(e, sin p+e, cosO cos p)e-jkH=g,uP(x, y, z)2元rZI1(eg cos O cos p - e, sin p)e-ikE=-2arC1For the x-directed electric current element, the directivity factoris completely differentfrom that of a z-directedone.The expression for the directivity factor will be different if theorientation of the antenna is changedHowever, onlythe mathematicalexpressionis changed.There is still no radiation in the direction along the axis of theelectric current element, while it is strongest along a directionperpendicularto the axis.UV
For the x-directed electric current element, the directivity factor is completely differentfrom that of a z-directedone. However, only the mathematical expression is changed. There is still no radiation in the direction along the axis of the electric current element, while it is strongest along a direction perpendicular to the axis. r Il z y x , P(x, y, z) o kr r I l j ( sin cos cos )e 2 j − = − + H e e kr r ZI l j ( cos cos sin )e 2 j − = − − E e e The expression for the directivity factor will be different if the orientation of the antenna is changed
2.Directivity ofAntennaswe will explore how to quantitatively describe the directivityofan antenna.It is more convenience to use the normalized directivity factor,anditis defined asF(0,0)= f(0,g)fmwhere f. is the maximum of the directivity factor f(e, d)Obviously,the maximum value of the normalized directivityfactor F. = 1.The amplitude of the radiationfield of any antenna can beexpressedas[E|=|EF(0,Φ)where E is the amplitude of the field intensityin the maximumradiationdirectionUEV
2. Directivity of Antennas we will explore how to quantitativelydescribe the directivity of an antenna. It is more convenience to use the normalized directivity factor, and it is defined as m ( , ) ( , ) f f F = Obviously, the maximum value of the normalized directivity factor Fm= 1. | | | | ( , ) E = E m F where is the amplitude of the field intensity in the maximum radiation direction. m | E | where fm is the maximum of the directivity factor f ( ,) . The amplitude of the radiation field of any antenna can be expressed as
The rectangular or the polar coordinate system is used to displaythe directivitypattern on aplaneIf the electric current element is placed at the origin and alignedwith the z-axis, then the directivity factoris f(,) = sin and themaximum value f. -l. Hence, the normalized directivity factorisF(0,d) = sin 0In the polar coordinate system, we have
The rectangularor the polar coordinate system is used to display the directivity pattern on a plane. If the electric current element is placed at the origin and aligned with the z-axis, then the directivity factor is and the maximum value . Hence, the normalized directivity factor is f (,) = sin f m =1 F(,) = sin y z y x In the polar coordinate system, we have
7ElectriccurrentelementThree-dimensionaldirectionHHpattern.The spatial directivitypatterninrectangularcoordinatesystemUV
Three-dimensional direction pattern. The spatial directivitypattern in rectangular coordinate system. x z y x y z r E E H H Electric current element
The direction with the maximum radiationis called the majordirection,and that without radiationis called a null direction.Theradiationlobe containingthemajor directionis calledthe mainlobe, and the others are called side lobesNullSideLobeDjrection2MainLobeBackLobe200.5200Major Direction172NullDirectionThe angle between two directions at which the field intensityisof that atthe majordirectionis calledthehalf-powerangle,andit is denoted as 20.s The angle between two null directionsis calledthe null-power angle, and it is denoted as 20uV
Major Direction Main Lobe Back Lobe Side Lobe Null Direction Null Direction 1 The direction with the maximum radiation is called the major direction, and that without radiation is called a null direction. The radiation lobe containing the major direction is called the main lobe, and the others are called side lobes. The angle between two directions at which the field intensity is of that at the major direction is called the half-power angle, and it is denoted as . The angle between two null directions is called the null-power angle, and it is denoted as . 2 1 2 0.5 2 0 2 0 2 0.5 2 1 2 1