Lec-2Antenna Parameters

(contd)

Radian and Steradian

• Radian

– A measure of a plane angle is a radian.

– One radian is defined as” the plane angle with its

vertex at the centre of a circle of radius r that is

subtended by an are whose length is r.

– Since the circumference of a circle of radius r is

there are rad ( ) in a full circle.

rC 2

r2r

r2

Radian and Steradian• Steradian

– The measure of a solid angle is a steradian.– One steradian is defined as “ the solid angle with its vertex

at the centre 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.

– Since the area of a sphere of radius r is there are ( ) in a closed sphere.

– The infinitesimal area dA on the surface of a sphere of radius r is

– Therefore the element of solid angle of a sphere can be written as

24 rA 2

24r

r

drdA sin2 2m

d

srddd sin

Steradian

Radiation Power Density The quantity used to describe power associated

with an electromagnetic wave is the instantaneous Poynting vector defined as:- W = E × H (W/m2)

W = instantaneous Poynting vector W/m2

E = instantaneous electric field intensity V/mH= instantaneous magnetic field intensity A/m

2

Radiation Intensity Power radiated by an antenna per unit solid angle Far field parameter U = r2 Wrad

where

U = radiation intensity (W/unit solid angle)Wrad = radiation density (W/m2)

or U = r2 Prad/A= Prad/A/ r2 = Prad/ Ω The total power is obtained by integrating the radiation

intensity over the entire solid angle of 4π Prad = ∫∫ U dΩ = ∫∫ U Sin(θ) dθdφ

Directivity Ratio of radiation intensity in a given direction to the radiation Intensity averaged over all directions. D = U/Uo = U / Prad / 4π

=4πU / Prad

If direction not specified – Direction of max radiation intensity Do

Dmax = Do = Umax / Uo =4π Umax / Prad

D = directivity (dimensionless quantity)Do = maximum directivity

U = radiation intensity (W/unit solid angle)Umax=maximum radiation intensity(W/unit solid angle)

Uo=radiation intensity of isotope (W/unit solid angle)

Prad= total radiated power (W)

Partial Directivities: For orthogonal polarization components

“ That part of radiation intensity corresponding to a given polarization divided by total radiation intensity “Do = Dθ + Dφ

Do = 4π Uθ /Prad + 4π Uφ /Prad

Implies how well a radiator directs em energy in a certain direction

Antenna GainAntenna Gain Another useful measure describing the performance of an Another useful measure describing the performance of an

antenna is the gain. Although the gain of the antenna is closely antenna is the gain. Although the gain of the antenna is closely related to the directivity.related to the directivity.

It is a measures that takes into account the efficiency of the It is a measures that takes into account the efficiency of the antenna as well as its directional capabilities. antenna as well as its directional capabilities.

Absolute gain of an antenna (in a given direction) is defined as “ Absolute gain of an antenna (in a given direction) is defined as “ the ratio of the intensity in a given direction to the radiation the ratio of the intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the intensity that would be obtained if the power accepted by the antenna were radiated isotropically. antenna were radiated isotropically.

Mathematically represented as:- Mathematically represented as:- Gain = Gain = 4π radiation intensity radiation intensity = = 4π U (θ,φ) total input (accepted) powertotal input (accepted) power Pin

Antenna GainAntenna Gain

An alternate way to define antenna gain is :-An alternate way to define antenna gain is :-GG == Power radiated by an antPower radiated by an ant

Power radiated by ref antPower radiated by ref ant The i/p power to both the antenna is the same and the reference The i/p power to both the antenna is the same and the reference

ant generally chosen is an isotrope. ant generally chosen is an isotrope.

Antenna Efficiency (eAntenna Efficiency (eoo)) eeoo is to take into account losses in antenna is to take into account losses in antenna

– Reflection and mismatch lossesReflection and mismatch losses– Conduction losses (IConduction losses (I22R)R)

eeo = o = eer r eec c eedd (overall efficiency)(overall efficiency) eeo = o = total efficiency total efficiency eer r = reflection (mismatch) efficiency == reflection (mismatch) efficiency = (1-| (1-|ΓΓ||22))

eed = d = dielectric efficiency dielectric efficiency ΓΓ= voltage reflection coefficient at the input = voltage reflection coefficient at the input terminals of antennaterminals of antenna

Beam EfficiencyBeam Efficiency To judge the quality of transmission/receptionTo judge the quality of transmission/receptionBE = BE = Power transmitted (received) within cone angle Power transmitted (received) within cone angle θθ11

power transmitted (received) by the antennapower transmitted (received) by the antenna

BandwidthBandwidth ““Range of frequencies within which performance of an Range of frequencies within which performance of an

antenna with respect to some characteristic conforms to a antenna with respect to some characteristic conforms to a specified standard” specified standard”

Characteristics within acceptable values of centre Characteristics within acceptable values of centre frequency (Gain, beam direction, side lobe level, frequency (Gain, beam direction, side lobe level, Polarization).Polarization).

Broadband antenna bandwidth described in ratio of upper Broadband antenna bandwidth described in ratio of upper to lower freq. (e.g. 10:1)to lower freq. (e.g. 10:1)

Narrow band antenna described in %age of B.W.Narrow band antenna described in %age of B.W. Antenna chars. don’t vary in the same mannerAntenna chars. don’t vary in the same manner Pattern Bandwidth, Impedance BandwidthPattern Bandwidth, Impedance Bandwidth

PolarizationPolarization Polarization is defined as “that property of the Polarization is defined as “that property of the

electromagnetic wave describing the time varying direction electromagnetic wave describing the time varying direction and relative magnitude of the electric field vector; specially and relative magnitude of the electric field vector; specially the figure traced out as a function of time by the extremity the figure traced out as a function of time by the extremity of the vector at a fixed location in space and the sense in of the vector at a fixed location in space and the sense in which it is traced as observed along the direction of which it is traced as observed along the direction of propagation.propagation.

Polarization is the curve traced out by the end point of the Polarization is the curve traced out by the end point of the arrow representing the instantaneous electric field. The arrow representing the instantaneous electric field. The field must be observed along the direction of propagation. field must be observed along the direction of propagation.

Polarization can be classified as linear, circular or elliptical. Polarization can be classified as linear, circular or elliptical. If the vector that describes the electric field at a point in If the vector that describes the electric field at a point in space as a function of time is always directed along a line, space as a function of time is always directed along a line, the field is said to be linearly polarized. the field is said to be linearly polarized.

Polarization (contd)Polarization (contd) In general however, the figure that the electric field In general however, the figure that the electric field

traces is an ellipse and the field is said to be elliptically traces is an ellipse and the field is said to be elliptically polarized. polarized.

Linear and circular polarizations are special cases of Linear and circular polarizations are special cases of elliptical and they can be obtained when the ellipse elliptical and they can be obtained when the ellipse becomes a straight line or a circle respectively.becomes a straight line or a circle respectively.

Polarization (rotation of wave)

Polarization Ellipse

polarization

Radiation Resistance• An important property of a transmitting ant is its radiation resistance

which is associated with the power radiated by the ant. If I = rms ant current= antenna radiation resistanceThen power radiated is I2 watts where is a fictitious resistance which accounts for the radiated power somewhat like a acct resistance which dissipates heat.

• The radiation resistance should be large as the greater is, the greater the power radiated by ant.

• In contrast, for a receiving antenna its i/p impedance is important. The i/p impedance is defined as the ratio of voltage to correct at its i/p and it should be matched to connecting lines or cables.

• The i/p impedance may or may not equal to its radiation resistance, though very often it does.

rR

rR rR

rR

Effective Length• An antenna with a non-uniform distribution of current

over its length l can be considered as having a shorter effective length le over which the current is assumed to be uniform and equal to its peak value. The relationship b/w le and l is given by:-

= area under non – uniform current distribution

area under uniform peak current distribution

lle

Effective Aperture • The power received by an antenna can be associated with a

collecting area. Every antenna may be considered to have such a collecting area which is called its effective aperture A.

• If is the power density at the antenna and is the received power then.

• = A watts or

For an antenna with power gain G, the effective aperture A at the operating wavelength λ is given by

dPrP

rP dP2m

PPA

d

r

4

2GA

End