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yoichi.aso - 21:52 Tuesday 20 April 2021 (16518) Print this report
PRM BF-LVDT replacement

Today, I started working on the replacement of the broken LVDT driver in PRM.


  • I took self-transfer functions of the BF-LVDTs with the old (broken) driver.
  • Found that the broken channel is V2.
  • I took single frequency transfer function at 2Hz to record the calibration of each LVDT with the old driver.
  • I took note of the resistance values of the gain setting resistors in the broken LVDT driver.
  • I replicated these values in the new LVDT driver.
  • I installed the new LVDT driver and confirmed some signal comes out of V2.
  • Took a single frequency transfer function of H1 and adjusted the demodulation phase to maximize the signal, which yields a slightly larger gain than with the old driver.
  • I will continue the phase adjustment tomorrow.


Characterization of the old LVDT driver

  • The problem of the old LVDT driver is not only the broken V2 channel, but also a design mistake in the wiring of the demodulator chip (AD630).
  • Since pin 18 of the chip is not grounded, the demodulation is performed asymmetrically. 
    • That is, the incoming signal is switched between the gain of +2 and -1 at the demodulation frequency.
    • This should be +2 and -2.
    • The gain imbalance allows DC signal to go through the demodulation process.
    • This is especially problematic for BF-LVDTs where the primary coil is used both for readout and actuation.
    • The low frequency actuation signal inevitably couples to the readback signal of the LVDT even if there is a DC cut capacitor.
    • The demodulation process is supposed to provide extra isolation of this actuation signal.
    • However, because of the asymmetry, the low frequency signal goes through the demodulation stage without much attenuation.
    • This is the source of the spurious coupling we observed in those LVDts.
  • The new LVDT driver I brought in from Mozumi has this problem fixed.
  • In order to see the improvement by the symmetric demodulation, I first measured the self-transfer functions of the LVDTs with the old driver boards.
    • What is self-TF ?
      • For example, we send actuation to the H1 coil, then measure the TF from this excitation to the output of H1 LVDT.
    • The results are shown in the attached plot.
    • As can be seen, the self-TFs are dominated by the spurious coupling at frequencies above 10Hz.
    • V2 has a flat TF at low frequencies, because it is broken and not sensing the suspension motion.
    • However, V2 has the same sprious coupling at high frequencies.
      • This indicates that the actuation signal is going to the primary coil and indeed couples to the LVDT readout.
      • Probably, the 10kHz reference signal is not sent to the secondary coil for this channel.

Record the calibration of the old LVDT driver

  • Before switching the driver to the new one, we need to make sure that the LVDT calibration will not change, or change by a known amount.
  • Therefore, I took a self-TF of each channel at 2Hz to measure the gain and phase at that frequency.
  • These values are used to recalibrate the LVDT signals with the new driver.
DoF Gain Phase
H1 -69.8dB -1.59deg
H2 -70.8dB -1.8459deg
H3 -79.2dB 16.5deg
V1 -92.4dB -5.9deg
V2 no coherence no coherence
V3 -90.3dB 7.82deg

Record the resistance of the old LVDT driver

The LVDT driver board has 4 channels. Each channel has two variable resistors for setting the gains for the excitation signal (10kHz) and the instrumentation amplifier to receive the signal coming back from the primary coil. I measured the values of those resistors to keep the same gains in the new LVDT driver. There is another variable resistor to set the demodulation phase of the LVDT. I will adjust this to maximize the gain of the LVDT.

Later, I changed my mind that preserving the resistance value is not necessary, as I will measure the new gain of the LVDTs using the self-TF and update the calibration factors accordingly.

Replicagtion of the resistance values in the new LVDT driver

This is indeed not really necessary, but I copied the resistance values of the gain setting resistors to the new LVDT driver.

Measure the gain of the new LVDTs

  • After installing the new LVDT driver to the rack, I measured the self-TF of the H1 LVDT at 2Hz. 
  • Then I tuned the variable resistor to set the demodulation phase to maximize the signal gain.
  • The obtained gain is -65.28dB, which is 4.5dB higher than the old one.
  • The phase is -1.64deg, which is almost the same as the old one.
  • It should be noted that because the gain asymmetry was removed, the LVDT demodulation gain should be increased by a factor of 2/1.5=1.25dB.
  • Time was up today at this moment. I will continue the work tomorrow.


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Comments to this report:
yoichi.aso - 21:17 Wednesday 21 April 2021 (16534) Print this report

Dramatic decrease in the LVDT spurious coupling was achieved

Today, I continued with the replacement of the PRM LVDT driver.
With the new LVDT driver, the spurious coupling at high frequencies is dramatically suppressed (40dB or more).
This will make the damping of tower modes at the BF stage much easier.

Corrections to the table reported yesterday

First of all, there were several mistakes in the table I reported yesterday for the calibration of the old LVDT channels at 2Hz.

The correct table is shown below:

Channel Gain Phase
H1 -69.8dB -1.59deg.
H2 -70.8dB -1.8deg.
H3 -68.5dB -1.75deg.
V1 -78.2dB 178deg.
V2 no coherence no coherence
V3 -79.2dB 178deg

Single frequency TF of the new LVDT driver

After taking note of the calibration values for the old LVDT driver, I adjusted the demodulation-phase tuning resistors of the new LVDT driver so that the DC value of the LVDT output signal becomes maximum.

Unfortunatelly, the demodulation phase cannot be set to the optimal one due to the limited adjustment range. By turning the trimmer of the resistor all the way from zero to maximum, the LVDT signal changed from negative to positive but never saturated. This means, the optimal phase is out of the tuning range. Anyway, I turned the trimmers maximally to the right, where the signal is maximum within the tuning range.

Then I measured the single-frequency TF at 2Hz with the new driver.

Channel Gain Phase
H1 -63.7dB -1.8deg
H2 -63.4dB -1.7deg
H3 -62.4dB -1.8deg
V1 -71.9dB 178deg
V2 -75.6dB -178deg
V3 -73.5dB -178deg

The gain was increased by about 6dB from the old driver. This is partially due to the increased demodulation gain by fixing the grounding problem of AD630. Another contribution comes from the demodulation-phase adjustment to maximize the signal gain. This increased gain could reduce the working range of the LVDTs. Currently non of the BF-LVDTs are close to saturation. In this case, the increased gain will give us more noise margin. So I will just leave as is.

Changing the calibration factors

In order to compensate for the increased hardware gain of the LVDT driver, I changed the gain values in K1:VIS-PRM_BF_LVDTINF_{H1, H2, H3, V1, V2, V3} so that the output from the filters should have the same gain as before. The old and new values are summarized here:

Channel Old New
V1 0.941 0.46
V2 -0.956 0.704
V3 0.954 0.495
H1 -0.973 -0.482
H2 -0.940 -0.401
H3 -0.945 -0.468

The calibration factor of V2 is computed in a different way from the others, because we don't know the single-frequency TF value of the old driver (V2 was broken).

For this channel, I excited the SF keystone LVDT at 2Hz. Assuming that the BF moves up and down without tilting, we can measure the relative gains between V channels. The transfer function values at 2Hz from the excitation amplitude to the LVDT output signals are the following:

Channel Gain Phase
V1 -53.7dB 178deg
V2 -57.4dB 179deg
V3 -55dB 179deg

From this, one can deduce that the gain of V2 is lower than V1 by 3.7dB. Therefore, the calibration factor of V2 should be 3.7dB(=1.53 times) larger than that of V1. This is how the calibration factor for V2 was computed. 

Self-TFs with the new LVDT driver

Finally I measured the transfer functions from an LVDT actuator to the readout of the same LVDT channel. The results can be found in the attached PDF. There is a dramatic improvement in eliminating the spurious coupling at high frequencies. This will allow us to increase the bandwidth and gain of the BF damper loops, which may be crucial in taming down the suspensions on a stormy day.

We should implement this new driver in all the BF-LVDTs. We may also want to replace the drivers to new ones for the LVDTs which do not share the actuation and readback coils. Even for those "normal" LVDTs, magnetic coupling between the actuation coil and the readback coil may create spurious couplings.


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