Antenna PARAMETERS

1. RADIATION & PROPOGATION -Fundamental Parameters of Antennas AJAL.A.J Assistant Professor –Dept of ECE, UNIVERSAL ENGINEERING COLLEGE Mob: 8907305642 MAIL: ec2reach@gmail.com AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

2. An antenna is a way of converting the guided waves present in a waveguide, feeder cable or transmission line into radiating waves travelling in free space, or vice versa. AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

3. Radiation Pattern Lobes Main lobe Full Null Beamwidth Between 1st NULLS Side lobes Back lobes

4. Only accelerating charges produce radiation. Idealized Point Radiator Isotropic AJAL.A.J- AP ECE Vertical Dipole Omnidirectional Radar Dish Directional UNIVERSAL ENGG COLLEGE

5. Two fields regions: oNear field or Fresnel region: The region within the radius of the smallest sphere which completely encloses the antenna is called Fresnel region. In sitting an antenna ,it’s crucial to keep objects out of the near field region to avoid coupling the currents in the antenna with objects. oFar Field or Fraunhofer region: The region beyond Fresnel region is called Fraunhofer region AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

6. Antenna parameters are: 1.Radiation Pattern 2.Directivity 3.Radiation Resistance and Efficiency 4.Power Gain 5.Bandwidth 6.Reciprocity 7.Effective Aperture 8.Beamwidth and Directivity 9.The Friis Formula: Antennas in Free Space 10.Polarisation Matching AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

7. The radiation pattern of an antenna is a plot of the farfield radiation from the antenna. More specifically, it is a plot of the power radiated from an antenna per unit solid angle, or its radiation intensity U [watts per unit solid angle]. This is arrived at by simply multiplying the power density at a given distance by the square of the distance r, where the power density S [watts per square metre] is given by the magnitude of the time-averaged Poynting vector: U=r^²S AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

8. Radiation Intensity Aside on Solid Angles surface area = r 2 ρ θ = 1.0 rad arc length = ρ total circumfrance = 2π radians r Ω = 1.0 sr total surface area = S o = 4π r 2 = Ω r 2 So Ω = 2 sr r infinitesimal area ds = r 2 sin(θ ) dθ dφ of surface of sphere ds dΩ = 2 = sin(θ ) dθ dφ r

10. The directivity D of an antenna, a function of direction is defined by the ratio of radiation intensity of antenna in direction to the mean radiation intensity in all directions. AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

12. The resistive part of the antenna impedance is split into two parts, a radiation resistance Rr and a loss resistance Rl. The power dissipated in the radiation resistance is the power actually radiated by the antenna, and the loss resistance is power lost within the antenna itself. This may be due to losses in either the conducting or the dielectric parts of the antenna. Radiation efficiency e of the antenna as e is the ratio of power radiated to the power accepted by antenna antenna with high radiation efficiency therefore has high associated radiation resistance compared with the losses. The antenna is said to be resonant if its input reactance Xa =0. AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

14. The power gain G, or simply the gain, of an antenna is the ratio of its radiation intensity to that of an isotropic antenna radiating the same total power as accepted by the real antenna. When antenna manufacturers specify simply the gain of an antenna they are usually referring to the maximum value of G. AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

15. Antenna Gain U (θ , ϕ ) G (θ , ϕ ) = 4π Pinput DIRECTIVITY POWER DENSITY IN A CERTAIN DIRECTION DIVIDED BY THE TOTAL POWER RADIATED GAIN POWER DENSITY IN A CERTAIN DIRECTION DIVIDED BY THE TOTAL INPUT POWER TO THE ANTENNA TERMINALS (FEED POINTS) IF ANTENNA HAS OHMIC LOSS… THEN, GAIN < DIRECTIVITY

17. The bandwidth of an antenna expresses its ability to operate over a wide frequency range. It is often defined as the range over which the power gain is maintained to within 3dB of its maximum value, or the range over which the VSWR is no greater than 2:1, whichever is smaller. The bandwidth is usually given as a percentage of the nominal operating frequency. The radiation pattern of an antenna may change dramatically outside its specified operating bandwidth. AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

19. Reciprocity theorem: If a voltage is applied to the terminals of an antenna A and the current measured at the terminals of another antenna B then an equal current will be obtained at the terminals of antenna A if the same voltage is applied to the terminals of antenna B. AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

21. Effective Aperture If an antenna is used to receive a wave with a power density S [W m2], it will produce a power in its terminating impedance (usually a receiver input impedance) of Pr watts. The constant of proportionality between Pr and S is Ae, the effective aperture of the antenna in square metres: Pr = AeS For some antennas, such as horn or dish antennas, the aperture has an obvious physical interpretation, being almost the same as the physical area of the antenna, but the concept is just as valid for all antennas. The effective aperture may often be very much larger than the physical area, especially in the case of wire antennas. Note, however, that the effective aperture will reduce as the efficiency of an antenna decreases. The antenna gain G is related to the effective aperture as follows G=4pi/ (lamda)2Ae AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

22. Effective Aperture Aphysical Pload Question: plane wave incident ? Pload = AphysicalWinc Answer: Usually NOT Pload = Aeff Winc ⇒ Aeff = Pload Winc

24. The directivity of an antenna increases as its beamwidth is made smaller, as the energy radiated is concentrated into a smaller solid angle AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

26. 2 Pr  λ   Dto Dro =  4π R  Pt   AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

27. Directivity and Maximum Effective Aperture (no losses) Antenna #1 transmit Atm, Dt Antenna #2 Direction of wave propagation R λ2 Aem = Do 4π receiver Arm, Dr

28. Directivity and Maximum Effective Aperture (include losses) Antenna #1 Antenna #2 Direction of wave propagation transmit Atm, Dt receiver Arm, Dr R λ2 * 2 ˆ ˆ Aem = ecd (1 − Γ ) Do ρ w ⋅ ρ a 4π 2 conductor and dielectric losses reflection losses (impedance mismatch) polarization mismatch

29. Friis Transmission Equation (no loss) Antenna #1 tran s Antenna #2 mit Atm , (θr,φr) Dt (θt,φt) receive R Arm , D r The transmitted power density supplied by Antenna #1 at a distance R and direction (θr,φr) is given by: Wt = Pt Dgt (θ t , ϕ t ) 4π R 2 The power collected (received) by Antenna #2 is given by: Pr = Wt Ar = Pt Dgt (θ t , ϕ t ) 4π R 2 2 Ar = Pt Dgt (θ t , ϕ t ) Dgr (θ r , ϕ r )λ2 4π R 2 Pr  λ  =  4π R  Dgt (θ t , ϕ t ) Dgr (θ r , ϕ r )  Pt   4π r

30. Friis Transmission Equation (no loss) Antenna #1 tran s Antenna #2 mit Atm , (θr,φr) Dt (θt,φt) R receive Arm , D r 2 Pr  λ  =  4π R  Dgt (θ t , ϕ t ) Dgr (θ r , ϕ r )  Pt   If both antennas are pointing in the direction of their maximum radiation pattern: 2 Pr  λ  =  4π R  Dto Dro  Pt   r

32. The polarisation mismatch loss is the ratio between the power received by the antenna and the power which would be received by an antenna perfectly matched to the incident wave AJAL.A.J- AP ECE UNIVERSAL ENGG COLLEGE

33. Appendices

34. Friis Transmission Equation: Example #1 A typical analog cell phone antenna has a directivity of 3 dBi at its operating frequency of 800.0 MHz. The cell tower is 1 mile away and has an antenna with a directivity of 6 dBi. Assuming that the power at the input terminals of the transmitting antenna is 0.6 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss. 2 Pr 2 2  λ  * 2 max max ˆ ˆ = ecdt ecdr (1 − Γr )(1 − Γt )  4π R  Dt Dr ρ w ⋅ ρ a  Pt   =1 λ= =1 c 3e8 = = 0.375m f 800e6 Dtmax = 103 /10 = 2.0 Drmax = 10 6 /10 = 4.0 =0 =0 =1 2 0.375   Pr = 0.6 watts ⋅   ⋅ 2 ⋅ 4 = 1.65 nW  4π ⋅1 609.344 

35. Friis Transmission Equation: Example #2 A half wavelength dipole antenna (max gain = 2.14 dBi) is used to communicate from an old satellite phone to a low orbiting Iridium communication satellite in the L band (~ 1.6 GHz). Assume the communication satellite has antenna that has a maximum directivity of 24 dBi and is orbiting at a distance of 781 km above the earth. Assuming that the power at the input terminals of the transmitting antenna is 1.0 W, and the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss. 2 Pr 2 2  λ  * 2 max max ˆ ˆ = ecdt ecdr (1 − Γr )(1 − Γt )  4π R  Dt Dr ρ w ⋅ ρ a  Pt   =1 λ= =1 c 3e8 = = 0.1875m f 800e6 Dtmax = 10 2.14 /10 = 1.64 Drmax = 10 24 /10 = 251.0 =0 =0 =1 2  0.1875  Pr = 1.0 watts ⋅   ⋅1.64 ⋅ 251 = 0.15 pW  4π ⋅ 781,000 

36. Friis Transmission Equation: Example #2 A roof-top dish antenna (max gain = 40.0 dBi) is used to communicate from an old satellite phone to a low orbiting Iridium communication satellite in the Ku band (~ 12 GHz). Assume the communication satellite has antenna that has a maximum directivity of 30 dBi and is orbiting at a distance of 36,000 km above the earth. How much transmitter power is required to receive 100 pW of power at your home. Assume the antennas are aligned for maximum radiation between them and the polarizations are matched, find the power delivered to the receiver. Assume the two antennas are well matched with a negligible amount of loss. 2 Pr 2 2  λ  * 2 max max ˆ ˆ = ecdt ecdr (1 − Γr )(1 − Γt )  4π R  Dt Dr ρ w ⋅ ρ a  Pt   =1 =1 c 3e8 λ= = = 0.025m f 800e6 Drmax = 10 40 /10 = 10,000 Dtmax = 1030 /10 = 1000.0 =0 =0 Pt = =1 100 ⋅10 −12 watts 2 0.025     ⋅10,000 ⋅1000  4π ⋅ 36,000,000  = 82 W

Antenna PARAMETERS

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