1. ECE 6345
Spring 2015
Prof. David R. Jackson
ECE Dept.
Notes 4

2. 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

3. Probe Inductance
Probe
Patch
Parallel-Plate Waveguide Model

4. 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

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 being infinite in the z direction.

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

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

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

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

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 Y0 Bessel 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