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 Wed Jun 9 11:46:01 2021, Anchal, Paco, Summary, AUX, Xend Green Laser PDH OLTF measurement Thu Jun 10 14:01:36 2021, Anchal, Summary, AUX, Xend Green Laser PDH OLTF measurement loop algebra Mon Jun 14 18:57:49 2021, Anchal, Update, AUX, Xend is unbearably hot. Green laser is loosing lock in 10's of seconds Tue Jun 15 15:26:43 2021, Anchal, Paco, Summary, AUX, Xend Green Laser PDH OLTF measurement loop algebra, excitation at control point Fri Jun 18 10:07:23 2021, Anchal, Paco, Summary, AUX, Xend Green Laser PDH OLTF with coherence
Message ID: 16213     Entry time: Fri Jun 18 10:07:23 2021     In reply to: 16202
 Author: Anchal, Paco Type: Summary Category: AUX Subject: Xend Green Laser PDH OLTF with coherence

We did the measurement of OLTF for Xend green laser PDH loop with excitation added at control point using a SR560 as shown in attachment 1 of 16202. We also measured coherence in our measurement, see attachment 1.

## Measurement details:

• We took the $\beta/\gamma$ measurement as per 16202.
• We did measurement in two pieces. First in High frequency region, from 1 kHz to 100 kHz.
• In this setup, the excitation amplitude was kept constant to 5 mV.
• In this region, the OLTF is small enough that signal to noise ratio is maintained in $\gamma$ (SR560 sum output, measured on CH1). The coherence can be seen to be constant 1 throughout for CH1 in this region.
• But for $\beta$ (PZT Mon, measured on CH2), the low OLTF actually starts damping both signal and noise and to elevate it above SR785 noise floor, we had a high pass (z:0Hz, p:100kHz, k:1000) SR560 amplifying $\beta$ before measurement (see attachment 2). This amplification has been corrected in Attachment 1. This allowed us to improve the coherence on CH2 to above 0.5 mostly.
• Second region is from 3 Hz to 1 kHz.
• In this setup, the excitation was shaped with a low pass (p: 1Hz, k:5) SR560 filter with SR785 source amplitude as 1V.
• We took 40 averaging cycles in this measurement to improve the coherence further.
• In this freqeuency region, $\beta$ is mostly coherent as we shaped the excitation as $1/f$ and due to constant cycle number averaging, the integrated noise goes as $1/\sqrt{f}$(see 16202 for math).
• We still lost coherence in $\gamma$ (CH1) for frequencyes below 100 Hz. the reason is that the excitation is suppressed by OLTF while the noise is not for this channel. So the $1/f$ shaping of excitation only helps fight against the suppression of OLTF somewhat and not against the noise.
$\gamma = \left( \frac{\eta}{A(s)} - \frac{\nu_e}{G_{OL}(s)} + \frac{\chi}{A(s) C(s)} \right)\frac{G_{OL}(s)}{1-G_{OL}(s)}$
• We need $1/f^2$ shaping for this purpose but we were loosing lock with that shaping so we shifted back to $1/f$ shaping and captured whatever we could.
• It is clear that the noise takes over below 100 Hz and coherence in CH1 is lost there.

## Inferences:

• Yes, the OLTF does not look how it should look but:
• The green region in attachment 1 shows the data points where coherence on both CH1 and CH2 was higher than 0.75.  So the saturation measured below 1 kHz, particularly in 100 Hz to 500 Hz (where coherence on both channels is almost 1) is real.
• This brings the question, what is saturating. As has been suggested before, our excitation signal is probably saturating some internal stage in the uPDH box. We need to investigate this next.
• It is however very non-intuitive to why this saturation is so non-uniform (zig-zaggy) in both magnitude and phase.
• In past experiences, whenever I saw somehting saturating, it would cause a flat top response in transfer function.
• Another interesting thing to note is the reduced UGF in this measurement.
• UGF is about 40-45 kHz. This we believe is due to reduced mode matching of the green light to the XARM when temperature of the end increases too much. We took the measurement at 6 pm and Koji posted the Xend's temperature to be 30 C at 7 pm in 16206. It certainly becomes harder to lock at hot temperatures, probably due to reduced phase margin and loop gain.
 Attachment 1: XEND_PDH_OLTF_with_Coherence.pdf  37 kB  Uploaded Fri Jun 18 11:09:37 2021
 Attachment 2: Beta_Amp.pdf  17 kB  Uploaded Fri Jun 18 11:26:48 2021
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