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 ...
Radian and Steradian• Steradian   – The measure of a solid angle is a steradian.   – One steradian is defined as “ the sol...
Steradian
Radiation Power Density The quantity used to describe power associated with an electromagnetic wave is the instantaneous ...
Radiation Intensity Power   radiated by an antenna per unit solid angle Far field parameter U = r2 Wrad  where  U = rad...
Directivity   Ratio of radiation intensity in a given direction to the radiation    Intensity averaged over all direction...
 Partial Directivities: For orthogonal polarization  components “ That part of radiation intensity corresponding  to a gi...
Antenna Gain   Another useful measure describing the performance of an    antenna is the gain. Although the gain of the a...
Antenna Gain   An alternate way to define antenna gain is :-    G =        Power radiated by an ant               Power r...
Antenna Efficiency (eo)       eo is to take into account losses in antenna    –      Reflection and mismatch losses    – ...
Beam Efficiency To judge the quality of transmission/receptionBE = Power transmitted (received) within cone angle θ1     ...
Bandwidth “Range of frequencies within which performance  of an antenna with respect to some characteristic  conforms to ...
Polarization   Polarization is defined as “that property of the    electromagnetic wave describing the time varying    di...
Polarization (contd)   In general however, the figure that the electric field    traces is an ellipse and the field is sa...
Polarization (rotation of wave)
Polarization Ellipse                       polarization
Radiation Resistance• An important property of a transmitting ant is its radiation  resistance which is associated with th...
Effective Length• An antenna with a non-uniform distribution of current  over its length l can be considered as having a s...
Effective Aperture• The power received by an antenna can be associated with a  collecting area. Every antenna may be consi...
End
Lec 2 terms  and definitions
Lec 2 terms  and definitions
Lec 2 terms  and definitions
Lec 2 terms  and definitions
Lec 2 terms  and definitions
Lec 2 terms  and definitions
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Lec 2 terms and definitions

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Lec 2 terms and definitions

  1. 1. Lec-2Antenna Parameters (contd)
  2. 2. 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.
  3. 3. 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
  4. 4. Steradian
  5. 5. 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
  6. 6. 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
  7. 7. 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)
  8. 8.  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
  9. 9. 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
  10. 10. 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.
  11. 11. 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
  12. 12. Beam Efficiency To judge the quality of transmission/receptionBE = Power transmitted (received) within cone angle θ1 power transmitted (received) by the antenna
  13. 13. 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
  14. 14. 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.
  15. 15. 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.
  16. 16. Polarization (rotation of wave)
  17. 17. Polarization Ellipse polarization
  18. 18. 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.
  19. 19. 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
  20. 20. 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
  21. 21. End

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