J. Kissel 

The HLTS damping loop design -- and the corresponding noise budgets that I produce to assess their performance -- had not been touched since July 2013 (LLO:7907). I've now updated the modeling infrastructure to receive the same updates as the HSTS, such that the HLTS modeling code
    - has the option to model of the input seismic noise for HAM2 (LHO:65639, CSWG:11238), 
    - has the option to change the DAC noise input model from 18-bit to 20-bit (using models from E1800243)
    - has the option to change the M2 and M3 stage coil driver from an unmodified TACQ driver response to a modified TACQ driver response (even though we would never do this)
    - which had the the same lever arm bug as the HSTS (LHO:65319), now also has the same math fix which impacted the actuator noise estimate in the R, P and Y budgets
    - plots many more loop metrics that we've come to expect including global transfer functions, impulse responses, etc.

Attached are the L, V, P and Y budgets for the HLTSs that's gotten a lot of attention recently - H1 PR3.
    :: dampingfilters_HLTS_H1PR3_18bitDACs_H1HAM2ISI_nosqrtLever_2022-11-09_totalbudget_LVPY.pdf

Hopefully, the H1 PR3 budget is what we can use directly compare and contrast against Elenna's REFL WFS noise budget from LHO:65495.
I show V in addition to the usual L, P and Y in my distilled collection of plots because in that budget, her multi-channel coherence estimate of the limiting noise sources showed that PR3 displacement noise is most coherent with V, P, and Y.

But let's sit in that statement for a second and clarify:
The sub-budget from LHO:65499 shows more clearly that there're two frequency regions dominated by different DOFs:
    - 1-10 Hz REFL WFS P and Y are dominated by actual PR3 P and Y, and
    - 10-30 Hz REFL WFS P and Y are dominated by PR3 V but also PR3 P and PR3 Y.
Some how, in all of the scattered conversations we've had, I had the mis-impression that the entire WFS ASD was limited by PR3 V across the entire 1-30 Hz band. That's false. It's really only the 10-30 Hz region that *contains* vertical, but it also *contains* P and Y coherence at a comparable level.

To further add to the confusion, in the HLTS, the (second) highest vertical mode and (third) highest pitch mode are at the virtually same frequency (3.50 Hz and 3.51 Hz, respectively), especially when the Qs of those modes are reduced by the top mass damping loops as they are during normal operation. So the first sanity check one typically does -- see what mode frequencies are present in the noise to tell you which SUS type and DOF is causing the noise, doesn't work. So some might have guessed that that 3.5 Hz mode was a vertical mode, and blamed the whole PR3 contribution from 1- 30 Hz on V. Also false.

But let's talk about what we do see from this modeled budget.
    - As we saw in LHO:65639, the HAM2 ISI, without ST0 L4C FF or fine vertical CPS, performs much worse than HAM5 and HAM7 in vertical in the  5 - 30 Hz region. This transmits all the way to the optic.
    - Thus, the residual vertical seismic noise contribution to PR3 M3 vertical FAR outweighs the contribution BOSEM sensor noise reinjection above 5 Hz in vertical.
    - By contrast the estimated displacement is very smooth in P and Y -- dominated by BOSEM sensor noise re-injection above ~3 Hz, following the shape of the damping loop filter's roll-off for these two DOFs.
    - The shape of the damping loop cut-off filter, and predicted optic motion, between 3-10 Hz is consistent with the shape of what's seen in the REFL WFS sub-budget for P and Y -- especially in say REFL WFS A and B RF9
    - The shape of the PR3 vertical estimate between 10-30 Hz is consistent with that from the residual vertical contribution.
    - As with the HSTSs (LHO:65317), the HLTSs are dominated by 18-bit DAC noise below 2.5 Hz, especially in P and Y.

I'm going to work with Elenna to try to get the REFL WFS budget cast in terms of PR3 optic displacement, so that we can put our results on the same plot.

Side conversations about "what would the budget look like it we added ST0 L4Cs, and we upgraded to 20-bit DACs?" will be answered in the comments below, where I budget H1 SR3, imagining it having 20-bit DACs.
The locations of the code and the model will also be spelled out in the comments.