The following are a few after thoughts on Propagation of Long Radio Waves. The section immediately below called "FROM ORIGINAL PART 4. DISCUSSION" was written as part of the original article but I left part of it out because I thought it unnecessarily complicated the article and there was not sufficient space to fully develop the subject so I present this discussion as a supplement for your consideration. It has been updated from when I originally wrote it. I would like to point out that there is probably a lot of learned discussion and information in learned papers on this subject which I don't have access to. Persons who know more than I might consider updating the information given here. The plot presented in Fig 14 gives information from two different sources as described below but allowing for the difference in frequency and radiated power the results from the combined graph agree fairly well by those given by "Gamal Soegiono" in an article "LF Propagation Abstract" in this web site.
In addition I have included a few new thoughts on "RADIATED POWER and/or ERP" and "Cutback". I would be interested on any comments particularly on the subject of radiated power and ERP.
Further Thoughts on "LACK OF HIGH ANGLE RADIATION ON LOW FREQUENCY"
As discussed above the lack of high angle radiation on LF is not surprising when you look at equation 7 and also observe Fig. 11. From equation 8, it is also obvious that at frequencies much above 200kHz the reflection coefficient at the conductivity discontinuity will be poor at even low angles.
All the above calculations for ionospheric reflection were derived from information given in chapter 3.3 of VLF Radio Engineering (ref 8) which deals with the ray theory of LF propagation mainly between 30kHz and 200kHz.. (Below 30kHz propagation is dominated by wave-guide modes and don't concern us). The aforementioned chapter only deals with reflection of the wave from the bottom edge of the conducting layer of the ionosphere by speculum type reflection. Originally when preparing this article I compared propagation graphs given in several writings particularly those given in Watt (ref. 8) and Davis (ref. 9).
Graphs shown by Davis give a slightly different picture see fig 14. From this graph, the signal is much higher at high angle although in most cases as with the example given here, the high angle signal is drowned out by the surface wave over medium distances. The graphs given by Davis are based on actual results. Why the difference? The data in Watt is based on the calculated reflection coefficient at the conductivity discontinuity between the ionosphere and the atmosphere only. This is probably correct for all or all practical cases below 200 kHz but is probably not the whole story.
There must be a transition between the type of reflection described in part 3 of this article and that in Part 2. What might happen is that, at a high angle of radiation, say at 200kHz, the reflection at the discontinuity is very poor. Some of the signal passes through the loss layer and is reflected by the E layer in the manner described in part 2 (HF type reflection). This is illustrated in fig 15. The transmission between these two modes of reflection should be more obvious with increasing frequency.
If a high angle signal exists it should be detectable with a dipole. A dipole should have a high rejection of the vertically polarized surface wave and enhance the high angle ionospheric wave. This effect is often used to advantage on 160 metres. In addition, if a dual path exists, it should also be detectable in the form of fading under certain conditions in the area beyond the ground wave range. The author has tried a number experiments at his QTH to detect high angle radiation from "Non Directional Beacons" but so far has not been able to detect any high angle radiation using dipole reception . A small dipole is very inefficient. The experiment is certainly worth repeating with a bigger dipole. There must be plenty of people in the rural areas who have big dipoles and could carry out such an interesting experiment. Fading caused by interaction between ionospheric waves might only be observed from a moving detector such as an aircraft because path lengths at LF change very slowly.
In the plot shown in fig 14 and if two ionospheric paths exist , fading should occur at about 900 km. as well as at the interaction with the surface wave at about 420 or 550 km (depending upon which curve is correct, the dotted or the solid). There should of course be another interaction at about 3000 km where the first hop ionospheric wave equals the second hop ionospheric wave.
REFERENCES
8. VLF Radio Engineering by Arthur D Watt Chapter 3.3.
9. Ionospheric Radio Propagation by Keith Davis section 9.7 see (fig. 9.20).
In "Radio Engineers Handbook" by F E Terman and also in "VLF Radio Engineering" by Watt the field strength curves are based on field strength in micro Volts per metre or field strength in dB above 1 micro Volt per metre for a radiated power of 1 kW. In the above article the curves were worked out for a radiated power of 100 watts. Obviously if a radiated power of 1 watt is being considered then the signal strength will be -20 dB of that shown.
What if we are talking about equivalent radiated power. I don't know how power is rated in countries having a Low frequency license but I will make a few observations on this matter.
Equivalent radiated power would be the power radiated by an isotropic (in space) which would give the same signal strength in the main lobe for the antenna in question. For an elemental (short) dipole the lobe has a gain of 1.78 dBi and for an elemental monopole, because all the radiation is above the ground only there is another 3db gain. This means that a vertical monopole would have a 4.78 dBi gain (in the main lobe at right angles to the antenna) over an isotropic for the same radiated power. This is a bit hypothetical for the distant field strength, as its radiation pattern does not include cutback.
In an actual antenna the radiated power is given by-
Radiated Power = Rr x I2 (11)
Efficiency % = (Radiated power/Input power to antenna) x 100 (12)
Where Rr is the theoretical radiation resistance and I is the actual current at the base of the antenna usually measured by an RF ammeter. Methods of estimating radiation resistance for medium and low frequency monopoles are given in the "Handbook of Wireless Telegraphy" (ref 10) and also in other suitable articles and computer methods. It should be understood however that, even if the estimated radiation resistance is accurate there is also some loss in near by objects, which reduce the radiated power. Also it is almost impossible to measure the radiation resistance of the antenna because the loss resistance in a low frequency antenna is enormous as compared with the actual radiation resistance. In theory, for example, the radiated power for an ERP of 1 watt should be 4.78 dB less than that for an actual radiated power of 1 watt. As stated above I don't know how ERP is usually defined in countries having an LF licence but I would be interested to know how my definition lines up with what is usually understood?
In the main article, cutback is observed to be modified by the effect of diffraction which bends the rays close to the ground and extends the distance of low angle hops beyond the horizon. The effect of cutback only applies to the distant radiation pattern and is not applicable to the surface wave. The idea of a negative radiation angle is based on drawing straight lines from the transmitter to the ionosphere to the receiver. This would suggest that the incident angle at the ionosphere is less than for a tangential ray to the earth. Because the ray bends above the earth it actually comes from a point above the earth and therefore the incident angle at the ionosphere is greater (or conversely the angle to the tangent at the ionosphere is less). I don't know how this difference can be taken into account in calculations except to say that it would improve the reflection coefficient of the ionosphere being at a lower angle.
Because the graph of cutback in the original article was limited to one frequency only I have worked out cutback for several frequencies relevant to amateur radio.
From tables and methods given in Watt
formulae 3.3.4 to 3.3.7, fig
3.3.7
and table 3.3.1 I have calculated cutback for these frequencies
(using
a spread sheet and the original tables) and these are shown in figs 16
to 20, some extrapolation was used based, on calculations including
ground
loss. I would say that the calculations may not extend to the lengths I
have taken them and therefore I could be corrected in the matter. I
offer
these graphs as a guide only. Please note, for anyone referring to the
original references that Watt gives cutback relative to an elemental
antenna
as if in space carrying the same current where as I have given cutback
relative to an elemental antenna above ground i.e.. relative to 0 dB.
The
final result is the same since I accounted for the parameters in a
slightly
different order.
Poor soil is taken as, pemittivity 5
condictivity .002. Good soil
permittivity 15 conductivity .01. Sea water permittivity 80
conductivity 4.0.
REFERENCES
10. Handbook of Wireless
Telegraphy 1938, British Admiralty.