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Linear array Directivity Index

Started by naumankalia 5 years ago7 replieslatest reply 5 years ago382 views

Hi

The linear array directivity index (DI) can be calculated as 10log10(n) or 10log10(2L/lemda) where n is no of sensors in linear array, L is acoustic length/aperture of array and lemda is wavelength.

If we have a uniform linear array whose elements have spacing greater than lemda/2 among them then what formula is more accurate for DI calculation?

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Reply by alcocer77August 27, 2016

For that particular question I would check Harry van Trees book series (estimation, modulation techniques) volume 4. It is devoted to radio waves, but math is the same for mechanical waves as well.

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Reply by naumankaliaAugust 28, 2016

Thanks. I will try to get this book series

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Reply by Fred MarshallAugust 28, 2016
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Reply by naumankaliaAugust 28, 2016

Thanks for literature

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Reply by shafie7August 28, 2016

Why would you want array spacing greater than half wavelength?

It would create Grating Lobe, Unwanted Lobe in undesired direction.

That is why all literature keep the spacing equal or less than half wavelength.

Best regards,

Shahram

https://ortenga.com/

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Reply by naumankaliaAugust 29, 2016

Dear Shahram

Thanks for reply. You are rigth but some times at higher frequencies, it is difficult to maintain lemda/2 spacing in an array due to sensors physical dimensions. This will of course limit the useful scanning area of the array but it is trade of b/w individual sensors sensitivity and scanning area

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Reply by shafie7August 29, 2016

You can look up equation 3.92 in Antenna Theory and Design by Warren Stutzman and Gary Thiele for directivity of linear array, equally spaced elements.

Keep in mind that, grating lobe is present for greater than half wavelength, and good portion of the energy/power is lost in the grating lobe.

You can contact me directly if there is any question.

Best regards,

Shahram

https://ortenga.com/about-2/