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| Deletions are marked like this. | Additions are marked like this. |
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| $ D = \lambda/2 $ | ||<:-3> $ D = L/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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| $ 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 ) ) $ ... or some variation of that. This assumes the spacing $ L >> \lambda $, a sparse array, so that the antennas do not couple (much). We can scale D and k, and also modify amplitudes across the array like a Hamming window, and see how that changes the sidelobes. |
... or some variation of that ( I originally tried $ D = \lambda/2 $ , with little effect). 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. |
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| MORE LATER | The signal is broadband, so there is not a well defined $ \lambda $. We may end up making k a function of x, y, and z as well. == 5x5x5 skewed, dithered array == {{ a4d21.png | | height=768 }} Annotated version with explanation coming soon. == 16x16x16 skewed, dithered array == {{ a4d21-16.png | | height=768 }} Annotated version with explanation coming soon. MoreLater |
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 = L/2 |
k = 2 \pi / N * L |
||||
\Delta x = D * ( \sin( k z ) + \cos( k y ) ) |
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\Delta y = D * ( \sin( k x ) + \cos( k z ) ) |
|
\Delta z = D * ( \sin( k y ) + \cos( k x ) ) |
|
... or some variation of that ( I originally tried D = \lambda/2 , with little effect). 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.
The signal is broadband, so there is not a well defined \lambda . We may end up making k a function of x, y, and z as well.
5x5x5 skewed, dithered array
Annotated version with explanation coming soon.
16x16x16 skewed, dithered array
Annotated version with explanation coming soon.