The Antenna's Radiation Pattern

Joachim Köppen Strasbourg 2009

The radio telescope's parabolic dish antenna is designed to concentrate the view into a small region. Or, if we were to use it on transmission, the radiated energy would be concentrated into a small angle in the sky. One speaks of the angular width of the antenna "beam" or "main lobe". It is useful to characterize it by its full width at half maximum power: Half Power Beam Width (HPBW).

Because electromagnetic radiation is in the form of waves, it is the diffraction of the waves impinging on the finite size of the antenna dish which determines this angular width. The HPBW is determined by the diameter of the antenna, measured in wavelengths:

HPBW = 58° * Wavelength/Diameter
which holds for small values (HPBW smaller than about 10°). This means that in order to have a beam width of less than 1°, the antenna must be larger than 60 wavelengths. For the Ku-band, with a wavelength of about 2.7 cm, we need a dish of 2.2 m diameter! Our 1.2 m dish thus would have a beam width of 1.3°, but it is about 1.7° because the dish is not fully illuminated; this is about three times the diameter of the Sun or the Moon!

When doing a drift scan across the sun, one simply measures the radiation pattern in the horizontal plane. The sky's apparent rotation makes a time intervall of 4 min correspond to 1° in angle. The plot below compares our results with the measurements of the prototype telescope. It can be seen that the prototype's HPBW was about 1.4° (as expected), but our antenna has a much broader beam of about 3.75 deg ...

... we found out the reason: the arm carrying the LNB had been bent, so that the antenna was out of focus! When it had provisonally been set up on the roof, one strong gust of wind blew it over, and not only the parabolic dish now is slightly distorted, but the LNB arm was bent by about 10°, but in a way that we took it as design! After repair in spring 2007 the horizontal HPBW is about 1.5°. Here is a comparison of the horizontal pattern before and after the repair:

In comparison with a perfectly symmetric gauss function, a slight East-West asymmetry becomes apparent:

This imperfection has no consequences for our observations! But what is really nice that as a consequence of the sharper beam, the peak signal from the sun is larger, and that now we were able to pick up the weak signal from the moon:

Here we caught the moon (which had been New Moon just a few hours ago) following the sun in the sky. We got that by pure chance: in 2008 Marina Lemberg wanted to observe the sun every day, but she had placed the telescope on a position slightly different from what we really had planned ... a great luck for us! (The dark blue curve is the moon signal, simply multiplied by ten).

Here is a JAVA applet which computes the radiation pattern of a square- or circle-shaped parabolic dish antenna. Click on Clear to start, enter Wavelength 2.5 (in cm), Dish diameter 120 (also in cm), and click on Compute Far Field to get the pattern when we look at large distances, as we do here. You can change the Y-axis to show the signal linearly (in V, but normalized to 1.0 at the maximum) or in dB. Also you can change from uniform illumination to perhaps a more realistic cosine law; what the real illumination of the dish by the LNB is, we don't know ... but this also affects the width of the antenna beam ... we can find out by measuring the HPBW (half-power beam width: the point at -3dB or at 0.71 in linear representation), which is 1.4 deg with cosine illumination but 1.0 deg with uniform illumination ... if you click with the mouse on the plot, it will show the x and y coordinates of that point!

Then we began to measure the antenna pattern both in horizontal and vertical direction, by observing the transit of the Sun every day, as it moved higher and higher up in the sky in late winter 2008. This contour plot shows the raw data obtained by Marina Lemberg, which are not corrected for the slight daily azimutal shift of the Sun. The colours indicate the different levels of sensitivity from the maximum (gray, red) downward:

Quite to our surprise (and delight) we found that far from the centre, there is apart from the low tail of the main lobe, another low secondary feature (the violet island) which indicates that our antenna pattern does not have a perfect shape. However this seems only a slight imperfection which does not compromise out observations. But it's nice to know! (Please note that the numbers at the coordinate axes are simply sequence numbers of the data ... the horizontal width of the yellow region is about the HPBW of 1.5°).

Another run could successfully cover both sides of the pattern. The nearly circular contours in the centre of the plot show that the pattern is quite symmetric. However, the outer contours indicate the presence of two pairs of "feet" in the pattern: a stronger one (upper right and lower left) but also a fainter pair at upper left and lower right. Since our dish is slightly distorted due to its initial been blown over by a strong wind, we suspect that the feet - which are point-symmetric to the centre - could be the result.

In a 3D representation of the same data, we see that the "feet" are at very low level, at about -15 dB from the maximum, so their presence does not have any effects on our interpretation of solar observations. The pattern is sufficiently symmetric in the top 10dB as to justify our assumption of a gaussian shape and use of the HPBW to compute the antenna filling factor!

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last update: Apr. 2013 J.Köppen