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ID Date Author Type Category Subject
  2207   Thu Jun 21 11:43:53 2018 anchalDailyProgressISSLISO Analysis of complete circuit

I did TF, input impedance, opamp stability and noise analyses of the complete circuit with feedback part, modeled AOM (by phase shifter) and modeled Cavity (by LPF+NOT). Attached are the results. In the process, I completed wrapping some more LISO functions in python. We can do calculate input referred noise, input impedance, opamp stability and plot only dominant noise sources. The circuit schematic is attached and for now uses OP27. Next steps are to figure out what adjustments (components and values) can lower the noise. Opamps are in the stable region only.

Attachment 1: ISSAOMCavity.pdf
ISSAOMCavity.pdf
Attachment 2: ISSAOMCavityNoiseAnalysis.pdf
ISSAOMCavityNoiseAnalysis.pdf ISSAOMCavityNoiseAnalysis.pdf ISSAOMCavityNoiseAnalysis.pdf ISSAOMCavityNoiseAnalysis.pdf ISSAOMCavityNoiseAnalysis.pdf
Attachment 3: ISSAOMCavity.fil
r R14 510 OUT n1
c C7 1u n1 n2
c C4 470p n1 n4
r R15 560k n2 n4
r R16 560k n3 gnd
c C6 1u n3 gnd
op ISS2 op27 n3 n2 n4

r R18 1k n4 n5
c C8 4.7n n5 n7
... 41 more lines ...
  2206   Wed Jun 20 17:54:45 2018 anchalDailyProgressISSLISO Analysis of Feedback Part of the circuit

OUr measurements of the actual circuit showed noise level in the order of several uV/sqrt(Hz). I did the noise analysis on LISO and the results indicate that the second stage amplifier's input current noise is causing most of the noise till around 30 Hz and then its input voltage noise dominates till around 200 kHz. I would work more on identifying ways to reduce the noise, would do the simulation for the loop gain transfer function and would do the stability analysis as well.

Attachment 1: ISSCircuitSchematic.jpg
ISSCircuitSchematic.jpg
Attachment 2: ISSLisoNoiseAnalysis.pdf
ISSLisoNoiseAnalysis.pdf ISSLisoNoiseAnalysis.pdf ISSLisoNoiseAnalysis.pdf
Attachment 3: ISS.fil
r R14 510 IN n1
c C7 1u n1 n2
c C4 470p n1 n4
r R15 560k n2 n4
r R16 560k n3 gnd
c C6 1u n3 gnd
op ISS2 op27 n3 n2 n4

r R18 1k n4 n5
c C8 4.7n n5 n7
... 20 more lines ...
  2205   Mon Jun 18 14:42:45 2018 anchalPhotosISSBreadboard circuit testing

Attached is the image of circuit implemented on breadboard with modelled AOM and cavity as phase shifter and low pass filter respectively.
In the image, all red/orange wires are at +15V, all white/grey wires are GND, all green wires are at -15V, all yellow wires are carrying signal and one violet wire is the voltage offset set to 0V right now. All the opamps are OP27G except the adder and an inverter which are OP27E. The circuit corresponds to the attached LTspice circuit.

Attachment 1: Breadboard_Circuit_Labeled.jpg
Breadboard_Circuit_Labeled.jpg
Attachment 2: ISSAOMCavity.pdf
ISSAOMCavity.pdf
  2204   Thu Jun 14 12:00:50 2018 anchalNotesPMCLatest PMC alignment

PMC in the North path got misaligned while working on the input path. We aligned it back again today. PMC locking method summary:

  • First increase the incoming power to around 13 mW. Make sure you note down the previous input power so that you can go back to it later.
  • Align the input path in order to see some lissajous figures from the output window. The try to minimize the the output path to a spot.
  • Drive the PMC PZT with signal generator at 5 Hz triangular wave with amplitude enough to transverse one full FSR.
  • Using the transmitted light which can be read from the PD measuring reflection from NCAV, try to supress other modes. TEM00 mode would be the dominant mode. Display this signal on oscilloscope trigered by the signal generator.
  • Once this has been supressed enough, align the reflection off the PMC to the PMC reflection PD. Display this signal also in the oscilloscope and align the input path further to supress all other modes as much as possible.
  • Go back to previous input power, connect back the PZT to the rack and wait for it to get autolocked.

We were able to achieve fringe visibility of 76.16% (measured by VIS program in labs programmable calculator). Also, we were able to get rid of all other modes enough that they were not visible anymore in the oscilloscope.

Keywords for future search: North Cavity Pre Mode Cleaner modecleaner visibility PMC

 

  2202   Wed Jun 13 18:04:32 2018 anchalDailyProgressISSLoop Gain Transfer Function analysis on LTspice

I implemented the feedback part of this circuit and measured the transfer function on SR785. Attached is the measured transfer function. It is close to the one given by LTspice except that there is a nearly flat top between ~100Hz to ~1.3kHz while analytically this was supposed to be a smooth peak.
I checked with attenuating the input signal to make sure the flat top is not due to saturation, it is in fact two peaks close together. By changing a capacitor C10 (see the last post for the circuit)., we can move these peaks closer or further. However, making them move closer decreases the overall gain of the point, so I stuck to 4.7uF value.
I'll now test this circuit with a low pass filter modeling the cavity and some delay for modeling the AOM and see if the loop gain is as expected.

Quote:

With the circuit of Johannes, I ran LT spice analysis with modeling cavity pole and AOM delay to get an estimate of how the loop gain would look like. Attached is a plot of the transfer function of loop gain and the circuit schematic used. Here I used this post of Johannes on elog to use DC Gain of AOM as 1.11 dB. But in case, this changes, I have a running code which will output the new unit gain frequencies and phase margins. I'll implement this into a board soon and move forward by optimizing the choice of elements with help from LISO.
I'm seeking input on anything which makes the frequency curve as shown here less than satisfactory.

 

Attachment 1: ISSMeasuredTF06-13-2018.pdf
ISSMeasuredTF06-13-2018.pdf
Attachment 2: ISSLTSpiceTF.pdf
ISSLTSpiceTF.pdf
  2201   Mon Jun 11 15:03:15 2018 anchalDailyProgressISSLoop Gain Transfer Function analysis on LTspice

With the circuit of Johannes, I ran LT spice analysis with modeling cavity pole and AOM delay to get an estimate of how the loop gain would look like. Attached is a plot of the transfer function of loop gain and the circuit schematic used. Here I used this post of Johannes on elog to use DC Gain of AOM as 1.11 dB. But in case, this changes, I have a running code which will output the new unit gain frequencies and phase margins. I'll implement this into a board soon and move forward by optimizing the choice of elements with help from LISO.
I'm seeking input on anything which makes the frequency curve as shown here less than satisfactory.

Attachment 1: ISSLoopGainAnalysis.pdf
ISSLoopGainAnalysis.pdf
Attachment 2: ISSLoopGainTFwithAOMDCG1.11.pdf
ISSLoopGainTFwithAOMDCG1.11.pdf
  2200   Thu Jun 7 17:18:03 2018 awadeDailyProgressComputersfb4 framebuilder downtime and time slippage

Rebooted the framebuilder fb4 on Tuesday May 29.  I didn't realize that it had hung on reboot.  There was a period of 24 hour after this in which no data was logged for the lab.

Also the framebuilder clock has reset back to 1980.  I can't really find documentation on the wiki or elogs on how this was configured sans ADCs.  I guess we'll just have to go Back to The Future and just use 80's dates for now. 

  2199   Thu Jun 7 13:08:38 2018 shrutiDailyProgressTempCtrlBasic gym environment - vacuum can and foam

I spent the past few days trying to troubleshoot errors that occurred while creating the basic gym environment for  thermal control of the vacuum can and finally got it to work. I also ran some tests on a jupyter notebook and the environment seemed to function as expected.

 

Features of this environment:

1. The state is a numpy array containing the current temperature of the can and the ambient temperature, initially set to a random value between 15 and 30 C, 20 C, respectively. 

2. The ambient temperature is currently modelled as a sinusoidal function oscillating with an amplitude of 5 C about 20 C with a time period of 6 hours.

3. Allowed actions are integer-valued heating powers between 0 and 20 W.

4. Each time-step lasts 10 seconds, and a single action is applied for this duration. The state updates itself after one time-step using scipy.integrate.odeint to calculate evolution of the vacuum can temperature. Heat conduction through the foam and heating influence the evolution. The heat conduction was modelled as per previous simulations and calculations.

5. A single episode of the game runs while the temperature of the can is within 15 and 60 C.

 

Tests:

1. gym.make('VacCan-v0') ran without any unusual error.

2. state, action, step() resulted in output as predicted.

3. Multiple iterations of step(), with zero heating, constant, and random heating seemed as was physically predicted.

4. The env was tested with a random agent i.e., one that applies a random action until the game terminates. Each time, the game terminated (temperature of the can rose above 60 C) in 150-200 timesteps (25-35 min : expected time while running in the lab).

 

It seems like this basic testing environment is ready to be used with a learning algorithm that would try and maintain the temperature. 

  2198   Wed Jun 6 22:08:33 2018 ranaSummaryTempCtrlMeasuring thermal decay time constant

We expect the vacuum can to have multiple time constants since there are multiple sources of heat loss. Don't worry too much about fitting, just tune the model so that it matches the observation. i.e. the model should have more than 1 conductive cooling path. Once it is accurate to ~20-30%, better to focus on the feedback than the tuning of the model.

  2197   Tue Jun 5 16:35:54 2018 awadeDailyProgressFSSMonitor channels overdrawing current in output buffers

After switching the FSS monitor channels to the Interface Controller box (with monitor read backs coming through the D25 connector) I found that the returned monitor signals were not working as expected. 

The XT1221 card installed in the interface controller box only gave positive voltages that latched near zero.  I think there is an issue with this particular unit. I've switch it out for a brand new card and have labeled in appropriately.

After switching I found that there were two further issues. The outputs were noisy and railed and latched to zero when driven above about 4.0 V.  The first of these issues was a grounding one: the Acromag XT1221 inputs are differential and need to be grounded on one side for differential inputs. I fixed this and gave all the channels a common ground referenced to the common ground of the rack.  After this the signal was a lot less noisy but railed and then dropped to zero when driven above 4.0 V.  Turns out the final buffer stage of the signals feed back through the D25 cable only has 50 Ω resistance in series (with the return pin giving a further 50 Ω).  It seems that the buffer is being overdrawn in current.  I switched out R101, R105, R118, R130 50 Ω for 1 kΩ.

In addition to the above changes I discovered last night that I had gotten the polarity of the wiring wrong in the acromag inputs.  The positive input was being sinked to ground, which is kind of bad and I don't really know how I was seeing any signal at all.  I've fixed this and now see the full range of voltages with very little noise. 

I'm not sure about the choice of 1 kΩ in series with the output (unity gain) buffer.  The ADCs are high impedance at the intput (100 kΩ) so it should be fine.  It does mean that there isn't a situation, say a short, where the output stage buffer will be drawn more than 15 mA.

Quote:

After switching the laser fast monitor channel from the front panel FASTMON pin to the FASTM_P/FASTM_N pins I found that the PID controllers that use this channel to adjust the laser slow frequency became unstable.  After turning down the gain the oscillations of laser temperature were very difficult to tune out.

It looks like the issue is with the fact that the FSS interface board (LIGO-D040423) low passes the monitor signal with a 0.8 Hz LP filter (200kΩ wt 1 µF cap).   The narrowed bandwidth of this 'sensor' in the PID loop limits the bandwidth of the total OLG.  We could turn down the P and up the I a little bit, but this seems less good than switching out some resistors.  

I replaced four 100 kΩ resistors R99, R100, R116 and R117 with 510 Ω resistors.  This brings the LP filter on the Fast monitor channels and mixer monitor channels up to 156 Hz: the new frequency is well above the ADC 10 Hz sampling rate but should still filter very high frequencies that are not of interest to the slow loop. I'm not sure what the ideal cut off point should be wrt digitizing signal and the loop, but this seems like a good first guess.

These modifications were made to North and South FSS interfaces boards (LIGO-D040423), serial 2010:005 and 2010:00? respectively. These changes are logged in the wiki page and with a label on the box back to this post. 

Quote:

Autolockers were not catching the resonances again. It turns out I had unplugged the excitation to the FSS acromag controller box that engages the binary channels.  It had been plugged back in but often fails to activate the logic because it is still being powered from a 5 V plug pack.

Decided it was time to make the switch to 9V. I installed some voltage dividers to set the excitation out to the FSS interfaces to 4.9 V with a low voltage of 0.66 V maximum (unpowered).  See PSL:2058 for the wiring, I used option D with R1 = 820 Ω  and R2 = 680 Ω.  The new wiring was tested to check the voltages were right, so I don't fry the FSS interface box again.  I also made some changes to the soft binary channels in the acromag IOC: the front medm panel Test1 and Test2 switches are now flipped (NOT operation) so they make sense from the users point of view.  Before the logic was inverted so turning TEST1 off actually activated this path in the circuit.

I also noted down the channels off the ADC card that picks off the monitors from the FSS D25 connector.  This should reduce the number of front panel BNCs as it can all be routed inside the Acromag interface controller box. These have remapped from Aidan's acromag crate into the FSS interface controller box.

 

 

  2196   Mon Jun 4 18:00:59 2018 shrutiNotesTempCtrlRL, SL, OpenAI Gym

Upgrade from PID to intelligent controls:

As seen from earlier elogs, PID control of the temperature of the cavities seems problematic - the time taken for the temperature to converge to the set-point is very large and moreover, the PID parameters may require non-trivial tuning that varies with the desired set-point. Intelligent controls, specifically neural networks, seem like an attractive upgrade to PID as such a network would be able to learn for itself the non-linearities in the model and predict the optimal actuation.

More precisely, in this system, the requirement for the intelligent control is to be able to predict the optimal amount of heat actuation to be supplied in each time-step that converges fastest to the set-point temperature. In its final form, this prediction would be implemented as a series of matrix multiplications, with optimal weights (matrix coefficients), simulating the non-linear function describing the required actuation on taking as input the current state of the system. 

 

Neural networks:

(Refer figure) A neural network consists of layers of nodes. The layers of nodes begin with an input layer, followed by one or more hidden layers, and finally an output layer. Each layer (represented as an n-dimensional vector, where n is the number of nodes in the layer) can obtained from the previous layer via multiplication by an m-by-n matrix on the previous m-dimensional layer. Each node also has an associated activation function which for the hidden layers is preferably non-linear (ReLU, tanh, etc) to take into account the non-linearities in the model. An optimisation algorithm then attempts to find a `fit' for the components of all matrices.

In order to achieve the final form, the weights need to be optimised via some learning algorithm that learns ‘from experience’. For this, a loss or cost function is calculated as a function of the current state, roughly representing the distance between the current state from the set-point. This is fed to the optimiser which moves over the parameter space of the weights associated to the nodes in the neural network (coefficients of all matrices that serve as a transformation from one layer to the next) to a point closer to the optimum. The weights predict an actuation which is applied to the system giving a new state for which the process is repeated until the minimum is reached. This learning algorithm can be implemented, in our case, either using reinforcement learning (RL) or supervised learning (SL).

Reinforcement Learning (RL):  RL deals with game-like problems where observations of the state are made and the algorithm learns to find the optimal action to perform based on the state. Each action has an associated reward which provides the basis for back-propagation or feedback that is used to predict future actions. In order to implement this, neither the internal working of the game nor a set of a priori `correct actions' need be known.

Supervised Learning (SL): SL operates on a set of labelled data, which includes a training and testing data set consisting of input states and their corresponding correct outputs. The algorithm learns to predict the output by learning with the training data set without any prior knowledge of the mechanism by which the outputs are obtained. In order to use SL in our system, a labelled data set must be obtained. This can be initially done using the model for thermal dynamics of our system and later on by taking real experimental data.

 

OpenAI Gym:

In order to train and test RL algorithms and also possibly SL algorithms, the physical system can be simulated as a `game environment' on which the neural net would learn the optimal action at each step. OpenAI, an open-source platform for Artificial Intelligence (AI) development, contains Gym and Baselines, which is a set of games on which RL algorithms can be trained and tested, and a set of high performance RL algorithms, respectively. 

 

Our particular system as a gym environment:

An initial model of the system only includes the vacuum can and the heat conduction through the foam surrounding it. The dynamics of this is represented as a first order differential equation and therefore the evolution can be predicted by knowing only the temperature of the can (assuming all system parameters are known accurately). The action or actuation would correspond to a specific value for heating power that would be applied to the can during the next time-step.

To formulate this as a gym game environment in python on which RL algorithms (such as those on baselines) may be trained and tested, the following methods are to be defined:

step(), reset(), seed(). 

render() and close() may also be used to visualise the gameplay. 

 

reset() begins a new game and returns an observation or initial state, deterministically or randomly as per choice.

def reset():

    return observation

 

step() accepts an action and returns a tuple consisting of the next state (observation), reward received after previous action (reward), boolean determining whether the game is over (done) and a dictionary for additional information, if any (info). This method is one time step of the evolution.

def step(action):

    return (observation, reward, done, info)

seed() contains seeds for the random number generators used in the program.

 

In addition, the environment also has the following attributes:

action_space - space of valid actions

observation_space - space of valid states or observations

reward_range - tuple of min and max possible reward

 

The action is given externally and should belong to the space of valid actions. In our case a learning algorithm, with a neural network, would feed this into the game at every time-step.

 

Attachment 1: intelligentcontrol.png
intelligentcontrol.png
  2195   Fri Jun 1 22:00:52 2018 CraigSummaryTempCtrlMeasuring thermal decay time constant

Hi shruti,

You might have more luck with scipy.curve_fit if you try taking the log of the y data, so log(y) = log(a * exp(-(t-c)/b) + d ) = some simpler expression, and create a new function around your simpler expression.

Quote:
 

The region of the data corresponding to the cooldown was fitted with an exponential decay using scipy.optimize.curve_fit() with:

 a\text{e}^{-(t-c)/b} + d

 

  2194   Fri Jun 1 16:30:09 2018 shrutiSummaryTempCtrlMeasuring thermal decay time constant

To develop an accurate physical model to be used as a testing ground for the machine learning controls to be implemented in the system, all parameters (material and dimensional) must be known as accurately as possible. The parameters A, k as in https://nodus.ligo.caltech.edu:8081/CTN/2191 are not known very accurately so a measurement of the time constant (time taken for the can to naturally cool to 1/e of its initial temperature) was attempted in order to gauge how well the model matches with experiment.

Several previous measurements of the time constant were undertaken, but results varying from 2-5 hours were obtained https://nodus.ligo.caltech.edu:8081/CTN/1728 and therefore, to further investigate what was going on another such experiment was undertaken.

Experiment:

On 23rd May, Andrew and I surrounded the assembly of the vacuum can with aluminium foil (as seen in the picture). A setpoint of 45 C was chosen on 23rd May at 20:24, then on 24th May at 15:40 after the set point was reached the heater and PID were turned off. The evolution of the system was recorded.

The steady state temperature obtained was 45.792 \pm0.005 C, where the uncertainty is calculated from a fit of steady state data as seen in the attached figure. A small region before cooldown was used for an estimate of the rms value for the noise obtained by subtracting a polynomial fit (10th order) to detrend the data. 

The region of the data corresponding to the cooldown was fitted with an exponential decay using scipy.optimize.curve_fit() with:

 a\text{e}^{-(t-c)/b} + d
The following are the parameters from the fit:

Fit parameters
Parameter Estimate Uncertainty
a 2.4e2 1.16e5
b 5.610 5e-3
c 2.1e-1 2.69e3
d 23.4 3.3e-3

The uncertainty here is taken from the square root of the correspoding covariance matrix for the fit parameters. This seems very unreliable given the unreasonably large uncertainties in a,c and relatively tiny uncertainties in b,d, even though visually the fit seems good.

According to the fit, the time constant should be 5.610 \pm0.005 hours. But there seems to be many issues with the model including the large uncertainty and the very large \chi^2 value that was calculated from the fit.

It seems like this model is an inaccurate description of the system at this level of sensitivity of measurement. The exponential decay curve does not even visually appear to fit the data to the level of the calculated rms noise value. This can be seen even in previous such experiments (as seen in https://nodus.ligo.caltech.edu:8081/CTN/1728). The possible reasons for this may be that the simple conduction model of the vacuum can may be leaving out conduction or radiation through other significant channels, the gradient across the foam is not linear at all time steps (as is assumed in the conduction equation), the geometrical effects of the foam and can may be more significant than is assumed, or the inner components of the can may be responsible for significant heat transfer. The answer to this may be evident from performing more complex models to fit the data.

The jupyter notebook can be found at https://github.com/CaltechExperimentalGravity/NonlinearControl/tree/master/TemperatureControl/Data/20180518_CoolDownTestVacCan

Attachment 1: VacCanTemp_analysis.pdf
VacCanTemp_analysis.pdf
Attachment 2: Setup_covered_in_aluminium.png
Setup_covered_in_aluminium.png
  2193   Thu May 31 14:17:42 2018 awadeDailyProgressFSSFixing FSS binary under voltage issue

After switching the laser fast monitor channel from the front panel FASTMON pin to the FASTM_P/FASTM_N pins I found that the PID controllers that use this channel to adjust the laser slow frequency became unstable.  After turning down the gain the oscillations of laser temperature were very difficult to tune out.

It looks like the issue is with the fact that the FSS interface board (LIGO-D040423) low passes the monitor signal with a 0.8 Hz LP filter (200kΩ wt 1 µF cap).   The narrowed bandwidth of this 'sensor' in the PID loop limits the bandwidth of the total OLG.  We could turn down the P and up the I a little bit, but this seems less good than switching out some resistors.  

I replaced four 100 kΩ resistors R99, R100, R116 and R117 with 510 Ω resistors.  This brings the LP filter on the Fast monitor channels and mixer monitor channels up to 156 Hz: the new frequency is well above the ADC 10 Hz sampling rate but should still filter very high frequencies that are not of interest to the slow loop. I'm not sure what the ideal cut off point should be wrt digitizing signal and the loop, but this seems like a good first guess.

These modifications were made to North and South FSS interfaces boards (LIGO-D040423), serial 2010:005 and 2010:00? respectively. These changes are logged in the wiki page and with a label on the box back to this post. 

Quote:

Autolockers were not catching the resonances again. It turns out I had unplugged the excitation to the FSS acromag controller box that engages the binary channels.  It had been plugged back in but often fails to activate the logic because it is still being powered from a 5 V plug pack.

Decided it was time to make the switch to 9V. I installed some voltage dividers to set the excitation out to the FSS interfaces to 4.9 V with a low voltage of 0.66 V maximum (unpowered).  See PSL:2058 for the wiring, I used option D with R1 = 820 Ω  and R2 = 680 Ω.  The new wiring was tested to check the voltages were right, so I don't fry the FSS interface box again.  I also made some changes to the soft binary channels in the acromag IOC: the front medm panel Test1 and Test2 switches are now flipped (NOT operation) so they make sense from the users point of view.  Before the logic was inverted so turning TEST1 off actually activated this path in the circuit.

I also noted down the channels off the ADC card that picks off the monitors from the FSS D25 connector.  This should reduce the number of front panel BNCs as it can all be routed inside the Acromag interface controller box. These have remapped from Aidan's acromag crate into the FSS interface controller box.

 

  2192   Mon May 28 17:36:58 2018 awadeDailyProgressFSSFixing FSS binary under voltage issue

Autolockers were not catching the resonances again. It turns out I had unplugged the excitation to the FSS acromag controller box that engages the binary channels.  It had been plugged back in but often fails to activate the logic because it is still being powered from a 5 V plug pack.

Decided it was time to make the switch to 9V. I installed some voltage dividers to set the excitation out to the FSS interfaces to 4.9 V with a low voltage of 0.66 V maximum (unpowered).  See PSL:2058 for the wiring, I used option D with R1 = 820 Ω  and R2 = 680 Ω.  The new wiring was tested to check the voltages were right, so I don't fry the FSS interface box again.  I also made some changes to the soft binary channels in the acromag IOC: the front medm panel Test1 and Test2 switches are now flipped (NOT operation) so they make sense from the users point of view.  Before the logic was inverted so turning TEST1 off actually activated this path in the circuit.

I also noted down the channels off the ADC card that picks off the monitors from the FSS D25 connector.  This should reduce the number of front panel BNCs as it can all be routed inside the Acromag interface controller box. These have remapped from Aidan's acromag crate into the FSS interface controller box.

  2191   Fri May 25 14:20:55 2018 shrutiDailyProgressTempCtrlSimulation and measurement of thermal conductivity time constant - Vacuum Can

A model of vacuum can was constructed taking into account the heat conduction across the foam, neglecting the geometry of the foam and approximating an effective cross-sectional area and thickness.

The analytically calculated time for the decay of temperature to 1/e of the initial value  (time constant) = d*m*C/k/A = 2.99 hours, with constant ambient temperature and no heating. The parameters used in this calculation :

Material and dimensional parameters of vac can
Mass of assembly m 15.76 kg
Specific heat of steel can C 505 J/kg-K
Heat conduction cross sec area A 1.3 m^2
Thickness d 5.08e-2 m
Thermal conductivity constant k 1.136*25.4e-3 W/m-K

'A' is not known very accurately and could even be as low as 0.48 m^2, and since the time constant is very sensitive to A a better estimate is required for a more accurate model. The units for 'k' in the spec sheet was confusingly W/m^2-K, nonetheless an approximation was made assuming it scales by thickness. An experiment to measure the time constant is now underway. This will give us a better idea of the values.

In order to study the evolution of temperature, scipy.odeint was used to perform numerical integration of the following equation:

\frac{\text{d}T_{can}}{\text{d}t} = -\frac{kA}{mC}\frac{(T_{can}-T_{amb})}{d} + \frac{H}{mC},

where 'H' is the heating power.

This can be done even in the presence of fluctuating ambient temperatures and variable heating power (taken as a lists, piecewise functions).

In the two trial plots shown, the ambient temperature was stepped up from 300K to 315K at 10000 s (~2.77hours). One plot shows the evolution without heating and the other with a heating power of 18.46 W.

Attachment 1: Temp_18W_StepTempAmbient.pdf
Temp_18W_StepTempAmbient.pdf
Attachment 2: Temp_NoHeat_StepTempAmbient.pdf
Temp_NoHeat_StepTempAmbient.pdf
  2190   Thu May 17 10:20:04 2018 awadeDailyProgressLaserPower drop south laser

There has been a distinct drop in laser power in the south path since yesterday.

It looks like the drop in power happened between GPS* 1209950712 s and 1209966050 s (18:24:54 and 22:40:32).  This was in the lab when nobody was there.

I've been tuning the temperature on the cavities to bring the beatnote into range and the current south laser slow voltage is -6.2759 V when the cavity is locked -- as an aside cavity heaters are set to 0.455 W diff heating and 0.56831 W common heating.   This is about where it was before and tuning the laser slow temperature around doesn't seem to get back to the original power levels as reported by the reflection and transmission PDs.  So it seems we are not in a mode hopping region.  I've attached a dataview screen shot showing that the prior to the drop the south trans PD was giving 4.25 V and the reflected 1.094 V (when locked).  After the change in power (after some unlock time for the cavities) the south trans PD was 3.11 V  and south refl PD was 0.488 V (when locked).

The points at which the cavity was unlocked show reflected power dropped from 3.81 V to 2.56 V.  This doesn't look great and its not clear what is going on with the laser.

For reference the current power going into each cavity is 3.1 mW for the north and 2.02 mW for the south.  Visibility is good on the south at 62% (Refl Vmin=0.592, Vmax =2.55  V)

Not clear what happen here, there is no mode cleaner or ISS applied in the south at the moment so seems like the only source of a power change would be a misalignment or a change in the laser.  Nobody has been in the lab since last night and looking around with the IR viewer there is no apparent clipping.

 

For now I think 3.1 mW for the north is a little bit too high.  I've turned down north power to 2 mW to match the south and we will watch the changes in power over the next few days in both lasers.

 

* Note: the GPS time on fb4 has now drifted by 9 days, so not clear if this is correct time, it is certainly in the early hours of this morning.

Attachment 1: Screenshot_from_2018-05-17_10-19-21.png
Screenshot_from_2018-05-17_10-19-21.png
  2189   Wed May 16 10:40:06 2018 anchalDailyProgressBEATInstalled Beatnote detector with known beam width at the point

Using the result of the beam profile analysis, I calculated the required position and lens to put in to decrease beam width to about 300 um at the RFPD (1/3 of detector size 2mmx2mm). Attached matlab code for the same. I used a 687.5 mm Fused Silica lens for this purpose. Finally, I installed the beatnote detector after taking beam profiles with the beam profiler and finding the right position. Attached is the screenshot of the beam profile at this position shows that beam has a width of ~300 um. I have positioned the RFPD such that beam is incident at 30 degrees from normal on it.

Attachment 1: Images.pdf
Images.pdf Images.pdf Images.pdf
Attachment 2: RFPDpositioning.zip
  2188   Tue May 15 18:19:05 2018 KojiNotesBEATAnalysis for idea of sending beam at Brewster angle to Photo diode

See https://dcc.ligo.org/LIGO-T1100564/public

See also: https://arxiv.org/abs/1710.07399 or https://doi.org/10.1364/AO.57.003372

  2187   Tue May 15 16:53:36 2018 anchalNotesBEATAnalysis for idea of sending beam at Brewster angle to Photo diode

Recently we were given the idea of sending the beam to the photodiode at Brewster angle. If we do so, ideally one particular polarization (parallel to the plane of incidence) will not reflect back. So if we send the beam polarized in this direction (or set the incidence plane such that these conditions are matched), we can minimize the reflection from PD significantly.
Sounded like a good idea, so I started reading about the InGaAs detector we have. Unfortunately, the datasheet of the C30642 detector we use does not mention either the fraction of In in InGaAs or the refractive index of it. So I went into the literature found these two papers:
Kim et al. Applied Physics Let Vol 81, 13 23 (2002) DOI: 10.1063/1.1509093
Adachi et al. Journal of Applied Physics 53, 5863 (1982); doi: 10.1063/1.331425
Using the empirical coefficients and functions from these paper, I calculated the refractive index for InGaAs for various fractions of x and the corresponding Brewster angles (Find Attached).
However, just after doing the analysis, we realized that doing this is not really possible. The Brewster angle is arctan(n2/n1) where n2 is the medium light is going into. This implies the Brewster angle would always be greater than 45 degrees and detector won't really absorb much light at this angle. So currently the conclusion is that this idea won't work.
However, there might be some error in our assumption of InGaAs as a transparent medium as the calculations do not take into account absorption of the photon at all. Attaching the python notebook too in case someone figures this out.

Attachment 1: InGaAsIncidenceAngleAnalysis.pdf
InGaAsIncidenceAngleAnalysis.pdf InGaAsIncidenceAngleAnalysis.pdf
Attachment 2: InGaAsIncidenceAngleAnalysis.zip
  2186   Tue May 15 14:29:47 2018 awadeDailyProgressTempCtrlBeat drift over the last few weeks

We haven't been paying attention to the beat frequency or its control in the last few weeks.  Yesterday it was apparent that the beat had drifted to ~2 GHz.  When I tuned the differential heating to ~0.42 W with a common offset of 0.56831 W I found that this had almost no effect on the beat note.

Initially I thought maybe the shield heater driver box was broken.  On closer inspection it seems that the Acromag IOC channels had been moved to a different output channel and the IOC process was only very recently reset to enact those changes.  

I've relabeled the cables and BNC ports to make it clear which components should plug into which.  I've set the differential heating to 0.422991 W and both lasers seem to be tracking in the right direction towards a 26 MHz beat note now.  It will take a few more hours to get close enough to stabilized. Currently at 250 MHz.

  2185   Tue May 15 14:24:25 2018 awadeDailyProgressBEATReinstalling beam splitter and beat detector

When I orient the beam into p-pol I noticed that the beam splitters give a lot of secondary reflections.  All these mirrors need to be switched out for p-pol optimized splitters and steering mirrors. 

We'll try to get all these beam dumps back in and bolted down soon.

Quote:

If I recall correctly, I placed those beam dumps everywhere because the transmission table ghost beams had gotten out of control.  Particularly bad was out of the cavity, it seems you have left those beam dumps there but I would double check their status.  There was also reflection from the first lenses back into the cavity that I tried to have the post-cav beam dumps block, unclear how successful I was. 

Also bad was reflection from the ND filter we had on our pre-RFPD lens, it seems like you have removed this lens which is great.  Also, there was some backscatter from the third camera I had installed at the other end of the recombination BS that unites the North and South path light, seems like that is gone as well, you might dump that light if you aren't already. 

Finally, the scatter from the IR cameras was like a diffraction grating pattern that went everywhere, it might be prudent to place those black glass beam dumps with the holes in front of them.

  2184   Mon May 14 09:25:44 2018 CraigDailyProgressBEATReinstalling beam splitter and beat detector

If I recall correctly, I placed those beam dumps everywhere because the transmission table ghost beams had gotten out of control.  Particularly bad was out of the cavity, it seems you have left those beam dumps there but I would double check their status.  There was also reflection from the first lenses back into the cavity that I tried to have the post-cav beam dumps block, unclear how successful I was. 

Also bad was reflection from the ND filter we had on our pre-RFPD lens, it seems like you have removed this lens which is great.  Also, there was some backscatter from the third camera I had installed at the other end of the recombination BS that unites the North and South path light, seems like that is gone as well, you might dump that light if you aren't already. 

Finally, the scatter from the IR cameras was like a diffraction grating pattern that went everywhere, it might be prudent to place those black glass beam dumps with the holes in front of them.

 

Quote:

I reinstalled the beam splitter, steering mirror and PD in the transmission path.  We have the beam profiling measurement and can reposition the detector more optimally in the near future.  But for now we need to get back to the scatter hunt: specifically the 500 Hz feature that haunts the area directly around the north path pre-mode cleaner (PMC).  

Some of the beam dumps were removed as they weren't bolted down or were in the way of the beam profiling (sorry Craig).

A few things to note:

  • I have now permanently removed the black cube steering mirror mount from the beat setup.  There are visable damage marks on the mirror that make it a dubious choice.  Also the mount just has too much close proximity surfaces on the reflection side that can be potential scatter points.  
  • I replaced the south path steering mirror (previously the black cube beam mount) with a Newport 10Q20HE.1 mirror.  The surface specs are ok 10-5 scratch dig and better than lambda/10.  Its optimized to be over 99% on both polarizations but not technically ultra good HR. We're out of the really good HR reflectors so I might be time to buy some more
  • After a bit of checking around I've concluded that the first beam splitters directly after the cavity are actually 50:50 splitters optimized for 45 deg on s-pol. The reflection is used to generate the beat and transmission of these splitters is used for ISS trans PDs and CCD cameras.  There is a 99% 45 s-pol splitter after the 50:50 splitters that picks most of the light off for the ISS PDs.  Its seems like we are wasting a lot of light going to the ISS here and should actually be using p-pol to get critical coupling into the InGaAs diodes.
  • We're still using two separate raised breadboards here in this optical setup.  I couldn't find any larger 3' by 1' boards in the Bridge West labs, might need to make a purchase to get this together all on one board.
  • I looks like John Martin will be using the ISS from the ATF lab in his SURF project.  I need to get onto getting more stuff fabricated so we can build the ISS better. Maybe a good task for Anchal would be to make a SolidWorks assembly of the new board to see how it will fit together.
  • There are still a few 1/4" adjustble hight mounts in the ISS part of the board.  These should be replaced with 1" mounts as we now have them in stock.

 

  2183   Sun May 13 21:18:55 2018 awadeDailyProgressBEATReinstalling beam splitter and beat detector

I reinstalled the beam splitter, steering mirror and PD in the transmission path.  We have the beam profiling measurement and can reposition the detector more optimally in the near future.  But for now we need to get back to the scatter hunt: specifically the 500 Hz feature that haunts the area directly around the north path pre-mode cleaner (PMC).  

Some of the beam dumps were removed as they weren't bolted down or were in the way of the beam profiling (sorry Craig).

A few things to note:

  • I have now permanently removed the black cube steering mirror mount from the beat setup.  There are visable damage marks on the mirror that make it a dubious choice.  Also the mount just has too much close proximity surfaces on the reflection side that can be potential scatter points.  
  • I replaced the south path steering mirror (previously the black cube beam mount) with a Newport 10Q20HE.1 mirror.  The surface specs are ok 10-5 scratch dig and better than lambda/10.  Its optimized to be over 99% on both polarizations but not technically ultra good HR. We're out of the really good HR reflectors so I might be time to buy some more
  • After a bit of checking around I've concluded that the first beam splitters directly after the cavity are actually 50:50 splitters optimized for 45 deg on s-pol. The reflection is used to generate the beat and transmission of these splitters is used for ISS trans PDs and CCD cameras.  There is a 99% 45 s-pol splitter after the 50:50 splitters that picks most of the light off for the ISS PDs.  Its seems like we are wasting a lot of light going to the ISS here and should actually be using p-pol to get critical coupling into the InGaAs diodes.
  • We're still using two separate raised breadboards here in this optical setup.  I couldn't find any larger 3' by 1' boards in the Bridge West labs, might need to make a purchase to get this together all on one board.
  • I looks like John Martin will be using the ISS from the ATF lab in his SURF project.  I need to get onto getting more stuff fabricated so we can build the ISS better. Maybe a good task for Anchal would be to make a SolidWorks assembly of the new board to see how it will fit together.
  • There are still a few 1/4" adjustble hight mounts in the ISS part of the board.  These should be replaced with 1" mounts as we now have them in stock.
Attachment 1: IMG_3368_DamageOnSouthBeatSteeringMirror.JPG
IMG_3368_DamageOnSouthBeatSteeringMirror.JPG
Attachment 2: IMG_CurrentBeatBoardLayout.JPG
IMG_CurrentBeatBoardLayout.JPG
  2182   Thu May 10 18:18:06 2018 AnchalDailyProgressBEATBeam Profiling Beatnote detector

Today I took more measurements after reflecting off the beam by 90 degrees to another direction and using the Beam Profiler Dataray Beamr2-DD. I used the InGaAs detector with motor spee dof 11 rps and averaging over 100 values.

Following is the fit with and without the new data taken. Data1 in the graph is the earlier data taken using razor blade and Data2 is the data taken today using beam profiler.

The two fits estimate same waist positions and waist sizes within error bars of each other. However, the reduced chi-square is still pretty high.

I've also added the data file and code in the zip.

Attachment 1: ModifiedFitWithNewData.pdf
ModifiedFitWithNewData.pdf
Attachment 2: DataAndCode.zip
  2181   Wed May 9 08:56:54 2018 NeoDailyProgressBEATBeam Profiling Beatnote detector

  2180   Wed May 9 00:51:45 2018 anchalDailyProgressBEATBeam Profiling Beatnote detector

PFA the results of beam profile analysis of transmitted laser from south cavity.

Description:

We are profiling the transmitted laser beam from the south cavity. All measurements of z-direction are from a reference line marked on the table. A razor blade mounted with a micrometer stand is used to profile the beam. The razor moves in the vertical direction and the whole mount is fixed using holes on the optical table so it moves in steps of 25.4 mm.

The beam is first split using a beam splitter and the other port is used as witness detector. The mean value of voltage from the photodetector over 4s time is normalized by the witness detector mean value to cancel out effects of laser intensity fluctuations. The peak to peak voltage from PD over 4 s is used to estimate the standard deviation of the signal. I assumed the error to be sinusoidal and estimated standard deviation as 1/sqrt(8) times the peak to peak voltage.

The profiles at each z point is then fitted with A*(0.5 - erf(norm_x)) + C where norm_x = (x - mu)*np.sqrt(2)/w . This gives estimates of beam radius w at each z position. This data is then fitted to w0*np.sqrt(1 + ((z-zc)*1064e-6/(np.pi*w0**2))**2) to estimate the beam wasit position and wasit size. I have also added the reduced chi-square values of the fits but I'm not sure how much it matters that our standard deviation is calculated in the manner as explained above.

Attachment 1: FitGraphs.pdf
FitGraphs.pdf FitGraphs.pdf FitGraphs.pdf FitGraphs.pdf FitGraphs.pdf FitGraphs.pdf FitGraphs.pdf FitGraphs.pdf
  2179   Thu May 3 22:05:23 2018 awade and anchalDailyProgressBEATBeam Profiling Beatnote detector

Today we made a new mount to be able to profile the laser beam for longer distances on the table.

Attachment 1: 20180503_193329.jpg
20180503_193329.jpg
  2178   Wed Apr 25 12:25:09 2018 awadeDailyProgressBEATBeam Profiling Beatnote detector

Please don't post plots in png, vector graphics only, preferably pdf with the correct transparency in the background. Here a note on plotting that summarizes some common sins: ATF:2137 

Also SI units only.  Sometimes technical drawings and other commercial technical documents and quotes are in limey units but we don't use them in the lab.

I can't really tell what is going on because of the weird units, but it looks like there isn't enough propagation distance for any meaningful change in the beam size.  

You can make a prediction of the expected beam waist size from the cavity waist (~180 µm) and by measuring the beam propagation path and taking into account the lens at output of the vacuum can. By propagating the Gaussian beam through the lens and along the beam path of the beat setup on the output you can make some predicted beam radius to compare to your measurements (in SI units, of course).  

 

 

Quote:

Today, we did the beam profiling for the beatnote detector just before the photodiode. I have attached the data taken. The z values mentioned are from a point which is 2.1 inch away from a marked line on the stage.

However, the analysis concludes that either the beam radius changes too slowly to be profiled properly with given method of measurement or something else is wrong. Attaching the the z vs w(z) plot from this data and few fit plots.

 

 

  2177   Tue Apr 24 14:37:39 2018 Anchal and AndrewDailyProgressBEATBeam Profiling Beatnote detector

Today, we did the beam profiling for the beatnote detector just before the photodiode. I have attached the data taken. The z values mentioned are from a point which is 2.1 inch away from a marked line on the stage.

However, the analysis concludes that either the beam radius changes too slowly to be profiled properly with given method of measurement or something else is wrong. Attaching the the z vs w(z) plot from this data and few fit plots.

 

Attachment 1: BeamradiusProfile.png
BeamradiusProfile.png
Attachment 2: Beam_Profile_Beatnote_-_Sheet1.csv
Ref Z: 2.1 inch,,,
Z-position (mils),Edge X Value (mils),Reading (mV),
-500,175,11,11
-500,180,11,11
-500,185,12,12
-500,190,15,16
-500,195,22,25
-500,200,39,42
-500,205,67,70
-500,210,99,105
... 175 more lines ...
Attachment 3: fitatz500.png
fitatz500.png
  2176   Sun Apr 22 22:00:15 2018 awadeDailyProgressscatterSwitching out NF1811 detector for KA25MHz

Rather than beating the NF1811 dead horse any more I've switched it out for the new KA 26 MHz detector.  

Installing detector and initial test

I found that after removing the focusing lens that was previously the last element before the BN detector, the beam size was roughly 300 µm (radius) about where the PD needed to go.  Here the photodiode size is 2 mm diameter. At this size the beam fits in about 1/3 of the diameter of the new detector area, so this looks like a perfect fit.  As a bonus we have one less optic in this critical part of the optical path.  

The new detector was mounted at 3" on two 1" diameter posts.  There are bolt holes at 1" and 2" spacing on the base of the detector but I didn't have a more solid base in stock.  This mounting should be good enough for now, but can be improved on.

The the incident beam was angled at 30 deg and when centered gave a DC output voltage of about 115 mV from a DC power of 170 µW.  This is about right for the DC path where from Koji's schematic (see PSL:2162) the DC path has transresistance of 10 Ω followed by gain of 101 (total G=1010): we should expect 129 mV, the small discrepancy could be my sloppy power measurement.  This power is down from the usual value of about 800 µW mostly because I refloated the table and didn't realign the refcav input beams. Hopefully I'll get to fixing that issue tomorrow.

The activity on the table unlocked the cavities a few times which caused the beat note PID to kick the frequency around quite a bit.  I was unable to relock the PLL tonight but the peak power as the beat note slewed across 26 MHz was about 55.2 mVrms (-12.2 dBm).  We should expect that with about 85 µW in from each path, 100% overlap, 0.75 A/W responsivity, and 1.27 kΩ gain that the beat note would be on order -2.8dBm (0.162 mVrms) in this case.  I'd say there is some optimizing to do with alignment.  Could have also missed the exact point where the BN crossed over 26 MHz.

Its going to take all night for the BN frequency PID to settle (bring on the intelligent NL controls). This will have to wait till tomorrow.

Max beat note power permissible ?

Not sure what the largest permissible beat note power can be here.  Koji went with a MAX4107 which has a slew rate of  500 V/µs. There were comments from in previous posts about slew rate (see PSL:2161). What is a good rule of thumb for slew rate of signal vs the rated response of an op amp in situations like this? 

Edit Mon Apr 23 13:47:34 2018 (awade): added detector diameter.

Quote:

no This beam is WAY too big for the PD. If the beam radius (wz) is 100 microns and the PD active area diameter is 300 microns, than you're always scattering a lot of beam off of the metal of the can. For new focus 1811, the beam radius should be ~30-50 microns.

 

  2175   Sun Apr 22 17:46:55 2018 awadeSummaryBEATCompensation for MAX4107 at G=4.5

For reference I have attached original schematic to this post.  Koji sent me the link to the original document that can be found here: https://labcit.ligo.caltech.edu/~rana/dale/Length_Sensing_and_Control/LSC_Photodiode/Version_B/D980454-01.pdf
 

This version of the document includes page 1 with the pinouts for the power connector.

Quote:

Performance of the modified photodetector unit:

Performance:

- Resonant frequency f_res = 26.0MHz
- Transimpedance gain at 26MHz is 1.27kOhm (560Ohm resistance of the resonant circuit x G=4.5 x 1/2 by 50Ohm termination)
- Input referred curent noise = 9pA/rtHz
- Shotnoise intercept current is 0.24mA

Remarks:

- There is a gain peaking at 280MHz as explained in the prev elog. If one does not like this, remove 700Ohm resistor from the max4107 stage. It will increase the amplifier gain from 4.5 to 5, and the gain peaking is reduced.

- The transimpedance gain might be still too high. Then, a shunt resistor at the location of R24 can be added to the resonant circuit. This way, the shunt resistance is seen only from the RF path. Of course, lowering the signal level has to be paid by the increase of the input referred current noise level.

 

Attachment 1: D980454-01.pdf
D980454-01.pdf D980454-01.pdf
  2174   Thu Apr 19 18:28:11 2018 ranaDailyProgressscatterBeam size on trans BN detector

no This beam is WAY too big for the PD. If the beam radius (wz) is 100 microns and the PD active area diameter is 300 microns, than you're always scattering a lot of beam off of the metal of the can. For new focus 1811, the beam radius should be ~30-50 microns.

  2173   Tue Apr 17 22:11:34 2018 awadeDailyProgressBEATSome final measurments before switching out NF1811

Note: I tried to attach the plot as a pdf but there is something wrong with backend processing this particular pdf and I'm getting a 502 error.  Have attached as a zip and a png

I thought it would be a good idea to document the current state of the BN spectrum before switching out the NF1811 post cavity BN detector for Koji's newly modified resonant detector.  The new detector has an area of 2 mm x 2 mm, much bigger than the 0.3 mm x 0.3 mm of the current configuration.  The larger PD means we can increase the beam size and hopefully reduce the scatter in the vicinity of the beat setup.

To compare apples with apples, I refloated the table. Also, I turned off the hepa fans around the  lab.   The current BN is 26 MHz and PID locked using the pre-cavity BN detector (Kp = -0.005, Ki = -0.000001).  It still hadn't settled from some disturbances earlier in the day, so was oscillating around ±200 kHz range about the set point. I didn't have time to wait, so I took the measurement with Marconi slope set to 10 kHz.  PLL bandwidth was ~16 kHz with SR560 gain of 100 and Marconi on slope 10 kHz/V.  In this range previous benchmarks of Marconi noise (see PSL:1588) would suggest that the PLL noise limit is 30 mHz/rtHz.  Therefore, PLL shouldn't be the limiting noise at the moment, notwithstanding PD dark noise (which isn't really quantified in the noise budget).

When I took the first measurement I found that the some of the scatter features had been improved since the last measurement (see attached figure razor blade in trace).  The noise floor seemed to be around 0.2 Hz/rtHz with a roll up at lower frequencies.  I realized, however, that I had left the razor blade profiler from the previous day's measurement (PSL:2172) in place, just above the beam.  I retook the measurement (see figure razor blade out trace).  There were a number of peaks that popped up broadly around 70 Hz, 180 Hz and 400 Hz.  Its likely that the razor blade was deflecting and dumping some of the light that has been causing these bumps in our spectrum.

I was a little suspicious of how flat the spectrum was above the characteristic scatter hump (up to 200 Hz).  In three separate measurements I blocked the beam from the BN detector, 50 Ω terminated the PLL at the BN input and then 50 Ω terminated at the ADC input .  These traces are also included in the figure below.  It shows that the apparent limit to sensitivity is the dark noise of the NF1811 photodetector.  

It should be noted that the power has been attenuated onto the NF1811 from ~ 1 mW by 3.0 OD neutral density filter down to 1 µW.  Any power much above this generates harmonics, that we are trying to avoid. So it seems that with improved dumping around the NF1811 detector we can reduce a number of mechanical resonances scatter peaks but that there is a limit to the amount of signal to noise because we are likely to saturate the RF AC path stages inside the NF1811.  Im not sure if this is the right way to calculated but dark noise (NEP) is 2.5 pW/rtHz with 0.75 A/W respositivity and 40kΩ gain PD gain the output noise of the detector is 75 nV/rtHz, For a 16 kHz loop bandwidth (preamp gain 100, VCO slope 10 kHz) the total gain, not including the mixer, is 1e6 which would place the noise floor at about 0.1 Hz/rtHz.  I need to work through exactly the right way to calculate this that treats the noise in a physically correct way at the mixer. 

So it seems that this measurement is getting closer to our previous best measurements. Data and plotting is attached in a zip below as well as being committed to the git.ligo.org ctn_labdata repository.

Attachment 1: plot20180417_ComparisonBNToNoiseFloors.pdf.zip
Attachment 2: 20180417_CompairNF1811ToNoiseFloor.zip
Attachment 3: plot20180417_ComparisonBNToNoiseFloors.png
plot20180417_ComparisonBNToNoiseFloors.png
  2172   Mon Apr 16 16:23:09 2018 awadeDailyProgressscatterBeam size on trans BN detector

I thought I'd have a look at how big the beam is on the current 1811 New Focus detector. Over focusing here might be a source of scatter so this is a number we should probably know.

Razor blade measurement of beam on NF1811 Trans BN detector

I borrowed one of the translation mounts mounted with razor blades from the 40m and did a quick measurement this afternoon.  

Because of the tightness of space on the transmission beat breadboard and the shape of the mount, the closest I could get the blade to the PD was about 1.0 cm.  I took a series of measurements cutting the beam and noting the transmitted DC power (in units of Volts). 

# Data: vertical sweep of razor blade 1 cm in front of post cav BN detector
ypos = np.array([6.,7.,8.,9.,10.,11.,12.,13.,14.,15.,16.,17.,18.,19.,20.]) / 1000. *25.4e-3  # In units of 1/1000s of inch converted to [m]
yPDVolt = np.array([1.74,1.86,2.64,5.10,12.9,28.2,53.4,82.8,112,132,143,148,149,150,150])  # [mV]

I fitted the integral of the Gaussian profile and plotted (see plot below).  This is a quick diagnostic measurement. Iused least squares fit, so no error analyses. Here are the fitted values:

Fitted beam center relative to zero of measurement 0.3240 mm
Fitted peak power 148.2308 mV
Fitted detector dark DC reading 1.6333 mV
Fitted beam width wz 97.3314 um

Time to make a switch?

This beam is quite small although the NF1811 detector diameter is only 0.3 mm.  Not sure how scatter scales with beam size here, is there a good reference I can look up on this?

Now might be a good time to switch to Koji's new PD.  I've managed to stabilize the beat note to 20 MHz it seems to stay within a <1 kHz (3.2 µK) range over a periods of sometime more than 6 hours.  Although, it can take 12 hours to settle down over night after a large disturbance. 

Attachment 1: IMG_2792.JPG
IMG_2792.JPG
Attachment 2: 20180416_RazorBladeProfileVerticalTransBNDector.pdf
20180416_RazorBladeProfileVerticalTransBNDector.pdf
Attachment 3: 20180416_BeamProfileAtPD.ipynb.zip
  2171   Fri Apr 13 11:34:09 2018 awadeSummaryDrawingsDrawings: 2in windows for vacuum can flang and clamp, steve's comments

I discussed the 2-in window flange design with Steve.  He had a couple of suggested changes.  I'm adding them here for reference as I update the drawings.

He says the angling of the optic into the main flange is fine, 8" 40m flanges have this design.

Changes:

  • The retaining ring should be made of Delrin, this will be more forgiving on the optic when at atmosphere if there happens to be any contact points.  Also easier/cheaper to machine.  The retaining ring is only there to hold the optic in place when not under vacuum;
  • The six #8-32 holding screws should be changed to four #10-24 s.  Orient these equidistant and with lower edge parallel to the table. No helicoil.;
  • Assembly drawing says o-ring part number #2-130 but description is is #2-223 (which is the next size class up). Choose one. The both are good in terms of groove size but maybe choose the smaller one;
  • Include screw part in assembly table;
  • It would be best practice to include a Teflon gasket on the flange side of the assembly between window and metal. Probably a thickness of 0.090".  Even if there is still an air gap left in the design dimensions. If the tolerances are a bit off then having a soft plastic surface is an good idea, it gives the optic something to rest against that won't apply hard localized stress points;
  • Place centering points on assembly drawing of the front face for two windows. Also, add center line on Detail B view; and
  • The two retaining rings are too close together.  Move spacing from 1.5" to 1.662".  This will mean the beams are not centered on the windows but will give some more space between the retaining rings.

Many of the finishing and tolerance parameters don't matter so much.  Over toleranced parts will cost more.  The only place where this might need to be careful is in the spec of the oring grove where vacuum is actually being held back, the 16 Ra in the drawing is fine.

Marco rubber and plastics have a good summary page for best practice design parameters, see: O-Ring Groove Design Directory.

  2170   Thu Apr 12 23:28:18 2018 awadeDailyProgressComputersRestarted fb4 framebuilder

I've made a number of changes to channels over the last week.  Channels haven't been logging for new shield channels and some minor channels I had renamed.  

I used Craig's scrape-and-make script for generating framebuilder .ini files (see PSL:2133). And restarted the daqd process as per PSL:2014. Looks like the new channels are up and logging.

I've been experimenting with different values of P and I in the shield controllers, the beat note seems to be settling to within 100's of kHz of the a set point but the convergence time is >12 hours.  It should be interesting it be able to see this data.

  2169   Thu Apr 12 22:00:13 2018 awadeSummaryTempCtrlSummary of parameters and dimensions for thermal modeling

This is a summary reference post for parameters to do with the thermal surfaces and bodies within the vacuum can. It brings together drawings and computed dimensions so we can begin to make an actuate physical model of the thermal dynamics of our system.

Design goals

At the center of the experiment are a pair of Fabry-Pérot cavities that need to be thermally stable enough to not drift more than 100 Hz in the time it takes to take a PSD of their relative brownian driven fluctuations.  

\Delta T = \frac{\lambda}{2c\alpha} \delta \nu

https://nodus.ligo.caltech.edu:8081/CTN/1874

Overview

[Insert SW cutaway with ballons]

Cavity parameters 

Refcav parameters
Property Value
Rough dimensions ø38.1mm x 36.83 mm (9.52 mm bore through middle)
Mass 112 g
Heat capacity  82.88 J/K
Outward facing surface area 75.5 cm^2
Emissivity rough fused silica 0.75
Emissivity polished fused silica 0.93
Coefficient of thermal expansion 5.5e-7 1/K
Optical frequency temperature shift @ 1064 nm 310 Hz/µK

Cavity cylindrical heat shields

https://nodus.ligo.caltech.edu:8081/CTN/1737

  2168   Wed Apr 11 16:06:31 2018 awadeSummaryDrawingsDrawings: 2in windows for vacuum can flang and clamp

Some updates for 2 inch window flanges.

Errors fixed

I noticed a few small errors in the 2 inch window flange design.  I hadn't factored the clearance of the window from the metal (0.5 mm) into the depth of the o-ring grooves, so as to get exactly 0.72 compression when assembled.  Also the clearance on the retaining ring side was wrong because I had computed the angling depth on the lower side of the optic based on the optic dimensions and not on the size of the cut hole with clearance.

To fix these issues and clarify the specified clearance, in the solidworks part itself, I have made the clearance explicit with two additional revolve cuts. One is around the face and around the circumference of the optic. This way the clearance will also be parameterize in the part: this should improve adaptability of the part to other applications. Groove depth is now set at the desired compression ratio and the correct real depth of the final groove is realized by the clearance cuts.

Also I changed the angling of the two windows to point inwards on the outside of the can.  This means that ghost beams will be maximally separated on the inside of the can, making it easier to mount a pair of beam dumps either side of each cavity.

Files uploaded to DCC

I've put the drawings and assembly on DCC for better version tracking. I've attached the solid works folder below in a zip for local reference.

How it fits together

I have yet to finish checking the whole tank assembly.  For now here is a pretty animation showing port and orings.

 

  2167   Mon Apr 9 20:44:41 2018 awadeDailyProgressTempCtrlBeatnote Stabilization: Configuring heaters to actuate differentially

In an effort to improve the CTN experiment's temperature control I've reconfigured the cavity heaters to operate with differential and common mode heating.  By making the actuation symmetric and elevating both cavities well above the vaccan temperature hopefully this will improve the linearity of the actuator.

The heating wire on the north path is 156.8 Ω and south is 85.6 Ω (don't know why they are different). I've configured an additional channels for the south heater (previously not hooked up).  Units of the new channel are in watts.  Two additional calcout channels were made that set the common heating value (in watts) for both channels and a difference between the heaters (in watts) that ranges from -1.1 W to +1.1 W.  After rebooting the IOC and setting the common and diff heating to produce 0 W on south and 0.7734 W on north I get roughly the same beat note frequency as before.

After the change PID feedback to the differential heater channel, it was possible to use PI feedback to drive the beat note to a set point of 100 MHz but tweaking gain values to kill oscillations was takes a very long time (still not there yet).  I reattempted to implement the relay auto tuning method from before (see PSL:2142). However, I had the same converging cycle limit to zero after a few hours.  I think that the large lag on the actuator/sensor/plant in these temperature tuning situations may rule out finding objective Kp, Ki, Kd values using relay tuning methods: the lag puts us away from the -pi first real axis crossing the nyquist curve and estimates of the plant's critical gain and frequency are bogus.  

Short of making some really smart controls that can anticipate the trajectory of the temperature and make more optimal estimates for the feedback I may need to vent the can and get some low noise platinum RTD sensors on the shields.

  2166   Fri Apr 6 15:57:30 2018 awadeDailyProgressOtherTuning up alignement into RefCavs

Since hard clamping down the vaccan, the alignment into the cavities has been suboptimal. 

South path was down to 45% fringe vis and north was down to 14%.  As we are using the trans PDs as reference for autolocker thresholds this is causing the FSS to unlock periodically.

I walked the south periscope so that the reflected DC voltage was V_min, Vmax = (0.292 V, 1.52  V) => Vis = 67%

Similarly the north was improved V_min, Vmax = (0.376V, 1.76V) => Vis 65%.

  2165   Fri Apr 6 04:48:02 2018 KojiSummaryBEATCompensation for MAX4107 at G=4.5

Performance of the modified photodetector unit:

Performance:

- Resonant frequency f_res = 26.0MHz
- Transimpedance gain at 26MHz is 1.27kOhm (560Ohm resistance of the resonant circuit x G=4.5 x 1/2 by 50Ohm termination)
- Input referred curent noise = 9pA/rtHz
- Shotnoise intercept current is 0.24mA

Remarks:

- There is a gain peaking at 280MHz as explained in the prev elog. If one does not like this, remove 700Ohm resistor from the max4107 stage. It will increase the amplifier gain from 4.5 to 5, and the gain peaking is reduced.

- The transimpedance gain might be still too high. Then, a shunt resistor at the location of R24 can be added to the resonant circuit. This way, the shunt resistance is seen only from the RF path. Of course, lowering the signal level has to be paid by the increase of the input referred current noise level.

Attachment 1: CTN25_transimpedance.pdf
CTN25_transimpedance.pdf
Attachment 2: current_noise_CTN25.pdf
current_noise_CTN25.pdf
Attachment 3: idet_CTN25.pdf
idet_CTN25.pdf
  2164   Thu Apr 5 02:04:49 2018 KojiSummaryBEATCompensation for MAX4107 at G=4.5

MAX4107 is stable only when G>+10. Because of this fact, the 25MHz PD has a too-high transimpedance for our purpose. To lower the gain without losing the stability of the amp, I have implemented a compensation network.

Attachment 1 shows the compensation network. This 10Ohm+100pF pair effectively makes the high freq noise gain higher (~10) while the low freq gain is G=4.5.

The actual implementation is found in Attachments 2 and 3. The overall schematic can be found in Attachment 5.
I also chose the resistor values so that their noise contributions are reduced.

The resulting output spectrum is compared with the one before the modification (Attachment 4).
Even with the lower gain, the gain peaking of the amplifier output is reduced.

LISO model (not shown here) indicates the input referred noise is ~1nV/rtHz. Considering the voltage division by the 50Ohm termination, the output voltage is as low as 2.25nV/rtHz. This is not a high number. Thus, we practically need a mid power / low noise amplifier attached to the output of the unit.

The total performance of the PD unit will be tested again shortly.

Attachment 1: max_circuit.pdf
max_circuit.pdf
Attachment 2: IMG_3667.JPG
IMG_3667.JPG
Attachment 3: IMG_3668.JPG
IMG_3668.JPG
Attachment 4: IMG_3665.JPG
IMG_3665.JPG
Attachment 5: CTN25_schematic_180404_KA.pdf
CTN25_schematic_180404_KA.pdf
  2163   Wed Apr 4 12:52:33 2018 awadeSummaryDrawingsDrawings: 2in windows for vacuum can flang and clamp

I've drafted up some new drawings for new view ports into our vacuum can.  We have 8 inch windows at the moment with AR coating and surface quality that could be better.  Given the criticalness of scatter we plan to replace the windows with a set of four 2 inch AR-AR coated windows; smaller windows will also reduce the exposed thermal surfaces to outside, thus improving thermal isolation of the cavity shields from the outside. 

Specifications of view port windows

Planned spec for the windows is 10-5 scratch-dig, lambda/10 flatness and AR of R<=0.25 % with a 30 arc second wedge. I've contacted a number of vendors for quotes. As we can't list prices publicly here I've made a summary page HERE with prices and specs from vendors that responded.

 

Design of flange and retaining ring

To deal with any residual beams from the surfaces of the window we will angle the windows at 3 degrees to normal by insetting them into the flange: centered beams on the optic that are normal the flange face will then be reflected at 3 degrees (52 mrad) which at a distances of roughly 20 cm will be 1 cm offset from main beam, this is plenty of space to fit in a beam dump. This design may present challenges for machining.  I'm pretty sure the groves can't just be milled, they need lathing with certain tool specifications to ensure there are no radially oriented scratches that might compromise the seal. The flange is a bulky piece, we need to ask a machinist what can be done.  The angled inset is the way to go, even if its a little harder to make.

I based these drawings partly off Johannes's design (see Cryo:1456). The particulars of their design meant that I couldn't reuse the parts, but I took cues from the design features (that made things much faster to draft). I rebuilt the flange parts and retaining ring with a more parametric design.  Within the part files dimensions are defined in a way that makes it easy to change wedging angles, groove dimensions and sinking depth of the optic.  Hopefully this will help future users adapt them to their needs quickly.  Johannes also had a good reference for view port designs Abbot & Scace in J. Vac. Sci. Technol. A 28, 573 (2010).  One thing that isn't addressed much in the literature is the extra loading applied on the inner o-rings when 1 atm of pressure is applied (vacuum).  For a 2 in^2 window area. 1 atm is about 20.9 kg of pressure (8.6 lb/in of oring). For 70 duro viton o-rings the additional compression looks to be on order of 7 %.  Provided there enough clearance is left between glass and metal, this shouldn't me much of an additional error: it just something to keep in mind for tolerances of the parts.

Drawings are attached below along with an ipython notebook used for the calculation of various dimensions (this can also be found in a gist on GitHub). A zip contains all the parts, drawings and assemblies.

The basic design criteria are for a 2.0" view port optic, wedge by 30 arc min, that is 9.35 mm on its thickest edge.  Clearance of 3/128" are made around the perimeter and 0.5 mm between the faces and metal of the flange and retaining ring.  The o-ring I selected is #130 which has ID of 1.612" and thickness (toroidal diameter) of 0.103".  With a set compression ratio of 0.72 for the o-ring it is possible to make an o-ring groove just deeper than half the o-ring thickness. An o-ring any smaller will be more than double any possible groove depth, which would be bad as would will pop out during assembly. Dimensions of the o-ring groove were chosen according to rules outlined in Abbot & Scace. I think at a 2" diameter it is a little too small to make dove tale o-ring grooves, so the inner diameter of the groove was made 2% larger than the o-ring so that it will be under a little tension while the unit is assembled.  The outer edge of the o-ring groove is 2 mm from the edge of the optic, this should be enough space for the o-ring to be clear of any edge imperfections. Calculations for all these quantities can be found in the ipython notebook.  

The rest of the dimensions were adjust accordingly to reach the correct clearances, an optic angle of 3 degrees to the front of the flange and leave 2 mm protruding on the lowest side of the optic.  The two windows are oriented about the center line of the 10" flange blank, spaced 3.0" apart.  The angle is currently set to point outwards on the outside  of the tank; this orientation might be wrong for our needs as we want to primarily dump light inside the tank and it would be easier to put the beam dumps not between the two beams.

I need to stop fiddling with this now.  It would be good if someone could look over the drawings and any raise issues. 

 

Attachment 1: VacuumViewportDesignNotebook.ipynb.zip
Attachment 2: TwoViewPort_10inchBlankFlange_Modified_v1.PDF
TwoViewPort_10inchBlankFlange_Modified_v1.PDF
Attachment 3: TwoInchViewportRetainingRing_v1.PDF
TwoInchViewportRetainingRing_v1.PDF
Attachment 4: 2inchWindowAssemb_3degangling_0.5degWedge.PDF
2inchWindowAssemb_3degangling_0.5degWedge.PDF
Attachment 5: SolidWorksFiles_NewVacCanFlanges.zip
  2162   Wed Apr 4 02:06:45 2018 KojiSummaryBEATFirst article of the CTN beat PD

Made the first article of the 25MHz resonant PD for CTN experiment.

Performance:

Resonant frequency f_res = 26.0MHz
Transimpedance R_res = 2.3kOhm
Input referred curent noise = 10pA/rtHz
Shot noise intercept current = 0.29mA

Remarks:

MAX4107 at G=10 gives a gain peaking at 260MHz. It is not tamed as the dark spectrum shows the peak does not have significant RMS.
But this might cause a trouble later. We can consider to replace the opamp with ones suggested by Rana. Rana bought "THS4271" to give it a try.

Attachment 1: PD_circuit.pdf
PD_circuit.pdf
Attachment 2: CTN25_schematic_180403_KA.pdf
CTN25_schematic_180403_KA.pdf
Attachment 3: CTN25_PHOTO.JPG
CTN25_PHOTO.JPG
Attachment 4: liso_model.zip
Attachment 5: CTN25_transimpedance.pdf
CTN25_transimpedance.pdf
Attachment 6: current_noise_CTN25.pdf
current_noise_CTN25.pdf
Attachment 7: idet_CTN25.pdf
idet_CTN25.pdf
  2161   Mon Apr 2 00:15:34 2018 ranaSummaryBEATThe design for a new beat PD

MAX4106 slew rate is 275 V/us, so almost half of 4107. LMH6611 is 460 V/us.

What about THS4271-EP ? (1000 V/us, can be used with a gain = 2, Vn = 3 nV, i_n = 3 pA)

Quote:

- Or do we have MAX4106 (min gain 5), or something else for a replacement?

Update: The "EP" model doesn't come in SOIC-8, so I just ordered the regular THS4271. It wants a 'PowerPad' heat sink, but we can try it without and see what happens as a test.

  2160   Fri Mar 30 20:12:22 2018 awadeDailyProgressOtherDisabling the air springs on the vac can: Shimming and clamping

Following up on the airspring issues.  Its not clear that suspending our vacuum can on 3 Hz air springs will improving things much in terms of noise hunting for now. As there is a leak and no stable supply of air, the air springs seem more a nuisance for now.  They are varying the alignment enough to change the power transmitted and reflected by about 12% (when using the wall supply of air).  Rana has suggested that it would be much better to have a really rigid connection to the table.

Craig placed metal shims under each of the four legs of the tank.  I have now clamped the tank down very tight using L-shaped pieces (see attachment).  I used a T-driver to get the tension nice and tight.  Alignment of the cavities will not have changed much as the tank was already resting on the shims.  

 

 

Quote:

Considering I can't even lock the North cavity today because of alignment drift, I'd upgrade this to super high priority.

Looks like you need to connect the air springs via this black tubing, and not the clear 1/4'' tubing.  There are 8 of these metal screw clamps on the North side of the table and 5 on the other side.  These are surely the cause of leaking, but I don't have any good ideas for how to eliminate them.  I'll google around for ways to eliminate this black tubing from the setup so we don't have 13 leaky connections.

At this rate, the cylinder will hit low 100's later this week.  This is why I'm disconnecting the air springs and shimming up the vaccan for now. 

Quote:

I guess going back to the wall supply would be a stupid step backwards.  We need to fix this leak, its either in the tubing or the air springs themselves.  

Can you check out what the connection to the air springs is and whether this can be connected to the standard clear tubing airlines?  We are using the standard 1/4" tubing (see Newport Pneumatic Isolator Accessories).  I'm not even sure if they are supposed to be permanently hooked up to air, the Newport air springs seem to have a Schrader valve (cars/bike valve) on the side and the description suggest that they only need to be pumped up and leveled once.   They do degrade. If that is the case then we need to assess if these older rubber diaphragms need replacing.

This is moderate priority. Scattering is top of the list.

---

We need to return this cylinder when getting a new one.  It will need to reach the low 100s, then we hit reorder on N2.

 

Quote:

Ever since I attached the vaccan air springs to the cylinder, it has been rapidly losing air pressure.  It is now down to ~1100 psi, where on Thursday it was ~1800 psi.  At this rate we will have to order a new cylinder, and figure out how to make the air springs less leaky, as this is affecting our alignment over time.

For now, I'll relock the cavities, replace the shims, and turn off the air springs as they are causing more harm than good.  We will rely on the floating table until then.

 

 

 

Attachment 1: 2018-03-30_17.24.30.jpg
2018-03-30_17.24.30.jpg
Attachment 2: 2018-03-30_17.24.24.jpg
2018-03-30_17.24.24.jpg
  2159   Fri Mar 30 17:34:52 2018 awadeDailyProgressOtherSign flip on Laser slow control PID parameters

I've been updating the IOC .db files to include new soft channels that break the refcav shield heaters into a common heating and differential heating component.  This should improve actuation on the cavity length by symmetrizing the temperature actuation.

However, after a few channel renamings and restarts to the IOC process I've found that the cavity auto lockers were no longer achieving lock.  On closer inspection it turns out that the PIDLocker on the laser slow frequency controls was switched to the beta version of the script which has a sign flip on the actuation direction. Autolockers were working fine but the PID was switching on and promptly unlocking the cavities by driving in the wrong direction.  I've flipped the sign of all the laser slow controls Kp, Ki and Kd.  The problem is fixed and cavities are now auto locking themselves again.

  2158   Thu Mar 29 11:14:52 2018 awadeNotesscatterHigher quality vaccan windows: 40m stock of wedged windows

I guess BK7 is fine, we're not going to be putting high power in.  I just though UV fused silica would be better practice if someone wanted to repurpose the flange in a few years.  Seems like a minor extra cost.

Bottom line is that I don't think we have four identical of anything we can use. Should order 1.5" W2s from CVI or somewhere else?

Quote:

That was unfortunate. But why does BK7 uncompatible with the purpose? We need UV fused silica only for the high power reason, I thought.

 

  2157   Thu Mar 29 02:51:35 2018 KojiSummaryBEATThe design for a new beat PD

DC photocurrent:
a few mA => A transimpedance of 1k Ohm will realize the output of ~a few V.
A few mA of DC current produces the shot noise photocurrent of 20~30pA/rtHz  

RF photocurrent: 
Resonant circuit resistance @25MHz: 100~300 Ohm.
Reduced to 100 by the shunt resistance of 150 Ohm
MAX4107 required minimum gain of 10 for the stability
-> Total Transimp. R=1K
-> Andrew said R=1K gives 13dBm output (1.4Vpk @25MHz)
-> This corresponds to 200 V/us of slewrate. This is ~40% of the full scale. (Too big)

input referred current noise ~ 12pA/rtHz ==> Shot noise intercept current ~0.44mA

 

If we reduce the shunt resistance to get the total transimpedance of 500Ohm
=> Beat output: 7dBm (0.7Vpk@25MHz, ~20% of the full slewrate)

input referred current noise ~24pA/rtHz ==> Shot noise intervept current ~ 1.8mA


Questions:

- Can we torelate this noise level (24pA/rtHz)?

- Or do we have MAX4106 (min gain 5), or something else for a replacement?
 

Attachment 1: PD_circuit.pdf
PD_circuit.pdf
Attachment 2: PDmodel_CTN_25MHz_opamps_run5.pdf
PDmodel_CTN_25MHz_opamps_run5.pdf
Attachment 3: PDmodel_CTN_25MHz_opamps_run6.pdf
PDmodel_CTN_25MHz_opamps_run6.pdf
Attachment 4: PDmodel_CTN_25MHz_opamps_run7.pdf
PDmodel_CTN_25MHz_opamps_run7.pdf
Attachment 5: PDmodel_CTN_25MHz_opamps_run8.pdf
PDmodel_CTN_25MHz_opamps_run8.pdf
Attachment 6: IMG_3608.JPG
IMG_3608.JPG
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