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Kraus-38096 book October 10, 2001 13:3CHAPTER 2Antenna Basics21 INTRODUCTIONWelcome to the wonderful world of antennas, its language and culture; to the aperture family(effective and scattering), the lobe family (main, side, back, and grating); to beamwidths,directivity, and gain.Antennas are three-dimensional and live in a world of beam area, steradians, squaredegrees, and solid angle. Antennas have impedances (self and mutual). They couple to allof space and have a temperature measured in kelvins. Antennas have polarizations: linear,elliptical, and circular.This chapter will make you uent in the language of antennas and comfortable in itsculture. The topics of this chapter include:I Basic parametersI PatternsI Beam areaI Beam efciencyI Directivity and gainI Physical and effective aperturesI Scattering aperture and radar crosssectionI The radio link (Friis formula)I Apertures of dipoles and /2 antennasI Radiation resistanceI Antenna impedanceI Antenna dualityI Sources of radiationI Field zonesI Shape-impedance considerationsI Polarization11Kraus-38096 book October 10, 2001 13:312 Chapter 2 Antenna Basics22 BASIC ANTENNA PARAMETERSA radio antenna may be dened as the structure associated with the region of transitionbetween a guided wave and a free-space wave, or vice versa. Antennas convert electrons tophotons, or vice versa.1Regardless of antenna type, all involve the same basic principle that radiation is pro-duced by accelerated (or decelerated) charge. The basic equation of radiation may beexpressed simply asIL = Q v (A m s1) Basic radiation equation (1)whereI = time-changing current, A s1L = length of current element, mQ = charge, C v = time change of velocity which equals the acceleration of the charge, m s2L = length of current element, mThus, time-changing current radiates and accelerated charge radiates. For steady-state harmonic variation, we usually focus on current. For transients or pulses, we focuson charge.2The radiation is perpendicular to the acceleration, and the radiated power isproportional to the square of IL or Q v.The two-wire transmission line in Fig. 21a is connected to a radio-frequency generator(or transmitter). Along the uniform part of the line, energy is guided as a plane TransverseElectroMagnetic Mode (TEM) wave with little loss. The spacing between wires is assumedto be a small fraction of a wavelength. Further on, the transmission line opens out in atapered transition. As the separation approaches the order of a wavelength or more, thewave tends to be radiated so that the opened-out line acts like an antenna which launchesa free-space wave. The currents on the transmission line ow out on the antenna and endthere, but the elds associated with them keep on going.The transmitting antenna in Fig. 21a is a region of transition from a guided wave ona transmission line to a free-space wave. The receiving antenna (Fig. 21b) is a region oftransition from a space wave to a guided wave on a transmission line. Thus, an antennais a transition device, or transducer, between a guided wave and a free-space wave, orvice-versa. The antenna is a device which interfaces a circuit and space.From the circuit point of view, the antennas appear to the transmission lines as aresistance Rr, called the radiation resistance. It is not related to any resistance in theantenna itself but is a resistance coupled from space to the antenna terminals.In the transmitting case, the radiated power is absorbed by objects at a distance: trees,buildings, the ground, the sky, and other antennas. In the receiving case, passive radiationfrom distant objects or active radiation from other antennas raises the apparent temperature1A photon is a quantum unit of electromagnetic energy equal to h f, where h = Plancks constant(=6.63 1034J s) and f = frequency (Hz).2A pulse radiates with a broad bandwidth (the shorter the pulse the broader the bandwidth). A sinusoidal variationresults in a narrow bandwidth (theoretically zero at the frequency of the sinusoid if it continues indenitely).Kraus-38096 book October 10, 2001 13:322 Basic Antenna Parameters 13TaperedtransitionTransmission lineGuided (TEM) waveOne-dimensional waveTransitionregionor antennaFree-space waveradiating inthree dimensionsGenerator or transmitterE lines~TRANSMITTING ANTENNAPlane waveTaperedtransitionGuided (TEM) waveTransition regionor antennaRECEIVING ANTENNAReceiverE lines(a) (b)Figure 21(a) Radio (or wireless) communication link with transmitting antenna and(b) receiving antenna. The receiving antenna is remote from the transmittingantenna so that the spherical wave radiated by the transmitting antenna arrivesas an essentially plane wave at the receiving antenna.RrVirtual transmission linelinking antenna with spaceTransmissionline terminalsAntennaVirtualresistanceTransmitteror receiverT( Rr )Region of spacewithin antennaresponse patternTxRxor Figure 22Schematic representation of region of space at temperature T linked via avirtual transmission line to an antenna.of Rr. For lossless antennas this temperature has nothing to do with the physical temperatureof the antenna itself but is related to the temperature of distant objects that the antenna islooking at, as suggested in Fig. 22. In this sense, a receiving antenna (and its associatedreceiver) may be regarded as a remote-sensing temperature-measuring device.As pictured schematically in Fig. 22, the radiation resistance Rr may be thought of asa virtual resistance that does not exist physically but is a quantity coupling the antennato distant regions of space via a virtual transmission line.11It is to be noted that the radiation resistance, the antenna temperature, and the radiation patterns are functions ofthe frequency. In general, the patterns are also functions of the distance at which they are measured, but atdistances which are large compared to the size of the antenna and large compared to the wavelength, the patternis independent of distance. Usually the patterns of interest are for this far-eld condition.Kraus-38096 book October 10, 2001 13:314 Chapter 2 Antenna Basics23 PATTERNSBoth the radiation resistance Rr, and its temperature TA are simple scalar quantities. Theradiation patterns, on the other hand, are three-dimensional quantities involving the variationof eld or power (proportional to the eld squared) as a function of the spherical coordinates and . Figure 23 shows a three-dimensional eld pattern with pattern radius r (fromorigin to pattern boundary at the dot) proportional to the eld intensity in the direction and . The pattern has its main lobe (maximum radiation) in the z direction ( = 0) withminor lobes (side and back) in other directions.To completely specify the radiation pattern with respect to eld intensity and polariza-tion requires three patterns:1. The component of the electric eld as a function of the angles and or E(, )(V m1) as in Figs. 23 and 24.zy x 0 85 0Main lobeaxisFieldpattern 30PEEFieldcomponentsMainbeamor mainlobeNullsSidelobesBacklobesField in, direction Figure 23Three-dimensional eld pattern of a directional antenna with maximumradiation in z-direction at = 0. Most of the radiation is contained in a mainbeam (or lobe) accompanied by radiation also in minor lobes (side and back).Between the lobes are nulls where the eld goes to zero. The radiation in anydirection is specied by the angles and . The direction of the point P is atthe angles = 30 and = 85. This pattern is symmetrical in and afunction only of .Kraus-38096 book October 10, 2001 13:323 Patterns 152. The component of the electric eld as a function of the angles and or E(, )(V m1).3. The phases of these elds as a function of the angles and or (, ) and (, )(rad or deg).Any eld pattern can be presented in three-dimensional spherical coordinates, as inFig. 23, or by plane cuts through the main-lobe axis. Two such cuts at right angles, calledthe principal plane patterns (as in the xz and yz planes in Fig. 23) may be required but ifthe pattern is symmetrical around the z axis, one cut is sufcient.Figures 24a and 24b are principal plane eld and power patterns in polar coordinates.The same pattern is presented in Fig. 24c in rectangular coordinates on a logarithmic, ordecibel, scale which gives the minor lobe levels in more detail.The angular beamwidth at the half-power level or half-power beamwidth (HPBW) (or3-dB beamwidth) and the beamwidth between rst nulls (FNBW) as shown in Fig. 24,are important pattern parameters.Dividing a eld component by its maximum value, we obtain a normalized or relativeeld pattern which is a dimensionless number with maximum value of unity. Thus, thenormalized eld pattern (Fig. 24a) for the electric eld is given byNormalized eld pattern = E(, )n = E(, )E(, )max(dimensionless) (1)The half-power level occurs at those angles and for which E(, )n = 1/2 =0.707.At distances that are large compared to the size of the antenna and large comparedto the wavelength, the shape of the eld pattern is independent of distance. Usually thepatterns of interest are for this far-eld condition.Patterns may also be expressed in terms of the power per unit area [or Poynting vectorS(, )].1Normalizing this power with respect to its maximum value yields a normalizedpower pattern as a function of angle which is a dimensionless number with a maximumvalue of unity. Thus, the normalized power pattern (Fig. 24b) is given byNormalized power pattern = Pn(, )n = S(, )S(, )max(dimensionless) (2)whereS(, ) = Poynting vector =_E2(, ) + E2(, )_Z0, W m2S(, )max= maximum value of S(, ), W m2Z0 = intrinsic impedance of space = 376.7 1Although the Poynting vector, as the name implies, is a vector (with magnitude and direction), we use here itsmagnitude; its direction is the far eld is radially outward.Kraus-38096 book Octob