40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  Engineering group Lab elog  Not logged in ELOG logo
Message ID: 219     Entry time: Tue Nov 19 09:36:56 2019
Author: Marie K. 
Type: Progress 
Category: BS BRDs 
Subject: 3 masses model check 

Following up elog 217, I want to make sure that the 2 BRD model is correct. Here is a comparison of the model with the 2 identical BRDs compared to the simple model with 1 BRD (the mass is twice the mass of an individual BRD but the Q is unchanged). In both cases the BRDs are tuned at the exact resonant frequency of the BS mode.

We can see that the models are perfectly overlapping. Hence, the 2 BRD model is in agreement with the 1 BRD model (see figure 1)

For the Roll mode, the poles and zeros of the 2 BRD model are:

  • z = {-104662,   -0.1031 +24.3398i,  -0.1031 -24.3398i,  -0.1031 +24.3398i,  -0.1031 -24.3398i}
  • p = {  -0.0547 +24.6018i,  -0.0547 -24.6018i,  -0.1031 +24.3398i,  -0.1031 -24.3398i,  -0.0513 +24.0809i,  -0.0513 -24.0809i}
  • We can see that 1 pair of poles and zeros is cancelling out.

The poles and zeros of the 1 BRD model are:

  • z = {-0.1031 +24.3398i,   -0.1031 -24.3398i}
  • p = {  -0.0547 +24.6018i,  -0.0547 -24.6018i,  -0.0513 +24.0809i,  -0.0513 -24.0809i}

**

If the frequencies of the BRDs are symetrically detuned from the BS resonant frequency in the 2 BRD model, the poles and zeros are:

For 1 % detuning:

  • p = { -0.1042 +24.5832i,   -0.1042 -24.5832i,   -0.1021 +24.0964i,   -0.1021 -24.0964i}
  • z = { -0.0782 +24.6978i,   -0.0782 -24.6978i,   -0.0564 +24.3377i,   -0.0564 -24.3377i,   -0.0746 +23.9869i,   -0.0746 -23.9869i}

For 0.1% detuning :

  • p = { -0.1032 +24.3641i,   -0.1032 -24.3641i,   -0.1030 +24.3154i,   -0.1030 -24.3154i}
  • z = { -0.0551 +24.6028i,   -0.0551 -24.6028i,   -0.1023 +24.3397i,   -0.1023 -24.3397i,   -0.0517 +24.0799i,   -0.0517 -24.0799i}

The resulting transfer function is presented in figure 2.

Attachment 1: Model_check.png  101 kB  | Hide | Hide all
Model_check.png
Attachment 2: Model_check_detuning.png  86 kB  | Hide | Hide all
Model_check_detuning.png
ELOG V3.1.3-