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Inviato: venerd́ 16 aprile 2004 15.40

GROUND WAVE PROPAGATION


Propagation Over Earth

Free Space Propagation
The RMS field intensity in free space in volts/metre is given by: where: The presence of the ground modifies the generation and propagation of radio waves so that the received power or field intensity is less than what would be found in free space. 
Electrical Properties of Ground
The electrical properties of the ground can be expressed by three constants which are the relative permeability, the dielectric constant and the conductivity. The relative permeability can be regarded as unity, so that generally only two of the three constants are required in propagation problems. where: The equation for wave propagation with a complex dielectric constant relative to a vacuum is: The effect of electrical characteristics of the ground upon propagation of the radio waves is given by:
 
E/E0=        1       +       Reiw         +    (1-R)Aeiw   +   ...........   ------------------ equation 3
            direct           reflected            surface             induction field
            wave             wave                 wave              and secondary effects

where R, A and w are all components of e' and
R = complex reflection coefficient of ground
A = surface wave attenuation factor
w = phase difference caused by the path difference between the direct and ground reflected waves 

Ground Wave Components
The behaviour of the equation 3 can be demonstrated using two limiting examples which allow the ground wave to be viewed as a surface wave or a space wave.

a) For antennas approaching ground level, w approaches zero and R approaches minus 1. The first two terms of the equation cancel leaving the surface wave. This term arises because the earth is not a perfect reflector, causing some energy to be transmitted into the ground.

b) For transmitting and receiving antennas which are elevated more than a few wavelengths, the surface wave can be neglected. The ground wave is now known as the space wave. For near grazing paths, R approaches minus 1 and the equation becomes:

For the wavelengths used in the HF band it is the surface wave that dominates the expression for the ground wave. This is because antennas are unlikely to be elevated greater than a few wavelengths.

The Surface Wave

For the surface wave, defraction is due to the earth, and the amount of defraction depends on the ratio of the wavelength to the radius of the earth. The degree of defraction increases steadily as the wavelength is decreased because the ground is not a perfect conductor. Energy is absorbed by the earth, the wave front is therefore tilted slightly forward due to the flow of energy downwards into the earth and hence the bending of the wave is assisted. For transmitting and receiving antennas both situated on the surface of the earth, the radiated field produced at a distance d from the transmitter is: Where: The factor F depends upon wave frequency, ground characteristics, wave polarisation and distance. F decreases with increasing wave frequency and also with decreasing ground conductivity. F is also much smaller for horizontal than vertical wave polarisation. 
Zonal Relationships
The dependence of F upon the distance from the transmitter is best explained using zonal relationships. There are 3 zones which have their own effect on attenuation. 
Effect of Antenna Height
Surface waves predominate when the antennas are close to the earth, but the presence of the two components of the space wave cannot be forgotten. When the antennas are close to the surface the two waves cancel. As the antenna height increases the path length of the reflected wave becomes greater than that of the direct ray. The two components therefore do not cancel. When heights of the antennas are raised above the surface of the earth the equation the radiated field becomes: Where H(h) is the height gain factor for an antenna at height h.

The effect of antenna height is greater over poor ground than over sea water. Height gain has a greater effect over horizontal polarisation than vertical polarisation, however when both the transmitting and receiving antenna heights become more than 3 wavelengths, polarisation has little effect.

The Space Wave

Zonal Relationships
When the transmitting and receiving antennas are more than 35l2/3 above the ground, the effect of the Earth's surface becomes small and thus the space wave predominates. There are three zones associated with the space wave:

1)Interference zone (line of sight)
For this zone the direct and the reflected waves make up the total field. The field strength of the direct wave is given by equation 1. The reflected waves field strength differs from the direct wave and as such is given by:

      ER = (GR/GD)1/2(dD/dR)DRE0 = aE0  ------------- equation 7
where: The total field now becomes: In practice this equation is more complicated since radio wave trajectories may not be linear.

2)Radio horizon zone
Reflection theory is only valid when when diffraction has a minor effect. If the grazing angle is less than:

where ma is the effective Earth's radius after tropospheric effects) then ray theory is invalid and the surface wave may contribute to the total field. In this zone the field strength calculation is rather difficult.
 
3)Diffraction zone
Beyond the radio zone the diffraction zone is entered and the attenuation settles to 0.62/l1/3 dB/km.
  
Effect of Antenna Height
If the reflection angle, q is greater than y from equation 9 , but is small enough to ensure a reflection coefficient of about -1, the difference in path length between the reflected and direct wave is approximately 2h1h2/d when h1 and h2 are less than d. When the angle q is increased the effects differ due to polarisation. For horizontal polarisation the modulus of the reflection coefficient decreases. For vertical polarisation the effects become complicated because both the phase angle and modulus of the reflection coefficient change rapidly with changes in q.

Effects of Outside Influences

General Considerations
The theory outlined so far must be modified to allow for physical effects and influences that are imposed on the radio wave as it propagates across the Earth's surface. It is not possible to make simple general statements regarding the influence of the terrain and the vegetation on propagation. It's a complex function of frequency, ground constants, tropospheric variations, path geometry, season and vegetation density.
  
Ground Conductivity
  1. Moisture content - this is a major factor in determining the electrical characteristics of the ground. The moisture of a particular soil may vary from sight to sight due to differences in geological formation, which affects drainage. At depths of greater than one metre the soil wetness tends to stay constant all year round at a particular sight.
  2. Temperature - Since the range of temperatures through the year decreases rapidly with depth, the temperature effects are likely to be important only at high frequencies for which the penetration of the waves is small.
  3. Geological structure - The ground over which a radio wave propagates is not usually homogeneous, so the effective ground constants will often be determined by several different types of soil. The effective constants are determined by the nature of the surface soils and also the underlying strata.
  4. Surface Objects - Surface objects contribute appreciably to the attenuation of ground waves. High attenuation rates are associated with transmission loss in forest terrain at frequencies above about 30 MHz. This may increase under the condition of rain while the trees are in leaf. 
Terrain Irregularities
Consider two waves reflected at points separated in height by Dh. Their phases are shifted with respect to each other by: where q  is the angle of the ray path to the ground. If the surface is to behave like a smooth surface, then waves reflected at all points must be only very slightly shifted in phase with respect to each other. Rayleigh proposed to consider a surface smooth if : Using equation 10 this sets up the Rayleigh criterion which catergorises the surface as smooth if: For radio waves in the HF band or for lower frequencies equation 12 shows that ground generally behaves like a smooth surface particularly with antennas near the ground. For VHF and higher frequencies the effect of the ground irregularities become apparent. The greater the irregularities the smaller the reflection coefficient. 
Mountainous Terrain
On long paths tropospheric-scatter may occur well above a mountain ridge, and the scattered and diffracted waves must be combined. With transmitting and receiving antennas elevated above the surrounding terrain, waves may be reflected before and after diffraction. When a wave passes close to the ground, an additional transmission loss caused by finite ground conductivity, may arise.

Mountain ridges can reduce fading and transmission loss below the values expected in the absence of the obstacle. This occurs when the direct path is non-optical, but both transmitter and receiver can be seen from the top of the mountain. This is known as obstacle gain. 

Vegetation
In the 30 to 2000 MHz range the average additional attenuation through wooden terrain is approximately proportional to exp(-bd/l) where b is a characteristic of the vegetation, d is distance and l is wavelength. Considerable variation of these values would be expected as a result of the density of the vegetation and the moisture content of the leaves.

At lower frequencies the vegetation can be modeled as a weak, lossy dielectric slab. The net effect is that the presence of vegetation produces a constant loss which seems to be independent of the distance between communication terminals.