The article NEC – vertical monopole radiation resistance study discussed ‘radiation’ in the strict sense, this article takes a look at ground wave propagation from the same antenna.

## NEC insight

Let us look at an example of a quarter wave monopole with 120 shallow buried radials, soil σ=0.005 ε_{r}=13, average ground, at 3.8MHz.

Above is the model geometry.

If the monopole was over a perfectly conducting earth (PCE) we would expect that E field is inversely proportional to radius of the observation point, ie \(E \propto \frac1r\), ie the same dispersion as ‘radiation’.

Requesting ground wave pattern calculation from NEC results in cylindrical model of ground wave E field intensity. In this case, data from X=500 to X=30,000m in increments of 500m was requested.

Above is a plot of NEC calculated E field vs r. Also plotted is the 1/r line (for PCE) and a prediction using Norton’s ‘exact’ formula for soil attenuation given soil parameters.

We can see that the E field of the ground wave falls more quickly than 1/r, the rate depends on soil parameters (mainly conductivity, but also permittivity).

Now these are predictions based on various assumptions including homogenous ground of known characteristics so there is scope for uncertaintly.

## E field survey

The E field strength is usually fairly easy to measure, an E field survey of a range of distances at various radials can provide a valuable source of data. Note measurement has its own uncertainties, and recent rain history may affect soil parameters somewhat.

## Cymomotive Force

A commonly used metric for ground wave assessment is the cymomotive force (CMF) (ITU-R 1986), it is the product of E field strength and distance without including the effect of finite ground conductivity. For example for 1000W into a lossless quarter wave monopole (Directivity assumed to be 3) over PCE, CMF=300V independent of distance.

(ITU-R 1986) allows for measurement of CMF, but the measurement must be at a point where reactive components of the field to be negligible, and given the requirement that it not include ground loss, the measurement must be made as close as possible within the previous constraint.

Let’s introduce a statistic being E*r, ie CMF with ground attenuation.

Above is a plot of E*r based on the NEC model and Norton’s ‘exact’ formula. As mentioned earlier, this scenario over PCE would have CMF=300V independent of distance, but we can see that the effect of real ground attenuation is that the E*r rolls off at several hundred metres and eventually a fairly constant slope downwards.

We could estimate CMF from field strength measurement, distance and Norton’s formula for |As|.

Above is a plot of estimated CMF based on the NEC model E field strength, distance and Norton’s formula for |As|. The slightly higher value at low r is evidence of some residual reactive field component.

## Ground wave system efficiency based on E*r and CMF

E*r calculated from measured E field at a distance gives us a view of system ground wave performance, we might call it system ground wave efficiency at that distance. Keep in mind that this is a two dimensional problem in the real world, E*r will depend on distance and radial direction when the ground is not homogeneous.

Above is a plot of ground wave system efficiency vs distance for the NEC model and using Norton’s ‘exact’ formula.

The expression \(GWSE=(\frac{E \cdot r}{CMF})^2 \cdot 100=(\frac{E \cdot r}{300 \cdot (\frac{P_{in}}{1000})^{0.5}})^2 \cdot 100\%\) shows the workup of the statistic.

Transmitter system losses such as ATUs, feed line, and antenna conductor and radial losses will all push the curve downwards overall, and the slope is very dependent on soil parameters.

This E*r efficiency is more relevant to a ground wave application than Radiation Efficiency. There are some factors that will reduce both Radiation Efficiency and GWSE, but one cannot be simply calculated or inferred from the other and each has its application. The apparent good ‘low angle’ performance of the surface wave is offset by its more rapid decay with distance than ‘radiation’ due to ground attenuation and it does not usually make a useful contribution to practical ‘low angle’ ionospheric paths.

## References / links

- IEEE. 2013. IEEE standard for definition of terms for antennas IEEE 2013.
- ITU-R. 1986. RECOMMENDATION ITU-R BS.561-2. Definitions of radiation in LF, MF and HF broadcasting bands. ITU-R.
- ITU-R 2007. Recommendation ITU-R P.368-9 (02/2007) Ground-wave propagation curves for frequencies between 10 kHz and 30 MHz. ITU-R.
- Norton, KA. Dec 1941. The calculation of ground wave field intensity over a finite conducting spherical earth. Proc IRE, vol 29, pp 623-639.
- ———. Oct 1936. The propagation of radio waves over the surface of the earth and in the upper atmosphere Part I. Proc IRE, vol 24, pp 1367-1387.
- ———. Sep 1937. The propagation of radio waves over the surface of the earth and in the upper atmosphere Part II. Proc IRE, vol 25, pp 1203-1236.