# Big Wheel Antenna Engineering Letter

The two variables you referenced are the Greek letter ‘Theta’, E and H refer to the ‘electric’ field and the ‘magnetic’ field respectively. Theta in mathematics designates the angle of an argument. When you use horizontal polarization the ‘E’ field lies within the horizontal plane parallel to the surface of the Earth. The ‘H’ is perpendicular to it. When we use antennas, we use (generally) vertical or horizontally polarized elements. There are other polarization configurations but to keep it simple right now lets just entertain vertical and horizontal polarities. Theta ‘E’ and ‘H’ are used to measure the beamwidth of the antenna in degrees or the area of a beam front propagated by an antenna of so many elements and length. We calculate the gain of an antenna by using: Gain (in dBi) = 10 Log (41253/theta ‘E’ X theta ‘H’). If we look at a point source inside a sphere of radius 1 radian and that point source is illuminating it the gain is 1. e.g. Area of the surface of a sphere = 4 X PI X R^2 (radians), a radian we know to be 57.3 degrees, therefore the surface of the sphere contains 41,253 (square degrees, actually steradial degrees). So, if we have an antenna that measures say 60 degrees in the ‘E’ plane and 30 degrees in the ‘H’ plane; 30 X 60 = 1800 and 41,253/1800 = ~23 and 10 log 23 = 13.6 dBi (i being over an isotropic source).

The wavefront transmitted from a horizontally polarized antenna will therefore have an ‘E’ plane that is horizontal. In order to receive the maximum amount of energy from the wave front of that propagated energy, the receiving antenna must also be horizontally polarized. If the receive antenna is moved out of the horizontal toward vertical or perpendicular to the plane of the transmit antenna the amount of received energy falls off as the cosine of the angle. For example: Let the receive antenna be positioned 45 degrees out of the plane of the transmitting antenna. the cosine of 45 degrees is 0.707. To find the amount of energy lost in decibels we take 20 Log of 0.707 and see that the loss is -3.01 dB, or half the power (actually half the voltage component of the power transmitted). If the angle between the transmit and receive antennas become 90 degrees the loss becomes -27 dB, this only in theory as I have, at best, working at the National Laboratories in Boulder, CO been only able to measure a loss of -22 dB between cross polarized elements. The reason being that there is no perfect horizontal or vertical wavefront. Each have components of the other to some degree.