New Spectrum Analyzer and Welcome Neil Gruending!

Wow, another status update in the same week means things are getting done!  Summary:

An engineer friend from my university days has joined the team and will be designing and building the feedback control for the magnetron.   A spectrum analyzer was purchased and the bent probes built.

You can read up about Neil Gruending in a recent EEweb article which mentions that he owns five multimetres – he is an engineer’s engineer.  Neil and I worked on a project together many many moons ago and it was only in the last year that I reconnected with him through Facebook.  After reading that article, I realized he was the perfect guy to build the feedback loop and the timing looks to be right as he has time and interest, yes!

Even better, Neil is a big supporter of open source hardware and has agreed to share his design, including software and any circuit layout.  Sharing the design is important if other groups want to duplicate the work.

For most of this week, he and I have been talking about what equipment he needs and one of the first pieces is a spectrum analyzer.  Which was something else I learned about this week, the difference between a network analyzer, which I use all the time in the lab, and a spectrum analyzer.  The network analyzer has both a source and an analyzer which allows for the characterization of a passive device under test, like the cavity.  A signal is injected into one port and the response recorded on the second and the network analyzer has special capabilities for calculating things like Q (screen shots of which I have sent around previously)  The spectrum analyzer is useful for looking at a signal and recording things like power, frequency and frequency-spread and typical spectrum analyzers have no output capability.

What took up the most time this week was looking at all the options available for getting a spectrum (or network analyzer).  The biggest problem is price.  The yearly demand for analyzer is low, quite likely on the order of tens of thousands of units a year and they are complicated devices because they deal with Ghz frequencies.  Up until a few years ago, analyzer have also always included a display, which adds to complexity and cost.  Add “complicated” to “low volume” and in a mature market, you get astronomical prices as spectrum analyzers start at $10K and go up.  The higher frequency, the higher the cost.

Even second hand analyzers tens of years old, hold their value and there is a huge business selling and repairing second hand analyzers.   For example, take a look at this ebay search which shows that if a spectrum analyzer is under $4K  it is either 25 years old, or more likely, doesn’t go up to 3Ghz.  Even if you do find one on the cheap, they weigh a ton, which means shipping is in the hundreds of dollars, not to mention the hundreds paid in GST and brokerage charges.  Meh.

It is only within the last few years that it has been possible to purchase an analyzer that uses digital technology, DSPs specifically, and a computer to display the results.

The options were short listed to :

  • $4K for a second-hand spectrum analyzer available here in Edmonton [ – an Anritsu MS2602A for when the link goes dead ]
  • Or $1k to $2k for a USB driven, display-less spectrum analyzer that uses a computer to display the results and the two considered were these:
    • Signalhound (.com) – a small US based company that also repairs analyzers and does LCD retrofits
    • Spectran (aka Aaronia) – a larger German based company and they sell both a USB based version and a version with a simple LCD display.

The winner was Signalhound and I purchased their spectrum analyzer for $1076CND today and it should be here next week.  Here ‘s a pic:

Signalhound won for a number of reasons:

  • Price – $919US (not including shipping, taxes, etc).
    • Aaronia has a better product that goes up to 6Ghz versus Signal hound’s 4.4Ghz, but costs $500 more
    • Aaronia doesn’t have an API or programmable interface (which is important and explained later)
    • Keeping the cost low will also help those who wish to duplicate our work.
  • Performance – up to 4.4Ghz
    • One important specification of a spectrum analyzer is how sensitive it is, however, in our case, because the magnetron signal has to be heavily attenuated before being injected into the spectrum analyzer, sensitivity isn’t an issue.
  • Custom programmable – This was the biggest reason Signalhound won because it can be used as part of the feedback loop!
    • I asked the designer to comment on using the Signalhound in our application and his response was “The Signal Hound API can stream 480K samples per second on a 240KHz bandwidth.  It will be more than fast enough for the feedback loop you have described.” and the feedback loop I described was:
      • “We are (quietly) duplicating the “demonstration engine” on the “EMDrive” ( in a university laboratory environment.  The EMDrive is essentially a magnetron, the heart of a domestic microwave oven, dumping upwards of a 1KW at 2.45Ghz into a finely tuned closed resonating cavity.  At the frequency the cavity will be tuned to, it will have a Quality factor in the tens of thousands, which means a bandwidth 2 to 6Khz wide.  By “bandwidth” I mean that the input frequency will need to be centered at the resonating frequency and not wander outside that range.  Commercial magnetrons are great at heating food, but not so great at delivering higher power in a narrow frequency range.  Our plan is to create a feedback loop by first, reading the magnetron output frequency, attenuating it, measuring it, then controlling the magnetron modified with electromagnets instead of permanent magnets.”

Once the spectrum analyzer arrives, then I will be bringing it up to the university to test it against the current magnetron setup.  I will then package everything up including the magnetrons, power supplies, circulator, tuning waveguide and coupler sections and get it all to Neil.  The intention is to use, as a guide, the paper written by William C Brown  “The Magnetron – A Low Noise, Long Life Amplifier” [PDF ]

Oh and I also got the bent probes finished today:

Whew!  This project might get completed after all!

I will be up at the university this coming week to test the bent probes.

Good Simulation Match to Shawyers Cavity


Going to build a bent probe first and test.

Two weeks ago, based on simulations, I had decided that a probe 280mm from the short, 28mm in diameter and 15mm in length would work best.  One last thing I had to check was the exact probe length and to that end, did a bunch of simulations:

Which looks like the lowest insertion loss is when the probe distance from the short is 17mm.  I then reran my simulations but with a much tighter frequency spread and got this:

Looks promising, right?  The insertion loss is great at 0.23dB but unfortunately, the mode is messed up:


And the Q dropped to 41K.  Oops.

I also modeled bent probes in order to put the probe at 280mm from the short, but without moving the probe hole (which already exists in the actual cavity).  The probes looked like this and the results were:


Not bad at 0.45dB, but it, too, lead to an impure TE0,1 mode (impure in the sense it didn’t have the circular TE0,1 mode through out the cavity) like this:


And the Q dropped to 48K from 60K.  Although it took me a while to realize it, the optimization has to happen with two variables at the same time, a high quality factor (Q) and low insertion loss.  There are a lot of resonances that have either a high Q or a low insertion loss, but the trick is to find one that has both (i.e. the TE0,1 mode!).

It is interesting to note that Shawyer has a few things to say about quality factor:

  • “The engine <the one we are duplicating> was built with a design factor of 0.844 and has a measured Q of 45,000 for an overall diameter of 280 mm.” (demonstratorengine.html,
  • “Conventional microwave technology limits the maximum Q of resonators to around 50,000, giving a specific thrust of 200 mN/kW” (applications.html,

I had hoped that we could get a Q of 60K or 70K because early simulations suggested we could, but I made a newbie mistake.  Those high Q factors are only possible with high losses.  As I noted in a previous update, I could get a Q of 32K from our actual cavity, but the insertion loss went up dramatically (over 6dB), making that particular resonance unusable.   Now looking back at Shawyer’s work, it would seem that our simulations are lining up with his results.  The best Q we can hope for is in the 41 to 48K range with an insertion loss between 0.23 and 0.45dB, as compared to our previous 60K with a 0.7dB loss, and that our simulations are showing exactly what we should expect.  Now to get the real cavity to work as it should.

I have two options, the first is to create a bent probe, which is what I will do first.

The second is to move the probe to 280mm from the short, closer to the narrow end and drill a new hole.   The probe needs to be straight up and down though and needs a mount.  One option was to build a ring that could be fastened to the cavity (shown below).  I modeled one in 3D and got a quote from, which is easier than it sounds, because their software calculates costs including shipping right from the program.  Turns out it would cost roughly $500 (including shipping).

Instead (and if the bent probe doesn’t work) then I am going to build my own probe mount with an extra square piece of copper I have.  The hardest part will be sanding the mount to fit the curve of the cavity.  The probe mount will look like this:

Having done a lot of simulations, I am now going to build a bunch of different shaped probes and test them.  I should then get a good idea of how well the simulations match the real cavity and what to change to give the best results.  Wish me luck.

I also contacted an old friend from my engineering days at SFU and he has agreed to take a look at building a feedback mechanism to control the magnetron frequency.  The great news is that he supports open source hardware and if he takes the job, we can publish the entire design! (for all those others who may want to reproduce our results.)


I Think I Know What To Fix!


Summary – From simulations, it looks like I can fix three things on the cavity, increase the probe length from 3mm to 15mm, move the probe backward to 280mm and get rid of the gap around the tuning plate.

For the test runs  below, I varied four variables

  • the probe loop diameter
  • the length between the probe mount and the probe loop (how far the loop stuck into the cavity)
  • the distance of both the measurement and power probe from the tuning plate
  • the gap around the tuning plate

Below is probably the most indecipherable graph ever but it shows all the test runs:


  • The best result seems to be a loop 28mm in diameter 15mm in length and 280mm from the short with no gap around the tuning plate.
  • The three variables that had the most dramatic affect, did so in two different ways:
    • Probe diameter and probe location affected the insertion loss dramatically but not the frequency, (E), (G) & (J) where the loop went from 20mm to 28mm and the insertion loss went from 1.5dB to 0.34dB.
    • Probe length seemed to affect the resonant frequency, starting at a high frequency of 2.4417Ghz with a probe length of 3mm, swinging as low as 2.435Ghz @ 20mm and then returning to 2.4414Ghz for a probe length of 30mm.
  • The current tuning plate has about a 1 to 2mm gap around the edge in order to avoid the tuning plate scratching the inside of the cavity.  However, as a previous status report showed, having a completely aluminum cavity has little affect on the TE0,1 mode and a few scratches from the tuning plate will have negligible effect.
    • The simulation results above suggest the tuning plate gap at 2mm, has a slight affect on both the insertion loss and the resonant frequency.  For example, for test run (G) without a gap and (H) with a 2mm gap, the frequency moved 3Mhz and the loss got better (?).
  • One of the surprises during this round of simulation was the 9dB loss for test (B).  This shows that not only is 292.5mm a bad match, but it is also more susceptible to other factors.  At 280mm, the probe length could vary from 3mm to 20mm in length and have little affect on the insertion loss, wheres as at 292.5mm, going from 3mm to 15mm, the loss went from 0.6dB to 9dB!!  The susceptibility to other factors at that probe location is likely the problem with the current cavity.

For the coming next week:

  • It is clear that having the probe at 280mm is much better then 292.2mm and I want to test, via simulation, if I can use the same probe location, but bend the probe backward such that the loop is in the right location (15mm above and 280mm from the short).
  • Once done the bent probe simulation, I will then decide if I need to drill a new hole or not.  I will then build a new probe and remove the gap around the tuning plate.

A Million Simulations – Some Results


I spent the rest of August running simulations to see if I could find the root cause of the difference between simulations and actual, without much luck.

Besides looking for the source of the problem, I am also trying to make changes that keep the shape of the cavity the same.  Changing the shape would mean ordering a new one, but it could very well produce the same results.  I need to be able to make sure that what I simulate makes a difference in the real world.

Here are the things I checked:

  • The location of the probes in the actual cavity are in the same position as simulated (99mm from the lip of the large end)
  • Whether a grounded tuning plate makes much difference –  it doesn’t – a couple dB insertion loss (it will be grounded when under high power)
  • Whether a large gap around the edge of the tuning plate makes much of a difference
    • 4mm

      The tuning plate is also ungrounded results in 1.2dB insertion loss, yuck.
    • 8mm (huge gap!)
    • Analysis – The plate needs to be grounded and the gap should not be more then 4mm.  With a gap at 4mm and no proper grounding of the tuning plate,  we could see up to 1.2dB of insertion loss.  The resonant frequency and the Q did not change.
  • I also moved the location of the probes forward and backward from the current location at 292.5mm from the tuning plate
    The probe here is in the zero point of the field and doesn't create a TE0,1 mode at all.
    Can start to see the resonance deform.
    This is the currently implemented distance, 292.5mm
    This has the lowest insertion loss
    The TE01 mode was really weak at this position even though the insertion loss was great


    • Analysis – As expected, the best match is when the probe is centered in the peak of the field, around 280mm, and the current location is slightly forward of that at 292.5mm.  The resonance at 280mm had the same Q (76K), the same frequency (2.4425Ghz) but had a better insertion loss (0.5dB).   It is possible to plug the current probe hole with round copper stock and move the power probe backwards and opposite the measurement probe.  However, I have to check if I can move the probe a centimeter backward and still stay on the probe mount ring (pointed to by the arrow)

      Note to self – Create a wider mounting ring for the next cavity.
  • I have also started to lengthen the probe and it does have an affect, for example, it moved the resonant frequency downward by 100Mhz.  Unfortunately, it seems to have messed up the TE0,1 resonance as shown below and dropped the Q to 60K.

    Probe is extended 15mm into the cavity with a 25mm diameter loop on the end. Q is lower, insertion loss is excellent. Frequency is 2.4411Ghz.

    The probe is 30mm deep with a 15mm diameter probe, the TE0,1 is impure but note it moved to 2.438Ghz
    • Background– One of the neat features of CST’s microwave studio is the ability to insert variable names instead of numbers, for example, the diameter of the probe can be “diameter_of_probe” which you (or an optimization routine) can then change.  In practice however, changing a variable by a large amount usually breaks the model, for example, using a large diameter probe loop means it is too close to the probe mount.  Thus when changing a variable, a few other variables have to be adjusted too.  Besides running simulations, I also spent time building a more robust model that can handle large changes without breaking.I am now on version 2.02 of the model and can change the depth of the probes and the probe loop diameter without breaking it.I also fixed another problem – With earlier model versions, the lofts I used to connect the probe loop to the probe had numerous “degenerate tetrahedrals” which are really thin tetrahedrals.  Degenerate cells mean convergence of the adaptive meshing takes a long time, up to 8 or more samples.  Each sample also uses a large number of mesh cells, for example, I have had counts as high as 750K.  Without degenerate mesh cells, the model uses ~450K cells, and takes 4 samples to converge mesh adaptation.  (The number of samples to simulate depend on the frequency range, for example, a range of 25Mhz takes nine samples, a 100Mhz range can take 16 samples.  Even then, if the TE0,1 mode moved, it requires another couple frequencies to be simulated in order to see which resonance is the TE0,1 mode and what the Q is at that frequency)
    • Method – One of the problems to fix is that the frequency of the actual cavity for the TE0,1mode is 18Mhz higher then simulated (2.467Ghz vs 2.449Ghz).  If a longer probe moves the resonant frequency lower, then it should be possible to simulate a probe length that is 18Mhz lower and then the actual cavity should be at the right frequency.  If I can also get a rock bottom insertion loss (0.3dB or 0.4dB) and the Q isn’t too bad, then it might work.  Probes are easy to fabricate, especially long ones and it will be a good test to see if the simulation can result in real-world outcomes.Making the probe longer moves the TE0,1 mode lower, but messed up the field configuration.  At first, I tried a larger loop but that lead to a worse field configuration, but going in the opposite direction with a smaller loop fixed it. The simulations suggest that the total length of the loop is important to create a clean TE0,1mode.  It doesn’t matter if the loop is near the probe, only that it is the same total length from probe mount to termination on the cavity wall.Which is my next task, to optimize the probe length and diameter.

Simulating is a big time sink, because the simulations never run under 400K tetrahedrals and take at least two hours, which means I can do about three to four a day.

  • In preparation for a future cavity, I tested to see if an aluminum cavity made much difference compared to copper.  I was a bit shocked to find that a completely aluminum cavity had an insertion loss that was almost the same as copper (0.8dB vs 0.72dB), the frequency of the TE0,1 mode didn’t change and the Q was almost as high (60K vs 76K)!!  After talking it over with Kevin, it would seem this is because the TE0,1 mode is zero along all the walls (but not at the end plates)  Aluminum has something like %60 less conductivity than copper!
Aluminum cavity

Here are the Q calculations between the two, first copper:

Frequency/Hz  2.44270000e+009
Energy/J      2.68158093e-007

Layer     Solid       Conductivity   Mue           Loss/W(peak)  Q
Copper (hard-drawn)   5.9600e+007    1.0000e+000   1.0743e-001   7.6618e+004
Resonator:Cavity                         9.3921e-002   8.7641e+004
Measurement Probe:Probe                  3.5290e-003   2.3325e+006
Power Probe:Probe                        2.4124e-003   3.4121e+006
Resonator:Tuning Plate                   7.5663e-003   1.0879e+006
Resonator:Tuning Plug                    4.3164e-006   1.9070e+009
PEC                   5.8000e+007    1.0000e+000   3.2168e-004   2.5588e+007
Power Probe:Probe Backing                1.1306e-004   7.2807e+007
Measurement Probe:Probe Backing_1        2.0863e-004   3.9455e+007
**Sum**                                            1.0775e-001   7.6390e+004

And then Aluminum

Frequency/Hz  2.44270000e+009
Energy/J      2.60714955e-007

Layer     Solid       Conductivity   Mue           Loss/W(peak)  Q
Copper (hard-drawn)   5.9600e+007    1.0000e+000   1.3125e-002   6.0973e+005
Resonator:Tuning Plate                   7.3542e-003   1.0882e+006
Measurement Probe:Probe                  3.4224e-003   2.3384e+006
Power Probe:Probe                        2.3446e-003   3.4134e+006
Resonator:Tuning Plug                    4.1946e-006   1.9079e+009
Aluminum              3.5600e+007    1.0000e+000   1.1812e-001   6.7750e+004
Resonator:Cavity                         1.1812e-001   6.7750e+004
PEC                   5.8000e+007    1.0000e+000   3.1734e-004   2.5219e+007
Power Probe:Probe Backing                1.1232e-004   7.1248e+007
Measurement Probe:Probe Backing_1        2.0501e-004   3.9036e+007
**Sum**                                            1.3157e-001   6.0828e+004

Note that this is version 2.00 of the cavity, built only in CST 2010 which uses the new static data for hard-drawn copper.

I have also been thinking about how to power the cavity and Kevin helped me nail down a few variables.  For example, because the cavity has a really high Q, we might be able to use a signal generator to power the cavity, even if it only outputs mW.   The benefit of the signal generator is that it has very fine frequency control and we can match it perfectly to the resonant frequency., thereby not reflecting unmatched frequencies.   Once resonance steady state has been reached, then very little would be reflected as well

As I understand resonance, if we have a high Q, it means that just a bit of input power at the right frequency can set it to resonant, whereas a low Q, means we need a lot more power to start and keep resonance alive.  From another perspective, if Q is high that also means we can use a very small input over a long period of time and end up with a very strong resonance.

Unfortunately, it will take much too long, on the order of days.  Most signal generators output 1mW and if the cavity can hold 100W at steady state, then it would take 100,000 seconds or 27 hours to reach.   27 hours is doable, however, Shawyer said that his cavity contained 17 MW of energy (17 megawatts!!, and it would simply take too long with only 1mW of input!

On a related note, there is something I don’t understand about Shawyer’s cavity – Shawyer said his cavity contains 17MW of energy, but at 1KW of power, it would take almost two thousand seconds (or ~ 30 minutes) to reach 17MW!!?  His test runs never last for more then a few minutes and movement occurs between 10 and fifteen seconds after startup.  Shawyer says that 15 second start-up delay isn’t pumping resonance either, but “The engine only starts to accelerate when the magnetron frequency locks to the resonant frequency of the thruster, following an initial warm up period.” – Hmm, thoughts anyone?

This status update turned out longer then anticipated because I wanted to be able to report something substantial and results seemed to be just one more simulation away.

The Conundrum – Why the Simulation Does Not Match Actual?


  • Simulations suggest rotated probes don’t make any difference
  • Upgraded computer to 16GB of faster memory and faster processor to handle larger simulations
  • Still trying to solve the conundrum – why the simulations don’t match real world results.

At the end of July, it was clear that simulated results were not matching the real world cavity, enough so that running a full-power test would not provide any useful information.  The problem is because of three things:

  • The resonant frequency of the cavity for the TE0,1 mode is 20Mhz higher then in the simulations (no matter the position of the tuning plate).
  • The insertion loss at the TE0,1 mode is 2.2dB versus an expected 0.5dB
  • The Q is 2500 versus an expected Q of 10,000+.

So far, here are all the things I have checked:

  • Size of cavity (length, diameter of narrow and large end) – cavity matches simulation
  • Size of probes (28mm, optimal size) – matches
  • Skin depth for microwaves – the electroplating thickness is more then enough (12.7 micrometers versus a skin depth of 2 micrometers)
  • Orientation of the probe –
    • In the simulation, I rotated the power probe by 5, 10, 15 and 25 degrees to see if it affected the resonant frequency, Q or insertion loss – it does not.  Below are the four examples which show the TE0,1 mode from 5 to 25 degrees (hold your mouse over to see the file name):
  • Tuning Plate at large end – I also ran a series of simulations with the tuning plate at the large end, but it didn’t lead to any conclusive results.  It did however, result in an interesting resonance in the center of the cavity:
  • Rebuilt the cavity model from scratch with better probes and a finer mesh for important parts.
    • Part of the problem with the old cavity model was that I had imported the probe from a previous model and the probe parameters (like diameter, height, etc.) could not be independently controlled (the power probe was a mirror of the measurement probe).  I also wanted to rebuild the model from scratch in the CST 2010 environment to double check all the variables and use any updated static data, for example, the conductivity of copper is now more accurate in CST 2010 because it differentiates between annealed and hard-drawn. (we use the later)
    • The two pictures below are good examples of the differences between v1 and v2 of the model:
      • The diagram below is from the first generation model which shows the sharp edges where the the probe loop connects and has a much rougher meshing.
      • The second diagram below is from v2.0 of the cavity model and has a finer mesh and probes that look much closer to the actual probe shape. The model still only takes about 350K+ tetrahedrals, but the meshing is now finer around important sections.

One thing I plan to check with the new version two is how the orientation and flatness of the tuning plate affects results.  My end goal is to see if I can duplicate what I see on the bench with a simulation. If I can, then I should be able to fix the problem.

I am currently running a simulation where I check to see how sensitive the TE0,1 mode is to the position of the probes from large end of the cavity.   That is one thing I haven’t check yet and from my preliminary results, it may be the cause of the problem.

In order to run higher accuracy simulations with more tetrahedrals (>500K), I upgraded my machine to 16GB of memory.  The CPU is also slightly faster now at 3.7Ghz instead of 3.2Ghz (stock) and the memory also runs at 1333Mhz versus 800Mhz ($350 in upgrades).  The upgrade also allows me to drop in the “Bulldozer” eight core AMD processor when it comes out in the fall.

No Great Resonances to be Found


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:


  • 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.


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:

New Probes Tested

I rebuilt the probes using a proper metal bending tool ($100 from Princess Auto) and got to within 1mm accuracy.

(The probe on the far right was my first attempt and you can see it is a bit out-of-round.  The 3mm diameter wire is stiff and difficult to work by hand.  Luckily, 3mm wire is readily available at the local Metal Supermarket and relatively inexpensive.)

After mounting the probes in the cavity, they are between 28mm and 29mm in diameter:

I say “between” because of two things – I drilled the threaded holes a little too far from the probe entrances (the white dielectric) which leads to a slight twisting (they should be straight up and down) and widens them a bit.

However, the new probes did not help the measured S-parameters get any closer to the simulations.


Expected (simulated)

The resonances below the TE0,1 mode have quite distinct shapes.  The most uniquely shaped and easiest to find resonance is the one that shows up at roughly 2.285Ghz (reference the expected results above).  (By resonance, I mean any place where the S1,2 (blue line) rises and the S1,1 (red line) drops)  The 2.285Ghz resonance is a large broadband resonance followed by two sharp resonances at 2.32Ghz and 2.34Ghz and then, between 2.33Ghz and 2.42Ghz, a long dropping S1,2 curve.  That series of resonances and the dropping S1,2 curve, I arbitrarily call “Marker Mountain”, also shows up in the measured data.

The problem is that simulated resonances above 2.42Ghz are not matching the simulated curves.  Simulated data shows another wide steep S1,2 (blue) line, a couple more resonances and then the TE0,1 mode.  The measured data above “Marker Mountain” does have a bunch of resonances, but none of them are as strong as they should be nor in the right places.

The only other difference between the actual cavity and simulated cavity was the tuning plate, which was easy to delete in the simulation and rerun – Here is what resulted (compare it to the measured above!)

Simulated Results without a Tuning Plate


Now the simulated and measure S-parameters are starting to look at least a bit more similar and more importantly, I think I can fix the problem!

A few asides:

  • Without the tuning plate, none of the four or five resonances above “Marker Mountain” are TE0,1 modes (I checked the field configurations for each and nada!)
  • I originally thought that removing the tuning plate would not change the S-parameter graph, except to move the resonances lower in frequency, but it would seem that is not the case.

My next task is to:

  • Mount the tuning plate and find the TE0,1 mode!

From last week:

  • Find a way to built mm accurate probes out of copper.  The good news is they are small and should be fairly inexpensive to get made.
  • Add the rest of the status updates to the blog. 82 posts now going back to 2007!
  • I will also run a monster simulation with the probe at 28mm, across a large frequency range that will probably take a day or so (likely running into hundreds of sample frequencies) .  With the resulting S-parameter chart, I can then compare it against the measured S-parameter chart and quickly find the TE0,1 mode.