance of50. Assume the antenna is made of copper wire 2.0 mm in diameter and theoperating frequency is 10.0 GHz. Assume the radiation pattern of the antenna is
Find the overall gain of this antenna
SOLUTIONFirst determine the directivity of the antenna.
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Example Problem: Continued
SOLUTIONNext step is to determine the efficiencies
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Example Problem: Continued
SOLUTIONNext step is to determine the gain
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Antenna Type Gain (dBi) Gain over Isotropic
Power Levels
Half Wavelength Dipole
1.76 1.5x
Cell Phone Antenna(PIFA)
3.0 2.0x 0.6 Watts
Standard Gain Horn
15 31x
Cell phone tower antenna
6 4x
Large Reflecting Dish
50 100,000x
Small Reflecting Dish
40 10,000x
Effective Aperture
plane waveincident
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Question:
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Directivity and Maximum Effective Aperture (no losses)
Antenna #2
transmit receiver
R
Direction of wave propagation
Antenna #1
Atm, DtArm, Dr
oem DA4
2
Directivity and Maximum Effective Aperture (include losses)
Antenna #2
transmit receiver
R
Direction of wave propagation
Antenna #1
Atm, DtArm, Dr
2*2
2 ˆˆ4
)1( awocdem DeA
conductor and dielectric losses reflection losses
(impedance mismatch)polarization mismatch
Friis Transmission Equation (no loss)
Antenna #2
Antenna #1
R
transmit
Atm , D
treceiver
Arm, D
r
The transmitted power density supplied by Antenna #1at a distance R and direction rr)is given by:
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R
DPW ttgtt
t
tt)
rr)
The power collected (received) by Antenna #2 is given by:
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4
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4
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2
2
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Friis Transmission Equation (no loss)
Antenna #2
Antenna #1
R
transmit
Atm , D
treceiver
Arm, D
r
tt)
rr)
),(),(4
2
rrgrttgtt
r DDRP
P
If both antennas are pointing in the direction of their maximum radiation pattern:
rotot
r DDRP
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Friis Transmission Equation ( loss)
Antenna #2
Antenna #1
R
transmit
Atm , D
treceiver
Arm, D
r
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rr)
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4)1)(1( awrrgrttgttrcdrcdt
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r DDR
eeP
P
conductor and dielectric lossestransmitting antenna
conductor and dielectric lossesreceiving antenna
reflection losses in transmitter(impedance mismatch)
reflection losses in receiving(impedance mismatch)
polarization mismatch
free space loss factor
Friis Transmission Equation: Example #1
A typical analog cell phone antenna has a directivity of 3 dBi at its operating frequency of 800.0 MHz. The cell tower is 1 mile away and has an antenna with a directivity of 6 dBi. Assuming that the power at the input terminals of the transmitting antenna is 0.6 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss.
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Friis Transmission Equation: Example #2
A half wavelength dipole antenna (max gain = 2.14 dBi) is used to communicate from an old satellite phone to a low orbiting Iridium communication satellite in the L band (~ 1.6 GHz). Assume the communication satellite has antenna that has a maximum directivity of 24 dBi and is orbiting at a distance of 781 km above the earth. Assuming that the power at the input terminals of the transmitting antenna is 1.0 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss.
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2
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r DDR
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= 0 = 0= 1= 1 = 1
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t
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me
e
f
c
Friis Transmission Equation: Example #2
A roof-top dish antenna (max gain = 40.0 dBi) is used to communicate from an old satellite phone to a low orbiting Iridium communication satellite in the Ku band (~ 12 GHz). Assume the communication satellite has antenna that has a maximum directivity of 30 dBi and is orbiting at a distance of 36,000 km above the earth. How much transmitter power is required to receive 100 pW of power at your home. Assume the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss.
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Radar Range Equation
Definition: Radar cross section or echo area of a target is defined as the area when interceptingthe same amount of power which, when scattered isotropically, produces at the receiver the samepower density as the actual target.
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lim mW
WR
R
WW
inc
s
R
inc
Rs
(radar cross section) m2
R (distance from target) mWs (scattered power density) W/m2
Winc (incident power density) W/m2
Radar Range Equation (no losses)
Power density incident on the target is a functionof the transmitting antenna and the distance between the target and transmitter:
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),(
t
ttgttinc
R
DPW
The amount of power density scattered by the target at the location of the receiver is then given by:
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),(
4 rt
ttgtt
r
incs RR
DP
RWW
The amount of power delivered by the receiver is then given by:
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),()4(
),( 2
2 rrgrrt
ttgttrsr D
RR
DPAWP
4
),(),(
)4( 2
2rrgrttgt
rtt
rDD
RRP
P ),,,( rrtt
Note that in general:
Radar Range Equation (losses)
2*
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rt
rrgrttgttrcdrcdt
t
r
RR
DDee
P
P
Radar Cross Section (RCS)
Definition: Radar cross section or echo area of a target is defined as the area when interceptingthe same amount of power which, when scattered isotropically, produces at the receiver the samepower density as the actual target.
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WR
R
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222
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scat
R
),,,( rrtt rtrt ,
Transmitter and receiver not in the same location (bistatic RCS)
rtrt , Transmitter and receiver in the same location (usually the same antenna) called mono-static RCS
Radar Cross Section (RCS)
RCS Customary Notation: Typical RCS values can span 10-5m2 (insect) to 106 m2 (ship). Due to thelarge dynamic range a logarithmic power scale is most often used.