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*Subject*: RE: [amsat-bb] variable phase delay / phased arrays*From*: "Tom Clark" <w3iwi@xxxxxxxxxxx>*Date*: Thu, 13 Nov 2003 00:27:31 -0500

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 ---- Sent via amsat-bb@amsat.org. Opinions expressed are those of the author. Not an AMSAT member? Join now to support the amateur satellite program! To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

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