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Bardwell J.Math and physics for the 802.11 wireless LAN engineer.pdf
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If an antenna with this polar coordinate graph were mounted on a pole in a warehouse, one could imagine that the signal strength would be represented as in the picture below in Figure 4.15.

Figure 4.15 The Directional Antenna’s Elevation Cut Seen in the Warehouse

The “E” Graph and the “H” Graph

Recall that the vector symbol for the electromotive field is “E” and the symbol for the magnetic field is “H”. Recall, too, that these two aspects of the electromagnetic field operate at right-angles to each other. You will see polar coordinate graphs referred to as “E” Graphs or “H” Graphs, depending

on whether they represent the electromotive force relative to an isotropic radiator, or the magnetic force relative to isotropic. Frankly, the “E” Graph is the most common, and most useful. But, if you encounter an antenna manufacturer or other reference using the “H” Graph itʼs a simple matter to mentally convert one format into the other. Remembering that the E and H vectors are 90O apart, it turns out that an antennaʼs “E” Elevation Cut is the same as its “H” Azimuth Cut. In like manner, an antennaʼs “H” Elevation Cut is the same as its “E” Azimuth cut. You can visualize the reason for this equivalence by thinking about how your view of the field changes when you move from the Elevation view to the Azimuth view. These two views are 90O apart, just as the “E” and “H” vectors are 90O apart.

Half-Power Beam Width

The magnitudes of Eθ and Eφ in the far field vary inversely as the distance. At any point in space around an antenna there is a particular Eθ value that has decreased by 3 dB and is half as powerful as the maximum signal. This value is represented as Eθm. When a Poynting vector is drawn in the direction of Eθm, an angle is defined thatʼs called the Half Power Beam Width. A side-view field pattern graph shows a representation of a cross-section of space on which the x and y axes lie and in which the antenna element is radiating outwards (towards positive and negative x). The plot shows the Half Power points. The angle between the Poynting vectors to the Half Power points define an angle called the Half Power Beam Width (HPBW), which is a standard measure of an antennaʼs directivity, as represented in Figure 4.16 below.

Math and Physics for the 802.11 Wireless LAN Engineer

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Copyright 2003 - Joseph Bardwell

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