Radio Frequency by Steve Winder and Joe Carr - HTML preview

11.4 Fresnel zones, reflections and multi-path fading

Signals which arrive at the receiver by more than one path as the results of reflection or diffraction may arrive in any phase relationship

 

₂₅₀ Station B
₂₀₀ Station A 0.6 × first Fresnel zone radius
150
100
50
Plane earth datum, K= 1.33
⁰ 01234567891011121314151617181920 Path length (kilometres)
Figure 11.2 Example of path profile

to the direct wave. When they arrive anti-phase to the direct wave, cancellations result. The intensity and phase of the spurious signal may not be constant, thus providing random multi-path fading.

Where a carefully drawn profile of a link path shows there to be a clear line of sight, the effect of waves reflected or diffracted from objects close to the line of the direct wave must then be considered. The effect of these indirect waves can be predicted by calculating where the reflection occurs in relation to a series of ellipsoids which can be drawn around the line-of-sight path between the transmitting and receiving antennas. These ellipsoids, known as the Fresnel zones, contain the points where reflected waves will follow a path of constant length, as shown in Figure 11.3.

d
d_{d3 2 d4d1}
d
₁ + ^d₂ = ^d₃ + ^d₄Figure 11.3 Fresnel zone: reflected path lengths

Waves reflected at the odd-numbered Fresnel zones will travel an odd number of half-wavelengths further than the direct wave but, because a 180^æ phase change usually occurs in the reflection process, will arrive at the receiver in phase with the direct wave. Waves reflected at even-numbered zones will arrive anti-phase to the direct wave with a cancelling effect. The effect of reflected waves diminishes with reflections from the higher order zones. The radius of a Fresnel zone in metres at the point of intrusion is given by:

First zone, F₁:

 

F

 

1

 

=

 

31

 

.

 

6 λd₁d₂ d or

 

F

 

1

 

=

548
d₁d₂ fd Second zone:

where

F₁ = radius in metres at point of intrusion d₁ + d₂ = d (path length in km)
λ = wavelength in metres
f = frequency in MHz

_F2 = √_{2× F1}

 

Third zone:

 

_F3 = √_{3× F1}

 

andsoon.

The degree of reflection from an object depends on its nature, the greatest reflection occurring from smooth flat ground or water. Where a path lies over the sea, variations in the path length of a reflected wave due to tides may render a path unusable. When the height of the antenna closest to the sea is varied, the effect of the reflected wave passes through a series of minima and maxima and adjustment of the height of that antenna can reduce or, occasionally, overcome the effect.

Atmospheric conditions change giving rise to fading and variations of the multi-path effects. The reliability of a link may be crucial to the success of a complete system and, where a critical path in terms of performance exists, long-term tests are advisable to ensure that variations of propagation do not reduce the reliability to an unacceptable level. Paths which contain obstacles in the line of sight which will cause additional losses are obviously suspect. So are those where objects or large stretches of water or flat ground which might produce diffraction or reflections of the wave lie close to the line of sight.