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Spring 2011

ECE 6345. Spring 2011. Prof. David R. Jackson ECE Dept. Notes 4. Overview. This set of notes discusses the probe inductance of a coax-fed patch. Introduce probe model for a parallel-plate waveguide Use this model to calculate the probe inductance. Probe Inductance. probe. patch.

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Spring 2011

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  1. ECE 6345 Spring 2011 Prof. David R. Jackson ECE Dept. Notes 4

  2. Overview This set of notes discusses the probe inductanceof a coax-fed patch. • Introduce probe model for a parallel-plate waveguide • Use this model to calculate the probe inductance

  3. Probe Inductance probe patch Parallel-Plate Waveguide Model

  4. Probe Inductance The probe current is assumed to be uniform in the z direction, and the metal is removed by the equivalence principle. Radiation from the coax “frill” is neglected. Assume that hollow tube of uniform surface current

  5. Probe Inductance (cont.) Assume since General solution: Choose m = 0, n = 0

  6. Probe Inductance (cont.) Hence finite at the origin infinite at the origin or incoming wave outgoing wave

  7. Probe Inductance (cont.) Model: hollow tube of current Note: The tube may be thought of as infinite in the z direction.

  8. Probe Inductance (cont.) (BC1) (BC2)

  9. Probe Inductance (cont.) BC 1: BC 2:

  10. Probe Inductance (cont.) BC 2 so Hence, eliminating A- using BC 1, we have or

  11. Probe Inductance (cont.) Wronskian Identity: Hence or so Next, use

  12. Probe Inductance (cont.) Hence Next, we use so Note: The imaginary part should be fairly accurate for the probe feed of a patch, but not the real part (the radiation effects are very different).

  13. Probe Inductance (cont.) Taking the imaginary part: For where

  14. Probe Inductance (cont.) Approximating the Y0Bessel function, we have or so

  15. Probe Inductance (cont.) Or, we can write or

  16. Probe Inductance (cont.) We can solve for the probe inductance as Hence The probe inductance is relatively constant with frequency.

  17. Example

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