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Magnetron cavity formula

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Coronafix

Thu Jun 16 2011, 12:44AM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Does anyone know what the formula is to ascertain the operating frequency in a magnetron cavity?
I know that the outer of the anode is the inductive part and the cavity openings create the capacitive part,
but I can't seem to find any design formulas of sizes and geometry vs operating frequency.
Thanks.

Ash Small

Thu Jun 16 2011, 01:19AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

"The core of the magnetron is a metal cylinder, not so different in appearance from the cylinder of a revolver-type pistol. The center of the cylinder is bored out, and a set of "cavities" are bored through the cylinder around the central hole. Each cavity is connected to the central hole through a slot. A conductive rod is placed in the central hole, to act as the negatively charged cathode, while the cylinder itself acts as the positively charged anode. The assembly is sealed inside a vacuum envelope, and magnets are placed top and bottom.

Electrons move at a right angle to a magnetic field, and so the magnets cause the electrons moving from cathode to anode to swirl around the cathode rod in a spiral. Electrons emit EM radiation when they are accelerated, and so as they are pulled around the cathode they emit EM radiation over a wide range. This radiation flowed into the cavities around the central shaft. The cavities act as "resonant chambers", with EM radiation of a specific wavelength building up inside them. The wavelength in practice is about 8 times the diameter, or a 1.2 centimeter cavity would produce a 10 centimeter / 3 GHz signal. One of these resonant cavities is tapped out to drive microwave power to the radar system.

The magnetron's operating wavelength can be adjusted within a limited range by lowering a set of slugs into the cavities to adjust their resonant frequency."

Coronafix

Thu Jun 16 2011, 02:39AM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Thanks Ash, that is something although not the formula I am looking for.
The slugs in a tunable magnetron adjust the cavity volume and therefore this would be part of the equation.
I think the 8 times factor might be for a 8 cavity resonator.

Ash Small

Thu Jun 16 2011, 03:04AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Wikipedia says this:

"The sizes of the cavities determine the resonant frequency, and thereby the frequency of emitted microwaves. However, the frequency is not precisely controllable. The operating frequency varies with changes in load impedance, with changes in the supply current, and with the temperature of the tube.[5] This is not a problem in uses such as heating, or in some forms of radar where the receiver can be synchronized with an imprecise magnetron frequency. Where precise frequencies are needed, other devices such as the klystron are used."

EDIT: This article mentions the inductance and capacitance of the resonant cavities:

Coronafix

Thu Jun 16 2011, 04:26AM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

I've read both of them already, the radartutorial site is excellent.
Is it just me, or do other people find that wikipedia is next to useless 90% of the time.
The frequencies are not precisely controllable and understandably so at such small wavelengths and heat, but enough to know that a
microwave oven operates at 2.54GHz.
I did find this which leads me to believe that they don't have an exact equation for the cavity/frequency structure.

But that was over sixty years ago.

Proud Mary

Thu Jun 16 2011, 09:29AM

Registered Member #543 Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992

The answer to your question is in here:

3-D Modeling of Cavity Magnetrons
by Lili Ma,
PhD Thesis,
University of London 2004.

Tip: you have two options open to you for altering the frequency of a modern oven magnetron:

1. Magnetron pushing - you can alter the value of anode current, on which the frequency depends, or

2. Magnetron pulling - you can alter the frequency of oscillation by modifying the reactive component of the load.

Magnetron pushing is the easiest to put into practice.

You may also be interested in the following paper, which looks at the spectral im/purity of a 2.45 GHz oven magnetron:

Tomohiko Mitani, Naoki Shinohara, and Kozo Hashimoto Fundamental Study on Spectral Purity of a CW Magnetron for Microwave Power Transmission

Coronafix

Thu Jun 16 2011, 01:15PM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Wow, that paper has a lot for me to read, a hopefull find.
Thank you Stella, will look at it in the morning.

Ash Small

Thu Jun 16 2011, 02:10PM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

How do you find all these papers, PM? I second what Coronafix said. The link you provided seems to cover it all.

@Coronafix, I agree that Wikipedia never seems to go into detail, and is often misleading. I posted those two links because they seemed to support what the first link I posted suggested.(They are among the first few that google brings up)

You may also find this link of some use (I'm not sure what you are planning to do, but it contains some practical advice, although some of doug's theories seem to be misplaced, ie he thinks 'frequency hopping' is due to manufacturing tolerances in the anode, rather than variations in the load, which would presumably be more exaggerated when running at low current):

(I wouldn't accept all of what he says as correct, but it does give some useful practical advice based on his own experience)

Coronafix

Tue Jun 21 2011, 12:26AM

Registered Member #160 Joined: Mon Feb 13 2006, 02:07AM
Location: Melbourne, Australia
Posts: 938

Stella, that paper didn't have what I was looking for either but I eventually found the right paper and I am posting it here in case anyone else wants this information.

Ash Small

Tue Jun 21 2011, 11:33AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Coronafix wrote ...

Stella, that paper didn't have what I was looking for either but I eventually found the right paper and I am posting it here in case anyone else wants this information.

I'm slightly confused now, I've had a quick glance at that paper, and it seems to be more relevant to waveguide cavities than magnetron cavities. While I appreciate that the dielectric constant of each is different (one being in a vacuum, and the other in air), at first glance it doesn't appear that the two are interchangable.

Maybe PM and I misunderstood your intitial question, Coronafix. Were you after magnetron cavity dimensions or waveguide dimensions, or am I missing something here?

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