Waveguide to coaxial line transition having rigid hollow cone portions

A system comprising:

• a first rigid portion comprising an inverted hollow cone, the first rigid portion having a first end and a second end, wherein the first rigid portion tapers inward at a first angle from the first end towards the second end;
• a second rigid portion comprising a hollow tube, the second rigid portion having a first end and a second end, wherein the first end of the second rigid portion is at least partially disposed within the second end of the first rigid portion;
• a third rigid portion comprising a hollow cone, the third rigid portion having a first end and a second end, wherein the first end of the third rigid portion is at least partially disposed within the second end of the second rigid portion, wherein the third rigid portion tapers outward at a second angle from the first end towards the second end;
• and
• a waveguide having a top plate and a bottom plate, wherein the first end of the first rigid portion is in contact with the top plate, wherein the second end of the third rigid portion is connected to the bottom plate, wherein the top plate has an opening therein configured to receive a pin of a coaxial cable therethrough.

A system comprising:

• a first rigid portion comprising an inverted hollow cone, the first rigid portion having a first end and a second end, wherein the first rigid portion tapers inward at a first angle from the first end towards the second end;
• a second rigid portion comprising a hollow tube, the second rigid portion having a first end and a second end, wherein the first end of the second rigid portion is at least partially disposed within the second end of the first rigid portion;
• a third rigid portion comprising a hollow cone, the third rigid portion having a first end and a second end, wherein the first end of the third rigid portion is at least partially disposed within the second end of the second rigid portion, wherein the third rigid portion tapers outward at a second angle from the first end towards the second end, wherein the first angle and the second angle are determined according to the equation
• Z
• c
• =
• 1
• 2
• ⁢
• π
• ⁢
• μ
• ϵ
• ⁢
• ln
• ⁢
• tan
• ⁡
• (
• θ
• 2
• 2
• )
• tan
• ⁡
• (
• θ
• 1
• 2
• )
• ,
• where Zc is the impedance, μ is permeability of a medium, ∈ is permittivity of the medium, θ1 is the first angle, and θ2 is the second angle;
• and
• a radial waveguide having a top plate and a bottom plate, wherein the first end of the first rigid portion is in contact with the top plate, wherein the second end of the third rigid portion is connected to the bottom plate, wherein the top plate has an opening therein configured to receive a pin of a coaxial cable therethrough, wherein the top plate, the first rigid portion, the second rigid portion, and the third rigid portion are sized such that when the pin of the coaxial cable passes through the opening, the pin becomes electrically connected to the third rigid portion.