ANTENNA

antennaLECTURES
lecture: BY Abdulmuttalib A. H. Aldouri
antenna& Mohammed Kamil
parameters

3. Finite Length Dipole

* ( )+
( ) {
* ( )+

𝑙
𝐼 𝑠𝑖𝑛 [𝛽 ( 𝑧)]

𝑙
𝐼 𝑠𝑖𝑛 [𝛽 ( 𝑧)]

Figure (12)

( ) ( )
[ ]

( ) ( )
[ ]

For the dipole, the average power density can be written as:

[ ]

( ) ( )
[ ]

And the total power radiated by the dipole is:

( ) ( )
∫ ∫ ∫ ∫ [ ]

* ( ) ( )+
∫

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antennaLECTURES
ANTENNA lecture: antenna
BY Abdulmuttalib A. H. Aldouri parameters
& Mohammed Kamil

This integral can be solved using Trapezoidal or Simpson's rule.

( ) ( )
[ ]

and:

( ) ( )
( ) [ ]

Elevation Plane Amplitude Patterns For a Thin Dipole with Sinusoidal Current Distribution

7
antenna lecture:
ANTENNA LECTURES antenna
BY Abdulmuttalib A. H. Aldouri parameters
& Mohammed Kamil

As the length of the dipole increases beyond one wavelength (l > λ), the number of
lobes begin to increase. The normalized power pattern for a dipole with l = 1.25λ is shown
in Figure below:

Radiation Resistance, Input Resistance and Directivity of a Thin Dipole with Sinusoidal
Current Distribution

8
 antennaLECTURES
ANTENNA lecture: antenna
BY Abdulmuttalib A. H. Aldouri parameters
& Mohammed Kamil

4. Half-Wave Dipole ( ⁄ )
One of the most commonly used antennas is the half-wavelength (l = λ/2) dipole.
Because its radiation resistance is 73Ω, which is very near the 75Ω characteristic impedances
of some transmission lines.
The electric and magnetic field components of a half-wavelength dipole can be obtained by
letting l = λ/2, thus:

( )
[ ]

( )
[ ]

The average power density and radiation intensity can be written, respectively, as:

( )
[ ]

( )
[ ] ( )

( )
( ) [ ]

* ( )+
∫

( ) ( )

and the radiation resistance is:

( )

( )

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 antennaLECTURES
ANTENNA lecture: antenna
BY Abdulmuttalib A. H. Aldouri parameters
& Mohammed Kamil

To find the HPBW:

( )
( )| [ ]

( )

( ) ( ( ))

By using trial and error, we can find the value of θh 51o

| | | |

Figure (13) shows the two and three dimensional radiation pattern for a λ/2 dipole.

0
330 30

300 60

1
0.5
270 90

240 120

210 150
180

Figure (13)

H.W. For a λ/4 dipole:

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antennaLECTURES
ANTENNA lecture: antenna
BY Abdulmuttalib A. H. Aldouri parameters
& Mohammed Kamil

Example:
A λ/2 dipole radiates a time-averaged power of 600 W at a frequency of 300 MHz. A second
λ/2 dipole is placed at a point ( ), where r = 200 m, = 90◦, = 40◦. It is oriented
so that its axis is parallel to that of the transmitting antenna. What is the available power at the
terminals of the second (receiving) dipole?
Solution:

( )

( )

( ) 1.643

( )

H.W: Find prad at r = 200 m, = 50◦, = 20?

Example:
A dipole is radiating into free-space. Input power to the dipole is 100 W. Assuming an
overall efficiency of 50%, find the power density (in W/m2) at (r = 500 m, = 60◦, = 0)?
Solution:

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