Yesterday, I was able to reproduce every resonance mode with just the antennae, not in a cavity. Today, I was not able to, but I think it's best to treat the modes I found as suspect until I get another set of equipment to verify the behavior of the cavity better.


I made a plaster cast of the cavity to measure the actual inner diameter of the cavity at the small plate. I had trouble getting the plaster out. I tried chipping it out and heating it for 15 minutes at 450o in a toaster and quenching it to shock it out. It did not come out until I heated it with the oxyacetylene torch. I took care not to anneal it by accident, but the flange is more bendable now. The finish is ruined.

The measured OD of the mandrel is 73.20 mm at the small plate. The measured OD of the plaster cast is 73.90 mm. This implies I lost approx. 0.70 mm between forming imperfections and polishing. This is an interesting benchmark for future fabrication.

I am interested that the diameter at the small plate is lower than dc @ the lower resonant frequency, 2351.999 MHz. This should have cut off that frequency. Feynman II suggests that, after the cutoff diameter, the signal does not die immediately, but dies out exponentially quickly so that it is a source of losses and is essentially gone within a distance of a (the radius). The chamber may hhave been past cut-off for such little distance that it wasn't visibly affected, but I would have expected it to affect the peak more than it seems to. This may speak to my theory that the cutoff frequency equation may be affected by the slope of the walls of the chamber.

I was thinking last night about the use of Raspberry Pis in a Hadoop cluster and I found that it is "difficult" to translate FFT to a MapReduce paradigm. However, I read more about DFT and found that it is possible to see whether a specific frequency is present in a signal with a technique called "correlation." This technique translates very well to MapReduce. Considering tracking the resonant frequency and feature recognition to determine if the resonant frequency is near the fc of the small plate radius (especially as the small plate expands in the heat) is essentially a search of the frequency domain, and a full characterization of the frequency domain probably isn't necessary, this could be a useful insight. Large transistor, slow speed processors running in a distributed MapReduce fashion may overcome processing limitations we could face.

2016-05-07 (2)

I have run the experiment with better resolution on the Spectrum Analyzer. The settings are as follows:

Signal Generator    
Freq Step 0500.000 MHz
Start Freq. 2300.000 MHz
Stop Freq. 2500.000 MHz
Step Delay 00.100 s
Attenuator Off  
Power +3 dBm
Spectrum Analyzer    
Freq Span 002.000 MHz
Start Freq. 2403.000 MHz
Stop Freq. 2405.000 MHz
Module 2.3 - 2.5 G  
Top dBm -065 dBm
Bottom dBm -107 dBm
Iterations 016  
Offset dB +000  
Units dBm  

The results are stored in RFExplorer_SweepData_2016_05_07_17_04_04.rfe. The samples at the edge of the peak around 2404 GHz were:

  • 2403.956 MHz@-99dBm
  • 2404.036 MHz@-100.41 dBm

This implies a Q factor of 26,710. I was skeptical of such a high rating on my first attempt, so I verified my approach with a physicist/engineer Richard Driver. He couldn't comment on my approach or experiment, but he believed I was calculating Q correctly.

I am also seeing a resonant mode at 2351.999 that I wasn't expecting,, and one at 2507.967 MHz, and maybe another at 2534.063 MHz. The analyzer doesn't got beyond that apparently. At least, I can't make it do so.

The wavelength in air of 2403.991 MHz (the average of the peak) is 124.7925 mm (according to, so the half-wavelength is 62.3962 mm. The measured height of the cavity is 62.70 mm - 1.36 mm = 61.34 mm (the plunge depth from teh calipers from the top of the base plate, minus the thickness of the base plate). I'm off by about 1 mm from matching the half-wavelength, and I can't tell if the that's close. Neither of the other nearly peaks (59.8094 mm and 63.7755) are any closer.

The cut-off radius of the target frequency is:

fc(mn) = X'mn/(2 * pi * a *sqrt(mu * epsilon)) c = 3 * 108
ac = X'mnc/(2 * pi * f) X'mn = 1.8412
ac = 0.03656870 m f = 2403.991 GHz
dc = 73.14 mm  

At the lower frequency:

ac = X'mn * c /(2 * pi * f) c = 3 * 108
ac = 0.03737707 m X'mn = 1.8412
dc = 74.75 mm f = 2351.999


The settings from 5/5 were:

Signal Generator  
Freq. Step 0500.000
Start Freq. 2300.000
Stop Freq. 2500.000
Step Delay 00.100
Attenuator Off
Pwr +3dBm
Spectrum Analyzer  
Freq. Span 060.000
Start Freq. 2367.000
Stop Freq. 2427.000
Module 2.3 - 2.5G


I have constructed a loop antenna from a SMA female-to-female adapter and a lenght of thin wire. I secured teh bottom plate to the cavity with 4 wing bolts and wing nuts. I inserted a straight antenna through a 3/8" hold about midway up the chamber, and inserted the loop antenna below the midpoint through a 1/4" hole. I prefer the 1/4" hold. Neither antenna was strongly secured, and the female-to-female adapter was connected physically (resting) to teh chamber wall. The straight antenna was connected to the RFExplorer Signal Generator. The loop antenna was cnnected to the RFExplorer Spectrum Analyzer and arranged approximately horizontal, parallel with the bottom plate. The settings of the devices are recorded later. The data recorded by the RFExplorer software is in file RFExplorer_SweepData_2016-05-05-22-28-52.rfe. The data show a steady peak at 2403.964 MHz that corresponds to turning the Signal Generator on and off. Using the contiguous data points 2403.429 MHz @ -91 dBm, 2403.964@-74dBm, and 2404.500@-90dBm to calculate Q, I get Q=2,244.598. I find this suspicious for several reasons:

  1. this is using contiguous data points, so it is more likely a commentary on the resolution of the equipment, meaning it is AT MINIMUM 2,244, and
  2. this seems suspiciously high considering I'm basically a mook and this is my first attempt.

This was done with:

  1. insufficient polishing,
  2. no silicone coating,
  3. no special geometry such as spherical endplates.

There remains in this experiment:

  1. tie the resonant frequency back to the actual dimensions of the cavity and
  2. resolve the resonant frequency with the ac of that frequency, and compare that to teh actual a of the cavity.


A number of problems have been bothering me that may be solved. I couldn't describe why the height of the chamber had to be dictated by the wavelength of the wave, or pinpoint where I read that. I didn't fully understand what a mode was. And, I didn't know whether the lambdag equation would work in a frustum as it did in a waveguide. This came from failing to understand that E is not oriented as in Feynmann II 23-11(a), but 23-11(b). It was very helpful to understand what was happening, but in a waveguide E goes across teh guide to allow the EM wave to propogate down it. (Feynmann II 24-3(a), Balanis Fig. 1, attached figure 1). So, figure 2 is wrong, figure 3 is more correct. This orients the propagation between the endplates, prevents the sloping sides from being near-tangential from E (meaning we are not at a non-zero portion of the Bessel function, preserving the lambeg equation) and changes the way I understand the current flow. It also explains why teh resonance modes in Tajmar were so clear; the sloped sides dampened resonance when the propagation was oriented sideways. Only TE resonance modes were appearing. This changes the way I will orient the antennas, at least. It also changes how I understand the connectivity of the loop antennas. I was so fixated on Feynmann II 23-15 that I missed Feynmann II 23-8, which shows a loop antenna and the obvious implication that the coaxial sheath shoudl be connected to the interior wall.

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