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Comment:

933

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 ) ) $  
Line 11:  Line 12: 
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 

\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). 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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