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# Array Antenna.....

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#### Rohit Chatterjee

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In an antenna array,why do grating lobes appear in the radiation pattern if the element spacing is greater than half-wavelength????

Studying and understand antennas is very similar to studying and understanding optical lenses. There are different phasing techniques, but consider a simple two horizontal dipole phased array. Then consider how light passes through an optical aperture or slit. Consider one dipole as metaphorically the source of light and the other the aperture.

In an optical system, diffraction will occur if the distance is too great, in a similar grating pattern as an antenna array.

Think of how lenses have corresponding focal lengths too. antennas are like lenses and focus the radiation pattern when the work together. The spacing of lenses is important just as it is with antenna arrays.

I am sorry but i really dont remember anythin about optics.....could u xplain mayb in terms of magnitude of primary lobes n secondary lobes or sumthn akin????

No hope othrwys???
i find optics very boring.....

"greater than half-wavelength???? " Antenna spacing > 1/2 does not matter. The receiver sees the energy from all the antennas. If the phaseing is such that the power adds the signal is strong. If the power substracts, because 180, then the signal is very small.

No hope othrwys???
i find optics very boring.....

Then you will find antennas boring. The same physics that governs optics governs antennas, practically speaking. But optical systems are easier to visualize. If you can visualize light behaving in much the same way as radio waves, then you will be able to visualize how radio waves are diffracted, refracted, reflected, and focused just like lenses do to light.

A good start in understanding optics is reading about monochromators, they are the principle behind the science of spectrometry. Lenses, mirrors, and apertures to seperate light into various wavelengths. Many of the same mathematical principles are used to design yagis and phased arrays.

A mathematical thesis on either subject is not needed. That is what textbooks are for. Many websites will offer tutorials on how lenses and mirrors bend light, and if you use strong analytical reasoning skills you will be able to make the connection between optics and antennas.

"greater than half-wavelength???? " Antenna spacing > 1/2 does not matter. The receiver sees the energy from all the antennas. If the phaseing is such that the power adds the signal is strong. If the power substracts, because 180, then the signal is very small.

Have you ever modelled antenna radiation with elevation or azimuth angle charts? Spacing DOES MATTER.

The texts that I have say that you get grating lobes when spacing exceeds 1 wavelength*. You can look at it this way, consider a simple driven array of two identical elements, which is the simplest array. When the spacing is less than 1 wavelength, it is impossible to find a direction beyond a single line through the array where there is complete constructive interference. For example, if the two elements are driven in-phase, the only direction in which their emissions add together perfectly in phase is broadside in a single line perpendicular to the plane of the elements. In all other directions, the emission from the two antennas do not combine perfectly in phase. Now, imagine that you increase the element spacing to 1 wavelength. Now, you can imagine that you will get perfect in-phase combination not only broadside to the array, but also on a line through the two elements as well. This must be so because we have spaced them one wavelength apart so emission from one element will be back in phase when it propagates to the other element and the total emission continueing in that direction will remain in phase from both elements.

As spacing goes beyond 1 wavelength, the direction in which you get in phase combination starts to move away from the axis through the two elements and when spacing reaches two wavelengths, you get a new grating lobe on that axis again for a total of 3 axes where there is perfect combination.

* ref: Kraus "Antennas For All Applications", 3rd Edition, page 598

I was trying to say that things do not change above/below 1/2 half-wavelength. Spacing does effect the pattern. Phase of the antennas effect the pattern. It is just "vector math". The energy adds/substraces via the phase. If the spacing is very close the pattern is simple. If the spacing is very large the number of lobes is large.

RadioRon has offered a good technical explanation for antenna phasing.

I'll add as an aside to my optics comments, that antennas also work like phased speaker systems, speaker enclosures and acoustics in general.

When a speaker diaphragm moves in and out, the audio waves come out the front and the back of diaphragm, out of phase with each other. Without proper design, the acoustics of the system can be quite a mess with cancellations masking certain frequencies and others echoing. But if the back-waves can be reflected back IN phase with the forward waves, the audio will be louder and more directionally focused. Enclosures in high quality systems utilize the back radiated waves in this way.

I found some really good animations on acoustic wave patterns, and the lesson here is that all wave generators behave with the same physical laws. grating and lobe patterns can even be seen in the waves of a pond.

Here is a good applet that shows how light is diffracted through slits. Grating lobes in a wave generation system are either caused by reflection or diffraction. This applet shows the diffracted gratings caused by laser light passed through slits

A pretty good description of optics, even covers X-ray diffraction theory. I maintain XRD equipment in my laboratory, as well as various spectroscopic diffractive and refractive test equipment.

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The texts that I have say that you get grating lobes when spacing exceeds 1 wavelength*.

Sorry it would be one wavelength....my apologies...

Btw,there may b secondary maximas even if the spacing is less than hlf wavlength,right????
How can we b sure that none of these will b a grating lobe?????

Btw,there may b secondary maximas even if the spacing is less than hlf wavlength,right????
How can we b sure that none of these will b a grating lobe?????

Yes, there may be secondary lobes in that case. However, the answer comes from the definition of grating lobes. For example, from Balanis*, the definition is "a lobe, other than the main lobe, produced by an array antenna when the inter element spacing is sufficiently large to permit the in-phase addition of radiated fields in more than one direction". It is simply not possible to meet this definition with smaller than one wavelength spacing. I think you might also be able to study this question in greater detail by studying a few individual cases using vector optical methods or a simulator.

* Constantine Balanis "Antenna Theory Analysis and Design" 2nd edition, page 311

Thnx 2 both of u guys once again.....u rock......\m/

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