I redid the optical POX transfer functions and updated the wiki at http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/POX.

I measured each transfer function several times to calculate uncertainties for each measured point. There is one large transfer function from 1 MHz to 500 MHz showing a resonance peak at 11 MHz and notches at 22 MHz and 55 MHz. I also made more detailed measurements around each of these resonance peaks. These measurements were fit to a resonance curve to determine the resonant frequency, transimpedance at resonance, and Q for each peak. These measurements agree with the shot noise measurement for the transimpedance at 11 MHz taken earlier considering that this measurement was made at 11 MHz instead of at the resonant frequency of 11.14 MHz.

I measured these transfer functions with the Agilent 4395a using the netgpib.py script last week. I realized that when using this script to save multiple copies of the same measurement after setting up the instrument, the first and second measurements are saved but all measurements saved after are identical to the second measurement until the instrument is physically reset. This happens because the analyzer switches the trigger from continuous to hold after making a measurement using this script. Kiwamu said that the script can be modified to return the trigger to continuous after saving the data so that multiple measurements can be saved without being at the analyzer physically. I did not want to waste more time figuring out how to modify the script to do this so I used one of the netbooks and sat at the analyzer manually returning the trigger to continuous after each measurement.

 The value of I_dc was a mistake. The value should be 240 µA.

The widths of the resonance peaks are listed below the fits to each peak on the wiki.

[Koji, Kevin]

We fit the entire POX optical transfer function from 1 MHz to 500 MHz in LISO. The fit is on the wiki at http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/POX. Using LISO's root fitting mode, we found that the transfer function has five poles and four zeros.

I will work on making plots of the residuals. This is difficult because by default, LISO does not calculate the fitting function at the frequencies of the data points themselves and I haven't figured out how to force it to do this yet.

[Rana and Kevin]

I measured the optical transfer function of POY and fit the data using LISO. The fit can be found at http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/POY. POY was missing the RF cage and back cover so I took those parts from AS55 in order to make these measurements.

POY does not have the unwanted oscillations at 225 MHz that POX has. Attachment 1 shows the transfer functions of POX and POY.

To measure the transfer functions, I used a 50/50 beam splitter to send half the light from an AM laser to POY and half the light to a New Focus 1611 reference photodiode. The transfer function for POY was measured as the transfer function of the signal from POY divided by the signal from the 1611. When I was measuring the transfer function for POX, I failed to ensure that the photodiodes were operating linearly. Before making the measurements for POY, I varied the RF power modulating the AM laser and recorded the magnitude of the transfer function at the 11 MHz peak. Attachment 2 shows these values. The measurements for POY were made in the linear region at an RF power of -10 dBm. The measurements for POX were made at 0 dBm and were most likely not in the linear region for POX.

[Koji and Kevin]

I measured the shot noise of POY and fit the data to determine the RF transimpedance at 11 MHz and the dark current. The transimpedance is (3.860 +- 0.006) kΩ. I realize that there are not many data points past the dark current but I did not want to take any further data because the light bulb was getting pretty bright. If this is a problem, I can try to redo the measurement using a lens to try to focus more of the light from the bulb onto the photodiode.

I also measured the spectrum and recorded a time series of the RF signal with the light to the photodiode blocked. These measurements do not show any large oscillations like the ones found for POX.

The plots of the measurements are on the wiki at http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/POY.

[Kevin, Rana, Koji]

I calculated the dark noise of POX and POY due to Johnson noise and voltage and current noise from the MAX4107 op-amp using nominal values for the circuit components found in their data sheets. I found that the dark noise should be approximately 15.5 nV/rtHz. The measured dark noise values are 18.35 nV/rtHz and 98.5 nV/rtHz for POX and POY respectively. The shot noise plots on the wiki have been updated to show these calculated dark noise sources.

The measured dark noise for POY is too high. I will look into the cause of this large noise. It is possible that the shot noise measurement for POY was bad so I will start by redoing the measurement.

The previous measurement for the shot noise of POY had the dark noise at ~100 nV/rtHz. I redid the measurement and got 26 nV/rtHz for the dark noise. I think that when I made the previous measurement, the spectrum analyzer had automatically added some attenuation to the input that I failed to remove. This added attenuation raised the noise floor of the measurement making the dark noise of POY appear larger than it is.

The updated measurement can be found on the wiki at http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/POY.

I measured the transfer function, shot noise, and dark spectrum of AS55.

From the shot noise measurement, the RF transimpedance is (556.3 +- 0.8) Ohms and the dark current is (2.39 +- 0.01) mA. The dark noise agrees with the approximate value calculated from the circuit components.

There are no anomalous oscillations when there is no light on the photodiode. I am working on fitting the transfer function in LISO but the other plots are on the wiki at http://blue.ligo-wa.caltech.edu:8000/40m/Electronics/AS55

I changed the heater circuit described in this elog to a current sink. The new and old circuits are shown in the attachment. The heater is  and is currently 24Ω; the sense resistor  is currently 6Ω. The op-amp is still an OP27 and the MOSFET is still an IRF630.

The current through the old circuit was saturating because the gate voltage on the MOSFET was saturating at the op-amp supply rails. This is because the source voltage is relatively high: .

In the new circuit the source voltage is lower and the op-amp can thus drive a large enough to draw more current (until the power supply saturates at 25V/30Ω = 0.8A in this case). The source and DAC voltages are equal in this case and so the current is . Since this is the same current through the heater, the drain voltage is . I observed this behavior in this circuit until the power supply saturated at 0.8A. Note that when this happens and the gate voltage saturates at the supply rails in an attempt to supply the necessary current.

Gautam and I looked into the DAC noise contribution to the noise budget for homodyne detection at the 40m. DAC noise is currently the most likely limiting source of technical noise.

Several of us have previously looked into the optimal SRC detuning and homodyne angle to observe pondermotive squeezing at the 40m. The first attachment summarizes these investigations and shows the amount of squeezing below vacuum obtainable as a function of homodyne angle for an optimal SRC detuning including fundamental classical sources of noise (seismic, CTN, and suspension thermal). These calculations are done with an Optickle model. According to the calculations, it's possible to see 6 dBvac of squeezing around 100 Hz.

The second attachment shows the amount of squeezing obtainable including DAC noise as a function of current noise in the DAC electronics. These calculations are done at the optimal -0.45 deg SRC detuning and 97 deg homodyne angle. Estimates of this noise are computed as is done in elog 13146 and include de-whitening. It is not possible to observe squeezing with the current 400 Ω series resistor which corresponds to 30 pA/rtHz current noise at 100 Hz. We can get to 0 dBvac for current noise of around 10 pA/rtHz (1.2 kΩ series resistor) and can see 3 dBvac of squeezing with current noise of about 5 pA/rtHz at 100 Hz (2.5 kΩ series resistor). At this point it will be difficult to control the optics however.

So it seems reasonable to reduce the DAC noise to sufficient levels to observe squeezing, but we will need to think about the controls problem more.

Gautam and I redid our calculations, and the updated plot of squeezing as a function of DAC current noise per coil is shown in the attachment. The current noise is calculated as the maximum of the filtered DAC noise and the Johnson noise of the series resistor. The total noise is for four optics with four coils each.

The numbers are worse than we quoted before: according to these calculations we can get to 0 dBvac for current noise per coil of about 2.4 pA/rtHz at 100 Hz.

I have been looking into whether we can observe squeezing on a short timescale. The simulations I show here say that we can get 2 dBvac of squeezing at about 120 Hz using extreme signal recycling.

The parameters used here are

• 100 ppm transmissivity on the folding mirrors giving a PRC gain of 40.
• 10 kΩ series resistance for the ETMs; 15 kΩ series resistance for the ITMs.
• 1 W incident on the back of PRM.
• PD quantum efficiency 0.88.

The first attachment shows the displacement noise. The red curve labeled vacuum is the standard unsqueezed vacuum noise which we need to beat. The second attachment shows the same noise budget as a ratio of the noise sources to the vacuum noise.

This homodyne angle and SRC detuning give about the maximum amount of squeezing. However, there's quite a bit of flexibility and if there are other considerations, such as 100 Hz being too low, we should be able to optimize these angles (even with more pessimistic values of the above parameters) to see at least 0.2 dBvac around 400 Hz.

We can get 1.1 dBvac at 210 Hz.

The first two attachments are the noise budgets for these optimized angles. The third attachment shows squeezing as a function of homodyne angle and SRC detuning at 210 Hz. To stay below -1 dBvac, the homodyne angle must be kept between 88.5 and 89.7 degrees and the SRC detuning must be kept between -0.04 and 0.03 degrees. This corresponds to fixing the SRC length to within a range of 0.07/360 * 1064 nm = 200 pm.

Yes, this SRC detuning is very close to extreme signal recycling (0° in this convention), and the homodyne angle is close to the amplitude quadrature (90° in this convention).

For T(SRM) = 5% at the optimal angles (SRC detuning of -0.01° and homodyne angle of 89°), we can see 0.7 dBvac at 210 Hz.

[Gautam, Kevin]

We redid the measurement measuring the voltage noise from the REFL PD demod board output monitor with an SR785 with the noise eater on and off. We used a 100x preamp to amplify the signal above the SR785 noise. The SR785 noise floor was measured with the input to the preamp terminated with 50 ohms. The spectra shown have been corrected for the 100x amplification.

This measurement shows no difference with the noise eater on or off.

[Gautam, Kevin]

We measured the MC coil driver noise at the output monitors of the coil driver board with an SR785 in order to further diagnose the excess IMC frequency noise.

Attachments 1 and 2 show the noise for the UL coils of MC3 and MC2 with various combinations of output filters engaged. When the 28 Hz elliptic filter is on, the analog dewhitening filter is off, and vice versa. The effect of the analog low pass filter is visible in MC3, but the effect of the digital low pass filter is swamped by the DAC noise.

We locked the arms and measured the ALS beatnote in each of these filter combinations, but which filters were on did not effect the excess IMC frequency noise. This suggests that the coil drivers are not responsible for the excess noise.

Attachment 2 shows the noise for all five coils on MC1, MC2, and MC3 as well as for ITMY, which is on a different DAC card from the MCs. All filters were on for these measurements.

The previous measurements were made from the coil driver output monitors. To investigate why the MC2 LR coil has less noise than the other coils, I also measured the noise at the output to the coils.

The circuit diagram for the coil driver board is given in D010001 and a picture of the rack is on the 40m wiki here. The coil driver boards are in the upper left quadrant of the rack. The input to the board is the column of LEMOs which are the "Coil Test In" inputs on the schematic. The output monitors are the row of LEMOs to the right of the input LEMOs and are the "FP Coil Volt Mon" outputs on the schematic. The output to the coils "Coil Out" in the schematic are carried through a DB15 connector.

The attachment shows the voltage noise for the MC2 LR coil as well as the UL coil which is similar to all of the other coils measured in the previous measurement. While the LR coil is less noisy than the UL coil as measured at the output monitor, they have the same noise spectrum as measured at the output to the coils themselves. So there must be something wrong with the buffer circuit for the MC2 LR voltage monitor, but the output to the coils themselves is the same as for the other coils.

I've been looking into recovering the seismic BLRMs for the BS Trillium seismometer. It looks like the problem is probably in the anti-aliasing board. There's some heavy stuff sitting on top of it in the rack, so I'll take a look at it later when someone can give me a hand getting it out.

In detail, after verifying that there are signals coming directly out of the seismometer, I tried to inject a signal into the AA board and see it appear in one of the seismometer channels.

1. I looked specifically at C1:PEM-SEIS_BS_Z_IN1 (Ch9), C1:PEM-SEIS_BS_X_IN1 (Ch7), and C1:PEM-ACC_MC2_Y_IN1 (Ch27). All of these channels have between 2000--3000 cts.
2. I tried injecting a 200 mVpp signal at 1.7862 Hz into each of these channels, but the the output did not change.
3. All channels have 0 cts when the power to the AA board is off.
4. I then tried to inject the same signal into the AA board and see it at the output. The setup is shown in the first attachment. The second BNC coming out of the function generator is going to one of the AA board inputs; the 32 pin cable is coming directly from the output. All channels give 4.6 V when when the board is powered on regardless of wheter any signal is being injected.
5. To verify that the AA board is likely the culprit, I also injected the same signals directly into the ADC. The setup is shown in the second attachment. The 32 pin cable is going directly to the ADC. When injecting the same signals into the appropriate channels the above channels show between 200--300 cts, and 0 cts when no signal is injected.

Steve, the pictures you posted are not the AA board I was referring to. The attached pictures show the board which is sitting beneath the GPS time server.

Steve secured the GPS time server in the rack above the AA board and removed the wooden block that it was resting on. The new rack is shown in attachment 1.

I then opened the AA board to see why the channels aren't working. Even though the board was powered and outputting 4.6 V, none of the chips were getting power. I must have shorted something while trying to diagnose this and the board is no longer powered either.

The schematic is given in D990147. The D68L8EX filter is bypassed on all the channels, as can be seen in attachment 3, so the board isn't really doing anything. Rana suggested that we could just bypass the whole circuit by wiring the IN channels directly to the OUT channels going to the ADC. I'll try that next for a single channel.

In the ongoing attempt to recover the seismometer BLRMS, I removed the AA board from the rack and modified the BS seismometer Z channel. The BS_Z BLRMs seem to be recovered after this modification.

I removed the three resistors from the output of the circuit and wired the input and from the seismometer directly to the input to the ADC. The modified schematic is shown in attachment 1. Attachments 2 and 3 show the top and bottom of the modified board. The board is doing nothing now other than serving as a connector for this channel.

I put the board back in the rack and injected a 2 Vpp signal into the BS_Z channel and saw +/- 1600 cts in C1PEM-SEIS_BS_Z. I then plugged the seismometer back into the board and took the spectrum shown in attachment 4. This shows the working Z channel giving a reasonable seismic spectrum. Note that X and Y are not modified yet.

If there are no objections, I will modify all the other channels on the board in the same way tomorrow.

I wired all 32 channels going to the AA board directly to the ADC as described in the previous log. However, instead of using the old AA board and bypassing the whole circuit, I just used a breakout board as is shown in the first attachment. I put the board back in the rack and reconnected all of the cables.

The seismic BLRMs appear to be working again. A PSD of the BS seismometers is shown in attachment 2. Tomorrow I'll look at how much the ADC alone is suppressing the common mode 60 Hz noise on each of the channels.

Steve: 5 of ADC DAC In Line Test Boards [ D060124 ] ordered. They should be here within 10 days.

Yesterday I wired the outputs from the seismometers directly to the ADC input bypassing the old AA board circuit as is described in this elog. The old circuit converted the single-ended output from the seismometers to a differential signal. Today I looked at whether 60 Hz noise is worse going directly into the ADC due to the loss of the common mode rejection previously provided by the conversion to differential signals.

I split the output from the BS Z seismometer to the new board and to an SR785. On the SR785 I measured the difference between the inner and outer conductors of the seismometer output, i.e. A-B with A the center conductor and B the outer conductor, with grounded input. At the same time I took a DTT spectrum of C1:PEM-SEIS_BS_Z_IN1. Both spectra were taken with 1 Hz bandwidth and 25 averages. The setup is shown in attachment 1.

The spectra are shown in attachment 2. The DTT spectrum was converted from counts to volts by multiplying by 2 * 10 V/32768 cts where the extra factor of 2 is from converting from single-ended to differential input. If there was common 60 Hz noise that the ADC was picking up we would expect to see less noise at 60 Hz in the SR785 spectrum measured directly at the output from the seismometer since that was a differential measurement. Since both spectra have the same 60 Hz noise, this noise is differential.

I was trying to plot trends (min, 10 min, and hour) in DataViewer and got the following error message

Connecting.... done
 mjd = 58235
leapsecs_read()
  Opening leapsecs.dat
  Open of leapsecs.dat failed
leapsecs_read() returning 0
frameMemRead - gpstimest = 1208844718
 

thoough the plots showed up fine after. Do we need to fix something with the leapsecs.dat file?

In light of the discussion at today's meeting, Guantanamo and I looked at how the series resistance for the test mass coil drivers limits the amount of squeezing we could detect.

The parameters used for the following calculations are:

• 4.5 kΩ series resistance for the ETM's (this was 10 kΩ in the previous calculations, so these numbers are a bit worse); 15 kΩ for the ITM's
• 100 ppm transmissivity on the folding mirrors giving a PRC gain of 40
• PD quantum efficiency of 0.88

Since we need to operate very close to signal recycling, instead of the current signal extraction setup, we will need to change the macroscopic length of the SRC. This will change the mode matching requirements such that the current SRM does not have the correct radius of curvature. One solution is to use the spare PRM which has the correct radius of curvature but a transmissivity of 0.05 instead of 0.1. So using this spare PRM for the SRM and changing the length of the SRC to be the same as the PRC we can get

• 0.63 dBvac of squeezing at 205 Hz for 1 W incident on the back of PRM
• 1.12 dBvac of squeezing at 255 Hz for 5 W incident on the back of PRM

This lower transmissivity for the SRM also reduces the achievable squeezing from the current transmissivity of 0.1. For an SRM with a transmissivity of 0.15 (which is roughly the optimal) we can get

• 1 dBvac of squeezing at 205 Hz for 1 W incident on the back of PRM
• 1.7 dBvac of squeezing at 255 Hz for 5 W incident on the back of PRM

The minimum achievable squeezing moves up from around 205 Hz at 1 W to 255 Hz at 5 W because the extra power increases the radiation pressure at lower frequencies.

To be quantitative, since we are looking at smaller squeezing levels and considering the possibility of using 5 W input power, it is possible to see a small amount of squeezing below vacuum with no SRM.

Attachment 1 shows the amount of squeezing below vacuum obtainable as a function of homodyne angle with no SRM and 5 W incident on the back of PRM. The optimum homodyne angle at 210 Hz is 89.2 deg which gives -0.38 dBvac of squeezing. Figure 2 is the displacement noise at this optimal homodyne angle and attachment 3 is the same noise budget shown as the ratio of the various noise sources to the unsqueezed vacuum.

The other parameters used for these calculations are:

• 4.5 kΩ series resistance for the ETM coils; 15 kΩ for the ITM coils
• 100 ppm transmissivity on the folding mirrors giving a PRC gain of 40
• PD quantum efficiency of 0.88

So maybe it's worth considering going for less squeezing with no SRM if that makes it technically more feasible.

As described in this elog, the ADC for the seismometers now has the signals wired directly to the ADC instead of going through an AA board or other circuit to remove any common mode noise. This elog describes one test of the common mode rejection of this setup. Guantanamo suggested comparing directly with a recent spectrum taken a few months before the new setup described in this elog.

Today I took a spectrum (attachment 1) of C1:PEM-MIC_2 (Ch17) and C1:PEM-MIC_3 (Ch18) with input to the ADC terminated with 50 Ohms. These are two of the channels plotted in the previous spectrum, though I don't know how that plot was normalized. It's clear that there are now strong 60 Hz harmonic peaks that were not there before, so this new setup does have worse common mode rejection.

Earlier today Kira and I reconnected the EX seismometer. I just took some spectra of all three seismometers, shown in the attachments, to compare with past data and to do a rough check of the calibration.

This elog has a spectra from 2010 (GUR1 is now EY) and this elog has one for BS at lower frequencies from 2017. Note that the EX seismometers now have strong peaks that are not at 60 Hz harmonics. Other than these peaks, these old spectra roughly match up with the ones taken today, so the callibration is still roughly the same. I couldn't find any old data for EX (GUR2) though so I don't know for sure that these peaks weren't there before.

gautam 20180517 0930: In 2017, Gur2 (now EX) looked like this. Still peaky, but the peaks seem shifted in frequency. Steve also informed me that the Gur1 and Gur2 cables were swapped n times, so perhaps we shouldn't read too much into that.

This goal of this test was to measure and map the AC (at 60 Hz) and DC magnetic fields around the interferometer. I've attached the final products which were drawn up with Google SketchUp.

The notes on the maps make them more or less self explanatory: for each numbered point there's an X, Y, and Z measurement produced by the magnetometer. For the AC numbers I measured the Peak-to-Peak value, while for the DC I simply measured the Mean. The magnetometer's axes were always oriented about the same way, with the X arrow on the magnetometer pointing north. I tried to keep variables such as the lights constant as much as possible (they were all on for most measurements, with the exception of a few noted DC ones) and all measurements had the top of the magnetometer at about 32 inches.  The map is pretty close to scale and all the walls and numbered locations were measured out (though the location of objects and the laser tubes is somewhat estimated). I added "landmarks" in the room, which were pretty much the laser tubes, computer racks, and ISC tables.

For each laser room measurement I also took a screenshot using the oscilloscope as a means of recording the shape of the wave for each measurement. Ch1 corresponds to the X value, Ch2 to the Y, and Ch3 to the Z. The screenshots are numbered 1-29 corresponding to the numbers on the map. The zip folders containing the screenshots can be found on the wiki:  PEM:Magnetometers

I should also mention that there is no point #24 and accordingly no 24 screenshot. I realized after I was done that I had messed up the location of that one and instead of risking bad data decided to just remove it.

I decided on the location of the points mainly based on the location of outlets in the room (since I had to plug in the oscilloscope for the AC numbers to set it to 60 Hz). After an initial pass of the room, I went back and filled in some of the larger gaps by moving the magnetometer as far as I could while the oscilloscope remained plugged in to the wall. I used the same points for DC numbers.

Prior to measuring the laser room, I measured the field in other rooms as well. I have

• AC numbers and screenshots for the control room and the adjoining office room.

• DC numbers for the entry room and the office room, not including the control room. The X-axis arrow is pointed south (instead of north) for these numbers.

These numbers were sort of a warm up for me to figure out the process and how I would go about recording my data. Since they're not in really important locations and aren't guaranteed to be accurate, I decided not to map them, though the screenshots are still on this Dell Inspiron 1300 Laptop and the measurements in my notebook.

Here are the settings I used on the oscilloscope for all measurements (I merely changed the Vertical Coupling between DC and AC depending on what I was measuring):

• Impedance: 1M ohms

• Bandwidth: Full

• Probe Setup: Voltage 1X

• Trigger Type: Edge

• Trigger Coupling: DC

• Fast Trig: Normal

• Trigger Mode: Auto

• Trigger Source: AC Line

• Acquire Mode: 512 Average

 The notebook that I used contains some additional info that I didn't include in the map, most importantly more precise descriptions of where each of the points is located and the measured distance between each of them (as well as slight changes I made to my measured distances in order to make the room a rectangle; the changes are slight enough that they shouldn't have any real effect on the data).

Since Kevin used our 3-axis Bartington Fluxgate magnetometer, we can guess that we can convert his voltage measurements (below) into magnetic field
by using the manual's guess of 10 uT /V or 10 V/Gauss. This is probably ok at the factor of 2 level, but one day we should calibrate it with a coil.

The punchline is that the DC fields in the lab are roughly what we expect from the Earth's field plus the rebar in our floors: ~1 Gauss. The 60 Hz fields are ~50-500 nT peak-peak.

Goal is to build a temperature sensor accurate to 1 mK. Schematic is shown below. This does not take into account the DC gain that occurs.

Parts that would be used for this: LM317 regulator, AD592 temperature transducer, OP amp (low input noise and high impedance), 100K (or maybe 10k) resistor. This is what is currently proposed, but the exact parts we use could be changed to better fit the sensor. The resistor and the OP amp will be decided depending on the output of the AD592.

Once this is built, I would like to create a few copies of it and put them into an insulated container and measure the output from each one. This would allow us to calculate the temperature noise of the circuit, as we can take out the variations due to temperature changes inside the container by comparing the outputs.

I can also model the noise in the circuit to see how much noise there is before building it. There are three terms to the noise that we have, and we need to decide which one dominates at low frequencies.

Our final goal is to create an additional circuit that could cancel out the DC gain. I have attached an additional schematic proposed by Rana that would help with this issue. I will leave this second half for when the first part works.

I decided to see what was inside the sensor that had been previously made. According to elog 1102, the temperature sensor is LM34, the specs of which can be found here:

http://www.ti.com/lit/ds/symlink/lm34.pdf

The wiring of this sensor confused me, as it appears that the +Vs end (white) connects to the input, but both the ground (left) and the Vout (middle) pins are connected to the box itself. I don't see how the signal can be read.

Since there seems to be little difference between AD590 and AD592, I guess we could just go with the AD590. The temperature noise spectrum in the first graph are for the AD590, so if we want to reproduce those results, we should use AD590.

For the AD581/AD587, we could go with a few varieties that have the least output voltage drift, although I am not sure what precision we will need. So maybe we could try AD587U and AD581L. We could also try AD587K and AD581K and see if those work as well.

We will also need to calibrate the sensor, as it takes an input of 5V, but the AD581/AD587 provides 10V, which will give about a 1 degree error according to the datasheet. It does state that this is only a calibration error, so it shouldn't be too much of an issue.

I will figure out the packaging once I construct the sensor and verify that it works. Maybe we could use a box similar to the existing sensor, but it depends on the size of the finished circuit.

Quick update: we actually have AD587KRZ and AD592, so we could start by using that and seeing how it works.

Used AD592CNZ and AD586 (5V output) to create a circuit that works and is responsive to temperature changes. At room temp, using ~1K resistor, it showed ~0.3V across it, as expected. The voltage went up when we heated it with a heating gun. Next step will be to add in an OP amp and design some experiments to check to see how accurate it is. Thanks to Gautam for helping me with it!

I have attached the working circuit and a close up of the connections.

Decided to try adding in an OP amp just to see if it would work. Added LT1012 and a 100k resistor to the circuit (I originally wanted to do AD743 as it seems to be the best choice according to Zach's elog here, but it said that they are very precious so I went with LT1012 for testing purposes). When heating it with a heating gun, the output voltage went down by a few 0.01V. The maximum voltage was 0.686V. Similar thing happened when I switched to a 10k resistor, where the maximum was 0.705V and it also went down by a few 0.01V upon heating.

I've attached a few pictures showing the circuit.

I didn't realize that the LT1012 needed an additional input to function. I added in +15V and -15V to pins 7 and 4, respectively and placed a 10k resistor and the numbers make more sense now. The voltage showed a negative value, but it became more negative as I heated it up (it's negative due to how a transimpedance amplifier works).

I have attached the new setup and the value it shows (~-3V). It became more negative by about 0.4V, which translates to about a 40K increase in temperature, which makes sense.

In addition, I have attached an updated sketch of the circuit. I will need to do more testing to determine how accurate this is. The next step would be to calculate how much noise there is currently and figure out how to remove this circuit from the breadboard and use a PCB or something like that for final testing in an insulated container.

The reason I chose AD743 initially for the OP amp is because at low frequencies (which is what we are working with), a FET amp such as AD743 will have a low current noise at high impedance, which is what we have in this case. While a FET amp has high voltage noise compared to other OP amps, the current noise becomes more important at high impedance, so it will work better. According to Zach's graphs, the AD743 is best at high impedances, followed by LT1012.

For the final packaging/mounting of the sensor to the seismometer, I have thought of two options.

1. Attach circuit to a PCB board and place it inside the can, while leaving the AD590 open to the air inside the can.

• This makes sure that the sensor gets a direct measurement of the temperature of the air in the can, as it is exposed to the air. 
• But, it takes a limited area of measurement, so it could be the case that the area we place it in happens to be a hot or cold pocket, and the measurement would be inaccurate.
• This can be solved by placing multiple copies of the circuit in various places of the can and averaging the values.

2. Attach the AD590 to a copper plate with thermal paste and put it into a pomona box.

• This solves the problem of having a limited sample area the first option had, as the copper plate should have a uniform temp distribution, thus we are sampling the temp of that whole area.
• Need to make sure that the response time to the temperature variations of copper is less than the frequency that we are measuring.
• This can be calculated using equations for heat transfer (listed below).

If anyone has input on which method is preferred or any additional options that we may have, I would appreciate it.

Heat transfer:

q = k A dT / s

• k = thermal conductivity
• A = area
• dT = temperature gradient
• s = thickness

For copper, k = 401 W/mK, x = 1.27 mm, A = 2.66x10^-3 m^2 (for the particular copper plate I measured), dT = 1K (assume). Thus the heat transfer will be 839 J/s.

I'm not completely sure what to do with this yet, but it could help us decide whether the copper plate option will be useful for us.

Tested to make sure that even when only the AD586 was heated that there was no change in the reading. I did so by placing the AD586 away from the rest of the circuit and blowing hot air only on it. There was, in fact, no change. 

Tried taking the circuit from the breadboard to the PCB. I attached all the components to adapters that would allow them to be connected to the PCB. From the first picture, the first component is AD586, the second is AD590, and the third is LT1012, along with a resistor across it. I then soldered the connections between the components, as can be seen in the second picture. When I tested out this version of the circuit by hooking it up to the DC source, I got a reading of ~-15V. I will have to check all the connections to make sure there is contact where there should be one, and no contact where there shouldn't be. I had issues attaching the tiny AD590 and LT1012 to its adaptor, so the issue may lie there as well. I'll also check that each component is in working order as well.

Once I figure out where my error is, my plan is to build two more of these and place a metal object such that it contacts only the surface of the AD590s. This would allow me to compare the three values to the actual temperature of the metal, which would then tell me how accurate this setup is.

Note on the resistor: I measured all the resistors and chose three that had exactly 10.00k Ohm. The voltage detected is dependent on the resistor, so if we are to take three identical copies, I ensured that there would be no error due to the resistors being a little different.

Got it to work. One of the connections was faulty. I decided to check the temperature measured against a thermometer. The sensor showed 26.1 C, but the thermometer showed 25.8 C after I let them both cool down after heating them up. The temperature of the thermometer was dropping at the time of measurement, but the temperature of the sensor was not. This is still a rough version of the final sensor, so I'm not sure what exactly causes this discrepancy.

On Friday, I cleaned up the circuit so that there are only three connections needed (+15V, -15V, GND) and a BNC connector for reading the output. Today, I added in bypass capacitors. The small yellow ones are 0.1 microF ceramic, and the large ones are 100 microF electrolytic. They are used to stabilize the +15V and -15V inputs to the OP amp and minimize fluctuations, since it doesn't have a regulator for stability. I have also attached the circuit diagram for the OP amp only, where 1 are the electrolytic and 2 are the ceramic. The temperature is still about 2 degrees off, but if that difference is constant for all temperatures in our range we can just calibrate it later.

Here is a helpful link on bypass capacitors (thanks to Kevin for sending it to me).

As a note, the electrolytic capacitors do have a polarity, so it is important to place them correctly (the negative side is towards the lower voltage potential, and not always towards ground).

I worked with Kevin and Gautam to create a heater circuit. The first attachment is Kevin's schematic of the circuit. The OP amp connects to the gate of the power MOSFET, and the power supply connects to the drain, while the source goes into the heater. We set the power supply voltage to 22V and varied the voltage of the input to the OP amp. At 6V to the OP amp, we got a current of 0.35A flowing through the heater and resistor. This was the peak current we got due to the OP amp being saturated (an increase in either of the power supplies did not change the current), but when we increased the voltage of the supply rails of the OP amp from 15V to 20V, we got a current of 0.5A. We would want a higher current than this, so we will need to get a different OP amp with a higher max voltage rating, and a resistor that can take more power than this one (it currently takes 5W of power, and is the best one we could find).

Kevin and I created a simulation of this circuit using CircuitLab to understand why the current was so low (second attachment). The horizontal axis is the voltage we supply to the OP amp. The blue line shows the voltage at the point between the output of the OP amp and the gate of the MOSFET. The orange line is the voltage at the point between the source of the MOSFET and the heater. The brown line is the voltage at the point between the heater and resistor. Thus, we can see that saturation occurs at about 2.1V. At that point, the gate-source voltage is the difference between the blue curve and the orange curve, which is about 4V, which is what we measured. Likewise, the voltage across the heater is the difference between the orange curve and the brown curve, which comes out to around 8V, which is also what we measured. Lastly, the voltage across the resistor is the brown curve, which is about 2V, which matches our observations. The circuit works as it should, but saturates too soon to get a high enough current out of it.

Gautam noted that it is important to measure the current correctly. We can't just use an ammeter and place it across the resistor or heater, because the internal resistance of the ammeter (~0.5 ohm) is comparable to the resistance we want to measure, so the current gets split between the circuit and the ammeter and we get an equivalent resistance of 1/R = 1/R0 + 1/Ra, where R0 is the resistance of the part we want to measure the current across, and Ra is the ammeter resistance. Thus, the new resistance will be lower and the ammeter will show a higher current value than what is actually there. So to accurately measure the current, we must place the ammeter in series with the part we want to measure. We initially got a 1A reading on the heater, which was not correct, and our setup did not heat up at all basically. When we placed the ammeter in series with the heater, we got only 0.35A.

The last two images are the setup for testing of the heater. We wrapped it around an aluminum piece and covered it with a few layers of insulating material. We can stick a thermometer in between the insulation and heater to see the temperature change. In later tests, we may insulate the whole piece so that less heat gets dissipated. In addition, we used a heat sink and thermal paste to secure the MOSFET to it, as it got very hot.

Our next steps will be to get a resistor and an OP amp that are better suited for our purposes. We will also run simulations with components that we choose to make sure that it can provide the desired current of 1A (the maximum output of the power supply is 24V, and the heater is 24 ohm, so max current is 1A). Kevin is working on that now.

I took off the AD590 and attached it to two long wires leading out from the board. This will allow us to attach the sensor to a metal block and not have to stick the whole board to it. I have also completed three identical copies of this and it's pretty much ready to be tested. According to Craig and Andrew's elog here, the sensor is very noisy and they added in a low pass filter to fix that, so that's something to consider for the final version of the circuit. I'll test what I have so far and see how that goes. We still need to figure out how to get readings from the sensors.

To attach the sensor to the metal block, I'll use some thermal paste and fasteners. I'll also put a thermometer on the block to record the actual temperature. I'll then wrap it in some insulation we have in the lab and have only some wires leading out of it to make measurements. I'll leave this setup overnight and record the outputs for about a full day. The fluctuations between the sensors will then indicate the noise of each individual sensor.

I decided to calculate the fluctuation in power that we will have in the heater circuit. The resistors we ordered have 50 ppm/C and it would be useful to know what kind of fluctuation we would expect. For this, I assumed that the heater itself is an ideal resistor that has no temperature variation. The circuit diagram is found in Kevin's elog here. At saturation, the total resistance (we will have a  resistor instead of  for our new design) will be . Therefore, with a 24V input, the saturation current should be .  Therefore, the power in the heater should be (in the ideal case) 

Now, in the case where the resistor is not ideal, let's assume the temperature of the resistor changes by 10C (which is about how much we would like to heat the whole thing). Therefore, the resistor will have a new value of . The new current will then be  and the new power will be . So the difference in power going through the heater is about 0.00088W.

We can use this power difference to calculate how much the temperature of the metal can we wish to heat up will change.  where  is the thermal conductivity and x is the thickness of the material. For our seismometer, I calculated it to be 0.012K.

Today, I stuck on the sensors to a metal block using a flag, rubber bands, and some thermal paste (1st attachment). I then wrapped the whole thing in about 4 layers of insulation and a lot of tape (2nd attachment). The only things leading out of the box were the three connections to the sensors and a thermometer. I then connected the wires to their respective places on the board of the sensor. To get the readings out we would need to use an ADC. Gautam and I checked to make sure the ADC we have inside the lab goes from -10V to 10V so that it would be able to measure the 3V value the sensor typically measures. We then tried to connect all three sensors to a DC source simultaneously, but unfortunately one of them seems to have disconnected somewhere during the process, as it only showed 1.2V instead of 3V. I plan to fix this tomorrow morning so that we can hopefully set this up soon.

to get the sensors to read the same values they have to be in direct thermal contact with the metal block - there can't be any adapter board in-between

for the 2nd attempt, I also recommend encasing it in a metal block rather than just one side. You can drill some 7-10 mm diameter holes in an aluminum or copper block. Then put the sensors in there and plug it up with some thermal paste.

Got it to work. A cable was broken and the AD586 also broke at the same time so it took a while to find the problem. I had to create a makeshift cable out of three parts so once I replace it for an actual cable, it will be good to go for a test.

Gautam and I measured the noise of the ADC for channels 17, 18, and 19. We plan to use those channels for measuring the noise of the temperature sensors, and we need to figure out whether or not we will need whitening and if so, how much. The figure below shows the actual measurements (red, green and blue lines), and a rough fit. I used Gautam's elog here and used the same function,  (with units of nV/sqrt(Hz)) to fit our results. I used a = 1, b = 1e6, c = 2000. Since we are interested in measuring at lower frequencies, we must whiten the signal from the temperature sensors enough to have the ADC noise be negligible.

We want to be able to measure to  accuracy at 1Hz, which translates to about  current from the AD590 (because it gives ). Since we have a 10K resistor and V=IR, the voltage accuracy we want to measure will be . We would need whitening for lower frequencies to see such fluctuations.

To do the measurements, we put a  BNC end cap on the channels we wanted to measure, then took measurements from 0-900Hz with a bandwidth of 0.001Hz. This setup is shown in the last two attachments. We used the ADC in 1X7.

I made a model for our seismometer can using actual data so that we know approximately what the time constant should be when we test it out. I used the appendix in Megan Kelley's report to make a relation for the temperature in terms of time.

 so  and 

In our case, we will heat the can to a certain temerature and wait for it to cool on its own so 

We know that  where k is the k-factor of the insulation we are using, A is the area of the surface through which heat is flowing,  is the change in temperature, d is the thickness of the insulation.

Therefore,

We can take the derivative of this to get

, or  

We can guess the solution to be

 where tau is the time constant, which we would like to find.

The boundary conditions are  and . I assumed we would heat up the can to 40 celcius while the room temp is about 24. Plugging this into our equations,

, so 

We can plug everything back into the derivative T'(t)

Equating the exponential terms on both sides, we can solve for tau

Plugging in the values that we have, m = 12.2 kg, c = 500 J/kg*k (stainless steel), d = 0.1 m, k = 0.26 W/(m^2*K), A = 2 m^2, we get that the time constant is 0.326hr. I have attached the plot that I made using these values. I would expect to see something similar to this when I actually do the test.

To set up the experiment, I removed the can (with Steve's help) and will place a few heating pads on the outside and wrap the whole thing in a few layers of insulation to make the total thickness 0.1m. Then, we will attach the heaters to a DC source and heat the can up to 40 celcius. We will wait for it to cool on its own and monitor the temperature to create a plot and find the experimental time constant. Later, we can use the heatng circuit we used for the PSL lab and modify the parts as needed to drive a few amps through the circuit. I calculated that we'd need about 6A to get the can to 50 celcius using the setup we used previously, but we could drive a smaller current by using a higher heater resistance.

I performed a test with the can last week with one layer of insulation to see how well it worked. First, I soldered two heaters together in series so that the total resistance was 48.6 ohms. I placed the heaters on the sides of the can and secured them. Then I wrapped the sides and top of the can in insulation and sealed the edges with tape, only leavng the handles open. I didn't insulate the bottom. I connected the two ends of the heater directly into the DC source and drove the current as high as possible (around 0.6A). I let the can heat up to a final value of 37.5C, turned off the current and manually measured the temperature, recoding the time every half degree. I then plotted the results, along with a fit. The intersection of the red line with the data marks the time constant and the temperature at which we get the time constant. This came out to be about 1.6 hours, much longer than expected considering that onle one layer instead of four was used. With only one layer, we would expect the time constant to be about 13 min, while for 4 layers it should be 53 min (the area A is 0.74 m^2 and not 2 m^2).