You should have read the notes on antennas .
You should also be attending antennas lectures this semester.
There is a xerox of a previous report on this lab for you to consult. You are presented with this report as a rough guide rather than a template. Some of the results are incomplete and even erroneous; if you merely adapt your data to those of the report and submit a copy of it I shall not be very impressed, and you may get an appropriate mark.
There is an excellent book; "Antenna Theory: Analysis and Design" By Constantine A Balanis, John Wiley, second edition 1997, ISBN 0-471-59268-4. There is a copy of this book in the lab for you to consult.
You are going to verify the inverse square law for far field power propagation from an antenna. Doubling the distance between transmit and receive antennas should reduce the received power by 6dB. You should take measurements at ranges of 0.25, 0.35, 0.5, 0.7, 1, 1.4, 2, 2.8, 4, 5.6, 8, 11.3 metres. Each increment of distance should give you 3dB less received power. The power is read on the VSWR meter assuming the detector is accurately square law. You are asked to estimate the errors, and plot suitable error bars. The plot of power vs distance on lin-log paper should give a straight line from which you can calculate the power law. You should also plot the Rayleigh distance 2d^2/lambda for this experiment. The separation between the antennas should be the sum of their Rayleigh distances for far field propagation to hold good. This will show up on your power vs distance plot.
An example of a previous experiment, at wavelength 3.3cm, is shown below.
Here, we show what a rough plot "plotted as you take the data" should look like. It is vitally important to PLOT EVERY POINT AS YOU TAKE IT. Here our first-pass data analysis shows a measured antenna gain of 16.5dB and a calculated antenna gain of 17.8dB. The error bars might at first sight allow for an uncertainty of +/- 2dB but actually the experiment is better than that as there is some data averaging involved in fitting the square-law theoretical line.
Note that in calculating the gain from the formula Gain = (4 pi A)/(lambda)^2 we have adjusted the effective aperture value down from the actual area of the horn mouth, to allow for the tapered illumination in the H-plane across the horn. This amplitude distribution is a half-cycle of a cosine function and the average value of (cos)^2 is 1/2. So we apply a factor ("aperture efficiency factor") to the actual area to derive the effective area. Since the fields add rather than the powers, the ideal aperture efficiency factor to apply would be 1/sqrt(2) or 70.7% assuming no phase errors across the mouth. In practice, the wave is not plane across the horn mouth as it sets out from a "phase centre" somewhere in the throat of the horn. Adjusting for the phase error as well puts the aperture efficiency somewhere in the region of 65-70% depending on the flare angle. There will also be a small contribution from resistive loss.
When you come to plot the polar radiation patterns you will see that even though the horn mouth is square, the E-plane pattern shows more pronounced sidelobes than the H-plane pattern. This is because of the cosine-law "edge taper" or "apodisation" in the H-plane section of the horn mouth.
You will measure the absolute gain of a pyramidal horn and compare it with the theoretical value given in the book by Constantine Balanis on antennas. You will find it possible to get agreement between measured and predicted gain of better than 0.5 dB with this apparatus.
You will take E-plane and H-plane polar plots for a pyramidal horn, and compare the positions of the first nulls with theory.
You will take polar plots for the sectoral horn, the polyrod antenna, and the single slot antenna. You will measure the interference pattern between the double slot antenna slots; this gives the array pattern of two elements. Note that for the sectoral horn, and the slot antennas, the E field direction is across the shortest opening of the slot. It is important to get this polarisation right when you set up the antennas.
You will investigate the polarisation directions of the pyramidal horn antennas, by rotating one around the line of sight joining the two antennas. Now you will demonstrate the use of the quarter wave plate to produce circular polarisation.
You will measure the gain improvement produced by the dielectric lens placed in front of a pyramidal horn. You will also investigate the effect of the artificial parallel plate lens.
You will estimate the Rayleigh distance of the parabolic reflector dish antenna, and try to get a measure of its boresight gain at as far a range as the lab will permit. This should be compared with the theoretical gain and an estimate of the antenna efficiency should be made.
This experiment runs in X-band which is roughly 8-12 GHz. Notionally the antennas are adjusted for operation at 10GHz, and you should measure the frequency of the Gunn oscillator with the inbuilt cavity wavemeter. The red scale on the wavemeter reads the guide wavelength directly in cm; you use the waveguide formula (waveguide notes) to find the free space wavelength and the frequency. The waveguide dimension "a" is 0.900 inches. Remember to convert it to cm.
Do NOT attempt to alter the frequency of the Gunn oscillator using the tuning screw.
For doing the calculations in this experiment you need a reasonably accurate measurement of the free space wavelength. The procedure above should give it to you within 1%. You can check the guide wavelength roughly using the slotted line on the transmit bench, generating the necessary reflections with a metal plate placed across the antenna mouth.
The free space wavelength at 10GHz is 3 cm.
You will probably think that the apparatus for making polar plots is rather rudimentary. The angle scales can be read at best to +/- about 2 degrees. Setting the antennas at the same height and pointing to each other on boresight is a matter of judgement rather than accurate measurement.
Nevertheless, it is satisfactory how much accurate scientific information can be obtained from this experiment.
Measuring side lobe shapes with all the scattering objects in the lab is quite inaccurate. You probably need to repeat the measurements of the far out sidelobes a number of times for differing configurations of scattering objects (get a colleague to walk around in the beam of the receive antenna) to get an idea of the sizes of the probable errors.
You will need to plot fairly accurately estimated error bars on both the angle and the received power axes. Then it will be possible to fit a calculated polar plot to your measurements and still lie within the experimental uncertainty.
There are sheets of blue cockled microwave absorber material which are on stands and can be placed to reduce the spurious reflections. They have much better absorption at normal incidence, but reflect a lot at grazing incidence.
If you have time to calibrate the diode detector square law, as you did in the microwave experiment, you will get better agreement between the theory and experiment on the power received vs distance experiment.
Do not take too many points when taking data. Take sufficient points near nulls or other features of interest to locate them accurately, as this information will be compared with theory later. But repeat points a few times (after resetting the apparatus) to get an idea of the potential accuracy. Remember, you are testing the theory in the lab, to find out how good a predictor it may be in the "field". The theory is perfectly accurate, but the model you use for the theory doesn't bear much relation to the complicated arrangement in the lab. It is part of the art of the engineer to assess how much to trust theory, link budget calculations, BER calculations, etc, and we hope this experiment will help you to get a feel for this aspect.
You do not need to adjust the triple stub tuners to get the best match, except possibly when using the single and double slot sheet antennas.
Do not adjust the frequency of the apparatus during the experiment.
Remember, DO NOT LOOK DIRECTLY UP THE BEAM, particularly at close range. The Gunn diode output is only about 15mW and there is little safety hazard, but it is wise never to subject the eyes to more microwave radiation than is necessary.
You will be working in teams, of about 6-9 people, so it is best to nominate a transmitter person, a receiver person, a data caller, a graph plotter (you should plot the results as you take them), and error estimator, a distance measurer, and a general factotum.
There is a very excellent report in the lab for you to consult. Can you please remember, accurately hand plotted graphs are much more informative than those produced on a computer. Lines should only be used to connect points if they are calculated lines from theory. It is poor practice to join points freehand with a "line to guide the eye".
Remember, you are testing the theory against experiment and it is good practice to have a convincing explanation for any observed discrepancies. I have been very happy on the whole with the standard of reports produced for the microwave measurements experiment in the first semester, with the exception that assessment of experimental errors, and inclusion of comparison with theory and critical discussions of errors, has been noticeably absent.
If you want to load the report with theory that is fine, but the intention of a report on a lab is to convey what happened when you yourself did the experiment. Therefore it is better to concentrate on experimental technique, assessment of errors, discussion of discrepancies, etc, and refer to the theory by references to the standard texts.
We hope you enjoy this lab.
The pyramidal horns used in this experiment have various apertures which you should measure; the diagonal width across the nearly square horn is about 11 cm so the area of the mouth of the horn is 11*11/2 or about 60 square cms. The wavelength at a nominal 10GHz (you should measure this frequency) is 3 cm so if it were true that the horn aperture was uniformly illuminated we would expect a numerical power gain G = 4 pi A/(lambda^2) of about 4*3.142*60/9 or about 84. Actually the illumination is not uniform, the variation in the H-plane being cosinusoidal with a maximum at the centre. You should refer to Balanis for details of the corrections required.
If the gain of the horn was 20dB or a numerical factor of 100, then at a rough approximation the energy is concentrated into 1/100 of the total area of a sphere surrounding the antenna. If we consider a circular disk of diameter d, and area pi*(d^2)/4, through which all the power is directed at distance R, then we find that 1/100 = [pi*(d^2)/4]/(4 pi R^2) and so d/R = 4/10. The half power beamwidth is therefore 4/10 radians, and the semi-angle subtended at the antenna is half this or 2/10 radians.
In our lab experiment the antennas are about 1 metre up off the floor, and measurements are made out to about 11 metres. Reflections from the floor will therefore be a problem at spacing greater than about 10 metres, since the edge of the beam falls 1 metre when travelling forwards 5 metres and the transmit and receive antennas are identical.
Thus you should expect to see deviations from square law at ranges above about 8 metres when you take your measurements, since there will be multipath propagation between the direct beam and the floor reflection at this distance and above. The ceiling is not a problem as it is at least 2 metres above the top of the antennas.
To find the far field radiation pattern of the horns it is necessary to take the Fourier Transform of the aperture illumination. With the simplest possible assumptions on aperture illumination for the pyramidal horn and for the sectoral horn, both of which you should have measured in the E-plane and the H-plane sections, the calculations proceed as on the following two pages:-
I have left the H-plane calculation for you to do. You should find the measured E-plane null positions within a few degrees of these predictions.
Here is a graph of a calculated H-plane plot, for an antenna horn mouth width in the H-plane of 7.6 cms and a wavelength of 3 cms (10GHz). Notice the first sidelobe is -23dB and is the only sidelobe inside an azimuth angle of 80 degrees. It is easy to miss the null when taking measurements. The beam semi-angle at -3dB is about 15 degrees.
If you can do your own plot like this and fit it to your own data I shall be pleased and impressed.
Copyright D.Jefferies 1996, 1998.