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Spring 2011

ECE 6345. Spring 2011. Prof. David R. Jackson ECE Dept. Notes 32. Overview. In this set of notes we examine the FSS and phased-array problems in more detail, using the periodic spectral-domain Green’s function. FSS Geometry. Incident plane wave. Reflected plane wave. z. y. a. L.

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Spring 2011

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  1. ECE 6345 Spring 2011 Prof. David R. Jackson ECE Dept. Notes 32

  2. Overview In this set of notes we examine the FSS and phased-array problems in more detail, using the periodic spectral-domain Green’s function.

  3. FSS Geometry Incident plane wave Reflected plane wave z y a L Metal patch b W x Dielectric layer Transmitted plane wave 3

  4. FSS Geometry (cont.) 4

  5. FSS Analysis Assume that unknown current on the (0,0) patch is of the following form: The EFIE is then Note that the “” superscript stands for “infinite periodic” (i.e., the fields due to the infinite periodic array of patch currents). The superscript “imp” denotes the impressed field (seen by the patches) that exists in the absence of the metal patches. That is, the incident plane-wave field plus that which reflects from the dielectric layer. The EFIE is enforced on the (0,0) patch; it is then automatically enforced on all patches. 5

  6. FSS Analysis (cont.) We have, using Galerkin’s method, Define We then have 6

  7. FSS Analysis (cont.) The (0,0) patch current amplitude is then We have 7

  8. FSS Analysis (cont.) For the RHS term we have The impressed field as a function of (x,y) can be written as where This gives us 8

  9. FSS Analysis (cont.) Hence, we have where 9

  10. FSS Analysis (cont.) For the incident field we have The field radiated by the patch currents for z > 0 is where 10

  11. FSS Analysis (cont.) The field of the specular-reflected (0,0) wave radiated by the patches for z > 0 is The total reflected field is The total FSS reflection coefficient is then 11

  12. Phased Array Geometry z Probe y L W a Metal patch b x Dielectric layer Ground plane Probe current mn: 12

  13. Phased Array Analysis Assume that unknown current on the (0,0) patch is of the following form: The EFIE (after Galerkin testing) is Hence we can write so 13

  14. Phased Array Analysis (cont.) The input impedance is Hence we can write 14

  15. Phased Array Analysis (cont.) From reciprocity, it follows that (though this is not obvious) To see this, consider the following: (single elements) Expressing the reactions in the general form of spectral integrals, we have where Since this holds for an arbitrary offset, we have 15

  16. Phased Array Analysis (cont.) Hence so or 16

  17. Phased Array Analysis (cont.) The “active” or “scan” input impedance can thus be written as where 17

  18. Phased Array Analysis (cont.) At a scan blindness point so Also, (no current on the patches) (The denominator has a much stronger singularity than the numerator, since the patches radiate much more of a surface-wave field than do the probes.) since 18

  19. Phased Array Analysis (cont.) From Waterhouse’s short-course slides Scan blindness 19

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