Notes 4

1
ECE 6345
Fall 2006
Prof. David R. Jackson ECE Dept.
Notes 4
2
Overview
This set of notes discusses the probe inductance
of a coaxially-fed patch.

• Introduce probe model for a parallel-plate
  waveguide
• Use this model to calculate the probe inductance

3
Probe Inductance
Parallel-Plate Waveguide Model
The electric field of the feed is spread out
vertically to become a uniform field.
Assume that
4
Probe Inductance (cont.)
Assume
since
General solution
m 0, n 0
5
Probe Inductance (cont.)
Hence
finite at the origin
or
outgoing wave
6
Probe Inductance (cont.)
Model
hollow tube of current
Note the tube may be thought of as infinite in
the z direction.
7
Probe Inductance (cont.)
(BC1)
(BC2)
8
Probe Inductance (cont.)
BC 1
BC 2
9
Probe Inductance (cont.)
so
BC 2
Hence, eliminating A- from BC 1, we have
or
10
Probe Inductance (cont.)
Wronskian Identity
Hence
or
Next, use
so
11
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).
12
Probe Inductance (cont.)
for
where
13
Probe Inductance (cont.)
Ignore 1 in order to neglect radiation effects.
Hence
or
so
14
Probe Inductance (cont.)
Or, we can write
or
15
Example