Differences between revisions 1 and 16 (spanning 15 versions)
 ⇤ ← Revision 1 as of 2012-11-30 05:35:20 → Size: 709 Editor: KeithLofstrom Comment: ← Revision 16 as of 2021-06-08 17:57:55 → ⇥ Size: 1373 Editor: KeithLofstrom Comment: Deletions are marked like this. Additions are marked like this. Line 6: Line 6: A smear function to try: A position dither function to try: Line 8: Line 8: $D = \lambda/2 $$k = 2 \pi / N * L ||<:-3> D = L/2 ||<:-3> k = 2 \pi / N * L |||| \Delta x = D * ( \sin( k z ) + \cos( k y ) ) || ||<-2> \Delta y = D * ( \sin( k x ) + \cos( k z ) ) || || \Delta z = D * ( \sin( k y ) + \cos( k x ) ) || Line 11: Line 11: \delta x = D * ( \sin( k z ) + \cos( k y ) )$$ \delta y = D * ( \sin( k x ) + \cos( k z ) )$$\delta z = D * ( \sin( k y ) + \cos( k x ) )$ ... or some variation of that ( 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. Line 15: Line 14: ... 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. 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. Line 18: Line 17: 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 ) ) \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.

ArrayPhasing (last edited 2021-06-08 17:57:55 by KeithLofstrom)