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 Fri Jun 11 08:58:44 2021, shruti, DailyProgress, PSOMA, Spurious peaks 6x Fri Jun 11 17:08:20 2021, rana, DailyProgress, PSOMA, Spurious peaks Wed Jun 16 10:29:58 2021, shruti, DailyProgress, PSOMA, Investigating the peaks Fri Jun 18 10:42:08 2021, aaron, DailyProgress, PSOMA, Investigating the peaks Mon Jun 21 13:54:08 2021, shruti, DailyProgress, PSOMA, Open Loop Transfer Functions 6x Mon Jun 21 15:34:09 2021, aaron, Electronics, Lab Work, swapping mixer Wed Jun 23 11:36:49 2021, shruti, Electronics, Lab Work, swapping mixer
Message ID: 2759     Entry time: Mon Jun 21 13:54:08 2021     In reply to: 2758
 Author: shruti Type: DailyProgress Category: PSOMA Subject: Open Loop Transfer Functions

Having added the attenuator, A(s), at the input A of the LB1005 the loop algebra is changed slightly: Attachment 3 has the algebra and Attachment 4 helps with understanding the symbols. I have just considered this attenuator separately from the plant and servo.

### Attachment 1: Open Loop TFs

• The yellow curve is the actual open loop transfer function after subtracting 5dB in the magnitude of the ratio between the PDH error signal and the LB error signal to compensate for the 10dB attenuator at the input A of the LB box
• The blue and orange magnitude curves were recorded directly from the Moku
• The phase of the Math channel saved from the Moku seems to be a copy of the magnitude for all three OLTFs even though the screenshots seem to show a real phase (the data for this is saved in Attachment 3 and shown in the previous elog) so I re-calculated the phase but I'm not sure if it fully makes sense. (The calculation is in Attachment 4)

Attachment 2 is all the individual closed loop transfer functions that were recorded to calculate the open loop ones.

Attachment 3 has the data, settings, and screenshots recorded from the Moku to calculate OLTFs

Attachment 4 is the Jupyter notebook used to generate Attachments 1 and 2

Attachment 5 has the loop algebra and diagram

Attachment 6 is a diagram of the setup depicting the loop components

 Quote: $\frac{V_\mathrm{PDH}}{B}=\frac{PG}{1-PG}\frac{A-B}{B}$ $\frac{V_\mathrm{LB,error}}{B}=\frac{1}{1-PG}\frac{A-B}{B}$ $\frac{V_\mathrm{control}}{B}=\frac{G}{1-PG}\frac{A-B}{B}$ ... ... Indeed, we were able to eliminate the oscillations we had been seeing by adding a 10 dB attenuator between the PDH error signal and LB box input A, and changing the attenuator at the LB box output from 20 dB to 10 dB. [We also swapped out our ZFM-3H-S+ for ZFM-2H-S+, which has a 2 MHz low frequency cutoff compared to 50 kHz. Swapping mixers did not resolve the oscillation]   ... ...

 Attachment 1: OLTF.pdf  51 kB  Uploaded Mon Jun 21 14:57:00 2021
 Attachment 2: IndividualTFs.pdf  47 kB  Uploaded Mon Jun 21 14:57:09 2021
 Attachment 3: OLTFs.zip  3.846 MB  Uploaded Mon Jun 21 15:11:37 2021
 Attachment 4: LoopTFs.ipynb  6 kB  Uploaded Mon Jun 21 15:13:10 2021
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