ECE 6345 Spring 2015 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 Parallel-Plate Waveguide Model

Probe Inductance Assume that 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

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

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

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

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

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

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

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

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).

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

Probe Inductance (cont.) Approximating the Y0 Bessel function, we have or so

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

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

Example