1. Fundamental Antenna Parameters
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.

2. Coordinate System

3. Types of Radiation Patterns
Idealized
Point Radiator
Vertical Dipole
Radar Dish
Isotropic
Omnidirectional
Directional

4. Radiation Pattern Lobes
Half-Power BEAMWIDTH
0dB
-3dB
Main lobe
Full Null Beamwidth
Between
1st NULLS
Side lobes
Back lobes
PEAK
SIDE LOBE LEVEL
( SLL )
~ -20dB

5. Radiation Pattern Lobes

6. Field Regions Reactive near-field region Far-field (Fraunhofer) region
Radiating near-field
(Fresnel) region R2

7. Radiation Intensity Aside on Solid Angles infinitesimal area
of surface of sphere

8. Radiation Intensity since decays as 1/r2 in the far field
will be independent of r

9. Radiation Intensity

10. Radiation Intensity Examples
1. Isotropic radiator
2. Hertzian Dipole

11. Directive Gain

12. Directivity Examples
1. Isotropic radiator
2. Hertzian Dipole

13. => => Antenna Gain POWER DENSITY IN A CERTAIN DIRECTION
DIRECTIVITY
=>
DIVIDED BY THE TOTAL POWER RADIATED
GAIN
=>
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

14. Antenna Gain Sources of Antenna System Loss
losses due to impedance mismatches
losses due to the transmission line
conductive and dielectric losses in the antenna
losses due to polarization mismatches
According to IEEE standards the antenna gain does not include losses due to
impedance or polarization mismatches. Therefore the antenna gain only
accounts for dielectric and conductive losses found in the antenna itself. However
Balanis and others have included impedance mismatch as part of the antenna gain.
The antenna gain relates to the directivity through a coefficient called the
radiation efficiency (et)
impedance mismatch
conduction losses
dielectric losses

15. Overall Antenna Efficiency
The overall antenna efficiency is a coefficient that accounts for all the different
losses present in an antenna system.

16. Reflection Efficiency
The reflection efficiency through a reflection coefficient (G) at the input (or feed)
to the antenna.

17. Radiation Resistance
The radiation resistance is one of the few parameters that is relatively
straight forward to calculate.
Example: Hertzian Dipole

18. Radiation Resistance
Example: Hertzian Dipole (continued)

19. Antenna Radiation Efficiency
Conduction and dielectric losses of an antenna are very difficult to separate and
are usually lumped together to form the ecd efficiency. Let Rcd represent the actual
losses due to conduction and dielectric heating. Then the efficiency is given as
For wire antennas (without insulation) there is no dielectric losses only conductor
losses from the metal antenna. For those cases we can approximate Rcd by:
where b is the radius of the wire, w is the angular frequency, s is the conductivity
of the metal and l is the antenna length

20. Example Problem:
A half-wavelength dipole antenna, with an input impedance of 73W is to be
connected to a generator and transmission line with an output impedance of
50W. Assume the antenna is made of copper wire 2.0 mm in diameter and the
operating frequency is 10.0 GHz. Assume the radiation pattern of the antenna is
Find the overall gain of this antenna
SOLUTION
First determine the directivity of the antenna.

21. Example Problem: Continued
SOLUTION
Next step is to determine the efficiencies

22. Example Problem: Continued
SOLUTION
Next step is to determine the gain

23. 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

24. Effective Aperture plane wave Aphysical Pload incident Question:
Answer: Usually NOT

25. Directivity and Maximum Effective Aperture (no losses)
Antenna #2
transmit
receiver R
Direction of wave propagation
Antenna #1
Atm, Dt
Arm, Dr

26. Directivity and Maximum Effective Aperture (include losses)
Antenna #2
transmit
receiver R
Direction of wave propagation
Antenna #1
Atm, Dt
Arm, Dr
conductor and
dielectric losses
reflection losses
(impedance mismatch)
polarization mismatch

27. Friis Transmission Equation (no loss)
Antenna #1
transmit
Antenna #2
(qr,fr)
receiver
Arm, Dr
Atm, Dt
(qt,ft) R
The transmitted power density supplied by Antenna #1
at a distance R and direction (qr,fr) is given by:
The power collected (received) by Antenna #2 is given by:

28. Friis Transmission Equation (no loss)
Antenna #1
transmit
Antenna #2
(qr,fr)
receiver
Arm, Dr
Atm, Dt
(qt,ft) R
If both antennas are pointing in the direction of their maximum radiation pattern:

29. Friis Transmission Equation ( loss)
Antenna #1
transmit
Antenna #2
(qr,fr)
receiver
Arm, Dr
Atm, Dt
(qt,ft) R
conductor and
dielectric losses
receiving antenna
reflection losses in receiving
(impedance mismatch)
free space loss factor
conductor and
dielectric losses
transmitting antenna
reflection losses in transmitter
(impedance mismatch)
polarization mismatch

30. Friis Transmission Equation: Example #1
A typical analog cell phone antenna has a directivity of 3 dBi at its operating frequency of 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.
= 0
= 1
= 1
= 0
= 1

31. 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.
= 0
= 1
= 1
= 0
= 1

32. 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.
= 0
= 1
= 1
= 0
= 1

33. Radar Range Equation
Definition: Radar cross section or echo area of a target is defined as the area when intercepting
the same amount of power which, when scattered isotropically, produces at the receiver the same
power density as the actual target.
(radar cross section) m2
R (distance from target) m
Ws (scattered power density) W/m2
Winc (incident power density) W/m2

34. Radar Range Equation (no losses)
Power density incident on the target is a function
of the transmitting antenna and the distance between the target and transmitter:
The amount of power density scattered by the target at the location of the receiver is then given by:
The amount of power delivered by the receiver is then given by:
Note that in general:

35. Radar Range Equation (losses)

36. Radar Cross Section (RCS)
Definition: Radar cross section or echo area of a target is defined as the area when intercepting
the same amount of power which, when scattered isotropically, produces at the receiver the same
power density as the actual target.
Transmitter and receiver not in the same location (bistatic RCS)
Transmitter and receiver in the same location (usually the same antenna) called mono-static RCS

37. Radar Cross Section (RCS)
RCS Customary Notation:
Typical RCS values can span 10-5m2 (insect) to 106 m2 (ship). Due to the
large dynamic range a logarithmic power scale is most often used.
100 m2
20 dBsm
10 m2
10 dBsm
1 m2
0 dBsm
0.1 m2
-10 dBsm
0.01 m2
-20 dBsm