Message ID: 16363
Entry time: Tue Sep 28 16:31:52 2021
In reply to: 16353
Reply to this: 16369

Author:

Paco

Type:

Summary

Category:

Calibration

Subject:

XARM OLTF (calibration) at 55.511 Hz

[anchal, paco]

Here is a demonstration of the methods leading to the single (X)arm calibration with its budget uncertainty. The steps towards this measurement are the following:

We put a single line excitation through the C1:SUS-ETMX_LSC_EXC at 55.511 Hz, amp = 1 counts, gain = 300 (ramptime=10 s).

With the arm locked, we grab a long timeseries of the C1:LSC-XARM_IN1_DQ (error point) and C1:SUS-ETMX_LSC_OUT_DQ(control point) channels.

We assume the single arm loop to have the four blocks shown in Attachment #1, A (actuator + sus), plant (mainly the cavity pole), D (detection + electronics), and K (digital control).

At this point, Anchal made a model of the single arm loop including the appropriate filter coefficients and other parameters. See Attachments #2-3 for the split and total model TFs.

Our line would actually probe a TF from point b (error point) to point d (control point). We multiplied our measurement with open loop TF from b to d from model to get complete OLTF.

Our initial estimate from documents and elog made overall loop shape correct but it was off by an overall gain factor. This could be due to wrong assumption on RFPD transimpedance or analog gains of AA or whitening filters. We have corrected for this factor in the RFPD transimpedance, but this needs to be checked (if we really care).

We demodulate decimated timeseries (final sampling rate ~ 2.048 kHz) and I & Q for both the b and dsignals. From this and our model for K, we estimate the OLTF. Attachment #4 shows timeseries for magnitude and phase.

Finally, we compute the ASD for the OLTF magnitude. We plot it in Attachment #5 together with the ASD of the XARM transmission (C1:LSC-TRX_OUT_DQ) times the OLTF to estimate the optical gain noise ASD (this last step was a quick attempt at budgeting the calibration noise).

For each ASD we used N = 24 averages, from which we estimate rms (statistical) uncertainties which are depicted by error bands () around the lines.

** Note: We ran the same procedure using dtt (diaggui) to validate our estimates at every point, as well as check our SNR in b and d before taking the ~3.5 hours of data.