Presentation on theme: "Antennas and Radiation"— Presentation transcript:
1 Antennas and Radiation ECE 3317Prof. Ji ChenSpring 2014Notes 22Antennas and Radiation
2 We consider here the radiation from an arbitrary antenna. Antenna RadiationWe consider here the radiation from an arbitrary antenna.Szr+-y"far field"xThe far-field radiation acts like a plane wave going in the radial direction.
3 Antenna Radiation (cont.) How far do we have to go to be in the far field?Sphere of minimum diameter D that encloses the antenna.r+-This is justified from later analysis.
4 Antenna Radiation (cont.) The far-field has the following form:xyzEHSTMzxyzHESTEzDepending on the type of antenna, either or both polarizations may be radiated (e.g., a vertical wire antenna radiates only TMz polarization.
5 Antenna Radiation (cont.) The far-field Poynting vector is now calculated:
6 Antenna Radiation (cont.) Hence we haveorNote: In the far field, the Poynting vector is pure real (no reactive power flow).
7 Radiation PatternThe far field always has the following form:In dB:
8 Radiation Pattern (cont.) The far-field pattern is usually shown vs. the angle (for a fixed angle ) in polar coordinates.0 dB30°60°120°150°-10 dB-20 dB-30 dBThe subscript “m” denotes the beam maximum.A “pattern cut”
9 Radiated Power The Poynting vector in the far field is The total power radiated is then given byHence we have
10 DirectivityThe directivity of the antenna in the directions (, ) is defined asThe directivity in a particular direction is the ratio of the power density radiated in that direction to the power density that would be radiated in that direction if the antenna were an isotropic radiator (radiates equally in all directions).In dB,Note: The directivity is sometimes referred to as the “directivity with respect to an isotropic radiator.”
11 Directivity (cont.)The directivity is now expressed in terms of the far field pattern.Hence we haveTherefore,
12 Directivity (cont.) Two Common Cases z +h y x -h Short dipole wire antenna (l << 0): D = 1.5Resonant half-wavelength dipole wire antenna (l = 0 / 2): D = 1.643y+hzx-hfeed-9-3-60 dB30°60°120°150°Short dipole
13 Beamwidth The beamwidth measures how narrow the beam is. (the narrower the beamwidth, the higher the directivity).HPBW = half-power beamwidth
14 The sidelobe level measures how strong the sidelobes are. In this example the sidelobe level is about -13 dBSidelobesSidelobe levelMain beam
15 Gain and Efficiency Prad = power radiated by the antenna The radiation efficiency of an antenna is defined asPrad = power radiated by the antennaPin = power input to the antennaThe gain of an antenna in the directions (, ) is defined asIn dB, we have
16 Gain and Efficiency (cont.) The gain tells us how strong the radiated power density is in a certain direction, for a given amount of input power.Recall thatTherefore, in the far field:
17 Infinitesimal DipoleThe infinitesimal dipole current element is shown below.xyzIlThe dipole moment (amplitude) is defined as I l.The infinitesimal dipole is the foundation for many practical wire antennas.From Maxwell’s equations we can calculate the fields radiated by this source (e.g., see Chapter 7 of the Shen and Kong textbook).
18 Infinitesimal Dipole (cont.) The exact fields of the infinitesimal dipole in spherical coordinates are
19 Infinitesimal Dipole (cont.) In the far field we have:Hence, we can identify
20 Infinitesimal Dipole (cont.) The radiation pattern is shown below.-9-3-60 dB30°60°120°150°45oHPBW = 90o
21 Infinitesimal Dipole (cont.) The directivity of the infinitesimal dipole is now calculatedHence
22 Infinitesimal Dipole (cont.) Evaluating the integrals, we haveHence, we have
23 Infinitesimal Dipole (cont.) -9-3-60 dB30°60°120°150°The far-field pattern is shown, with the directivity labeled at two points.
24 Wire Antenna A center-fed wire antenna is shown below. z +h y+hzI (z)x-hFeedI 0I (z) vs. zA good approximation to the current is:
25 Wire Antenna (cont.)A sketch of the current is shown below for two cases.+h-hlI 0+h-hlI 0Resonant dipole (l = 0 / 2, k0h = / 2)Short dipole (l <<0)Use
26 Wire Antenna (cont.) Short Dipole +h I 0 l -h The average value of the current is I0 / 2.+h-hlI 0Infinitesimal dipole:Short dipole (l <<0 / 2)Short dipole:
27 Wire Antenna (cont.)For an arbitrary length dipole wire antenna, we need to consider the radiation by each differential piece of the current.y+hzx-hFeedrRdz'z'I (z')Far-field observation pointInfinitesimal dipole:Wire antenna:
28 Wire Antenna (cont.) z R +h r dz' y x -h Far-field observation point FeedrRdz'Far-field observation point
29 Wire Antenna (cont.) z R +h r dz' y x -h Far-field observation point FeedrRdz'Far-field observation pointIt can be shown that this approximation is accurate whenNote:
30 Wire Antenna (cont.) z R +h r dz' y x -h Far-field observation point FeedrRdz'Far-field observation pointHence we have
31 Wire Antenna (cont.) We define the array factor of the wire antenna: We then have the following result for the far-field pattern of the wire antenna:The term in front of the array factor is the far-field pattern of the unit-amplitude infinitesimal dipole.
32 Wire Antenna (cont.)Using our assumed approximate current function we haveHenceThe result is (derivation omitted)
33 Wire Antenna (cont.)In summary, we haveThus, we have
34 Wire Antenna (cont.) For a resonant half-wave dipole antenna The directivity is
36 Wire Antenna (cont.)Radiated Power:Simplify using
37 Wire Antenna (cont.) Performing the integral gives us After simplifying, the result is then
38 Wire Antenna (cont.) The radiation resistance is defined from z +h y+hzI (z)x-hFeedCircuit ModelZ0ZinI0I0For a resonant antenna (l 0 / 2), Xin = 0.
39 Wire Antenna (cont.) The radiation resistance is now evaluated. Using the previous formula for Prad, we havel0 / 2 Dipole:
40 Wire Antenna (cont.)The result can be extended to the case of a monopole antennaI (z)hFeeding coax(see the next slide)
41 Wire Antenna (cont.) This can be justified as shown below. Vmonopole +-DipoleVdipoleI0Virtual ground+VmonopoleI0-
42 Receive AntennaThe Thévenin equivalent circuit of a wire antenna being used as a receive antenna is shown below.+-VThEincl = 2h+-VThZTh
43 Find the Thévenin voltage (magnitude of it). ExampleTwo lossless resonant half-wavelength vertical dipole wire antennas+-VThReceivexrTransmit Prad [W]Pradz+-VThZThReceive Thévenin circuitFind the Thévenin voltage (magnitude of it).
45 Example (cont.) Assume these values: f = 1 [GHz] (0 = 29.979 [cm]) Prad = 10 [W]r = 1 [km]The result is+-3.00 [mV]73 Receive Thévenin circuit
46 Example (cont.)Next, calculate the power received by an optimum conjugate-matched load+-VThZThFor resonant antennas:
47 Effective AreaAnother way to characterize an antenna is with the effective area.This is more general than effective length (which only applies to wire antennas).Receive circuit: Assume an optimum conjugate-matched load:+-VThZThPL = power absorbed by loadAeff = effective area of antenna (depends on incident angles)Pinc = average power density incident on antenna [W/m2]
48 Effective Area (cont.) We have the following general formula*: G(,) = gain of antenna in direction (,)*A poof is given in the Antenna Engineering book:C. A. Balanis, Antenna Engineering, 3rd Ed., 2055, Wiley.
49 Effective Area (cont.)Effective area of a lossless resonant half-wave dipole antennaAssuming normal incidence ( = 90o):Hence
50 Effective Area (cont.) Example Find the receive power in the example below, assuming that the receiver is now connected to an optimum conjugate-matched load.f = 1 [GHz] (0 = [cm])Prad = 10 [W]r = 1 [km]ReceivexrTransmit Prad [W]Pradz
52 Effective Area (cont.) Effective area of dish antenna In the maximum gain direction:Aphy = physical area of disheap = “aperture efficiency”The aperture efficiency is usually less than 1 (less than 100%).