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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
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
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