I What causes the unexpected annihilation point in the Magic-Tee configuration?

[Leopold89]

I have some problems understanding the magic-tee. There is a configuration for the E and H arm, where the signal output is blocked. As far as I understand you should be able to set one arm to 0 and the other to 1/4 of a wavelength, so the reflected wave's phase will be shifted by pi compared to the incoming and they will annihilate.
But now I found a setup where the annihilation happens at 3/8 of a wavelength. As far as I understand there are two possibilities:
1. is the impedance at the reflecting arm not matched, leading to a different phase of the reflecting wave?
2. maybe a phase shift from optics (reflection at a medium with n2>n1)?

Could you explain this really weird phenomenon to me, please?

 

[tech99]

Is it possible to send a diagram so we are certain which ports we are discussing?

 

[Leopold89]

Here is the image. I used port 1 as input, port 2 as output, blocked port 3 and 4. Then I set the height of port 4 to 0mm and of port 3 to 3/8 of the wavelength.

 

[tech99]

I suspect the disparity is caused by the wavelength in the waveguide.

 

[Leopold89]

If you mean this conversion from vacuum wave length to waveguide wavelength, then unfortunately no, I have considered this.

 

[tech99]

Is Port 2 terminated in a matched load?

 

[tech99]

If you terminate arm 4 with a non contacting variable short circuit (https://www.ainfoinc.com/waveguide-...sliding-short-plates-4-9-7-05-ghz-fdp58-udr58) then the zero setting is lambda/4 not zero. This may give the offset you are observing.
It is also possible that mismatch on arms 1 and 2 may be happening.

 

[Leopold89]

Is Port 2 terminated in a matched load?

Yes, the load of around 523Ohm (even though I would have expected around 533.9Ohm) is the same at port 1 and 2.

If you terminate arm 4 with a non contacting variable short circuit (https://www.ainfoinc.com/waveguide-...sliding-short-plates-4-9-7-05-ghz-fdp58-udr58) then the zero setting is lambda/4 not zero. This may give the offset you are observing.

I do not understand why. If the wave in arm 3 gets phase shifted by pi and the wave that would go into arm 4 instead is unchanged, I would expect destructive interference. But if both are phase shifted by $\pi$, then I would expect constructive interference.
Also the offset is $\phi = 2\pi\frac{2\Delta x_i}{\lambda_w}$, right? So if I set arm 4 to 0, I get an offset of 0.

 

[Leopold89]

So, I now set both arms, 3 and 4, to $\frac{\lambda_w}{4}\approx 43$mm length, but get the minima for dampening at $\approx 2.4$GHz with -70dB and $\approx 2.6$GHz with -50dB, referring to the frequency of the signal generator, while I would have expected 2.45GHz.

 

[tech99]

That is only a 2% error. Maybe the offset of the movable short circuits is not so precise.

 

[tech99]

Even air has sufficient relative permittivity to slow radio waves a little, as I found when I passed them through a bell jar for a demonstration. When I pumped the air out of the bell jar I found the jar was slightly defocusing the beam.

 

[Leopold89]

Usually I would agree, but in this case I have a computer simulation, so everything is perfect. Perfect vacuum, precise control, perfect conductor and so on.

 

[Baluncore]

Usually I would agree, but in this case I have a computer simulation, so everything is perfect. Perfect vacuum, precise control, perfect conductor and so on.

And a perfect mesh generator. I am so jealous. I wish I had one of those.

 

[tech99]

I am not sure if you have done the experiment or are using a simulation. If the latter, how can we discuss errors arising from it, in view of its being perfect?

 

[Leopold89]

It is a simulation, CST to be precise.

how can we discuss errors arising from it, in view of its being perfect?

Here is a misunderstanding. I was not suggesting that the setup/simulation was wrong, but that I may have missed something in my calculation of the arm position. Maybe the corners add a weird contribution. Maybe I was reading the wrong books, because I thought the S matrix would have entries dependent on something like $e^{2\pi i\frac{2\Delta x}{\lambda_w}}$.

But if you say you block the signal at $\frac{\lambda_w}{4}$, then I have to try another simulation software and perform an experiment.

 

[Leopold89]

Could it be that $\frac{\lambda_w}{4}$ only works, if you have $\cos\alpha=\frac{\lambda}{\lambda_w}=\frac{1}{\sqrt{2}}$? Because otherwise you have a different $\lambda_w$ in the arms than at the input?