Help matching this circuit resonator

[yefj]

Hello , I have created a resonator as shown below in CST.
The waveguide port automatickly sets impedance as he sees along the line.
I got a TEM mode of quarter wavelength as shown below.
However the matching is very bad.
Where did i go wrong creating this resonator?
Thanks.

E-Field:

 

[marcusl]

The quarter wave transmission line transforms the short at the far end to an open circuit. Congratulations, It’s hard to achieve a worse match!

This thread and your other one suggest that you lack understanding of the fundamentals of waveguides, transmission lines, resonators and microwave engineering. No amount of fooling around with numerical solvers can make up for that deficit. Back up and do some studying.

I can recommend Smith’s original book “Electronic Applications of the Smith Chart; in Waveguide, Circuit and Component Analysis” which covers lines, matching circuits and transformations. Then read one of the standard books on microwave electronics such as Collin (older but very good and inexpensive on the used market) or Pozar (the current standard text and also excellent).

With comprehension, you can then use your numerical solver to validate and refine your design.

EDIT: When you are ready, Collin’s “Field Theory of Guided Waves” is an outstanding advanced book.

 

[yefj]

Hello, actually I managed to match the resonator circuit by placing lumpled capacitor with series resistance.
by tuning the place of the capcitor and values I got it matched.
but as you said i have mo theory.
Could you give me theorectical intuition regarding how this lumpted capactior plays with the TEM mode and maked the matching ?(smith chart wise)

 

[Baluncore]

I do not know where your lumped capacitor was placed.

A resonator should be lightly coupled to the external circuit. If that is not done, the Q will be very low, and the resonator would be pointless.

A resonator, like the λ/4 stub you have designed, would be coupled with either a small capacitive patch inside the wall, or a small inductive loop inside the wall. Each would be driven through a small hole in the outer wall of the resonator.

The position along the resonator of that coupler, would match the impedance, and set the Q of the resonator. High impedance close to the open end, low impedance close to the shorted end.

I would expect the inner conductor at the open end, to be fully enclosed by the outer, to prevent electrostatic radiation, since that end will have a high RF voltage.

The inner conductor would be cut slightly short, then the centre frequency could be trimmed with a small screw adjustable capacitive patch, in the end cap of the resonator.

 

[yefj]

Hello,My question is linking theory with whar i saw in simulations.
I want to know the relations between the lumped capacitor and the resonance frequency shift.
What do you think caused the shift in resonance as i moved arround the lumped element in the shirt circuit coax resonator?
Thanks.

 

[marcusl]

Even though your resonator is an extended EM structure, it can be thought of as an LC. Hanging extra parallel capacitance in random locations will lower the frequency by various amounts.

As for theory, you need to learn some. We can help you clarify a small point but can’t do your work for you.

 

[yefj]

Hello, Yes when we are doing lumped element theory then I understand there are good theory and exct equetions.
But based on the E and H fields how can i turn them into lumpled element models?
Thanks.

 

[marcusl]

I gave references above. Also you can see volumes in the Rad Lab series. The volume on Microwave circuit theory (and maybe also the one on transmission lines). You can find them free online.

 

[yefj]

Hello,I have built a a resonator but I want to understand the physics behind it.
The mode is TEM ,Why when I make the resonator 1.5mm shorter I have the resonator frequency going up?
Why when I increase the permitivity of the dielectric inside I have the resonance frequency going down?
Why the permitivity changes the matching of the resonance?
Is there any mathematics that could exlaing why TEM mode acts this way?
Thanks.

 

[Baluncore]

Hello, I have built a resonator but I want to understand the physics behind it.

You are going about this the wrong way. If you do not understand the physics, you will not be able to design a sensible resonator, one worthy of analysis. First study the physics, then design and model a simple example as an exercise.

,Why when I make the resonator 1.5mm shorter I have the resonator frequency going up?

If you make a structure smaller, the resonant wavelength will be smaller, so the frequency will be higher.

Why when I increase the permitivity of the dielectric inside I have the resonance frequency going down?

Your resonator is a short coaxial transmission line. The velocity factor on that line is proportional to 1/√(L⋅C), where L and C are the inductance and capacitance per unit length of line. Increasing permittivity Er, increases C, which reduces velocity, so the line is slower, and the resonant frequency is lower.

Why the permitivity changes the matching of the resonance?

The characteristic impedance of a transmission line, is proportional to √(L/C). When you increase the permittivity Er, you increases C, so you lower the impedance of the line, which changes the impedance of the interface port.

At the same time, you are changing the velocity factor, so you are scaling the size in wavelengths and centre frequency of the resonator. Moving the centre frequency will change the Q and the matching at the original design frequency.

Is there any mathematics that could exlaing why TEM mode acts this way?

Yes. This is all trivial RF engineering for beginners. Once you read the first references you were given earlier in this thread, you will begin to understand the principles. You will not become a microwave engineer overnight. It will remain a fascinating "black art", until you make it a "science", by doing a few years of solid study.

Looking at the state of your knowledge, and your lack of study, I see that you are so far behind, that you think you are first.

Study first, then model to test your understanding.

You are wasting your time, and ours, by going about this in the wrong way.