Guide Radio Antennas and Propagation: Radio Engineering Fundamentals

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In this case, the reflected signal phase would shift degrees at the point of reflection. However, the ground is not a perfect reflector. Its characteristics as a reflector depend on its conductivity, permittivity, the polarization of the signal, and its angle of incidence. In the Mathcad worksheet we have accounted for polarization, angle of incidence, and permittivity to find the reflection coefficient, which approaches -1 as the distance from the transmitter increases.

The signals reaching the receiver are represented as complex numbers, since they have both phase and amplitude.

Radio Antennas Propagation Engineering Fundamentals

Also shown is a plot of free space field strength versus distance dotted line. In both plots, signal strength is referenced to the free space field strength at a range of 3 meters. Notice in Figure 5.

Beyond meters, signal strength decreases more rapidly than for the free space model. Whereas there is an inverse distance law for free space, in the open field beyond meters for these parameters the signal strength follows an inverse square law.

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Increasing the antenna heights extends the distance at which the inverse square law starts to take effect. This distance, dm, can be approximated by. In plotting Figure 5.

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When vertical polarization is used, the extreme local variations of signal strengths up to around 50 meters are reduced because the ground reflection coefficient is less at larger reflection angles. However, for both polarizations, the inverse square law comes into effect at approximately the same distance. This distance in Figure 5.

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