# Resonant Cavity Combiner Q Factor - RF Cafe Forums

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Jeanalmira
Post subject: Resonant cavity combiner Q factor Posted: Wed Feb 07, 2007 1:52 am

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hi All :

I have a question regarding resonant cavity combiner. As it is mentioned that this combiner disadvantage is narrow-band as it has high Q (Quality factor).
By formula :
BW = (fresonant)/Q

But I am not sure how to determine/ derive Q?
It is my guess that it derives from permittivity and conductor properties?
I am trying to relate that Q= (1/R) * (sqrt (L/C)) ?
and I also read that the Q somehow related to eigenvalues or number of waves?

and please recommend good textbook on waveguide combiners

Thanks and Regards,
Jean

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nubbage
Post subject: Posted: Wed Feb 07, 2007 10:31 am

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Joined: Fri Feb 17, 2006 12:07 pm
Posts: 218
Location: London UK
The formulas you need are
a) for a cylindrical cavity length L diameter D in TMlm0 mode
Q = (lambda0/skin depth) * (Xlm/(PI*(2+r)))
where r is the ratio of diameter to length
Xlm is the mth root of Jl(x) = 0
For higher modes the expression is more complicated (!!)
b) rectangular cavity, of width a height b length c, the TE10n mode expression is
Q = (lambda0/skin depth)*(0.5*a*b*c)*(p^(2)+r^(2))^(1.5)/(p^(2)*c*(a+2*b)+r^(2)*a*(c+2*b))
where p = 1/a r = n/c
Again, other modes, other expressions.

I have the formulas for resonant wavelengths lambda0, as well if you need them. Skin depth is on the encyclopedia on the home page.
The formulas can be found in "The Microwave Engineers Handbook and Buyers Guide" 1966 where there are also graphs for the cavity modes.

If there is a text book, I regret I do not know of one.

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Jeanalmira
Post subject: Posted: Thu Feb 08, 2007 12:12 am

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hi nubbage :

I will try to find the handbook.
By the way, am I right to say that the mode numbers, which is the eigen numbers actually represent the number of waves?

Thanks and Regards,
Jean

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nubbage
Post subject: Posted: Thu Feb 08, 2007 7:40 am

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Joined: Fri Feb 17, 2006 12:07 pm
Posts: 218
Location: London UK
Hi Jean
Yes, the mode number is the number of cycles the field goes through.
If it varies from zero through a peak and down to zero it is mode 1.
If there is no variation, so the field value is constant, it is mode number 0.
I will try to upload a scan of the Handbook pages in the next couple of days. The 1966 "Handbook and Buyers Guide" is very difficult to obtain these days. I am not sure when Microwave Journal stopped issuing this, but it was a very valuable source of design data.

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Jeanalmira
Post subject: Posted: Thu Feb 08, 2007 9:02 pm

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hello Nubbage :

I am very new to this waveguide issues. I found that eigen numbers (mode numbers) are represent by 3 variables, e.g. n,m,p. So the resonant frequency is given as fmnp. But I am not sure what this n,m,p exactly represents?

You are right, I can't find the handbook.

Best Regards,
Jean

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Jeanalmira
Post subject: Posted: Thu Feb 08, 2007 9:07 pm

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hi :

I have another question, what does it mean by mode spacing? and how to calculate that?

Thanks again.

Cheers,
Jean

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nubbage
Post subject: Posted: Fri Feb 09, 2007 6:32 am

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Joined: Fri Feb 17, 2006 12:07 pm
Posts: 218
Location: London UK
I have uploaded (I hope) the 3 images for the design graphs

I hope those work OK[/url]

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nubbage
Post subject: Posted: Fri Feb 09, 2007 6:34 am

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Joined: Fri Feb 17, 2006 12:07 pm
Posts: 218
Location: London UK
Here is another try

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Jeanalmira
Post subject: Posted: Sun Feb 11, 2007 9:46 pm

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hello Nubbage :

However, there is only one graph that can be viewed.
If you do not mind, please send me the article/ link to j_almira@yahoo.com

By the way, I have another question related to resonant cavity waveguide combiner :
why as the modes increase, the combining efficiency decreases?

Thank you.
Best Regards,
Jean

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Jeanalmira
Post subject: Posted: Sun Feb 11, 2007 9:48 pm

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hello Nubbage :

I managed to view all graphs.

Thanks a lot

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Jeanalmira
Post subject: Posted: Sun Feb 11, 2007 10:05 pm

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore
Hi :

regarding the number of modes and combining efficiency, am I right to say :

as dimension increases--> lambda increases--> Q decreases and therefore, combining efficiency decreases.

and as dimension increases, the number of modes increases and therefore, by relating both cases:
as the number of modes increase, the combining efficiency decrease?

Thanks and Regards,
Jean

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nubbage
Post subject: Posted: Mon Feb 12, 2007 5:07 am

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Joined: Fri Feb 17, 2006 12:07 pm
Posts: 218
Location: London UK
Hi Jean
Broadly you are right, except the Q does not fall as the wavelength and size increases. I think, intuitively, that with larger dimensions (for example in a microwave oven) the number of supportable modes increases, whereas coupling is usually designed for peak efficiency into only one of the modes (or a few anyway).
Consequently some energy in the cavity is not coupled, and either gets reflected to the sources or dissipated as metal resistive losses.

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Jeanalmira
Post subject: Posted: Tue Feb 13, 2007 12:06 am

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Joined: Tue Mar 15, 2005 11:43 pm
Posts: 65
Location: Singapore

Best Regards,
Jean

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tjunqueira
Post subject: Posted: Thu Mar 08, 2007 11:24 am

Lieutenant

Joined: Thu Mar 08, 2007 11:07 am
Posts: 1
Hi Jeanalmira and nubbage!
I read your messages about designing resonant cavity combiner. It was really useful for me. I need to design a combiner with 10 inputs of 2,5 KW each one, the frequency is 476 MHz. For now I have no idea how to do this, but I have two months for this.
I’ve been studying transmission lines and wave guides, but it too far from developing a combiner.
As you shown on your discussion, both of you are advanced on designing. Could you give me some tips about where to study, where to look for more information, basic projects you did. Everything is well come.
Another thing, do you use anything to simulate this combiners? HFSS, CST, or any else thing?

Thanks!

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