Antenna Parameters Part 2

BEAM EFFICIENCY
A parameter used to judge the quality of transmitting and
receiving antennas.
The beam efficiency will indicate the amount of power in the
major lobe compared to the total power.

BANDWIDTH
Defined as the range of frequencies within which the
performance of the antenna, with respect to some
characteristic, conforms to a specified bandwidth.
Because the characteristics (input impedance, pattern, gain,
polarization, etc.) of an antenna do not necessarily vary in
the same manner or are even critically affected by the
frequency, there is no unique characterization of the
bandwidth.
Pattern bandwidth – gain, side lobe level, beamwidth,
polarization, and beam direction
Impedance bandwidth – input impedance and radiation
efficiency

POLARIZATION
Polarization of an antenna in a given direction is defined as
the polarization of the wave transmitted by the antenna.
Polarization of a radiated wave is defined as that property of
an electromagnetic wave describing the time varying
direction and relative magnitude of the electric-field vector

POLARIZATION
1. Linear - the electric field vectors are oriented in the same
direction in space
i. Vertical – the electric field progresses in the direction
of the propagation in the vertical plane
𝜀 𝑦 ≠ 0, 𝜀 𝑥 = 0
ii. Horizontal – the electric field progresses in the
direction of the propagation in the horizontal plane
𝜀 𝑥 ≠ 0, 𝜀 𝑦 = 0

POLARIZATION
2. Circular – the electric field vector rotates in circular
fashion as it progresses in the direction of propagation
𝜀 𝑥 = 𝜀 𝑦 = 0
i. Right-handed – the electric field vector rotates in a
clockwise manner as it recedes in the direction of
propagation
ii. Left-handed – the electric field vector rotates in a
counter- clockwise manner as it recedes in the direction of
propagation
3. Elliptical – a variation of circular polarization where
electric field rotates in elliptical way
𝜀 𝑥 ≠ 𝜀 𝑦 ≠ 0

POLARIZATION
4. Random – the electric field vector has no definite pattern
or orientation

INPUT IMPEDANCE
Defined as the impedance presented by an antenna at its
terminals or the ratio of the voltage to current at a pair of
terminals or the ratio of the appropriate components of the
electric field to magnetic fields at a point
𝑍 𝐴 = 𝑅 𝐴 + 𝑗𝑋𝐴

INPUT IMPEDANCE
Transmitting antenna and its equivalent circuit
In general, the resistive part consists of two components
𝑅 𝐴 = 𝑅 𝑟 + 𝑅 𝐿

INPUT IMPEDANCE
Antenna and its equivalent circuits in receiving mode

ANTENNA RADIATION EFFICIENCY
The conduction-dielectric efficiency is defined as the ratio
of the power delivered to the radiation resistance Rr to the
power delivered to Rr and RL. The radiation efficiency is
For a metal rod of length l and uniform cross-sectional area
A, the dc resistance is
The high-frequency resistance can be written, based on
uniform current distribution as

ANTENNA VECTOR EFFECTIVE
LENGTH AND EQUIVALENT AREAS
Vector effective length – it is a quantity that is used to determine
the voltage induced on the open-circuit terminals of the antenna
when a wave impinges upon it
Uniform plane wave incident upon dipole and aperture antennas

Effective area (aperture) – in a given direction is defined as
the ratio of the available power at the terminals of a
receiving antenna to the power flux density of a plane wave
incident on the antenna from that direction, the wave being
polarized-match to the antenna.

The effective area is
The scattering area is
The loss area is
The capture area is
Capture area = Effective Area + Scattering Area + Loss Area

Apertune efficiency – is defined as the ratio of the maximum
effective area of the antenna to its physical area
Partial effective area – this is the ratio of the available power
at the terminals of a receiving antenna to the power flux
density of a plane wave incident on the antenna from that
direction and with a specified polarization differing from the
receiving polarization of the antenna
The effective area of an antenna is not necessarily the same
as the physical aperture

MAXIMUM DIRECTIVITY AND
MAXIMUM EFFECTIVE AREA
The radiated power density of an isotropic antenna at a
distance R with transmitted power Pt and a directive gain of
Dt is
Two antennas separated by a distance R
With this, the power received

MAXIMUM DIRECTIVITY AND
MAXIMUM EFFECTIVE AREA
The maximum effective aperture of any antenna can be
related to its maximum directivity by
To accommodate conduction-dielectric losses (radiation
efficiency), maximum effective aperture is

FRIIS TRANSMISSION EQUATION AND
RADAR RANGE EQUATION
Friis transmission equation - elates the power received to
the power transmitted between two antennas separated by a
distance R > 2D2/λ, where D is the largest dimension of
either antenna.
Geometrical orientation of transmitting and receiving antennas for Friis
transmission equation

If the input power at the terminals of the transmitting antenna is Pt,
then its isotropic power density W0 at distance R from the antenna is
The ratio of the received to the input power is
For reflection and polarization-matched antennas aligned for
maximum directional radiation and reception, the equation above is
reduced to
This equation is referred to as Friis transmission equation. The term
(λ/4πR)2 is called the free-space loss factor.

The radar cross section or echo area (σ) is defined as the
area intercepting that amount of power which, when
scattered isotropically, produces at the receiver a density
which is equal to that scattered by the actual target. The
scattered power density is
For polarization-matched antennas aligned for maximum
directional radiation and reception
This equation is referred to as the radar range equation.

ANTENNA TEMPERATURE
The amount of energy radiated by an antenna is usually
represented by an equivalent brightness temperature TB

ANTENNA TEMPERATURE
The temperature appearing at the terminals of an antenna is
Assuming no losses or other contributions between antenna
and receiver, the noise power transmitted to the receiver is

ANTENNA TEMPERATURE
Antenna, transmission line, and receiver arrangement for system noise
power
calculation
The effective antenna temperature at the receiver terminals
is

ANTENNA TEMPERATURE
The antenna power can be modified to
If the receiver itself has a certain noise temperature Tr (due
to thermal noise in the receiver components), the system
noise power at the receiver terminals is given by

Antenna Parameters Part 2

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Antenna Parameters Part 2