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Spring 2011

ECE 6345. Spring 2011. Prof. David R. Jackson ECE Dept. Notes 34. Overview. In this set of notes we overview the segmentation method for obtaining the input impedance of an arbitrary shaped patch. This is an extension of the cavity model. Segmentation Method. PMC.

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Spring 2011

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  1. ECE 6345 Spring 2011 Prof. David R. Jackson ECE Dept. Notes 34

  2. Overview In this set of notes we overview the segmentation method for obtaining the input impedance of an arbitrary shaped patch. This is an extension of the cavity model.

  3. Segmentation Method PMC The perimeter has been extend to account for fringing. (arbitrary shaped patch) Note: the effective complex wavenumber may be determined iteratively – once the field is known inside the patch, the stored energy and the radiated power may be computed, and from this the Q may be determined.

  4. Segmentation Method (cont.) (2) (3) (1) The patch is divided into a number of rectangular-shaped patches.

  5. Segmentation Method (cont.) Along the edges where the rectangular patches connect, we introduce ports. The ports connect the patches together.

  6. Segmentation Method (cont.) For each rectangular patch, we calculate the Z matrix for the ports that connect to it.

  7. Segmentation Method (cont.) To illustrate, consider one patch: port 1 port 2 We can calculate Zmnby using the cavity model.

  8. y port 2 We PMC port 1 x Le Segmentation Method (cont.) This figure shows a general two-port system for a rectangular patch. (the input impedance at port 1) port 1: (the input impedance at port 2) port 2:

  9. y port 2 We PMC port 1 x Le Segmentation Method (cont.) Assume

  10. y We PMC x Le Segmentation Method (cont.) Note: Bm is a function of the location of port 1 Use the mode-matching method: so that

  11. Segmentation Method (cont.) Note: The feed is considered one of the ports on patch 1. Once the Z matrices of all the patches have been computed, an overall Z matrix of the entire system ZP is calculated, by connecting the individual Z matrices and using circuit theory. If there is a single feed, then ZP is a 11 matrix (a single number Z11P).

  12. Segmentation Method (cont.) port 1 The input impedance is then given by

  13. Desegmentation Method This is a variation of the segmentation method, in which we have a rectangular patch shape in which a set of smaller rectangular patches have been removed.

  14. d q p q p Segmentation Method (cont.) c We next show how to combine two Z matrices into a single Z overall matrix. The ports p and q are the external ports, while c and d represent the internal (connected) ports.

  15. d q p q p Segmentation Method (cont.) c (1) (3) (4) (2)

  16. d q p q p Segmentation Method (cont.) c Also, from Kirchhoff’s laws we have (5) (6)

  17. Segmentation Method (cont.) Substituting (3) and (4) into (6) and using (5) yields Hence so that (7)

  18. Segmentation Method (cont.) Next, insert (7) into (1): (8) Similarly, from (2) we have (9) From the definition of the Z matrix of the overall system, we can also write (10) (11) Comparing (8) and (9) with (10) and (11), we have the following results:

  19. Segmentation Method (cont.)

  20. d c feed Segmentation Method (cont.) To find the input impedance, assume that the feed port is located on patch , and that all other patches have been reduced (one pair at a time) to a single connecting patch .

  21. Segmentation Method (cont.) first of the previous set of equations then specializes to In this equation Zin is the input impedance of the patch that the feed is connected to (patch ) when this patch is not connected to the other patches.

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