Antenna Radiation Patterns Directivity and Gain |
Antenna Radiation Patterns Directivity and Gain. No physical antenna radiates uniformly in all directions. Rather, antennas radiate EM waves better in certain directions than others. In fact, many antennas will not radiate in some directions at all. A radiation pattern is a plot that shows the relative far field strength of `E (or `H ) versus angular direction (q,Æ) at a fixed distance from the antenna (again, in the far field). It is often a polar plot. We’ll take the Hertzian dipole antenna as an example. From equation (12) in the previous lecture we found in the far field that The magnitude of this phasor electric field is What is of interest in an antenna radiation pattern is the variation of |`E| in q and Æ at a fixed r, which is in the far field of the antenna. In the case of the Hertzian dipole antenna in (2), this variation is simply | sinq| : This radiation pattern indicates a number of characteristics of this Hertzian dipole antenna: 1. Maximum radiation is at q = 90° . This is called broadside radiation. 2. There is no variation in Æ, as expected. 3. There is no radiation in directions along the ends of the antenna (q = 0, 180°). Radiation Patterns of Longer Dipole Antennas The radiation patterns of dipole antennas get far more interesting as their electrical length increases. We’re only considering the electrically short Hertzian dipole antenna in this course, but we’ll show a couple of radiation patterns for two other dipole antenna lengths without proof. Dipole antenna radiation patterns stay roughly the same shape up to lengths ? 0.5 l . The main beam then sharpens for lengths from ? 0.5 l to 1 l . There is only one beam of radiation for these lengths. There are no so-called side lobes. (You can experiment with this yourself by adjusting the dipole antenna length L in the VisualEM worksheet “Radiation Pattern of a Dipole Antenna.”) For lengths longer than 1 l , the radiation patterns change considerably with the addition of multiple main beams and the appearance of side lobes: Beamwidth? E plane, H plane? Directivity and Gain An important characteristic of an antenna is its ability to focus radiated power in a given direction in the far field. The directivity D(q ,Æ ) of an antenna is the ratio of the power density radiated in the (q,Æ) direction at some distance in the far field of the antenna to the power density at this same point if the total power were radiated “isotropically” (i.e., equally in all directions. Mathematically, directivity is defined as While there is no such thing as a physical antenna that radiates equally well in all directions (i.e., isotropically), we use this artifice as a normalization quantity in the denominator of (3) to assess the focusing ability of a given antenna. If a total power P_{rad} is radiated isotropically by an antenna, then the time average power density anywhere on a sphere of radius r Is Using (4) in (3) along with the definition of S_{AV}, then (3) Becomes The gain of an antenna is defined similarly as directivity. In particular, the gain G(q ,Æ ) of antenna is the ratio of the power density radiated to some point in the far field of an antenna to the total power accepted by the antenna, P_{in}, when radiated isotropically. Mathematically, antenna gain is defined as The radiation efficiency e_{r } of an antenna is defined as Using this in (6) and comparing to (5) we find that G(q,Æ) = e_{r} D (q,Æ) In short, the gain G(q ,Æ ) of antenna includes the effects of losses in the antenna (and other surrounding structures), if present. The directivity of an antenna is determined solely by the pattern shape of the antenna. Example N33.1. Calculate the directivity of a Hertzian dipole antenna of length ÑL with current a_{z} I A. If the antenna is made of steel, is 62” long and 1/8” in diameter, and is operating at 1 MHz, calculate the antenna gain. In the far field of this antenna Substituting (1) into (9) The total power radiated by this antenna is found by integrating this power density over a closed surface, the simplest of which is an imaginary sphere centered on the dipole antenna: There fore Substituting (10) and (11) into the definition of directivity in (3), and using (4) gives Consequently, The maximum directivity, D, occurs for this antenna when q = 90º at which To calculate the gain of the antenna, we first must compute its radiation efficiency. The efficiency of this antenna was computed previously in Example N32.1. As we saw in that example, the equivalent input circuit at the terminals of the Hertzian dipole antenna is The total time average power delivered to the input terminals of this antenna is while the total radiated time average power is Substituting (12) and (13) into the definition of radiation efficiency (7) gives It was this last equation for e_{r }that was used previously in Example N32.1. There it was found that e_{r} = 8.95% for this steel antenna. Using we find that G(q , Æ) = 0.0895.1.5. sin ^{2} q = 0.134 sin ^{2} q And the maximum gain G occurs for this antenna at q = 90° Where G = 0.134 or G_{dB} = 10log_{10} G = -8.72 dB Conclusion To conclude, it is important to realize that there is no real “gain” associate with such antennas. These are made of metal and are completely passive devices. There is no signal amplification. The “gain” that has been defined in this lecture refers to the focusing properties of the antenna beyond that of an isotropic radiator. |