Directivity

Directivity is a fundamental antenna parameter. It is a measure of how 'directional' an antenna's radiation pattern is. An antenna that radiates equally in all directions would have effectively zero directionality, and the directivity of this type of antenna would be 1 (or 0 dB). [Silly side note: When a directivity is specified for an antenna, what is meant is 'peak directivity'. Directivity is technically a function of angle, but the angular variation is described by its radiation pattern. Hence, directivity throughout this page will mean peak directivity, because it is rarely used in another context.] An antenna's normalized radiation pattern can be written as a function in spherical coordinates: Because the radiation pattern is normalized, the peak value of F over the entire range of angles is 1. Mathematically, the formula for directivity (D) is written as: This equation might look complicated, but the numerator is the maximum value of F, and the denominator just represents the "average power radiated over all directions". This equation then is just a measure of the peak value of radiated power divided by the average. Example As an example consider two antennas, one with radiation patterns given by:     Antenna 1     Antenna 2 These patterns are plotted in Figure 1. Note that the patterns are only a function of the polar angle , and not a function of the azimuth angle (uniform in azimuth). The radiation pattern for antenna 1 is less directional then that for antenna 2.

Figure 1. Plots of Radiation Patterns. The directivity is calculated for Antenna 1 to be 1.273 (1.05 dB). The directivity is calculated for Antenna 2 to be 2.707 (4.32 dB). Again, increased directivity implies a more 'focused' antenna. In words, Antenna 2 receives 2.707 times more power in its peak direction than an isotropic antenna would receive. Antennas for cell phones should have a low directivity because the signal can come from any direction, and the antenna should pick it up. In contrast, satellite dish antennas have a very high directivity, because they are to receive signals from a fixed direction. As an example, if you get a directTV dish, they will tell you where to point it such that the antenna will receive the signal. Finally, we'll conclude with a list of antenna types and their directivities, to give you an idea of what is seen in practice.

Antenna Type	Typical Directivity	Typical Directivity (dB)
Short Dipole	1.5	1.76
Half Wave Dipole	1.64	2.15
Patch (Microstrip) Antenna	3.2-6.3	5-8
Horn Antenna	10-100	10-20
Dish Antenna	10-10,000	10-40

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