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# calculating resonant frequency of reentrant cavity

## calculating resonant frequency of reentrant cavity

(OP)
Hello folks,
I need to construct a re-entrant cavity whose resonant frequency is 10.3 GHz. I have been told that taking a known cavity of some frequency and shape can then be scaled proportionately to the desired frequency. However, I need to build the first model. My constraints are that the cavity be cylindrical and slightly longer than wide. Please go easy on the jargon, as I haven't dealt with Hi-freq stuff in 40 years. I seem to get ignorter and ignorter the older I get.

Thank you,
Morg

### RE: calculating resonant frequency of reentrant cavity

You are correct about the resizing, but it's never perfect when you build it. Aperture coupling effects can give slight errors.

http://www.rfcafe.com/references/electrical/waveguide.htm

I think the formulas for resonant cavities are simple calculator formulas using waveguide cutoff info (which is all based on physical sizes of your waveguide/cavity).

could you explain the phrase re-entrant and what you plan to use the cavity for?

Normally a cavity is 1/2 wavelength long electrically.
kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
Thank you Higgler.
A re-entrant cavity brings the two opposite sides close together to intensify the electrical field between the gap. Like in a Klystron. Picture a small "stub" whose diameter is less than half the diameter of the cavity, emerging from one end of the cavity and reaching nearly to the other end forming a small gap of intense field.

Morg

### RE: calculating resonant frequency of reentrant cavity

Thanks, that helps,
I did see a klystron photo via Google, looks like a can of tuna, or metal hollow donut with the center area squeezed with a C clamp to bring them closer to each other. Sounds correct?

Is the purpose for material measurement?

kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
I am checking fiber strands for impurities.

morg

### RE: calculating resonant frequency of reentrant cavity

The Q of the cavity goes down with increasing frequency typically. So if you have a design with a Q at low frequencies, it'll probably be lower Q at 10 ghz.

Losses in metal increase with frequency. Smooth walls and low loss plating help improve the Q.

kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
Most of my RF work has been with power grid tubes up to 40kw in a Hartley-Colpitts configuration. This was many years ago. This application is 2 orders of magnitude above those frequencies, and the components and effects are smaller than my eyes and fingers are accustomed. Thanks for the information on the Q. I will be sure and detail the finish on the drawings. Would you have any thoughts about whether the uWaves should be launched via current or voltage coupling into the cavity?

Morg

### RE: calculating resonant frequency of reentrant cavity

My original experience is launching a wave into a cavity  through a wave propagating in X band waveguide which enters the cavity through a small iris (say 20 mils diameter). The waveguide was X band and the cavity was a cube with around 0.45" size per side. Used for dielectric constant measurement (empty cavity vs. dielectric loaded cavity frequency shift).

I've recently worked on a microwave plasma spark plug that used a small loop to couple energy. That makes a grounded center conductor which is better for heat transfer since the center conductor heating/melting is often a concern with higher rf powers.

kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
Higgler,
Thanks for the input. Interesting about measuring Epsilon. I recall the resonant Frequency changes by the factor of the square root of the Epsilon of the material.

Having thought about this problem some more. Does it make since to couple via voltage (antenae) since I will be looking at changes in the electric field TE mode, as opposed to TM mode requiring magnetic coupling (current)?

Morg

### RE: calculating resonant frequency of reentrant cavity

morg,
that's correct, you measure the change in frequency, say from 17 ghz down to 10 ghz and your Er is (17/10)^2 in that case. Being square, you can remove your test article and rotate it two more times to see if it's homogeneous or if the frequency changes alot. Air spaces and imperfect cubes add error however, but it's a good simple method to measure Er in x,y and z.

The waveguide to coax transition is essentially an antenna poking into waveguide (spaced 1/4 wave from it's back wall). Our use did not care about efficiency since our 0.45" cube had irises on two sides and we measured energy propagating in one iris and out the other iris of the cavity. The through loss looked like a spiky picket fence. The loss in the dielectric was determined by how thin the spikes (or low loss points) in the picket fence, and taking the 3 dB width down from a peak (say 10 Mhz) and dividing that by the frequency (say 10 ghz) then the loss tangent of the material was 0.01/10 or 0.001. very simple, and fairly accurate.

kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
Higgler,

You've discerned the process exactly. Well done. Yes, the mechanism is fairly simple for determining good/bad. Fortunately for me, it is enough.

On the narrow band patch antenna, I have no experience there. Would you suggest a source or site that I could learn enough to make an evaluation? Could be a possibility.

As I said before I have been away from this stuff a long time. I retired from EE 12 years ago when I worked as a consultant for companies needing sensing methods for material separation. I moved to the country, started a sawmill, got splinters and went broke. Back to consulting.

Morg

### RE: calculating resonant frequency of reentrant cavity

are you looking at a single fiber or a sheet?

### RE: calculating resonant frequency of reentrant cavity

here are a few links on patch antennas.
http://en.wikipedia.org/wiki/Patch_antenna

here's a good photo http://www.emtalk.com/images/calculator/mpa_model.jpg

In wikepedia, it shows a cable connected to a piece of metal suspended above a ground plane. The field between the piece of metal and ground plane is concentrated. You would make the length proper to set the frequency, and set the width narrow so that the field is more concentrated. The bandwidth of the antenna is made narrow by making the height of the metal patch above the ground plane very small. i.e. bandwidth is directly proportional to it's height. Bandwidth is also proportional to the dielectric constant if you replace the metal patch with a piece of dielectric with metal cladding on the top (instead of the metal sheet in the wikipedia). Dielectric has loss which lowers the Q, there is etchable foam dielectric that can maximize your Q.

I would picture having the fiber run close to the center conductor along the long direction of the patch. You could also run 2 fibers or 4 fibers at a time under the patch and speed up your test time if your yield is high possibly. This all depends on the needed Q.

Other options are possible dealing with making an S21 measurement between two patches.

One thing that new software technology has provided through two programs (Ansoft HFSS and CST Microwave Studio) is the ability to calculate a result so accurately, that you can analyze any potential setup before you build. The bad part is the software is \$50K and it takes some skill to get accurate answers.

kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
Hacksaw, I am looking at a single fiber strand.

Higgler, thanks for the info and direction. Most of what I've seen may require more measurement equipment than I have at my disposal. Although HP (now Agilent) used to be really good at sampling equipment for a couple of weeks if there was a reasonable expectation to buy or lease. The quality of measurement information is not very critical to the process. I just need to ensure absence of fairly gross particles. 20 to 40 micron range. Hence the frequency. I've even thought about a high voltage wire off of a toner that would short through any impurities thus snapping the fiber. Anyway, this project is less than 20K to prove the technology. So I probably don't need to branch into new science just yet.

Having said that, the narrow-band patch antenna presents some intriguing ideas for some other projects that need a simple way to detect gross frequency and amplitude shifts.

I did find a teaching website for the student from the University of Taiwan (in English) that explained many of the constraints for a given frequency, plus many configurations.

The greatest drawback I have found in using cavities as  detection elements is their temperature sensitivity due to thermal expansion. Thay can make quite a good temperature monitor. Particularly, if they are embedded in a process with changing temps. I am thinking the patch antenna may eliminate this sensitivity.

morg

### RE: calculating resonant frequency of reentrant cavity

A patch antenna will vary too with temp. Rogers corp makes a material called RO6002 that was formulated to not change frequency over temperature and they made it for patch antennas specifically. Since patch antennas were very narrow bandwidth when they were invented, 0.3-3.0% bandwidth, dielectric constant changes would vary the frequency so much it made the antenna unusable.

6002 is +12 ppm/deg. C variation in dielectric constant with temp from -50 to +150C, and frequency varies proportional to sqrt (diel. constant).

My recollection of putting a heat gun on a 1575 Mhz patch was a 2 Mhz shift in frequency when it was pretty toasty.

What type accuracy do you need in your frequency over what temp range? and how much did the resonator vary on you?

kch

### RE: calculating resonant frequency of reentrant cavity

(OP)
I need less than 10Mhz drift over 20 degrees. The resonating cavity (brass with silver plate) over time drifted over 50Mhz in a 20 degree span. And because the block of brass had so much mass there was a great deal of temperature hysteresis making it difficult to separate the temperature curve from the signal. As I recall S/N from the temperature effects was right on the margin for the size particulate we were interested in detecting.

Morg

### RE: calculating resonant frequency of reentrant cavity

Sounds like the patch is more stable over temperature than your brass air cavity. It would only change 1.2 MHz over that temperature range with 10 ghz frequency. Looking at the Rogers curves, the greatest change in the material 6002 is from 40C to 140C, and the change from +40 to less than 0C is much less based on their curves. I expect that my heat gun experiment producing 2 Mhz shift at 1.5 ghz frequency was a +23C to +150C temp shift, though calculations show it'd only change 1 MHz over that range.

kch

### RE: calculating resonant frequency of reentrant cavity

We have built similar cavities for some of our customers over the years. For your frequency shift requirement, a suggestion I would make is to use Invar steel with a high surface finish(very low coefficient of thermal expansion) and copper or silver plate. You could likely get away with fairly thin (~50-100thou wall) and plated aluminum flanges to keep weight low. If you are interested.. please send inquiry to sales@custommicrowave.com and we can quote price and delivery to fabricate this for you.

www.custommicrowave.com
Space Qualified Multifrequency Antenna Feeds - Advanced Microwave & Mechanical Design - Full Catalog of Standard Product

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