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

Largest

dimension of

the antenna

Patten is flat (no

main lobes are

formed)

Main lobe

begins to

develop

Pattern is

well formed

with dominant

Main lobe

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 DensityThe power radiated per unit surface area from the antenna surface (in spherical

coordinates system) is called Radiation Power Density (in W/m2).

Instantaneous

Poynting vector

The poynting vector can also be expressed as:

Average poynting

vector or Average

power density

Real (calculated

over one time

period):

Imaginary part is

eliminated

Radiation Power Density

Peak Values (not

RMS)

Analogous to Ohm’s law :

P=1/2 VI*

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, D•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

implied.”

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

General Formulation of Directivity

Let,

The values of directivity will be equal to or greater than zero and equal to or less

than the maximum directivity (0 ≤ D ≤ D0).

Normalised Radiation

intensity

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

perpendicular planes

Symmetrical and

Approximate Methods to Calculate Directivity

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•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.

Relative Gain

•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

antennas.

Partial Gains

Ps=Pg+Pr+PL ( Conjugate Matching)

Receiving Mode

Antenna in Receiving Mode…

Vector Effective Length of Antenna

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.

2

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.

Aem=?

Emf induced= VT= E* length of dipole