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  Coating Ring-down Measurement Lab elog, Page 3 of 18  Not logged in ELOG logo
ID Date Author Typeup Category Subject
  388   Wed Aug 2 13:47:47 2017 ZachElectronicsModelingArm width Sweep


  • I ran a sweep of the width of the ESD arms. There appears to be a linear relationship across the modes except for mode 25. Mode 25 exhibits a very similar behavior as in the arm gap sweep. I realized that the abrupt change in direction (also noticeable in mode 14) is likely caused by the fact that the force profile is calculated as absolute value, there might be an exponential relationship that gets converted into that shape by the absolute value function. 

  389   Wed Aug 2 15:40:00 2017 ZachElectronicsModelingParameter diagram

I am posting a diagram of the geometric parameters that I swept. The only one not included is the vertical space between the ESD and sample that sweeps perpendicularly out of the image


  394   Mon Aug 7 13:19:48 2017 ZachElectronicsModelingNormalized data


  • I included the modal mass factors in the code and renormalized my data. The normalization has a noticeable impact, but does not change the general trends of the data
  • In fact the impact is not even significant enough to warrant a change in the ideal parameters I picked for the rectangular ESD in my interim report

  398   Tue Aug 8 16:20:24 2017 ZachElectronicsModelingRotated ESD


  • I rotated the ESD and calculated it's modal projections by rotating the data array that MATLAB extracts from COMSOL. I confirmed that this was properly done by plotting the profile and then computed and plotted both the rotated and normal projections.
  • The rotated ESD actually increases the force in some of the modes but decreases the forces in others. It markedly improved the force in 7 of the modes: 3, 6, 12, 18, 19, 22, and 26 while being quite weaker in about 4 of the modes: 9, 13, 14, and 15. This suggests that it may actually be useful to rotate the ESD as it excites some of the higher order modes a noticeable amount more. I am including plots of both modal profiles as well as a chart with mode numbers, shapes, and frequencies.


  399   Wed Aug 9 12:10:47 2017 ZachElectronicsModelingPreliminary improvement from ESD optimization


  • I created a plot of the ratio of the force in the optimized design to the force in the original design. The improvement factor is huge, some modes are excited by more than a factor of 100. I took the same ratio keeping the gap between the ESD and the sample constant and it decreased the excitation by almost a factor of 10. Keeping that gap constant, the geometric modifications to the ESD give an improvement factor ranging from almost 2 to almost 4 for most of the modes. Modes 10 and 25 are outliers but in the original geometry they are barely excited at all, so this could easily be a numerical artifact where those modes were excited at a minimum in the original geometry.

  400   Wed Aug 9 15:57:28 2017 ZachElectronicsModelingTriangular Geometry


  • I compared the triangular geometry to the original geometry and the excitation was only improved in 7 of the of 20 modes. In four of those modes the improvement factors ranged from almost 2 to over 3 while the other modes where only improved by about 25%. The other 13 modes were diminished drastically, 9 of them where less than half as excited. Given more time it may have been interesting to try and optimize the geometry of a triangular drive, but that would easily take the better part of a week. 

  401   Wed Aug 9 17:07:57 2017 ZacharyElectronicsModelingOptimization Summary


  • From the data I have gathered from a variety of MATLAB sweeps, I think that the optimal geometry I can produce has the parameters in the attached image. Neither the original or optimized drawing is to scale. The gap between the arms of the electrodes should be 1.25 mm, the arm width 0.55 mm, the arm length 16 mm, and the offset of the arms 3.5 mm.

  • It is also optimal to place the ESD as close to the sample disk as can reasonably be achieved, at around 0.5 mm away. Since the force on the disk scales exponentially with the distance from the ESD, decreasing that gap is the most substantial way to impact the excitation. Decreasing the gap from 1 mm to .5 mm increases the excitation of the modes by approximately a factor of 8.

  • From my simulations, the shift in geometry alone still has a useful impact on the excitation. Modes 1 and 3 are the only two modes that are less excited by the new geometry, mode 1 is 10% weaker  and mode 5 is 5% weaker. Modes 5 and 6 are nearly unaffected by the shift, mode 5 is 2% stronger and mode 6 is 5% stronger.  Modes 7, 18 and 19 are outliers, 7 is excited by a factor of 7, 18 by a factor of 4 and 19 by a factor of 17. The rest of the modes are improved by between a factor of 1.5 and 3. For mode numbers, shapes, and frequencies a plot is included.

  402   Thu Aug 10 10:47:54 2017 ZachElectronicsModelingGeometry Ratios


  • The attached plots compare the new and old geometries with .5 mm and 1 mm sample gaps. They are the same plot on linear and logarithmic axes respectively



  407   Tue Aug 15 00:09:01 2017 ZachElectronicsModelingESD Improvements


  • I did my best to increase the excitation in the higher order modes. By making the ESD narrower (a 6mm electrode overlap) the higher order excitation is improved drastically, by factors of between 10 and 30 for most modes.  I also created a double ESD (see image) that excited the modes by a factor of 3 or more better than the thinner drive. The plotted ratios are relative to the original geometry, but both of these geometries do better than previous geometries by factors of 2 or 3. 
  • After a lot of experimentation, I think that there are non-trivial numerical artifacts from the force projection method. I have noticed that in the modes that are almost entirely unchanged by modifications, both the mode and its doublet have equal regions of positive and negative antinodes directly above the ESD force profile. This can be more clearly seen in the attached mode plot, the rectangle represents the region of the ESD. As a result of this, when the mode shape and force profile are multiplied and integrated the resultant force is very small. I expect this does not appear in the lab because the modes could be rotated at a different angle relative to the ESD. I am not sure how to effectively resolve this, perhaps checking other rotations of the mode shapes could be productive though I am unsure how to effectively accomplish this. 

  409   Tue Aug 15 16:43:58 2017 ZachElectronicsModelingUnchanged Mode Insight


  • It appears to me that the major factor limiting the improvement of the modes that either remain equal or diminish is that the original design was already quite good at exciting those modes. As can be seen in the attached plots, the original design is about as well centered over the 5 modes as a rectangle on the x axis can be. As a result, maintaing a constant potential on the ESD it would be difficult to improve the coupled force without specifically tailoring the force profile to a certain mode.
  • In order from left to right, the frequencies of the given modes are 14.2 kHz, 16.2 kHz, 16.3 kHz, 23.8 kHz, and 27.4 kHz.

  411   Wed Aug 16 10:04:24 2017 ZachElectronicsModelingESD along edge


  • I placed created a very narrow ESD placed along the edge of the sample. The thought behind this is that it will not cross over into any other modes that will cancel out the force. However, it does not appear to couple force into enough of the area of the disk to cause a worthwhile improvement, as can be seen in the plot, more modes lost amplitude than gained and some were worse by as much as a factor of 1000.

  412   Wed Aug 16 11:36:13 2017 ZachElectronicsModelingMiddle ESD


  • I created a model with a drive offset in the middle. It improved one of the modes by a factor of 14 or so, but overall, it diminished the vast majority of the modes by as much as a factor of 100. 

  414   Wed Aug 16 16:05:09 2017 ZachElectronicsModelingTwo ESD First test


  • I created a model with two ESD's, essentially a combination of my previous two attempts with one ESD on the edge and one closer to the center of the disk. This test was quite successful compared to previous trials, the improvement seems to be on an average of a factor of 10. No modes are weakened by this design. I am going to run a sweep adjusting the central ESD and see what placement is best.
  • Attached is an overlay of the force profile and all of the modes. Note that this image is very large, and is useful as a digital reference or very large print only.

  415   Thu Aug 17 14:19:04 2017 ZachElectronicsModelingTwo ESD Optimization


  • I ran a sweep of the position of the middle ESD to determine the optimal arrangement. From the original geometry I offset the central ESD between -2 mm and 11 mm. From the plots below I conclude that the optimal geometry is the one that is shifted 2 mm to the right of the original design. 
  • The first plot is the sweep data as a ratio to the data of the current geometry for all modes. The second plot is the root mean square of the eight high frequency modes that change the most over the course of the sweep, those are modes 9, 11, 13, 14, and 17-20. The frequencies of those modes in order are 9.5kHz, 11 kHz, 14 kHz, 16 kHz, 19 kHz, 20 kHz, 21 kHz, and 23 kHz. There is a very apparent peak at 2 mm which is the driving force behind my conclusion that it is the optimal design. The next two plots are the 2mm shifted design and the original design as ratios to the original geometry. The 2mm shifted geometry is much more consistent than the original design, there is a very noticeable minimum in the original design (improvement by a factor of 2) for the 23 kHz mode that is resolved in the shifted design to a factor of 9.
  • The final plot are ratios of the two designs relative to each other. I found this plot useful to convince myself that the 2 mm shifted design was better than the original, particularly in the region above 1.5 kHz.

  416   Thu Aug 17 23:34:51 2017 ZachElectronicsModelingOptimized ESD Drawing


  • I made a drawing of the Optimal ESD design. The bottom combs (right hand in the rotated image) are set to ground and the 5 arm comb is set to a positive voltage and the 2 arm comb is set to a negative voltage. 

  417   Fri Aug 18 10:50:53 2017 ZachElectronicsModelingESD's with positive voltage


  • With both electrodes driven at a positive voltage, the results are still an improvement over the original design, but by smaller factors, particularly in 3 of the higher frequency modes at around 2 and 3 kHz. With another parametric sweep I may be able to find a better design. The opposite voltage was useful because it could couple force in opposite directions to adjacent anti-nodes with opposing signs. An adjusted configuration could probably be found to interact with anti nodes with the same signs. An alternative option would be to leave the radial position of the more central ESD constant but rotate it relative to the sample by some amount, though this would also require an additional parametric sweep as well as a much larger ESD. 

  419   Fri Aug 18 14:15:47 2017 ZachElectronicsModelingSame Voltage ESD Sweep


  • I ran a sweep of the central position in the two ESD setup with both set at the same voltage. There were two designs that maximized excitation by different metrics, the design with a 3 mm shift from the original design maximized excitation overall, but the 20 kHz mode was worse by a bout a factor of 5. The design with a -2 mm shift maximized the high frequency modes, particularly the modes most affected by the shift.
  • MATLAB crashed shortly after the sweep so I will have to recreate the RMS plots of the dynamic modes later.


  420   Fri Aug 18 15:10:23 2017 Zach, GabrieleElectronicsModelingESD prototype


  • We created a prototype of PCB for the ESD design. Unfortunately the orientation of the two combs was flipped, so it will require some creative mounting to get right. The final design had a 6 mm offset between the two combs, .5 mm traces and 1 mm gaps between them The vertical traces are 12 mm long and there is a 3.75 mm gap between the end of the vertical traces and the opposite horizontal one. The ESD will arrive on Tuesday to be installed Wednesday and we will see how the new design works out.


  421   Wed Aug 23 14:11:13 2017 Zach, GabrieleElectronicsMeasurementsInstalling ESD Prototype


  • Installed ESD Prototype design by taping it to the older design, we then lowered the mount until it was as close as we could reasonably get it. The new PCB lines up when the top of the new PCB is lined up with the last electrode on the old one. The new PCB was slightly too narrow, the mounting holes are very close to the edge of the PCB, this can easily be corrected in later models.
  • Installed sample S1600541 into the single sample apparatus
  • Roughing pump on at 12:32
  • Turbo pump on at 2:28pm

Link to image1.JPG Link to image2.JPG

  456   Tue Jan 30 15:56:36 2018 Gabriele, CraigElectronicsConfigurationTemporary data acqusition for PSL lab beat note and accelerometers

We set up the model x3tst to acquire at 65kHz four signals coming from the PSL lab:

  • X3:TST-BEAT_OUT_DQ: beat note
  • X3:TST-ACC_X_OUT_DQ: accelerometer X
  • X3:TST-ACC_Y_OUT_DQ: accelerometer Y
  • X3:TST-ACC_Z_OUT_DQ: accelerometer Z
  9   Mon May 2 11:46:45 2016 GabrieleFacilityDaily ProgressTable and vacuum chambers in the lab

Elogs for the new Coatin RIng-down MEasurement lab had to start somewhere, so here is a couple of pictures of the optical table with shorter legs and of one of the two vacuum chambers that have been moved in.

  10   Tue May 3 11:57:47 2016 GabrieleFacilityDaily ProgressTable and vacuum chambers in the lab

We discovered a couple of days ago that the table was sitting on three legs only and the fourth one was dangling. I managed to adjust the height of the fourth leg using the large screw on the leg support. Now the table is properly supported by all four legs.


Elogs for the new Coatin RIng-down MEasurement lab had to start somewhere, so here is a couple of pictures of the optical table with shorter legs and of one of the two vacuum chambers that have been moved in.


  21   Tue Jun 7 14:07:55 2016 GabrieleFacilityGeneralRack and workstation

I moved the unused rack from the Crackling Noise lab to the C.Ri.Me lab. It will be used for the new cymac. I also started putting the new workstation together, but I'm missing some adaptors for the monitors.

  31   Thu Jul 7 17:44:11 2016 GabrieleFacilityDaily ProgressVacuum chamber tests

[Alena, Gabriele]

This afternoon we opened the tall belljar vacuum chamber, and took everything out of it. All the stuff that was inside the chamber is "temporarily" stored on the floor beside the optical table.

We installed a "spacer" into the chamber, made from one of the optical table legs that were sitting in the hallway. We installed one of the aluminum base plates on top of it, so that the optical components will be at the level of the viewport. Another leg and a thinner base plate are installed out of the chamber, at a similar level.

After this we closed the chamber with one of the flats used for the old chamber, and a rubber o-ring. We started the roughing pump, quickly reached a pressure below 1 mTorr and switched on the turbo pump. Unfortunately, it seems that the low pressure gauge is not working properly, so we don't know what's the pressure right now. We'll check the gauge and controller tomorrow morning and swap it out if needed.

  33   Fri Jul 8 15:26:37 2016 AlenaFacilityDaily ProgressVacuum chamber tests

Fixed the 307 gauge controller (a missing contact on the rair panel). The low pressure gauge was connected to 1G port and has measured 1.7E-6 torr. We are not sure since how long the turbo was operating (no vacuum logger yet).



  36   Mon Jul 11 14:56:45 2016 AlenaFacilityDaily ProgressVacuum chamber tests

Installed a gate valve between the roughing and tubbo pump. See below a pump down curve. The convection gauge is not calibrated. the turbo started at 14th min (at about 3 torr)

  38   Mon Jul 11 17:04:06 2016 AlenaFacilityDaily ProgressVacuum chamber tests

At 5pm the pressure was 6.5e-6 torr.

Checked again at:

  • 9am, pressure was 2e-6 torr
  • 11:30am, pressure was 1.5e-6 torr
  • 5pm, pressure was 1.4e-6 torr

Installed a gate valve between the roughing and tubbo pump. See below a pump down curve. The convection gauge is not calibrated. the turbo started at 14th min (at about 3 torr)


  41   Thu Jul 14 16:56:00 2016 AlenaFacilityDaily Progresstest vacuum system

Please see prosidures for pumping down and venting with air for the test vacuum chamber here https://dcc.ligo.org/T1600304

  45   Sat Jul 16 14:15:44 2016 GabrieleFacilityDaily ProgressPump down started

Following Alena's procedure, at about 1:30pm LT I started the chamber pump down. At 14:15pm LT the pressure was still 240 mTorr

At 6:20pm the pressure was about 70 mTorr, so I started the turbo pump.

  46   Mon Jul 18 13:39:45 2016 GabrieleFacilityDaily ProgressPump down started

Today at 1:40pm pressure is 8.5e-7 Torr


Following Alena's procedure, at about 1:30pm LT I started the chamber pump down. At 14:15pm LT the pressure was still 240 mTorr

At 6:20pm the pressure was about 70 mTorr, so I started the turbo pump.


  52   Tue Jul 19 17:15:37 2016 GabrieleFacilityDaily ProgressVacuum pressure acquired

[Alena, Gabriele]

We connected the analog output of the vacuum gauge controller to one of the ADC channels. The signal is calibrated so that the pressure is 10^(X3:CR1-PRESSURE_LOGTORR_OUT). Unfortunately the RTG does not know how to compute 10^x...

  65   Wed Jul 27 11:27:11 2016 GabrieleFacilityGeneralPumps stopped and venting

11:25am LT: closed valve between roughing and turbo pumps, switched off both pumps. Turbo pump is slowing down

After lunch I opened the chamber and removed everything from the inside.

The chamber around the vacuum gauge is really dirty now, see picture:

In addition, the electrostatic driver shows some signs of "burn" even though it was still working quite well. Unfortunately, whatever happened contaminated our sample:

  66   Wed Jul 27 15:43:02 2016 GabrieleFacilityDaily ProgressVacuum chamber dismantled and ready for cleaning

[Alena, Gabriele]

As decided at out Red Door meeting, we're going to clean the vacuum chamber and move it to the large table, which will be enclosed in a clean room.

So today we disassembled and packaged the vacuum chamber, which is now ready to be trasnspoted to be cleaned and baked.

  81   Sat Aug 13 11:17:17 2016 GabrieleFacilityDaily ProgressSpot the differences

  90   Fri Aug 19 13:46:55 2016 Alena, Calum, Jon, Liz, Steve, GabrieleFacilityDaily ProgressClean room and vacuum complete

This morning we installed the clean room curtains and washed them. It turns out that the air filters are supposed to be powered at 277V (?) instead of 115V. So right now the flux is quite low. We are looking into the problem: either replace them with 115V modules or install a small transformer.

We also installed the vacuum chamber on the table and connected all the pumps and gauges. There are no leaks and we could pump down easily the empty chamber. We left for lunch when the pressure was at a few 1e-6 Tor and still going down.

  113   Thu Sep 15 11:23:13 2016 GabrieleFacilityGeneralChamber open

Turbo pump off and spinning down at 9:37am LT. Pumo completely stopped at 11:15am LT

Openend the chamber and removed the sample at ~11:20am LT

  126   Mon Sep 26 15:54:01 2016 GabrieleFacilityConfigurationMoved vacuum controllers

I moved the turbo pump controller out of the clean room. Also, I installed the gauge controller on the Cymac rack.

  216   Tue Nov 29 17:02:06 2016 GabrieleFacilityNoise huntingSuspending the roughing pump

I suspended the roughing pump with four springs. The reduction of the 58 Hz peak is similar to what I got when the pump was sitting on a box. So most of the coupling is due to acousting noise.

  265   Thu Jan 19 12:49:17 2017 GabrieleFacilityVacuumSkyhook installed

The SkyHook has been put in place and bolted down to the floor.

  430   Thu Sep 14 15:59:10 2017 GabrieleFacility All wrapped up for Saturday plumbing work


  26   Wed Jun 29 16:44:17 2016 GabrieleGeneralConfigurationFirst disk eigenfrequency

The following table shows the lowest eigenfrequency (Hz) for different sizes of disks

Diameter \ Thickness [mm] 0.125 0.250 0.500 1.000
75 137 273 545 1090
100 77 154 307 613
150 34 68 136 272
200 19 38 77 153

  37   Mon Jul 11 15:21:12 2016 GabrieleGeneralDaily ProgressOne disk installed into the chamber

[Alena, Gabriele]

We attached one of the silicon lenses to a 1" optical post using some kapton tape, and installed it into the vacuum chamber. We built a simple periscope using standard optical component, and managed to send the optical level beam into the disk and back out.

To set a reference for the horizontal position of the disk we used the LMA method: we put a small container with water in place of the disk, and mark on a reference where the reflected beam hits out of the chamber:

We then put back the disk, and aligned it to have the beam hitting the same position. During pumdown we couldn't see any shift of the disk, judging from the position of the optical lever beam.

  44   Fri Jul 15 17:56:50 2016 GabrieleGeneralDaily ProgressQPD connected to digital system

I connected the QPD to the ADC interface with a temporary cable running on the floor.

I could get signals. I still have a problem with the digital system: I can't access test points with dataviewer, but I get them with DTT. This will have to be fixed.


  48   Mon Jul 18 14:29:07 2016 GabrieleGeneralDaily ProgressStatus of the test setup

I checked that the QPD electronics works as expected, and that I can acquire the signals using the ADCs. A new model (x3cr1) is up and running. It acquires the four quadrants, convert them from counts to volts, and compensate for the analog whitening filter. The four quadrant signals are X3:CR1-Q1_OUT, X3:CR1-Q2_OUT, X3:CR1-Q3_OUT, X3:CR1-Q4_OUT.

A matrix is used to compute the X and Y signals, defined as X = (Q1+Q4-Q2-Q3) and Y = (Q2+Q4-Q1-Q3). The SUM signal is also computed as SUM = (Q1+Q2+Q3+Q4).

Finally, the X and Y signals are normalized with the sum to produce X3:CR1-X_NORM_OUT and X3:CR2-Y_NORM_OUT.

A filter bank (ESD) is connected to the DAC channel #0 to produce the excitation that will be sent to the high voltage amplifier. I checked that the DAC is working properly (adding offsets). The input to the ESD filter bank is in volts.

The normalized X and Y signals, the sum of all four quadrants and the output of the ESD driver filter bank are saved to frames. The model runs at 65kHz.

  49   Mon Jul 18 17:46:04 2016 GabrieleGeneralDaily ProgressFirst look at QPD signals

Here's the first spectrum of the QPD X and Y signals, acquired with the digital system. Roughing and turbo pumps are still on.

The noise floor seems quite non stationary. To be investigated.

  53   Tue Jul 19 17:21:48 2016 GabrieleGeneralDaily ProgressFirst modes excited!

We can't generate any arbitary signal with the real time model, since awg is not working properly yet. For the moment being I added a uniform random number generator in the model (only option I found for noise) and send it into the ESD filter bank. In this way I can generate band-passed noise.

I plugged in the DAC output to the HV amplifier input, and I could send white noise to the electrostatic drive. Behold: I was able to excite quite a few modes. In the following trace blue is a reference and red is right after I sent white noise (3 V peak to peak) to the disk for a while (less than 1 minute). Excitation stopped at 4:56pm LT.

Using COMSOL and tuning the disk thickness at 1.018 mm I could hit the frequency of the first butterfly mode (1109 Hz) and get a reasobly good estimate of the other modes.

After about half a hour of ring down, most of the modes are gone but the two lowest are still going strong.

Note that the flattish background noise seems to be generated by some sort of glitches. I tried to swap the laser and the power supply, without change. More investigations are needed.

Note that the roughing pump was still on during the test.

  56   Thu Jul 21 12:10:14 2016 GabrieleGeneralDaily ProgressGlitch hunting

Yesterday I could clearly see the glitches as jumps in the time domain plot of X and Y signals, and trace them to somewhat harder to see jumps in the quadrant signals. 

  • I tried to catch them with an oscilloscope looking at the analog signals, but couldn't see any. However, for a brief period I had a persistent square wave oscillation in all transimpedance stages
  • I hooked the single ended output of the whitening filter to an ADC, and I could see the jumps there too. So I can exclude it's a problem of the differential drivers

One suspect was an intermittend oscillation of the transimpendance amplifier, so I looked into the schematics (D1600196) to see what could be the optimal value of the compensating capacitor C7. Following some useful notes online I computed the optimal value of C7 to be close to 2pF (instead of 10pF). I used 30-35 pF as the QPD capacitance, and 10 MHz has the gain-bandwidth product of the opamp. I swapped all 10pF capacitors with 2pF. After this I can still see the glitches in the spectra, but I can't find them anymore in the time domain. So things seem to have improved, although I still have annoying glitches.

Rich suggested to test the stability of the transimpendance stage by driving the output with a square wave and looking for the signal ringing. Here's his note:

I tried this for both the TI stage and the whitening stage, using 1k and 1uF and a square wave at 10 kHz. Here are the results, which look reasonable to me (firts is the TI, ringing at about 0.5 MHz, second is the whitening, almost no ringing):

So now I'm quite confident that the electronics is working. In the first trace you can see some intermittend background noise, due to the ambient light leaking into the QPD.

More investigations will follow.

  68   Thu Jul 28 14:01:27 2016 AlenaGeneralDaily ProgressClean room

Ordered the clean room (hardware+hepa filters) and vacuum gauges

  70   Fri Jul 29 14:08:31 2016 GabrieleGeneralDaily ProgressPeak tracking code for real time model


I wrote a C function to reconstruct the amlplitude and frequency of a line. It can be added as a block into a real time monitor. The idea is to use it to track in real time the frequency and amplitude of the disk modes, during the ring down. I did some tests and finally managed to get the function to compile and run on the cymac2 (the crackling lab cymac).

The following plot shows a simulation, since I can't run the code on the new cymac and I don't have the disk installed anymore. The top panel gives the amplitude of a decaying line, and the bottom panel the frequency offset from a reference local oscillator (more below). The nominal values are an initial amplitude of 1, frequency of 1109.375 Hz to be compared to a 1109.0 local oscillator. The fitted decay time is 10.005 seconds, to be comapred with 10 seconds nominal. There is some additive gaussian noise, that causes the ring down to be unmesurable after about 70 seconds of data.

This code will be used for real time estimation of the disk modes, once theot frequency has been roughly estimated with FFTs. The estimation of the frequency work remarkably well. In the first 20 seconds the mean value is 0.3747 Hz, with a standard deviation of 1.5 mHz. When the SNR gets worse (between t=30s and t=50s) the mean value is 0.3745 with a standard deviation of 20 mHz. 

Because of the way it's built (see below) the code is sensitive to DC offsets, so the input signal must be high-passed.  

Details on the implementation

The code is based on demodulation of the input signal with a reference local oscillator thta must have a frequency as close as possible to the line we want to track.  The inputs to the block are: the signal to be monitored, sine of the local oscillator, cosine of the local oscillator. The outputs are: amplitude squared of the peak, frequency offset in Hz from the local oscillator.

Here's the math. Let's assume that the signal is

x(t)=A \sin (2\pi f t + \phi)

and the local oscillator has a frequency f0:

s(t)= \sin (2\pi f_0 t) \qquad c(t)= \cos (2\pi f_0 t)

The code multiply the signal by the two local oscillators and average the result over 65kHz / 8 Hz samples. Therefore we get two output streams at 8 Hz which are

\left< x(t) s(t) \right> = -\frac{A}{2} \sin\left[2\pi(f-f_0)t + \phi \right]

\left< x(t) c(t) \right> = \frac{A}{2} \sin\left[2\pi(f-f_0)t + \phi \right]

Then the sum of the two squared 8 Hz streams give an estimate of the amplitude squared. The code computes this every second

\hat A = 4 \left[ \left<x(t) s(t)\right>^2+\left<x(t) c(t)\right>^2\right]

while the arctangent of the ratio gives a phase that varies linearly with time.

\arctan \frac{\left< x(t) c(t)\right>}{\left< x(t) s(t)\right>} = \phi + 2\pi(f-f_0)t

For each of the 8Hz samples the code computes the arctangent (using a home-brewed function based on a lookup table, since we can't import math.h in the RCG). It unwraps it, and then every second fit a line to the unwrapped arctangent, to estimate the frequency offset with respect to the local oscillator.

The C function has some parameters hard coded: the main sampling frequency (65536 Hz), the number of points per second to use for the frequency estimation (8 Hz), the fact that the output is computed every second. The first two parameters can be changed, the third one cannot for the moment being.

  74   Mon Aug 8 10:42:46 2016 GabrieleGeneralGeneralDependency of eigenmode frequencies on thickness and diameter

I ran a set of COMSOL simulations to determine the dependency of the frequency of each eigenmode on the disk thickness and diameter, within the tolerances. I chose wide ranges: diameter 75.0 +- 0.1 mm and thickness 1.0 +- 0.1 mm, much more than the expected tolerances. It turns out that the frequencies depends almost exactly linearly on both variables: mostly on the thickness and negligibly on the diameter. The following plots shows: the mode shape and frequency (left), the frequency dependency on the two variables (center), the residual of a linear fit and the functional form of the fit (right).

I'm including only the modes that will be measurable by our system (no motion in the center, frequency below 32kHz. Since the disks in my simulation is completely round, I'm showing only one mode for each doublet.

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