wire antennas

2007-08 CRL-715 Radiating Systems for RF Communications
• The dipole and the monopole are arguably the two most widely used antennas across the UHF, VHF and lower-microwave bands.
• Arrays o dipoles are commonly used as base-station antennas in land-mobile systems.
• The monopole and its variations are perhaps the most common antennas or portable e!uipment, such as cellular telephones, cordless telephones, automobiles, trains, etc.
• An alternative to the monopole antenna or hand-held units is the loop antenna, the microstrip patch antenna, the spiral antennas, inverted-" and inverted-F antennas, and others.
LINEAR WIRE ANTENNASLINEAR WIRE ANTENNAS

INFINITESIMAL DIPOLE
%onstant current distribution$ Top-hat antenna

appro&imation valid or the ininitesimal dipole

#n spherical coordinates

eatures o the ield vectors o a current element
• "ongitudinal (r -components) components decrease with distance as *+r or aster. eglected in the ar one.
• Transverse component have a *+r term / dominant at large distances
• Transverse E and H ield components are orthogonal to each other (E Θ and H φ)

Po!er densit" o a current element

Radiated po!er o a current element
Radiation resistance o a current element (ideal dipole)

SMALL DIPOLE
The Vector 3otential integral is obtained as$

The solution assuming R 4 r $
• This result is e&actly one-hal o the result obtained or vector potential o an ininitesimal dipole.
• #s this e&pected5 678999

The normalied ield pattern is the same as that o the ininitesimal dipole$
The power pattern$
The beam solid angle$
The directivity

The radiated power is our times less than that o an ininitesimal dipole because the ar ields are twice smaller in magnitude

FINITE LEN#T$ DIPOLE
A good appro&imation o the current distribution along the dipole:s length is the sinusoidal one$

The inite-length dipole is subdivided into an ininite number o ininitesimal dipoles o length dz 2. 7ach ininitesimal dipole produces the elementary ar ield$
Using the ar-ield appro&imations$

Using the superposition principle, the total ar ield is obtained as$
7lement actor • Field o a unit length
ininitesimal dipole located at a reerence point (origin)
• ;epends on type o current and its direction
8pace actor (pattern actor)

For the current distribution or inite length dipole, the pattern actor is$
The above integrals are solved using$

The ar ield o the inite-length dipole is obtained as
The amplitude pattern$
3atterns (in d<) or some dipole lengths l = >$

The pattern o the dipole l 1 *.?>

The power pattern$
The radiated power
The total radiated power is given by$

ℑ is solved in terms o the cosine and the sine integrals$
@here,

adiation resistance$
#nput resistance
# the dipole is lossless, the input power is e!ual to the radiated power$

@hen the overall length o the antenna is a multiple o λ,
the input current$
#n practice, the current is not e&actly sinusoidal, hence r is
not ininite but has very large values.
The current is not e&actly sinusoidal due to nonero radius
o the wire and inite gap spacing at t%e terinals.
0in
r
I
R
Finite eed gap$
To account or nonero current at the eed point, the
sinusoidal current distribution is modiied by adding a
!uadrature term$
z
z
l l I z a I z jpI z z l
l l I z a I z jpI z l z
β β β
β β β
= − + − ≤ ≤ ÷

÷ = + + − − ≤ ≤ ÷ ÷

$alf&!avelengt% dipole
This is a classical and widely used thin wire antenna$
adiated power low density$
adiation intensity$
adiated power

adiation resistance$
#nput resistance
• The imaginary part o the input impedance is 4 E j .? G.
• To ac!uire ma&imum power transer, this reactance has to be removed by matching (that is shortening) the dipole
• thic dipole l ≈ B.I> • thin dipole l ≈ B.J>
• The input impedance o the dipole depends strongly on the ratio l +>
• The input impedance is also inluenced by the capacitance associated with the physical Kunction to the transmission line.

#nput resistance #nput reactance
Met%od of iages

'ertical electric current eleent a(ove perfect conductor
• The ield at the observation point P is a superposition o the ields o the actual source and the image source, both radiating in a homogeneous medium o constitutive parameters.
• The actual source is a current element (I Ll ) (ininitesimal
dipole).
For the amplitude term

The total ar ield

As the vertical dipole moves urther away rom the ininite conducting (ground) plane, more and more lobes are introduced in the power pattern. This eect is called scalloping o the pattern.
The number o lobes is$

Total radiated power
• As Mh B, the radiated power o the vertical dipole above→
ground approaches twice the value o the radiated power o a dipole o the same length in ree space.
• As Mh N, the radiated power o both dipoles becomes the→
same
adiation resistance
As M h N, the radiation resistance o both dipoles becomes the same→
As M h B, the radiation resistance o the vertical dipole above→

adiation intensity
The ma&imum o ! (O) occurs at O 1π + (e&cept or Mh N)$→
This value is times greater than ! ma& o a ree-space dipole o the
same length.
Da&imum directivity
# Mh 1B, " 1 C, which is twice the ma&imum directivity o a
ree-space current element (" id 1 *.?).
The ma&imum o " as a unction o the height h occurs when
Mh 1 .JJ* (h 1 B.?J?> ). Then, "#$.%$$.

Monopoles
• A monopole is a dipole that has been divided into hal at its center eed point and ed against a ground plane. #t is normally a quarter wavelength long.
• The vertical monopole is e&tensively used or AD broadcasting (f 1?BB to *?BB H, > 1BB to PBB m), because it is the shortest most eicient antenna at these re!uencies and vertically polaried waves suer less attenuation at close-to-ground propagation.
• Usually multiple radial wire rods, each B.? Q B.C?> long, are buried at the monopole base in the ground to simulate perect ground plane, so that the pattern appro&imates closely the theoretical one, i.e., the pattern o the >+-dipole.

• The ield distribution in the upper hal-space is the same as that o the respective ree-space dipole.
• The currents and the charges on a monopole are the same as on the upper hal o its dipole counterpart but the terminal voltage is only hal that o the dipole. The input impedance o a monopole is thereore only hal that o the respective dipole$

T%e )uarter&!avelengt% onopole
• This is a straight wire o length l1>+ mounted over a ground plane.
• The !uarter-wavelength monopole is very similar to the hal- wavelength dipole in the hemisphere above the ground plane.
• #ts radiation pattern is the same as that o a ree-space >+-dipole, only that it is non-ero only or B°RORSB°.

• The radiation resistance o the >+-monopole is hal that o the >+-dipole$
• The directivity o the >+-monopole is$

Appro*iate Forulas for Rapid +alculations , Design
"et,
Then
;etermine the length o the dipole whose input resistance
is ?BG.
$ori-ontal current eleent a(ove a perfectl" conducting plane
• The analysis is analogous to that o a vertical current element above a ground plane.
• The dierence arises in the element actor &' O) because o the horiontal orientation o the current element.
•The current element is oriented along the ( -a&is.

The ar-ield appro&imations$
The ar-ield$
The normalied pattern

The radiated power and the radiation resistance o the horiontal dipole
adiation intensity
Da&imum ;irectivity
For small Mh

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