MF HF Groundwave Model
This tutorial article describes the effect of the surrounding environment on the radiation from a vertically-polarised antenna. The article contains a summary of a new empirical groundwave model developed by Luo Lichun [1]. This new model is an extension of Norton’s ground wave model and may be used to predict the power loss of Electromagnetic (EM) waves in an Urban environment. The model covers propagation in the Medium (MF) and High (HF) Frequency bands.
When an antenna is radiating, power is emitted in the form of a wave front. The power is consequently spread over an increasing surface-area with respect to time. The radiation at the source is concentrated near the current node close to the feed and conceptually at a point. But as we move further from the antenna the radiation must spread out to form a spherical wave front.
The power passing through a selected surface-area of the wave front of radius R is described by the flux equation:
Where Gt is the gain of the transmitting antenna, Pt is the transmitted power, and 
MF HF Groundwave Model – Equation 1a[/caption] is power flux described as the measure of Watts divided by area at the distance R meters from the transmitter [2].
The amount of power that a receiving antenna can recover from this power flux is related to the receiving antenna’s effective receiving area (Ae). This is the area that captures a quantity of power flux and converts it to power [2][3].
The power available at the receiver, discounting feeder and other losses, is described by:
The effective capture area is related to the geometry of the antenna and can be accounted for by the antenna gain. The direct relationship between the gain and the effective capture area is described by the following equation:
So now we can express (Eqn 2) in terms of the gain of the transmitting and receiving antennas by substituting (Eqn 3) into (Eqn 2) yielding:
Thus the available power at a receiver is proportional to the gain of the transmitting and receiving antennas, the radiated power and the square of the wavelength; and the power is inversely proportional to the square of the distance between the receiving and transmitting antenna. (Eqn 4) describes the propagation of power between two antennas in free-space.
As an aside, the effective capture area of a dipole has been found to be (3 l2 /16 p) ~ 0.119 l2 which can conceptually be thought of as a circle at the radial distance of l / (1.6 p) from the dipole centre [3]. The physical significance of this is that a sphere of approximately this radial distance surrounding the antenna can be thought of as enclosing the reactive (or near-field) whilst the region outside the sphere contains the radiative (or far-field).
As the radiation propagates further into the far-field the radiation front tends to become linear and the flux lines tend towards being parallel. E.g. light emitted from a star can be considered as parallel rays on earth and the wave front can thought of as linear rather than spherical. A camera lens is said to be focused at infinity when all light rays seem parallel to its axis and this occurs at distances much closer than most people would think.
Equation (1) may also be used to derive the electric field strength at a receiving antenna by the following relation:
Where
is the intrinsic impedance of free-space (~ 377 ohms).
With the aid of a quantity called the effective height, (Eqn 5) can be used to determine the input voltage at the receiving antenna input:
V = ER he [V] (Eqn 6)
The Effect of the Earth
The effect of the earth is complicated, it is curved and the signal is modified by the conductivity and dielectric constants of the soil layers, the antenna heights and antenna separation and by refraction in the atmosphere.
As a first approximation consider that the earth is flat and a perfect mirror; all power transmitted towards the ground would be reflected from the earth back into the hemisphere containing both the transmitting and receiving antennas. The reflection of the power from the radiator back into the half-space (that above the ground) accounts for a gain factor of 2 (3 dB) because the radiation resulting from the same power is only required to fill half the space compared to a radiator in free space.
If we could now stand on the perfect ground and look towards the antenna and see the radiation we would notice that there appears to be another equally “bright” antenna below the ground. The fact that there appears to be two antennas radiating with the same intensity accounts for another gain factor of 2 (3 dB).
Overall, the improvement due to a perfect ground is 4 or a gain of 6 dB compared with the same antenna radiating in free space.
Radiation over an Imperfect Ground
Some of the radiated power is absorbed in the ground when the ground is not a perfect conductor so not all energy is reflected into the half-space above the ground and the antenna image intensity also depends on the effectiveness of the ground reflection.
The effectiveness of the image reflection is termed the reflection coefficient. This reflection coefficient is low at high angles of incidence, near 90 degrees, and tends to improve as the angle is decreased. Because of complex ground constants (soil conductivity and permativity) the reflection coefficient becomes negative below the Brewster angle. This is caused by phase changes between the signal from the image and the signal from the antenna so the combined signal tends to cancel resulting in diminished radiation at those lower angles.
You can expect up to 5 dB gain over an isotropic (5 dBi) when using a real ground; for a vertically polarised half-wave dipole this amounts to approximately 7.15 dBi.
These ground effects have been studied by Zenick, Sommerfeld and Norton [1],[5]. For vertical antennas, these studies have found that the wave front is slowed-down at the ground interface and that the EM field tilts so it is no-longer perpendicular to the ground. Just another effect that must be accounted for when studying antennas above an imperfect earth. This tilting effect is put to good use when receiving MF signals via a Beverage wave antenna.
Norton has proposed a ground-model which is still in use today. Sommerfeld expanded Norton’s work and derived complex calculations which take into account ground-losses in the near and far-field. The Sommerfeld ground calculations are used in the Numerical Electromagnetic Code (NEC) [5] and its derivatives.
Radiation of Power is a Loss
Propagation or Radiation from an antenna is a loss of Power. (Eqn 1), (Eqn 3) and (Eqn 4) can be cast into terms containing loss, for linear values the equation is expressed as:
Pr = Gt Gr Gh Pt / Lt [W] (Eqn 7)
Where Gh is the height gain and Lt is the total loss due to radiation.
Equation (7) can more conveniently be expressed with addition and subtraction when adopting decibel notation (powers of 10). This new form follows:
Pr = Gt + Gr + Gh + Pt – Lp dB[W] (Eqn 8)
Lp is the total loss over the path. Lf is the free-space propagation loss, which takes into account the inverse-square law. Lg is the ground loss, and Lm contains other losses which will be described by the new propagation Model (introduced in reference [1]). For the traditional propagation model Lm=0.
Lp = Lf + Lg + Lm dB[ ] (Eqn 9)
Traditional Propagation Model
Taking all losses and gains in dB we can assign values to the terms of (Eqn 8) and perform calculations with addition and subtraction.
Free Space Propagation Loss
Lf = 32.45 + 20 log f + 20 log R dB[ ] (Eqn 10)
Ground Loss
The ground loss term is:
Lg = 20 log A dB[ ] (Eqn 11)
Where A is the field attenuation due to ground effects:
A = (2 + 0.3p) / (2 + p + p2) when p > 10. (Eqn 12)
p = 1.75×10-1 (f R cos ß) / s ? (is called the numeric distance) (Eqn 13)
ß = arctan[(e + 1) f / (1.8×10-4 s) ] (Eqn 14)
Where f is MHz and R is in km, e is the relative dielectric constant, s is the soil conductivity in S/m, and ? is the wavelength in m.
Now for most ground and large radial distances A can be approximated as 1 / 2 p.
Height Gain
Gh is the gain improvement due to antenna heights above the ground.
Gh = 15 log(ht +hr) dB[ ] (Eqn 15)
The antenna heights are taken as the distance from the ground to the antenna mid-points and are measured in wavelengths.
The new Lou Lichun HF and MF propagation model [1]
I now expand the Lm from the work of Lou Lichun as:
Lm = Ld + Lb + Ls + Le (Eqn 16)
Ld = 16 log R (Eqn 17)
This term is proposed to account for the increase in path due to the presence of buildings, it contains no other factors other than the radial distance between the transmitter and receiver (I cannot justify the numeric basis).
Building density losses
Lb = 95 log(1 + rb) (Eqn 18)
Rb is the building density, it is calculated by dividing the area of a plan map of the suburban region by the sum of the area of all buildings (assuming that these enclosed area are shadows).
Sight losses
Ls = 80 log(1+rs) (Eqn 19)
rs is the sight parameter which is calculated by executing the following procedure along the route between the transmitter and receiver:
- When a building is located in the route increase the number of building (nb) by 1
- Measure the height of the building (hb) and measure the height of the intersect of the ray with the building (hl).
- Compare hb and hl, if hb > hl, then increase the number of buildings which are not lower than the Line Of Sight intersect (ns) by 1. If hb < hl then ns is not modified.
- Repeat 1 to 3 until all buildings between the transmitter and receiver have been encountered.
- Calculate rs = ns / nb, unless nb is zero, in which case Ls = 0
Receiving environment losses
Le = 125 log(1 + re) (Eqn 20)
Re is the environment parameter representing the environment around the receiving antenna. This is a relative value that has been determined by empirical placement of antennas in various environments. It assumes that the transmitting antennas is well placed.
Suitable Le values can be chosen from the following tables:
For MF
For HF
Luo Lichun also modified Gh because he found that it depends on distance and the frequency, he states the Gh factor as:
Conclusion
This article is a tutorial explaining some of the features of propagation for vertically polarised signals in the MF and HF bands. It is a summary of the feature article [1] by Luo Lichun. In that article the traditional Lp and Gh terms have been expanded to form a new propagation model which Luo Lichun states helps to describe propagation in an Urban environment. He has also stated that he hopes to verify the model for distances greater than 40km. At any rate, his work represents an attempt to quantify the effects of nearby buildings (and possibly trees) on antennas. He assumes that the buildings are composed of re-enforced concrete and that they shield and scatter the RF energy.
Originally posted on the AntennaX Online Magazine by Ralph Holland, VK1BRH
Last Updated : 27th May 2024