ABCDx: Miscellaneous Notes

Contents:

1. Propagation Notes

2. Antenna Notes

D/2 = R*c/(180/pi), so that D = (2R/57.3)c

Since the angles a, b, c of the triangle must add to 180, we then have

D = (2R/57.3)*(90 - a - b)

By the Law of Sines,

R/sin(b) = (r + H)/sin(90 + a)

so

b=arcsin {[(R/(R + H))]*sin(90+a)}

and we finally have

D = (2R/57.3)*arcsin {[(R/(R + H))]*sin(90+a)}

The diameter of the Earth at various latitudes may be approximated by the average of the polar and equatorial diameters [Polar diameter ~ 7,900 mi (12,720 km); Equatorial diameter ~ 7,926 mi (12,760 km)], or R = 6370 Km. Below are the results of some calculations using an Excel macro to replicate the Table 1 of the WR column. Note from the figure that as the radiation angle increases, the signal ray incident angle, b, decreases, and so the angle (90 - b) increases.

From the table, we can see immediately that as the ion-region height (H) increases, the skip does indeed increase, but the MUF decreases! The reason is clear from the data because as H increases, the incident angle decreases, bringing the ray closer to vertical incidence and therefore allowing less opportunity for the wave to be refracted, so that it exits into space unless the frequency is decreased (i.e., lower M-factor => lower MUF). Just another interesting aspect of radio wave propagation!

**************

- WWV Reports

Archives of the eight WWV SFI reports for each day may be seen at www.sec.noaa.gov/ftpmenu/forecasts/wwv.html.

Below is a summary of the reports for two days, reduced to the SFI, A, & K indices only, and arranged in row-order to better appreciate the change-over of the A-index at 2100UTC. Note the date change at 2100UTC and the estimated A-index at that time.

2. Antenna Notes

- Understanding Elevation & Azimuthal Plots

Antenna modeling programs commonly produce output graphics and data showing the expected radiation pattern of the antenna in one of 3 viewing options: as a 3-dimensional figure; a vertical slice ("Elevation Plot") through the 3-D pattern; or a horizontal slice ("Azimuthal Plot") through the 3-D pattern. The elevation view tells us about the radiation angle and the azimuthal view is the one that we most often use for evaluating direction of radiation. Below are the Elevation and Azimuthal plots of a simple 20m 3-element Yagi antenna used for illustration. Elements are 1" OD untapered and lengths are: Reflector = 35.0 ft; Driven = 32.7 ft; Director = 30.0 ft. Boom length is 28 ft and modeling is done for the antenna at a height of 66 ft (one wavelength) above real ground.

The modeling software automatically labels the outer-most point of the radiation pattern maxima as "0 dB" because the intent of the plots on the circular graph is to show the pattern of energy distribution in comparison to the maximum. The modeling program has calculated the maximum gain over an isotropic radiator to be 13.02 dBi (10.7 dBd), so the outer ring of the plot is set to that value. We can then see from the two plots that there is quite a bit of interesting variation in the energy distribution as it radiates from the source. Note also that the scale of the rings is compressed as they get smaller, because decibels are logarithmic numbers that compress as they get larger or smaller.

Note from the data in the Elevation plot (left), that there are two major beam lobes emerging from the antenna, with a radiation maxima in the lower lobe at an angle of 14^o. In addition to the angle of maximum radiation power emission, the "thickness" or "width" of the beam is also calculated between the two angles above and below 14^o at which the power is reduced by half, that is, reduced by 3 dB. If we look at the -3 dB ring (inwards from the 0 dBi max), we see where the power is down by half from the maximum, indicated by the two purple lines at 7.0^o and 15.3^o. This is called the "Half-power Beamwidth", or just the "Beamwidth". It should be clear that antennas generally radiate energy in beams and not single rays; however, it is theoretically possible (and feasible at UHF and above) to design antennas that produce extremely narrow beamwidths. Additional information can be likewise determined for the other lobes.

Let's now look at the horizontal, or Azimuthal, radiation pattern, which can be viewed as a slice from any angle. Since for DX, we are interested in a low angle of radiation, for this antenna model we will use 14^o above ground from which to view the azimuthal pattern. In the figure on the right, we see from the data that the horizontal forward gain at the chosen radiation angle (14^o) is 13.02 dBi (10.7 dBd), as we already knew from the Elevation plot. In addition, the calculated data tells us that the antenna has a F/B of 18.64 dB, a figure that we can easily read from the plot, as diagrammed below.

Here is another look at the azimuthal view, labeled and annotated to explain the numbers in the figure. The modeling software automatically labels the outer-most point of the radiation pattern maxima as "0 dB" because the intent of the circular graph is to show the radiation energy distribution within 360^o, relative to the maximum.

The azimuthal beamwidth is seen to be 65.0^o (purple lines defining -3db points), a fairly wide "funnel". That's why exact "pointing" of your 20m beam is not extremely critical, as long as you are within a few degrees of the proper beamheading.

Why is a negative scale used? Remember that gain in dB is a logarithm of the power ratio, and that logarithms of fractions are negative numbers. Since any "gain" at a point inside of the outer-most circle will have to be less than the maximum, it will then be a fraction, hence negative. Even if the data were not printed out, we could, as illustrated above, get an estimate of the F/B ratio by reading the chart.

Another important point to remember is that these patterns from which we derive the antenna gain are viewed in the far-field, many wavelengths from the antenna. Note that the "gain" at the radiation source (antenna at the center of the pattern) is not a consideration and is shown to be essentially zero ( -50dB or less).

- Gain, F/B, & Bandwidth

To see how the forward gain and F/B ratio are related to frequency, here is a set of superimposed azimuthal plots of the above 3-el Yagi produced by having the modeling software sweep the frequency from 14.0 MHz - 14.4 MHz in 0.2 MHz steps:

We see that the forward gain is less affected by frequency change than is the F/B, which ranges from approximately 24 dB at 14.0 MHz (Blue-line), down to about 15 dB at 14.4 MHz (Black-line). Data figures are for the sweep end-frequency (Black-line patter @ 14.4 MHz).