Double Ridged Waveguide help (pretty well documented :)

[ardiware]

Hi everybody. Excuse my english, I speak spanish. I'm doing my thesis project.


INTRODUCTION
It consist of a Low Noise Amplifier, for the band 10.7 to 13.3 GHz. I use a transistor to get a gain of 12 dB with a Noise Figure no more than 1 dB for the band.

In order to accomplish this, the transistor need a 16 ohm impedance at its input. I use a WR-75 waveguide with a caracteristic impedance of 500 ohms, so a impedance transformer is due.

3 sections Chebyshev transformer design (1/3)
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3 sections Chebyshev transformer design (2/3)
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3 sections Chebyshev transformer design (3/3)
According to CST MW Studio, this is the impedance at port 3 of the 3 sections transformer.
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I design a 3 sections chebyshev transformer to reduce the 500 ohms to 174 ohms, then I can add a line of 50 ohms (lambda_g/4) with a stub of 6 mm (50 ohms also) to reduce the 174 ohms to 16 ohms.

Transformer plus subsystem design (1/4)
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Transformer plus subsystem design (2/4)
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DEVELOPMENT
I "build it" in CST Microwave Studio 5.0.1, being the waveguide of vacuum material, all of its boundaries Electrics, and the ports (1 and 2) boundaries vacuum too.

The "ridges" inside the waveguide are of PEC, with 1 mm thick. Each section has its own lambda, and ist lenght is a quarter of lambda.

I determine the impedance of each section according with the equations I attach, and then, I use CST to calcule the impedance of each section having only one "ridge" and varing its separation "s", then I wrote down the impedance calculated at 12 GHz until I got a "impedance table": for each "possible" separation 's' between "ridges" it correspond a impedance 'Z', its own lambda and its own f_cut.

So, I use the impedance calculated for CST to make each section of the transformer.

PROBLEM
As you can see in the pictures below, I'm not getting the "right" results with CST. Some of them are close (179 ohms instead of 174), but they had a very high reactance part, which should not be there.

And when I add the extra line a stub "subsystem", the results are worst. No matter the stub's length I use (from 1 to 6.25 mm, 0.2 mm step) the impedance at ports 3 and 5 stills almost the same.

Transformer plus subsystem design (3/4)
According to CST MW Studio, this is the impedance at port 3 of the transformer, plus the "subsystem"
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Transformer plus subsystem design (4/4)
According to CST MW Studio, this is the impedance at port 5 of the transformer, plus the "subsystem"
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I don't know whats wrong, what I'm not doing right. I suspect that my theorical calcules are not accurate, since they doesn't consider the "ridges" thickness. I have done all the calcules again using the famous chebyshev tables to determine each section impedance, but the results I get are pretty bad too.


I've hear of another approaching to calcule the impedances of each section of the transformer, they take the thickness for the calcules. If you know about them, I appreciate your help.

Anyway, thanks for reading too.

THEORICAL CALCULES
(The description is in spanish, but the equations are crystal clear)


Wave guide WR-75 and Transistor specifications
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3 Sections transformer, "extraline and stub" subsystem diagram
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RED: If we use a "extraline" of 50 ohms (51.9 exactly) we need a impedance matching system from 500 ohms to 173.8 ohms.
BLACK: equations used to compute each section impedance (1/2)
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BLACK: equations used to compute each section impedance (2/2)
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I attach the file too, if you need it.

 

[biff44]

I am not a mw studio guy, so I am having a little trouble following all your stuff. But it looks like the initial design was pretty close to what you wanted (making the assumption that the polar plot of S33 was normalized to 174 ohms). My comments:

1) If you could negate out the inductance shown in the first S33 plot, you would be there! Try working on the coaxial probe part. Try a fatter diameter, maybe step up to a disk or something with more shunt capacitance. You could even try something in pure coax built into the waveguide metal wall.

2) Who told you that the input waveguide was 500 ohm characteristic impedance? Even if that were true, it would only be true at ONE frequency, not over your entire band of interest. You should check that!

 

[ardiware]

Thank you very much for your answer.

I just got the HFSS v10 software and i'm gonna do it all again from scratch to compare results with CST.

1) Well, I don't have a coaxial probe, so I can't make it fatter. The thickness of the "ridges" (I don't know how to call the squared columns in the middle of the waveguide) is fixed according to my teacher (1 mm), due to real life components, so does the waveguide length (50mm), so, the 3 sections transformer can't be longer than 23 mm.

The shunt capacitance I don't know if I'm allowed to do that. In the middle of the waveguide there shall be the transistor (with 4 'legs') and nothing more. One of the 'legs' is connected to the stub, and it decrease the impedance from 16+7j to 16+0j ohms. I'm taking that 'leg' in account, that's why the transformer with the stub should match 16 ohms only.

2) The characteristic impedance of any rectangular waveguide is calculated as follow:

a = 19.050e-3; % [m] height
b =  9.525e-3; % [m] width
c = 3e8;       % [m/s] light velocity
m = 1;
n = 0;         % for mode TEmn = TE10
f = 12e9;      % [Hz]    

lambda = c / f;
     k = 2 * pi / lambda;
 nabla = 120 * pi;
  beta = sqrt( k^2 - (m*pi/a)^2 - (n*pi/b)^2 );
Z_TEmn = k * nabla / beta

acording to this, the impedances for the band are
ZTE @ 10.7 GHz = 556.8
ZTE @ 12.0 GHz = 499.6
ZTE @ 13.3 GHz = 467.8

I'm trying to match everything at 12 GHz.

 

[biff44]

Maybe this will help:

https://epaper.kek.jp/p95/ARTICLES/WPR/WPR16.PDF