40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  Coating Ring-down Measurement Lab elog, Page 17 of 18  Not logged in ELOG logo
ID Date Author Type Categoryup Subject
  862   Tue Apr 14 12:19:57 2020 GabrieleGeneralMeasurementsS1600775 S1600784 S1600788 S1600791


  • 12:18 pm in chamber
    • S1600775 in CR1
    • S1600784 in CR2
    • S1600788 in CR3
    • S1600791 in CR4
  • 12:19 pm roughing pump on
  • 12:29 pm turbo pump on
  863   Tue Apr 14 18:35:59 2020 GabrieleGeneralMeasurementsS1600785 S1600789


  • 6:35pm in chamber
    • S1600785 in CR1
    • S1600789 in CR2
  • 6:40pm roughing pump on
  • 6:48pm turbo pump on
  864   Thu Apr 16 14:23:11 2020 GabrieleGeneralMeasurementsS1600775 S1600784 S1600788 S1600791


  • 2:21 pm in chamber
    • S1600775 in CR1
    • S1600784 in CR2
    • S1600788 in CR3
    • S1600791 in CR4
  • 2:22 pm roughing pump on
  • 2:30 pm turbo pump on
  865   Fri Apr 17 10:18:17 2020 GabrieleGeneralMeasurementsS1600785 S1600789


  • 10:17am in chamber
    • S1600785 in CR1
    • S1600789 in CR2
  • 10:20am roughing pump on
  • 10:28am turbo pump on
  866   Thu Apr 23 14:02:25 2020 GabrieleGeneralMeasurementsS1600776


  • 2:00pm in chamber
    • S1600776 in CR1
  • 2:02pm roughing pump on
  • 2:12pm turbo pump on
  867   Fri Apr 24 10:53:40 2020 GabrieleGeneralMeasurementsS1600801 S1600802 S1600803 S1600804


  • 10:51 am in chamber
    • S1600801 in CR1
    • S1600802 in CR2
    • S1600803 in CR3
    • S1600804 in CR4
  • 10:52 am roughing pump on
  • 11:00 am turbo pump on
  868   Mon Apr 27 10:26:29 2020 GabrieleGeneralMeasurementsS1600805 S1600806 S1600807 S1600808


  • 10:25 am in chamber
    • S1600805 in CR1
    • S1600806 in CR2
    • S1600807 in CR3
    • S1600808 in CR4
  • 10:28 am roughing pump on
  • 10:38 am turbo pump on
  869   Thu May 28 11:43:19 2020 GabrieleGeneralMeasurementsS1600801 S1600802 S1600803 S1600805 S1600806


  • 11:40 am in chamber
    • S1600801 in CR1
    • S1600802 in CR2
    • S1600803 in CR3
    • S1600805 in CR4
    • S1600806 in CR0
  • 11:43 am roughing pumps on
  • 11:53 am turbo pump CR1-4 on
  •  turbo pump CR0 on not on yet
  870   Fri May 29 10:10:51 2020 GabrieleGeneralMeasurementsS1600806


  • 10:00 am in chamber
    • S1600806 in CR1
  • 10:05 am roughing pumps on
  • 10:15 am turbo pump CR1-4 on
  871   Tue Jun 2 10:16:40 2020 GabrieleGeneralMeasurementsS1600801 S1600802


  • 10:15 am in chamber
    • S1600801 in CR1
    • S1600802 in CR2
  • 10:20 am roughing pumps on
  • 10:30 am turbo pump CR1-4 on
  872   Fri Jun 5 18:55:27 2020 GabrieleGeneralMeasurementsS1600803 GaAs


  • 6:50 pm in chamber
    • S1600803 in CR1
    • GaAs in CR2
  • 6:55 pm roughing pumps on
  • 7:05 pm turbo pump CR1-4 on
  873   Tue Jun 9 11:04:28 2020 GabrieleGeneralMeasurementsGaAs S1600805


  • 11:00 am in chamber
    • GaAs in CR1
    • S1600805 in CR2
  • 11:04 am roughing pumps on
  • 11:15 am turbo pump CR1-4 on
  874   Mon Jun 15 19:32:31 2020 GabrieleGeneralMeasurementsS1600803 GaAs


  • 7:32 pm in chamber
    • S1600803 in CR1
    • GaAs in CR2
  • 7:36 pm roughing pumps on
  • 7:46 pm turbo pump CR1-4 on
  875   Tue Jun 16 15:43:29 2020 GabrieleGeneralMeasurementsS1600805


  • 3:42 pm in chamber
    • S1600805 in CR1
  • 3:45 pm roughing pumps on
  • 3:55 pm turbo pump CR1-4 on
  876   Thu Jun 18 17:46:51 2020 GabrieleGeneralMeasurementsS1600806


  • 5:45 pm in chamber
    • S1600806 in CR1
  • 5:50 pm roughing pumps on
  • 6:00 pm turbo pump CR1-4 on
  877   Tue Jun 23 16:22:42 2020 GabrieleGeneralMeasurementsS1600806


  • 4:20 pm in chamber
    • S1600806 in CR1
  • 4:21 pm roughing pumps on
  • 4:31 pm turbo pump CR1-4 on
  878   Wed Jun 24 14:17:45 2020 GabrieleGeneralMeasurementsS1600805 S1600806


  • 2:26 pm in chamber
    • S1600805 in CR1
    • S1600806 in CR1
  • 2:27 pm roughing pumps on
  • 2:37 pm turbo pump CR1-4 on
  879   Thu Jun 25 08:49:24 2020 GabrieleGeneralMeasurementsS1600803 S1600805 S1600806


  • 8:47 am in chamber
    • S1600803 in CR1
    • S1600805 in CR2
    • S1600806 in CR3
  • 8:49 am roughing pumps on
  • 9:00 am turbo pump CR1-4 on
  880   Wed Jul 1 13:43:53 2020 GabrieleGeneralMeasurementsS1600803 in


  • 1:42 pm in chamber
    • S1600803 in CR1
  • 1:43 pm roughing pumps on
  • 1:53 pm turbo pump CR1-4 on
  881   Thu Jul 2 14:43:09 2020 GabrieleGeneralMeasurementsS1600794 S1600795 S1600796 S1600797


  • 2:41 pm in chamber
    • S1600794 in CR1
    • S1600795 in CR2
    • S1600796 in CR3
    • S1600797 in CR4
  • 2:42 pm roughing pump on
  • 2:52 pm turbo pump on
  882   Tue Jul 7 15:40:44 2020 GabrieleGeneralMeasurementsS1600809 S1600810 S160081 S1600812


  • 3:39 pm in chamber
    • S1600809 in CR1
    • S1600810 in CR2
    • S1600811 in CR3
    • S1600812 in CR4
  • 3:40 pm roughing pump on
  • 3:50 pm turbo pump on
  351   Thu Jun 22 13:16:37 2017 ZachElectronicsModelingBeginning with COMSOL


  • 4:30 pm- Installed COMSOL, began modeling current ESD by creating parameters and the first arm of the comb
  352   Thu Jun 22 15:37:20 2017 ZachElectronicsModelingBeginning modeling


  • Created the geometry of the ESD by creating blocks and joining them with Unions. I then created a block to serve as the domain and added air to that region
  • This plot is a combination of a Surface plot of the potential and a Streamline plot of the electric field
  • I created another model of the ESD with more accurate measurements to the real thing and added the silica disc to the model
  353   Fri Jun 23 12:02:12 2017 ZachElectronicsModelingPlots


  • I created plots of the E field and potential from my rough model of the ESD. This model has 1mm electrode arm widths and spacings, the length of each arm is 16 mm, and the resulting total size is 38mm x 20 mm x 0.1 mm. One comb has ten arms while the other has nine to match the actual ESD currently in use in the lab. 
  • I set the ten arm comb to a potential of 100 V and the other to ground. I then used physics controlled mesh with an extremely fine element size to computer the simulations. With mesh sizes larger than extra fine, there was clearly non-physical error in the electric field and potential graphs that appeared as inexplicable field lines, spikes, and coarseness in the plots. 
  • To create readable plots of the potential I created a Cut Plane in the center of the ESD perpendicular to both the arms and the plane of the device. The plots are attached with a milimeter length scale. I created a filled contour plot of the potential that is very clean, I tried a couple of different options for the electric field because it is harder to represent well. I created a contour plot for the norm of the electric field as well as superimposing a streamline plot of the field lines over that. Everything behaves generally as expected though I do suspect the spikes in electric field at the edges of each electrode are due to the fact that they are sharp corners and not smooth edges.



Attachment 1: Potential.png
Attachment 2: E_w_Lines.png
Attachment 3: Mesh.png
  356   Tue Jun 27 14:17:47 2017 ZachElectronicsModelingFurther plots and improving models


  • I built a new model of the ESD to determine whether or not the spikes in the electric field at the corners was affecting the results enough that it had to be accounted for in further models. To create the model, I created a 2D profile of the arm used in my original model and filleted the corners at a radius of .05 mm, since the electrode model is .1 mm thick, this made completely rounded edges. In creating this model I caught an earlier mistake in the original one, I only set one half of the surface of the electrodes to have a potential or to ground, the "bottom" was left with no charge. I fixed this mistake and then compared the two models at a potential of 1000 V. For speed of computation I ran both models with a finer mesh size and then calculated the electric field at approximately the middle of the ESD, 1mm above the fourth electrode arm. For the rounded electrodes the field had a value of 84024 V/m and for the rectangular electrodes the field had a value of 80728 V/m, which is less than a 4% difference in field magnitude. Furthermore, the field shapes appear nearly indistinguishable; I am confident from this test that I can proceed modelling the arms of the ESD as rectangles.
Attachment 1: E_field_corner.png
Attachment 2: E_field_round.png
  359   Thu Jun 29 16:40:41 2017 ZachElectronicsModelingAccurate model and force profile


  • I created a much more accurate model of the current ESD setup from the technical drawings. My resulting ESD has dimensions of 21.3x24.3x.1mm with 1 mm spacings and 17.5 mm long electrode arms. The sample has a diameter of 75 mm and thickness of 1mm, the ESD is 1mm below the sample in the current model. I still have to compare the technical drawings to confirm that is the actual distance in the current lab setup.
  • I was able to calculate the force profile on the disk from the ESD. COMSOL struggled to resolve the data with a small mesh size over the whole domain, so I created a region of extremely fine mesh around the ESD and the disk and then made the rest of the mesh size normal sized. Over the domain near the ESD my mesh size ranges from 2.5*10-3 to .25 mm and over the rest of the domain it's automatically setup at the normal size.
  • The force on a single dipole is given as F = (P \cdot \nabla)E, since fused silica is isotropic it's polarization is proportional to E so F = \chi_e \epsilon_0 \nabla (E^2). The electric suscepitibility of fused silica is 1.09, I plotted the profile of the force perpendicular to the plane of the disk and exported data files of the full vector quantity of the force for use with Matlab.


  360   Fri Jun 30 11:02:18 2017 ZachElectronicsModelingMatching Forces


  • I adjusted the plot parameters slightly so that it only showed the actual force profile on the sample in the direction perpendicular to the sample surface. Additionally I compared the two methods of computing the force, as \vec{F} = -(\vec{P}\cdot \nabla)\vec{E} and as \vec{F} =- \chi_e \epsilon_0 \nabla \vec{E}^2. The profile of the force in both instances appear equal, but they differ in magnitude by exactly a factor of 2, I plotted the force computed with the explicit polarization doubled and the force magnitudes matched exactly. I'm still not entirely sure where this factor of two could be coming from.

  361   Fri Jun 30 16:27:56 2017 ZachElectronicsModelingDouble Checking Model


  • In order to confirm the accuracy of my model I checked some easily computable quantities between what real values and what COMSOL produced. My expected electric field magnitude between the electrodes is 106 V/m and COMSOL reads out 1.015*10which is less than a 2% error. When I went to compute the electric field gradient however, I discovered that I had been calculating my derivatives wrong, I was calculating full derivatives when I needed partial derivatives. Due to some subtleties of the numerics involving curl calculations are the order of the variables, in order to calculate a partial I belive that I have to map the results of the electric field to Lagrange elements.
  363   Wed Jul 5 12:01:51 2017 ZachElectronicsModelingForce plots-Correct plots, force issue


  • I sorted out my mathematical lapse in logic and computed the correct force profiles in the perpendicular direction in both disks. The issue is that now the force profiles don't match up. The fact that there is a measured force distribution for the E^2 case outside the disk is only an artifact of the numerics because it is being calculated only from the electric field data which is defined outside the sample. It can be easily removed for final plots once the force distributions are matched by either redefining the cut plane or putting a data filter specifically on the E^2 plot. The jumps in the E^2 plot suggest that the meshing is still too large, I will try to fix this first, hopefully it will help resolve the difference.

  364   Wed Jul 5 16:40:51 2017 ZachElectronicsModelingForce disparity-improvement


  • In order to improve my data I shrunk the region of the finer meshing slightly and made the mesh even smaller and then recalculated the force profiles. This time I tried sampling regions inside the disc rather than immediately at the surface. The attached graphs were sampled at the center of the disc. These two techniques vastly improved the data, now the profiles appear the same, but the magnitudes differ by a factor of 2 again. Previously this was due to an error in my calculation of the force, now I do not believe this to be the case. I will leave my work here for the purposes of my first report, it is an interesting result. I also restricted my data set to the finely meshed box which resolved the earlier data display issue. 

  365   Thu Jul 6 12:08:35 2017 ZachElectronicsModelingChecking physical parameters


  • I compared the electric field and the polarization to make sure that those calculations made sense. Since P = \epsilon_0 \chi_e E due to the linear dielectric, I plotted the electric field and the polarization divided by the proportionality constant and they match exactly.
  • This confirms both the constant value and the polarization distribution but gets me no closer to resolving the factor of two

  366   Thu Jul 6 12:48:54 2017 ZachElectronicsModelingResolving the factor of two


I resolved the factor of two from Griffiths' discussion of dipoles in non-uniform electric fields. The force on a dipole in a non-uniform field is \textbf{F}=\textbf{F}_+ + \textbf{F}_-=q(\Delta \textbf{E}) where \Delta \textbf{E} is the difference in the field between the plus end and the minus end. Component wise, \Delta E_x = (\nabla E_x) \cdot \textbf{d} where d is a unit vector. This holds for y and z, the whole thing can also be written as \Delta \textbf{E} = (\textbf{d} \cdot \nabla) \textbf{E}. Since p=qd, we can write \textbf{F} = (\textbf{p} \cdot \nabla) \textbf{E}

Jackson derives it differently by deriving the electrostatic energy of a dielectric from the energy of a collection of charges in free space. He then derives the change in energy of a dielectric placed in a fixed source electric field to derive that the energy density w is given by w = -\frac{1}{2} \textbf{P} \cdot \textbf{E}_0. This explicity explains the factor of two and is an interesting alternative explanation.

  367   Wed Jul 12 15:08:59 2017 ZachElectronicsModelingModel of actuator and sample


  • I am attaching the first fully functioning model of the actuator and sample. I cleared both meshes and solutions to make the file a reasonable size, but they can quickly be built/solved again. 
Attachment 1: Force_Model.mph
  368   Fri Jul 14 16:43:24 2017 ZachElectronicsModelingForce profile matlab script


  • I have completed a rough, but functioning script that calculates the modal force profiles. The force values are still coming out incorrect (on the order of 10^14) but the script can take in my model as a .m file and return an array with a force value per mode. I am attaching both the .m file and the matlab script
  • I have done very little work with the numerical integration itself, based on the 2D numerical integration code I received I just appended a z component and left it at that so when I return from Livingston I will  fix that component
Attachment 1: forces.m
par.a = 75e-3/2;    % radius [m]
par.h = 1.004e-3;   % thickness [m]
par.E = 73.2e9;     % Young's modulus [Pa]
par.nu = 0.155;     % Poisson's ratio
par.rho = 2202;     % density [kg/m^3]

%Calculate fundamental modes of the disk
[freqs, modes, shapes, x, y] = disk_frequencies(par, 10000, 1, 'shapes', 0.5e-3);

%Now we extract the force profile from the COMSOL model
... 41 more lines ...
Attachment 2: faster.m
function out = model
% faster.m
% Model exported on Jul 14 2017, 14:47 by COMSOL

import com.comsol.model.*
import com.comsol.model.util.*

model = ModelUtil.create('Model');
... 403 more lines ...
  371   Thu Jul 20 11:37:01 2017 ZachElectronicsModelingMatlab Script


  • I believe my MATLAB script successfully calculates the force distribution into each of the modes specified by the parameters. My previous error was caused by my neglecting the proportionality factor of \frac{1}{2}\chi_e\epsilon_0. Now the force order of magnitude is on the order of 103. I am currently unclear how to think about the units of the mode shapes from the disk_frequencies script, but I will pick it apart more carefully and try to figure that out. Then it will be a matter of converting units so that it matches with the N/m^3 from the COMSOL script and then comparing with real lab results. It seems to me that the error in force distribution should be inversely proportional to the number of modes calculated, in which case it would be useful to determine an appropriate number of modes to calculate. 
Attachment 1: forces.m
par.a = 75e-3/2;    % radius [m]
par.h = 1.004e-3;   % thickness [m]
par.E = 73.2e9;     % Young's modulus [Pa]
par.nu = 0.155;     % Poisson's ratio
par.rho = 2202;     % density [kg/m^3]

%Calculate fundamental modes of the disk
[freqs, modes, shapes, x, y] = disk_frequencies(par, 10000, 1, 'shapes', 0.5e-3);

%Now we extract the force profile from the COMSOL model
... 27 more lines ...
  375   Mon Jul 24 09:13:45 2017 ZachElectronicsModelingParametric Sweep


  • I wrote a MATLAB script that is capable of sweeping parameters, the code is attached. The next step is to create nested loops so that I can sweep multiple parameters in a single run. I also should add a function in the script to eliminate the modes that cannot be measured by the experimental setup.
  • My first sweep was for the gap between electrodes and swept from 1 to 2 mm. In the plot the gap grows from steps 1 to 6 and the only obvious effect in the plot is a decrease in force from the highest mode. Intuitively it makes sense that a wider gap would decrease the force because the electric field is diminished by spreading out the electrodes.
  • I would like to add a parameter for the overlap of the electrodes, but this would require substantial redesigning of the COMSOL model due to the multilevel dependency on parameters. 

Attachment 2: forcesweep.m
fpro = zeros(6, 27);
no = 1;
for count = 1:.2:2
    gap = strcat(num2str(count), ' [mm]')
    model = fst2(gap);
    fpro(no, :)= product(:);
    no = no + 1;
  378   Tue Jul 25 13:38:30 2017 ZachElectronicsModelingParametric Sweep of ESD gap


  • I completed a short sweep of the gap between the drive and the sample, between .5 and 1 mm in .1 mm increments. It appears that a 1 mm distance is the ideal distance by approximately a factor of two. I will next sweep larger distances and see how the force profile behaves at greater distances.

  379   Wed Jul 26 09:27:40 2017 ZachElectronicsModelingSweeping the space between ESD and sample


  • I ran a sweep of the gap between the ESD and the sample, first from .5 mm to 1 mm. That sweep suggested that there is a significant jump in force across almost all of the modes at 1 mm. To confirm this I double checked the geometry and it appears that COMSOL is building everything as expected when changing the spacing parameter. Then I ran a finer sweep in .02 mm increments for the spacing between .9 and 1.1 mm. Once again it appears there is a large jump as the gap approaches 1 mm, but the behavior does not seem to be symmetric about that point, the force appears to diminish linearly as the gap increases beyond 1 mm. I will run a sweep of the ESD arm spacing along with the vertical gap to confirm that the jump occurs when the gap between the ESD and the sample is equivalent to the spacings between the ESD arms.

Attachment 1: Gap_near_one.jpg
  381   Wed Jul 26 21:22:50 2017 ZachElectronicsModelingParametric Sweep Results


  • I resolved the major bugs in the parametric sweep scripts and ran low resolution sweeps of the gap between the ESD and sample (Gap Sweep) and the spacing between the ESD arms (ESD Arm Gap Sweep).
  • The arm gap sweep largely behaved in a reasonable way with a maximum excitation at a 1.25 mm gap. However modes 14, 19, and 25 did not follow the general trends and had sharp drops and increases compared to the other modes.
  • The sample gap sweep had less intuitive behavior, all of the modes followed the same general double peak trend that drops to zero when the gap is 1.5 mm. I cannot explain exactly why it is behaving that way, I will run a higher resolution sweep and examine the geometry in greater detail.


  382   Thu Jul 27 13:37:31 2017 ZachElectronicsModelingCorrected sample gap sweep


  • I resolved a couple more data processing bugs and calculated a sweep of the ESD-Sample gap from a distance of .5 mm to 1.5 mm. The resulting data behaves far more like I would expect from a force generated by an electric field, it seems to drop off like distance squared. This is a very strong correlation with a good intuitive explanation, and would suggest that it is prudent to place the ESD as close to the sample as possible.
  • I also computed a higher resolution sweep of the gap between the arms of the ESD. It did not resolve the strange behavior at all, so I will investigate coupling into the mode pairs as a possible source.

Attachment 1: Fine_sample_gap.jpg
Attachment 3: fine_arm_gap.jpg
  383   Thu Jul 27 16:56:03 2017 ZachElectronicsModelingOffset Sweep


  • I ran a low resolution sweep of the offset in the arms of the ESD, the space between the end of the arm and base of the opposite combs. The trends are much more subtle and are not coherent across as many of the modes. The lower frequency modes decrease slightly, while the force in the higher frequency modes increase more drastically. This is an interesting parameter, I will definitely run another sweep once I have written code that accounts for the mode pairs. Assuming the apparent trends are physically accurate, this could be a useful parameter because a greater offset gives a greater relative increase to the higher order modes while still leaving a substantial force on the lower order modes that are excited more easily anyway.

Attachment 1: Offset.jpg
  386   Tue Aug 1 16:10:42 2017 ZachElectronicsModelingImproved Gap Sweep


  • I completed an improved sweep of the gap between the ESD arms. I resolved some code issues, since it was passing the maximum value not the most extreme, smaller magnitude positive values were being included rather than the strongest force calculation.
  • There are still three modes that show unique behavior relative to the others: 14, 19, and 25. Mode 14 is the (2,2), mode 19 is the (2,3) and mode 25 is (3,2).
  • Plots of the mode shapes are included for reference. The black rectangle represents the region covered by the ESD.

  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

Attachment 1: Arm_gap.pdf
Attachment 2: Arm_width.pdf
Attachment 3: Offset.pdf
Attachment 4: Sample_Gap.pdf
  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.


Attachment 1: ESD.pdf
Attachment 2: Rotated.pdf
Attachment 3: resonantmodes.pdf
  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.

Attachment 1: Ratio.jpg
  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.

Attachment 1: resonantmodes.pdf
  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



Attachment 1: Optimization_plot_lin.pdf
Attachment 2: Optimization_plot_log.pdf
ELOG V3.1.3-