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 C = 2πr there are 2πr rad ( 2πr r ) in a full circle.
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 A = 4πr there are 2 ( 4πr 2 2 ) in a closed sphere. r – The infinitesimal area dA on the surface of a sphere of radius r is dA = r 2 sin θdθ m 2 – Therefore the element of solid angle dΩ of a sphere can be written as dΩ = sin θdθdφ sr
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/m H= 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)
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 Gain Another useful measure describing the performance of an antenna is the gain. Although the gain of the antenna is closely related to the directivity. It is a measures that takes into account the efficiency of the antenna as well as its directional capabilities. Absolute 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. Mathematically represented as:- Gain = 4π radiation intensity = 4π U (θ,φ) total input (accepted) power Pin
Antenna Gain An alternate way to define antenna gain is :- G = Power radiated by an ant Power radiated by ref ant The i/p power to both the antenna is the same and the reference ant generally chosen is an isotrope.
Antenna Efficiency (eo) eo is to take into account losses in antenna – Reflection and mismatch losses – Conduction losses (I2R) eo = er ec ed (overall efficiency) eo = total efficiency er = reflection (mismatch) efficiency = (1-|Γ|2) ed = dielectric efficiency Γ= voltage reflection coefficient at the input terminals of antenna
Beam Efficiency To judge the quality of transmission/receptionBE = Power transmitted (received) within cone angle θ1 power transmitted (received) by the antenna
Bandwidth “Range of frequencies within which performance of an antenna with respect to some characteristic conforms to a specified standard” Characteristics within acceptable values of centre frequency (Gain, beam direction, side lobe level, Polarization). Broadband antenna bandwidth described in ratio of upper to lower freq. (e.g. 10:1) Narrow band antenna described in %age of B.W. Antenna chars. don’t vary in the same manner Pattern Bandwidth, Impedance Bandwidth
Polarization Polarization is defined as “that property of the electromagnetic wave describing the time varying direction and relative magnitude of the electric field vector; specially 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 which it is traced as observed along the direction of propagation. Polarization is the curve traced out by the end point of the arrow representing the instantaneous electric field. The field must be observed along the direction of propagation. Polarization can be classified as linear, circular or elliptical. If the vector that describes the electric field at a point in space as a function of time is always directed along a line, the field is said to be linearly polarized.
Polarization (contd) In general however, the figure that the electric field traces is an ellipse and the field is said to be elliptically polarized. Linear and circular polarizations are special cases of elliptical and they can be obtained when the ellipse becomes a straight line or a circle respectively.
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 Rr = antenna radiation resistance Then power radiated is I2 Rr watts where Rr 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 Rr 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.
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:- le = area under non – uniform current distribution l area under uniform peak current distribution
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 Pd is the power density at the antenna and Pr is the received power then.• Pr = Pd A watts or Pr 2 A= m Pd For an antenna with power gain G, the effective aperture A at the operating wavelength λ is given by Gλ2 A= 4π