EE335 – Antenna Radiation Characteristics
20 Lecture
pp 380-387
9-2
Antenna Pattern: The far field directional properties of an antenna when measured at a
fixed distance from the antenna
3-D plat that displays the strength of the radiation field or power density as a function of
direction, zenith angle: θ and azimuth angle φ.
Solid angle:
dA R 2 sin θ dθ dφ
dΩ = 2 =
= sin θ dθ dφ (steradians)
R
R2
Solid angle of a sphere is 4π and a hemisphere is 2π
20-1
r
r
dPrad = S ave ⋅ dA = SdA = R 2 S (R, θ , φ )dΩ
S is power density
The normalized radiation intensity is given by: F (θ , φ ) =
S (R, θ , φ )
S max
The total power radiated by an antenna through a spherical surface at a fixed distance R is
obtained by integrating:
2π
Prad = R
2
π
∫ ∫ S (R,θ ,φ )sin θ dθ dφ = R
φ θ
=0 =0
2π
2
S max
π
∫ ∫ F (θ , φ )sin θ dθ dφ = R
φ θ
=0 =0
2
S max ∫∫ F (θ , φ )dΩ
4π
This is the total radiated power
The plot of F(θ,φ) as a function of the angles gives a 3-D plot of the antenna radiation
pattern.
An isotropic antenna (unreal) radiates evenly in all directions therefore F = 1
Some antenna have highly directional patterns with narrow beams that require a decibel
scale to note the features:
F(dB) = 10 log F
20-2
The beamwidth, half-power beamwidth, 3-dB beamwidth is defined by the angles
where the F has reduced to half of its maximum values (-3dB on the decibel scale)
β = θ 2 − θ1 :
θ1 and θ2 are the half-power angles
Null beamwidth: βnull : the width of the spacing between the first nulls on the sides of the
peaks
Antenna Directivity:
D=
Fmax
=
1
Fave
4π
1
∫∫ π F (θ , φ )dΩ
=
4π
4π
≈
Ω p β xz β yz
4
Represents the ratio of maximum power to the average usually expressed in decibels
D(dB) = 10 log D
Radiation efficiency: the ratio of the power radiated to the total power supplied to the
antenna
ξ=
Prad
Prad
=
Pt
Prad + Ploss
4π R 2 S max
Gain of the antenna is defined as G =
=ξ D
Pt
Gain accounts for ohmic losses in the antenna materials whereas the directivity does not.
For a lossless antenna the efficiency is one.
20-3
The transmission line sees the antenna as an impedance, part of the power is radiated and
part is dissipated as heat in the antenna.
1 2
I 0 Rloss
P
Prad
Rrad
2
=
Æ ξ = rad =
1 2
Pt
Prad + Ploss Rrad + Rloss
= I 0 Rrad
2
Ploss =
Prad
20-4