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Prof. David R. Jackson ECE Dept.

ECE 6341. Spring 2014. Prof. David R. Jackson ECE Dept. Notes 47. Notes 42. Periodic SDI. z. y. b. L. W. a. x. Calculate the fields from a 2D periodic array of currents in a layered media. Layered media. Radiation angles:. Periodic SDI (cont.).

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Prof. David R. Jackson ECE Dept.

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  1. ECE 6341 Spring 2014 Prof. David R. Jackson ECE Dept. Notes 47 Notes 42

  2. Periodic SDI z y b L W a x Calculate the fields from a 2D periodic array of currents in a layered media Layered media Radiation angles:

  3. Periodic SDI (cont.) The current on the periodic structure is represented in terms of Floquet waves: where and To solve for the unknown coefficients, multiply both sides by and integrate over the (0,0) unit cell.

  4. Periodic SDI (cont.) Use orthogonality:

  5. Periodic SDI (cont.) The current Js0 is the current on the (0,0) patch.

  6. Periodic SDI (cont.) Hence the current on the 2D periodic structure is We now calculate the Fourier transform of the 2D periodic current (this is what we need in the SDI method): Use

  7. Periodic SDI (cont.) Hence Calculate the field:

  8. Periodic SDI (cont.) Hence, we have:

  9. Periodic SDI (cont.) Therefore, we have

  10. Periodic SDI (cont.) Compare: Single element (non-periodic): Periodic array of elements:

  11. Periodic SDI (cont.) Conclusion: where The double integral is replaced by a double sum, and a factor is introduced.

  12. Periodic SDI (cont.) ky kx

  13. Periodic SDI (cont.) For a skewed lattice: where

  14. Microstrip Patch Phased Array z y b L W a x Example Microstrip Patch Phased Array Find Ex(x,y,0)

  15. Phased Array (cont.) Single Patch:

  16. Phased Array (cont.) 2D Phased Array: where

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