# 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.