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KU EECS 622 - C. Antenna Pattern

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5/4/2005 Antenna Pattern present 1/1 Jim Stiles The Univ. of Kansas Dept. of EECS C. Antenna Pattern Radiation Intensity is dependent on both the antenna and the radiated power. We can normalize the Radiation Intensity function to construct a result that describes the antenna only. We call this normalized function the Antenna Directivity Pattern. HO: Antenna Directivity The antenna directivity function essentially describes the antenna pattern, from which we can ascertain fundamental antenna parameters such as (maximum) Directivity, beamwidth, and sidelobe level. HO: The Antenna Pattern We find that conservation of energy requires a tradeoff between antenna (maximum) directivity and beamwidth—we increase one, we decrease the other. HO: Beamwidth and Directivity11/20/2006 Antenna Directivity 1/7 Jim Stiles The Univ. of Kansas Dept. of EECS Antenna Directivity Recall the intensity of the E.M. wave produced by the mythical isotropic radiator (i.e., an antenna that radiates equally in all directions) is: 04radPUπ= But remember, and isotropic radiator is actually a physical impossibility! If the electromagnetic energy is monochromatic—that is, it is a sinusoidal function of time, oscillating at a one specific frequency ω—then an antenna cannot distribute energy uniformly in all directions. The intensity function ()U,θφ thus describes this uneven distribution of radiated power as a function of direction, a function that is dependent on the design and construction of the antenna itself. Tx radP ()0U, Uθφ=11/20/2006 Antenna Directivity 2/7 Jim Stiles The Univ. of Kansas Dept. of EECS Q: But doesn’t the radiation intensity also depend on the power delivered to the antenna by transmitter? A: That’s right! If the transmitter delivers no power to the antenna, then the resulting radiation intensity will likewise be zero (i.e., ()0U,θφ= ). Q: So is there some way to remove this dependence on the transmitter power? Is there some function that is dependent on the antenna only, and thus describes antenna behavior only? A: There sure is, and a very important function at that! Will call this function (),Dθφ—the directivity pattern of the antenna. The directivity pattern is simply a normalized intensity function. It is the intensity function produce by an antenna and transmitter, normalized to the intensity pattern produced when the same transmitter is connected to an isotropic radiator. Tx radP ()U,θφ11/20/2006 Antenna Directivity 3/7 Jim Stiles The Univ. of Kansas Dept. of EECS ()()0intensity of antennaintensity of isotropic radiatorU,D,Uθφθφ== Using 04radUPπ= , we can likewise express the directivity pattern as: ()()4radU,D,Pπθφθφ= Q: Hey wait! I thought that this function was supposed to remove the dependence on transmitter power, but there is radP sitting smack dab in the middle of the denominator. A: The value radP in the denominator is necessary to normalize the function. The reason of course is that ()U,θφ (in the numerator) is likewise proportional to the radiated power. In other words, if radP doubles then both numerator and denominator increases by a factor of two—thus, the ratio remains unchanged, independent of the value radP. Another indication that directivity pattern (),Dθφ is independent of the transmitter power are it units. Note that the directivity pattern is a coefficient—it is unitless! ()()0U,D,Uθφθφ=11/20/2006 Antenna Directivity 4/7 Jim Stiles The Univ. of Kansas Dept. of EECS Dependent on Tx power Perhaps we can rearrange the above expression to make this all more clear: () ()4radPU, D,θφθφπ= Hopefully it is apparent that the value of this function (),Dθφ in some direction θ and φ describes the intensity in that direction relative to that of an isotropic radiator (when radiating the same power radP). For example, if ()10,Dθφ= in some direction, then the intensity in that direction is 10 times that produced by an isotropic radiator in that direction. If in another direction we find ()05,D.θφ=, we conclude that the intensity in that direction is half the value we would find if an isotropic radiator is used. Q: So, can the directivity function take any form? Are there any restrictions on the function (),Dθφ? A: Absolutely! For example, let’s integrate the directivity function over all directions (i.e., over 4π steradians). Dependent on Tx power and the antenna. Dependent on antenna only.11/20/2006 Antenna Directivity 5/7 Jim Stiles The Univ. of Kansas Dept. of EECS ()()()()()22000 0020020001444radradradU,D,sindd sinddUU,siU,sinddPnddUPPππ ππππππθφθθφθθφφθθφ θθφθφθθφπππ=====∫∫ ∫∫∫∫∫∫ Thus, we find that the directivity pattern (),Dθφ of any and all antenna must satisfy the equation: ()2004D,sinddππθφθθφπ=∫∫ We can slightly rearrange this integral to find: ()2001104D,sindd .ππθφ θ θ φπ=∫∫ The left side of the equation is simply the average value of the directivity pattern (aveD), when averaged over all directions—over4π steradians!11/20/2006 Antenna Directivity 6/7 Jim Stiles The Univ. of Kansas Dept. of EECS The equation thus says that the average directivity of any and all antenna must be equal to one. 10aveD.= This means that—on average—the intensity created by an antenna will equal the intensity created by an isotropic radiator. Æ In some directions the intensity created by any and all antenna will be greater than that of an isotropic radiator (i.e., 1D> ), while in other directions the intensity will be less than that of an isotropic resonator(i.e., 1D<). Q: Can the directivity pattern (),Dθφ equal one for all directions θ and φ? Can the directivity pattern be the constant function ()10,D.θφ=? A: Nope! The directivity function cannot be isotropic. Tx (),Dθφ ()1,Dθφ=11/20/2006 Antenna Directivity 7/7 Jim Stiles The Univ. of Kansas Dept. of EECS In other words, since: ()0,UUθφ≠ then: ()()()000010,,,UUUUUDU.θφθφ θφ≠⇒ ≠ ≠⇒ Q: Does this mean that there is no value of θand φfor which (),Dθφ will equal 1.0? A: NO! There will be many values of θ and φ (i.e., directions) where the value of the directivity function will be equal to one! Instead, when we say that: ()10,D.θφ≠ we mean that the directivity function cannot be a constant (with value 1.0) with respect


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