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| Deletions are marked like this. | Additions are marked like this. |
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| || $ D = \lambda/2 $ || $ k = 2 \pi / N * L $ || $ \Delta x = D * ( \sin( k z ) + \cos( k y ) ) $ || $ \Delta y = D * ( \sin( k x ) + \cos( k z ) ) $ || $ \Delta z = D * ( \sin( k y ) + \cos( k x ) ) $ || | ||<:-3> $ D = \lambda/2 $ ||<:-3> $ k = 2 \pi / N * L $ || || $ \Delta x = D * ( \sin( k z ) + \cos( k y ) ) $ || ||<-2> $ \Delta y = D * ( \sin( k x ) + \cos( k z ) ) $ || || $ \Delta z = D * ( \sin( k y ) + \cos( k x ) ) $ || |
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| We can scale D and k, and also modify amplitudes across the array like a Hamming window, and see how that changes the sidelobes. | Try scaling D and k, and also modifying amplitudes across the array like a Hamming window, and see how that changes the sidelobes. |
Array Phasing
When we randomly dither the position of the emitters in a 3 dimensional phased array, it smears out the grating lobes. I am looking for a better function.
A position dither function to try:
D = \lambda/2 |
k = 2 \pi / N * L |
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\Delta x = D * ( \sin( k z ) + \cos( k y ) ) |
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\Delta y = D * ( \sin( k x ) + \cos( k z ) ) |
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\Delta z = D * ( \sin( k y ) + \cos( k x ) ) |
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... or some variation of that. This assumes the spacing L >> \lambda , a sparse array, so that the antennas do not couple (much). Try scaling D and k, and also modifying amplitudes across the array like a Hamming window, and see how that changes the sidelobes.
This happens on top of the array of perhaps hundreds of emitters on the thinsat itself, which beamforms to a few degrees of angle, reducing power splattered far from the target.
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