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RE: variable phase delay / phased arrays

David  -- the Symposium papers are posted at http://www.gpstime.com. Let me
offer a few comments about what I had in mind. The paper only sketched out
the ideas.

Lets think that we are at the spacecraft, looking back at the earth. The
spacecraft has an n x n array of patch antennas (perhaps 4 x 4). One the
ground we would have one or two beacon stations with known positions. At the
spacecraft we would employ an n^2 channel receiver (16 in the case of a 4x4
array) with a common local oscillator. [An aside -- if you think this is a
lot, remember that a 12 channel $200 GPS receiver really has 12 independent
DSP receiver backends.]

On each of the n^2 channels we would extract the apparent carrier phase of
the beacon signals. Since the patch array is 2 dimensional, this represents
the 2-D (i.e. Az & El) set of phases that can be used to "point" the antenna
array. If the beacons are not at the center of the earth (as seen from the
spacecraft), a phase correction can be developed in the on-board computer to
tweak each of the antenna phases.

OK -- so I have this [n x n] set of phases derived from the ground-based
beacon. How do I phase the array for the real transponders? The signal from
each of the antennas can be re-phased by changing the phase of the LO
associated with that element, and then all the signals simple summed to pass
on to the transponder's TX.

Now lets phase the array for TX. I am supposing that each element has a
separate PA so that ~0 dBm is needed to "light up" the element. The baseband
IF is split n^2 ways, and fed to n^2 mixers. Again, the LO phase for each
element is set by the on-board computer to point the downlink beam where it
is desired.

So the problem is really reduced to making 2*n^2 baseband LO phase shifters
which are at easy-to-handle VHF frequencies). And you are right that only a
finite number of phase "taps" are needed. An m=2^x (i.e. x=3 gives m=8)
linear array can be used to generate m independent beams (overlapping at
the -3 dB point) using x*m/2 0/180 deg sum/dif hybrids and fixed
transmission lines. In the antenna array world, this array of hybrids is
called a Butler matrix (see
http://www.anaren.com/docs/app_notes/VLBUT&HYBINTRO.PDF for a 4x4 and 8x8
example and see http://www-mtl.mit.edu/research/sodini/hayashi02.pdf for a
4x1 implemented in microstrip). [Aside: If you look at how the Butler matrix
works, it is exactly the same as the Cooley-Tukey FFT algorithm. Butler
invented his combiner before the FFT algorithm was formulated.]

A ground-based user could do precisely the same, except he would want to
phase both the RX and TX arrays to point at the spacecraft (and not
off-pointed as I allowed on the satellite).

You asked about gain and the number of patches needed. Each patch has a
collecting area about equal to a half-wave dipole. Since they are on a
ground-plane, the typical gain ("on-axis") will then be about 6 dBi (just
like a dipole). If the patches are properly spaced so that their collecting
aperture barely overlaps (about 3/4 wavelength), the array will pick up 3 dB
each time the number of elements in the array is doubled (i.e. 2 elements
gives +3dB, 4=+6dB, 8=+9dB, 16=+12db, etc). So for my example of 4x4 we
would get about 6+12 = 18 dBi of gain.

Hope this sparks some discussion -- 73, Tom

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