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PNF, radiated=Re(E x H*)=|E||H|Cos(90o) Watts=0
PNF, stored=Im(E x H*)=|E||H|Sin(90o) Watts=Max
PRNF, radiated=Re(E x H*)=|E||H|Cos(0≤theta≤90o) Watts>0
PRNF, stored=Im(E x H*)=|E||H|Sin(0≤theta≤90o) Watts<Max
PFF, radiated=Re(E x H*)=|E||H|Cos(0o) Watts=Max
PFF, stored=Im(E x H*)=|E||H|Sin(0o) Watts=0
Patten is flat (no
main lobes are
infinite distances are not realizable in practice, the most commonly used criterion
for minimum distance of far-field observations is 2D2/λ.
One radian is defined as the plane angle with its vertex at the center of a circle of
radius r that is subtended by an arc whose length is r.
One steradian is defined as the solid angle with its vertex at the center of a sphere of
radius r that is subtended by a spherical surface area equal to that of a square with
each side of length r.
Radiation Power Density
The power radiated per unit surface area from the antenna surface (in spherical
coordinates system) is called Radiation Power Density (in W/m2).
The poynting vector can also be expressed as:
vector or Average
over one time
Imaginary part is
Radiation Power Density
Peak Values (not
Analogous to Ohm’s law :
Instanatious Total Power = Integration of normal component of poynting
vector (power density) over the entire surface
Average (total) radiated power
(Radial component of radiated
power density) Given
Radiation intensity (W/unit solid angle) in a given direction is defined as “the
power radiated from an antenna per unit solid angle.” Obtained by multiplying
radiation density (in W/m2) with square of distance r.
Radiation is equal in all directions, i.e. U will be independent of the angles θ and φ,
The beamwidth of a pattern is defined as the angular separation between two
identical points on opposite side of the pattern maximum.
Half-Power Beamwidth (HPBW ) is defined as: “In a plane containing the direction
of the maximum of a beam, the angle between the two directions in which the
radiation intensity is one-half value of the beam.”
The angular separation between the first nulls of the pattern is referred to as the
First-Null Beamwidth (FNBW )
•directivity of an antenna defined as “the ratio of the radiation intensity in a given
direction from the antenna to the radiation intensity averaged over all directions.
•The average radiation intensity is equal to the total power radiated by the antenna
divided by 4π.
•If the direction is not specified, the direction of maximum radiation intensity is
directivity of a nonisotropic source is equal to the ratio of its radiation intensity
in a given direction over that of an isotropic source.
Radiation power density of infinitesimal
linear dipole of length l <<λ.
General Formulation of Radiation Power Density & Radiation Intensity
The values of directivity will be equal to or greater than zero and equal to or less
than the maximum directivity (0 ≤ D ≤ D0).
The beam solid angle ΩA is defined as the solid angle through which all the
power of the antenna would flow if its radiation intensity is constant (and equal to
the maximum value of U, i.e. Umax) for all angles within ΩA.
Instead of using the exact expression of (2-23) to compute the directivity, it is often
convenient to derive simpler expressions, even if they are approximate, to compute
the directivity. These can also be used for design purposes.
For antennas with one narrow major lobe and very negligible minor lobes, the beam
solid angle is approximately equal to the product of the half-power beamwidths in two
The total antenna efficiency e0 is used to take into account losses at
the input terminals and within the structure of the antenna.
1. reflections because of the mismatch between the transmission line and the antenna
2. I 2R losses (conduction and dielectric)
•Gain of an antenna (in a given direction) is defined as “the ratio of the intensity, in a
given direction, to the radiation intensity that would be obtained if the power accepted
by the antenna were radiated isotropically.
•The radiation intensity corresponding to the isotropically radiated power is equal to
the power accepted (input) by the antenna
divided by 4π.”
•gain of the antenna is closely related to the directivity, it is a measure that takes into
account the efficiency of the antenna as well as its directional capabilities.
•directivity is a measure that describes only the directional properties of the antenna,
and it is therefore controlled only by the pattern.
•the ratio of the power gain in a given direction to the power gain of a reference
antenna (a lossless isotropic source).” The power input must be the same for both
Definition: 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 polarization-matched to the antenna.
RT (load) Rr RL
Finally the capture area is defined as the equivalent area, which when multiplied by the incident
power density leads to the total power captured, collected, or intercepted by the antenna.