Hello,
1) I simulated an open-ended WR-90 rectangular waveguide (F = 9.6 GHz, air-filled, L = 40 mm) in CST.
According to the formula Zin=Z0cot(βL), the input impedance should be purely imaginary, and my calculation gives Zin≈j4122.
However, as shown in the attached results, the input impedance is approximately 773−j289. This result is different, with a real part added to the input impedance.
I have also introduced an air space with a lambda distance from the structure, but the result is still not as expected. What could be the mistake in my simulation setup?
2 )I conducted another simulation for a short-circuited WR-90 rectangular waveguide (F = 9.6 GHz, air-filled, L = 40 mm) in CST. Zin=Z0*Tan(βL),
In this case, the input impedance is 0.86−j217 , or approximately −j217 ohm. However, my calculation predicts it should be j61Ω. Could you help me understand where the problem lies?
Open ended waveguide is not open circuit. It usually radiates fairly well, so your result for the open circuit makes sense. The real part represents significant radiation. If you want a proper open circuit, put a magnetic wall onto the open end of the waveguide.
I don't know about the phase for the short. It looks to me as if the shorted guide should be about 337 degrees long. Double this to get the two way phase and it comes close to 1.87 times round the smith chart (clockwise). This is very close to a capacitance with a reactance equal to about half the characteristic impedance, so -j217 seems close to what I would expect, then with a bit of loss added to get a small series resistive part.
I get tan(Bl) as -.428, so I think you have calculated the wavenumber or tangent wrong. Was it expecting degrees or radians?
Thank you, Malcolm White, for your explanation.
1)For the open-ended waveguide, the magnetic wall works well, and my calculations require correction. The results are approximately the same.
However, without boundary conditions to establish a magnetic wall, is there any other approach?
If I use a dielectric with high permittivity near the output or at the output of the waveguide, it does not behave like a magnetic wall.
2)Yes, my calculations have an issue. They now yield the same result.
I appreciate your kind response.
You can put a choke around the end of the waveguide - it only really needs it on the top and bottom walls, but it is easy to model all the way round. A 2 mm high air gap 1/4 wavelength deep ending with a shorting wall. Like a shorted length of rectanguar coax back along the outside of the guide wall. The 2 mm gap surrounding the open end will look like a good open and stop currents continuing along the outside of the guide, so making the end of the guide a low current point. I think this will also hamper the radiation.
Dielectric with a high permittivity will look more like a s/c. High permeability material (magnetic) looks more like o/c.
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