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Message ID: 2062     Entry time: Wed Oct 7 06:26:09 2009
Author: rana 
Type: HowTo 
Category: IOO 
Subject: MC_L calibration + some DTT lore 

I drove MC2 in POS and used the resulting response in MC_F to calibrate the IOO-MC_L channel.

Yoichi did an excellent job of calibrating MC_F last year. I have used his calibration of MC_F (220 Hz/count @ DC) to get the MC_L calibration at DC as well as at high frequencies. The hardware dewhitening was OFF for all these measurements.

Method

1. For the DC measurement I excited C1:SUS-MC2_MCL_EXC at 0.0731 Hz. At these frequencies, the MC_L path has much more gain than the MC_F path. So this excitation at the error point makes the length path to drive itself to cancel the digital excitation. Since the overall MC servo gain is huge, this causes the MC_F path to compensate the residual MC_L motion. One can simply take the ratio of MC_L/MC_F to get the calibration of MC_L in Hz.

2. For the AC measurement, I engaged FM9 of the MC2_MCL filter bank. This guy is an elliptic LP with a notch at 660.38 Hz. I then drove MC2_LSC at 660.38 Hz with a sine wave of 500 counts amplitude. The notch makes the gain of the MC_L feedback zero at that frequency. So MC_F has to do all the work. We can simply measure the ratio of MC2_LSC/MC_F to get the AC calibration of MC2_MCL_OUT (aka IOO-MC_L) and MC2_LSC_OUT (aka LSC-MC_L).

 

Results:

MCF/MCL @ 0.0731 Hz = 569.4. So the MC_L calibration at DC is 220 x 569.4 = 125 kHz/count or 6.02 nm/count.

From this we would expect the AC calibration to be (6 nm/count)*(660.38/f_pend)^2 = 13.0 x10^-15 m/count.

The AC measurement gave 1445 counts_peak** of MC_F for the 500 counts (peak) excitation in MC2_LSC. From Yoichi's entry we get that the high frequency calibration of MC_F should be 0.089 Hz/count. So the MC_L calibration at 660 Hz is 0.089*1445/500 = 0.25 Hz / count or 12.3 x 10^-15 m/count. So the AC/DC ratio is close to 1.

Splitting the difference, the new official MC_L calibration is 5.87 nm/counts @ DC with a complex pole pair at 0.972 Hz.

 

** note:  To convert from the peak height observed in DTT with a 50% Overlap Hanning window you must use the following intuitive formula:  counts_peak = (counts / rHz) * sqrt(2 * BW). In this case, BW is the number that DTT reports as BW on the screen, NOT the BW that you asked for on the measurement tab.

*** note: when measuring peak heights in a DTT FFT, make sure to unclick the box for 'Bin' under the config tab. Bin suppresses peaks in a plot with a lot of points and is ON by default.

**** note: I have updated the MCF reference in the Templates directory with the Yoichi calibration - spectrum attached. This is probably the most accurate MCF spectrum we have ever put in the elog in the history of the 40m. The implication is that the VCO phase noise is ~5 mHz/rHz. Not bad.

***** note: with the OAF off, I drove a 1.55 Hz sine wave into MC1 and measured the ratio of MC1_MCL_OUT/IOO-MC_L. This gives the DC calibration of MC1_MCL_OUT = 7.98 nm/count.

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