No Great Resonances to be Found

Summary:

Resonances with quality factors of 1000 are common, the cavity is the right size and all that can be updated/fixed are the probes and tuning plate.

I verified that the cavity dimensions match the simulations and then spent another good couple of hours playing with the cavity yesterday.  Here is what I learned (pictures taken with my iPhone):

  • Resonances with insertion losses of under 1dB and with Q’s higher then 1000 are common and easy to find.  Here are pictures of two of them:
    • This resonance is the “Best Hope” one which I have shown before and is in the unknown mode (insertion loss 0.5, 1261Q, frequency of 2.44GHz):
    • The resonance below was chosen at random and shows an uncalibrated result, which means the insertion loss measures is really about 0.7dB and the Q about 1000 (f of 2.47GHz).  Again, some unknown mode.

I also wanted to see what a high Q resonance looked like and found one:

A few things to note:

  • The bandwidth (shown as “BW” above) is only 160KHz which would explain the Q of 16000
  • The loss, even after subtracting the amount calibration would adjust for, is 3dB!
    • I think I remember being told once that having a high insertion loss would help Q and I can reproduce that here if I tune the insertion loss even higher,  I can get a Q of 32000.
  • Note how sharp the spike is compared to the first “Best Hope” graph above, both of which have about the same width of 5MHz

The last diagram is what the TE0,1 mode should look like but with a much better insertion loss.

I have brought the cavity home to work on some more.  The first thing I am going to do is bring the probes closer to the simulations by making them rounder and more horizontal.  The probes are twisted slightly which may be the reason for the insertion loss.  I will then fix the tuning plate by putting some copper mesh around it’s outside edges to connect it properly to the cavity.  I will also make sure it is as flat as possible and doesn’t twist when moved in and out.  Kevin pointed out that it may be necessary to investigate another way of tuning and perhaps a movable plate from the large end??  I don’t think it should make any difference, but I will run that through a simulation to see and I will also think about other ramifications, for example, won’t a larger plate flex even more?

Fixed Calibration, Not Working Yet

The short version:

After fixing calibration problems, the cavity still needs work, although it isn’t clear where.  The copper electroplating is thick enough at 12 micrometers.

After sending out the previous status update, I noticed that S1,1 was going above zero!

See?  That should not be the case for a passive cavity because it has no mechanism to generate energy and is obviously a problem with calibration.  I confirmed the problem on Thursday.

In the end, with the help of Kevin, we fixed it and I learned a few things.  Turns out the cables connecting the network analyzer to the cavity had been bent too much, quite likely by me, and were no longer working correctly.  I learned how to check for a proper calibration by using the smith chart to check for phase.  With a calibrated short load, the “dot” should be on the left and slightly above the middle line, with a load, it should be in the middle of the smith chart and with an open connection, it should be to the right and slightly below.  Those values should also not change no matter what orientation (within reason) the cables are set to.  This was the problem with the previous cables, which, when their orientation changed, so did the phase with a short signal.

After replacing the cables, the calibration started working as expected.

I also realized that I had been using the default number of points for my previous measurements, 201, not the maximum at 1608.  Below are the new results with the fixed calibration, maximum number of points and the automated Q calculation showing the proper loss.  The first two graphs show the overlap between simulated and measured results:

Sections “A”, “TE0,1” and “B” all correspond to each other between the two graphs.  An then zoomed in:

Analysis:

  • It is pretty clear that we have the right resonance because both sets of graphs have similar features as outlined by the labeling.
  • It is also clear they are miles apart because:
    • The insertion loss expected is 0.5dB and measured is 2.2dB (which, on a logarithmic scale, is a big difference!)
    • The Q is substantially different, 2500 vs 67,000
    • The frequencies are also different, the simulated cavity is resonating at 2.449Ghz and the actual cavity is resonating at 2.467Ghz.  As noted in previous status updates, the tuning plate doesn’t actually move the resonant frequencies by much, it just affects how strong a resonance is.  The tuning has been set such that the least amount of insertion loss is present with a maximum Q.
  • As an aside – The “B” in the first zoomed out graph is not the same dip as the “B” in the second zoomed in graph.

I am going to fiddle with the cavity over the coming week to see if it is fixable, primarily starting with the probes and checking the cavity dimensions against the simulated one.  It is curious that the TE0,1 mode is happening at a frequency 20 Mhz higher than simulated, 2.4676Ghz vs 2.4485Ghz .

There was the other resonance that has a better insertion loss:

The resonance is at 2.45Ghz, has a Q of 1000 and an insertion loss of 0.7dB.  Unfortunately, I have no idea what mode it is and would need to match it to a simulated result to really know for sure.  It should also be noted that the first cavity created by Shawyer produced 83mN worth of force for a Q of 5000.

Hmm….

In related news:

I think I might have found someone local who can machine a cavity and I have a preliminary quote back for $730 (not including the 12″ diameter aluminum round stock which will run about $900).  A local supplier would allow faster iterations of the cavity and I could film the CNC lathe in action!  If I can find the problem with the current machined cavity and it is a dimension problem, I will definitely go for another cavity.

If I do get a new cavity, I will have to send it away to get electroplated with copper given aluminum has only 60% of the conductivity of copper.  I was talking over the electroplating depth with my supervisors and to be effective, they noted that I should make sure the skin depth used by the microwaves is less than the electroplating.  To explain further, microwaves only utilize a very thin skin on the inside of the cavity and it is known as the “Skin Effect” [wikipedia].  For example, at 10Ghz with copper, the skin depth is less then a micron at 0.65um.  At 2.45Ghz, using this online calculator, the skin effect is 1.32 micrometers using copper’s resistivity of 1.673 micro-ohm-centimeters and a relative permeability of one.  The current copper plating is 0.0005 inches or 12.7 micrometers, which is more then enough.

Usable Q(!) and Tuning Plate Tilt

Results are rolling in now, hot and fast.  I played with the cavity again today and got better results, even, maybe ones we can actually power up the cavity with.  The first result is from the “best hope” resonance that I mentioned in the last part of the previous email, which I zoomed in on today and got this:

A few things are notable:

  • The insertion loss is pretty high (1.9dB) when our simulations predict 0.7.  A cavity with a loss of 3dB or greater, is useless (3dB is a log scale which means each step looses exponentially more power).
  • The Q is the best I have measured yet at nearly 3000 (subtract markers 3 from 2 which resulted in 2467.140Mhz divided by 0.838)
  • It isn’t clear from trying to match the simulation s-parameter curve, if this is the TE0,1 mode.  However, if the insertion loss can be brought into the sub zero range (see below) and the Q is still high, then this is the resonance to use!

As mentioned at the beginning of the previous email, I then tuned and zoomed in on the location which looked to have the best match with the simulated location of the TE0,1 mode.  Here are the results (got some reflection in the picture):

An analysis:

  • Wow – an insertion loss of only 0.5dB! Excellent! (WAIT – this is not right – look at the graph, S1,1 goes above zero!!! Check out the next blog for an explanation)
    • However, that insertion loss was finicky and could only be created by pushing the tuning rod toward the back as the diagram shows (note the arrow).

      I think the reason is the tuning plate rests at a slight angle and when straightened, the insertion loss dropped by about one dB.  The Q didn’t change at all though.
  • The Q isn’t as high as the “Best Hope” but was still very decent at 1500
  • I also figured out how to get the network Analyzer to automatically calculate Q, as you can see above.  It should be noted that it says “loss: -10.718 dB” however, it is taking that result from the wrong s-parameter as the loss is 0.57dB
  • I had a bit of trouble with calibration which produced some funky results like this (note the jagged lines):

    I’m not sure what happened, but you can tell it’s a calibration problem because all the other graphs were smooth and the S1,1 actually protrudes momentarily above zero which is nigh impossible.

If we do end up with a resonance that we can use, I have been thinking about how to power it.  The problem is this:

A high Q means the energy will only be accepted by that mode over a small frequency range, usually under a megahertz.  However, the magnetron from a microwave is built for power not pin-point frequency control and wanders as it heats up or there are changes in input power.  Worse, the better the Q, the narrower the frequency range over which it will accept energy.  If we are going for a Q of 50,000, it will have a bandwidth of 0.05Mhz or 50 Khz!

Possible solutions:

  • The one thing that might save us is that a microwave transmits over a wide range of frequencies, usually 30Mhz or more, which means if we can center it on the resonant frequency, some of the energy will excite the resonance.
  • Most of the energy will be reflected, not only because it is outside the frequency bandwidth of the resonance, but also because once resonance has reached steady state, all the energy will start to be reflected.  For much longer runs, once steady state is reach, it should be possible to turn the magnetron off periodically in order to just pump in enough energy that only a bit of it is reflected.   An analogy is like pushing a kid on a swing, when getting them up and going, you need to push hard, and the fastest way is to run behind them and push from one side to the other.  After they are swinging high enough, you can just use a single hand to keep the resonance going.

I will be back up at the university tomorrow to test if changing the angle of the tuning plate at the 3000Q resonance makes any difference to the insertion loss.  I also plan on getting the new water cooled magnetron up and running too!

My attempts to avoid reflection when taking pictures of the results, means I spend most of my time like this:

Tuning Plate Added – Still Crappy Q

I got the tuning plate attached and got good results at the university, although, as usual, as expected.

The tuning plate fit this cavity very well, with a fairly uniform and small gap between it and the cavity walls.

The measured results are at least a bit like the expected results and here is a side by side comparison at one location of the tuning plate:

That was the best match I could get across the tuning spectrum and it is close.  Notice the little “hill” just before the “Marker 1” location, labelled “A”?  That seems to match the little hill just before the the TE0,1 mode in the simulations.  There is also the wider bandwidth resonance immediately after (“B”) and although “Marker Mountain” is not as clear as the measurements, that can probably be explained by the lack of measurement points, only 1500 across the entire spectrum from 2.3Ghz to 2.5Ghz, of the network analyzer.  If we were to zoom into the important points of “Marker Mountain”, it would probably resolve a few details.

The unfortunate part is it looks like the resonance only dips to  -13dB, meaning the cavity isn’t very well matched and the insertion loss is unacceptably high at 2dB+!  I will zoom in, recalibrate, and retake measurements this week, but from previous experience, I am guessing the results won’t change much.

However, while I was moving up and down the tuning range, I did find this:

Again, notice the marker mountain on the far left and marker 1 shows the location of interest.  The match is very good at -38dB and the insertion loss also stellar at 0.6db!  Unfortunately,  Q still only looks to be in the hundreds because the 3dB points look to be about 6 to 7 Mhz apart.  From the graph, which has 20Mhz per division, the 3dB points look to be about a fifth or so of that width.  Q is then just 2446Mhz divided by 6Mhz or roughly 407 (unitless), ironically not much of an improvement over the plastic cavity!!  To get a Q in the thousands, the width between the 3dB points has to be 2Mhz or less!  Besides a low Q, it is hard to tell if that resonance is even the TE0,1 mode we want because it doesn’t closely match the simulated results.

Again, I will take a closer look this week but I’m not holding my breath.

Playing with the tuning plate also showed something else – that “Marker Mountain” is pretty much stationary no matter where the tuning plate is.  Tuning does change the mountain’s shape, but it doesn’t move it in frequency.  Moving the tuning plate mostly affects the higher order resonances, like the TE0,1 mode we are looking for, but it isn’t clear if they are moving frequencies or just appearing and disappearing.  Click on the graphic below to see a looping animation that gives you and idea of how the s-parameters change as the tuning plate moves up (making the cavity longer).

Here’s a shot from the documentary footage: