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Entry  Mon Jul 11 11:56:40 2022, he Yehonathan, Update, BHD, MICH AS55 noise budget Control_Diagram.pdfMICH_AS55_Noise_Budget.pdf
    Reply  Tue Jul 12 09:14:50 2022, rana, Update, BHD, MICH AS55 noise budget 
       Reply  Wed Jul 13 10:54:39 2022, Yehonathan, Update, BHD, MICH AS55 noise budget BS_MICH_ACtuation_Calibration.pdfMICH_AS55_Model_Measurement_Comparison.pdfMICH_AS55_Noise_Budget.pdf
          Reply  Wed Jul 13 13:30:48 2022, Yehonathan, Update, BHD, add Laser RIN to MICH budget 
             Reply  Mon Jul 18 16:49:57 2022, Yehonathan, Update, BHD, add Laser RIN to MICH budget Laser_RIN.pdfMICH_AS55_Noise_Budget.pdf
                Reply  Mon Jul 18 18:33:38 2022, Koji, Update, BHD, add Laser RIN to MICH budget 
Message ID: 16984     Entry time: Mon Jul 11 11:56:40 2022     Reply to this: 16989
Author: he Yehonathan 
Type: Update 
Category: BHD 
Subject: MICH AS55 noise budget 

I calculated a noise budget for the MICH using AS55 as a sensor. The calculation includes closed-loop TF calculations.

The notebook and associated files can be found on https://git.ligo.org/40m/bhd/-/blob/master/controls/compute_MICH_noisebudget.ipynb.

Attachment 1 shows the loop diagram I was using. The equation describing the steady-state of the loop is

\left[\mathbb{I}-G \right]\begin{pmatrix} \gamma \\ \delta \\ \Delta\end{pmatrix} = \begin{pmatrix} \alpha \\ \beta \\ \epsilon\end{pmatrix}

, where G is the adjacency matrix given by

G=\begin{pmatrix} 0 & 0 & AE_2\\ 0 & 0 & BE_2 \\ E_1C & E_1D & 0 \end{pmatrix}

First, the adjacency matrix G is constructed by stitching the small ABCDE matrices together. Once the inverse of (I-G) is calculated we can simply propagate any noise source to \delta and then calculate \left[\mathbb{I}-E(CA+DB)\right]B^{-1}\delta to estimate the displacement of the optics. 

Attachment 2 shows the calculated noise budget together with Yuta's measurement.

All the input and output electronics are clumped together for now. Laser noise is irrelevant as this is a heterodyne measurement at 55MHz.

It seems like there is some mismatch in the calibration of the optical gain between the measurement and model. The missing noise at 3-30Hz could be due to angle-to-length coupling which I haven't included in the model.

Attachment 1: Control_Diagram.pdf  50 kB  Uploaded Mon Jul 11 12:59:31 2022  | Hide | Hide all
Control_Diagram.pdf
Attachment 2: MICH_AS55_Noise_Budget.pdf  70 kB  Uploaded Mon Jul 11 13:15:00 2022  | Hide | Hide all
MICH_AS55_Noise_Budget.pdf
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