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Understanding Dyadic Green's Function for Finite Source and Phased Current Sheet Analysis

This document delves into the application of Dyadic Green's Function in analyzing finite sources and phased current sheets within electromagnetic theory. It covers the spatial representation of electric fields generated by planar currents and provides insights through the 2D Fourier transform. The content includes examples and results relevant to current modeling, such as vertical planar currents, and offers definitions and calculations necessary for understanding electric potential and its relationship to current sources. Key identification parameters and spectral-domain functions are also discussed comprehensively.

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Understanding Dyadic Green's Function for Finite Source and Phased Current Sheet Analysis

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  1. ECE 6341 Spring 2014 Prof. David R. Jackson ECE Dept. Notes 39

  2. Finite Source For a phased current sheet: Recall that

  3. Finite Source (cont.) Hence Note: Wavenumber plane Spatial coordinates

  4. TEN Model for We can also write Comparing with the previous result, we have Similarly, This motivates the following identifications:

  5. TEN Model (cont.)

  6. TEN Model (cont.)

  7. TEN Model (cont.)

  8. Example Find

  9. Example (cont.) Hence

  10. Example (cont.)

  11. Dyadic Green’s Function where due to the unit-amplitude electric dipole at From superposition: We assume here that the currents are located on a planar surface. where

  12. Dyadic Green’s Function (cont.) This is recognized as a 2D convolution: Taking the 2D Fourier transform of both sides, where

  13. Dyadic Green’s Function (cont.) Assuming we wish the x component of the electric field due to an x-directed current Jsx (x , y ), we have In order to indentify , we use

  14. Dyadic Green’s Function (cont.) Recall that Hence

  15. Dyadic Green’s Function (cont.) We the have The other eight components could be found in a similar way. (The sources in the TEN that correspond to all possible sources are given on the next slide, and from these we can determine any component of the spectral-domain Green’s function that we wish, for either an electric current or a magnetic current.)

  16. Summary of Results for All Sources These results are derived in Notes 44. Definition of “vertical planar currents”:

  17. Sources used in Modeling • Vi = voltage due to 1[A] parallel current source • Ii = current due to 1[A] parallel current source • Vv = voltage due to 1[V] series voltage source • Iv = current due to 1[V] series voltage source + -

  18. Sources used in Modeling (cont.) • Vi = voltage due to 1[A] parallel current source • Ii = current due to 1[A] parallel current source • Vv = voltage due to 1[V] series voltage source • Iv = current due to 1[V] series voltage source + -

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