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 Wed Jan 30 15:07:32 2019, awade, anchal, HowTo, FSS, Shot noise in FSS loops? Fri Feb 1 14:59:01 2019, awade, anchal, HowTo, FSS, Noise tallies Fri Feb 1 20:20:11 2019, awade, HowTo, FSS, Modifying North FSS EOM path Tue Feb 5 11:40:02 2019, awade, HowTo, FSS, Modifying South FSS boost Tue Feb 5 20:39:52 2019, anchal, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis Wed Feb 6 19:13:06 2019, anchal, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis Wed Feb 6 21:30:24 2019, awade, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis Thu Feb 7 10:33:27 2019, anchal, Summary, FSS, Complete model of TTFSS box with TF and crossover analysis
Message ID: 2306     Entry time: Wed Feb 6 21:30:24 2019     In reply to: 2305     Reply to this: 2307
 Author: awade Type: Summary Category: FSS Subject: Complete model of TTFSS box with TF and crossover analysis

Hmm... Last estimate of V_rms applied to EOM can't be true.

If laser frequency noise is

$\dpi{100} S^\textrm{Laser}_f (f)= \frac{1 \textrm{Hz}}{f} \times 10^4 \quad [\textrm{Hz}/\sqrt{\textrm{Hz}}]$

Total frequency noise down to 1 kHz should then be 316 Hz_rms. As you've noted in your jupyter notebook the EOM frequency domain response to actuation signal goes as f, i.e.

$\dpi{100} \delta f(t) = \frac{1}{2\pi}\frac{d \Delta\phi}{dt} = \frac{m_s}{2\pi} \frac{d V_{EOM}}{dt}$

where ms is EOM phase slope (15 mrad/V) and V_EOM is the applied actuation voltage. As you wrote, that leads to

$\dpi{100} \delta \tilde f(f) = \frac{m_s}{2\pi} (-i 2 \pi f) \tilde V_{EOM}(f) = -i m_s f\tilde V_\textrm{EOM}(f) \quad [\textrm{Hz}/\textrm{V}]$

If we assume that the EOM is taking 100% of the load for canceling laser frequency noise at a given frequency then it follows that the applied voltage to exactly cancel laser frequency noise is

$\dpi{100} \delta \tilde V_\textrm{EOM}(f) = \frac{S^\textrm{Laser}_f (f)}{\delta \tilde f(f)} = i \frac{10^4}{m_s} \frac{1}{f^2}\quad [\textrm{V}/\sqrt{\textrm{Hz}}]$

This would indicate that the burden on the EOM becomes 1/f heavier in frequency because of the laser noise roll up and 1/f heaver because the EOM responds as f to signals in the Fourier domain.  The above puts an upper bound on the ASD curve of load that the EOM is absorbing to cancel laser frequency noise.

Integrating the above V_EOM PSD down from high frequency will give the total V_rms load that the loop would need to apply to suppress laser frequency noise:

$\dpi{100} V_\textrm{rms}(f) = \sqrt{\int^\infty_f (\frac{10^4}{m_s} \frac{1}{f^2})^2 \textrm df} \quad [\textrm{V}_\textrm{rms}]$

or

$\dpi{100} V_\textrm{rms}(f) = \frac{10^4}{m_s}\frac{1}{f^{3/2}} \quad [\textrm{V}_\textrm{rms}]$

I've plotted this below and attached the notebook used for the calculation.  It kind of looks like the maximum load at 1 kHz hits about 200 Vrms.  Maybe I've gotten some factors wrong here but you can sort of see the scaling of how the maximum load on the EOM will look.

One thing to note is that the above estimates are an upper bound assuming that the EOM is taking all of the load down to that frequency point and that the PZT path isn't fighting or out of phase with EOM.  To correctly compute the load on the EOM you are going to have to break down the EOM only portion of the loop from the laser frequency to the point of voltage injected into the EOM.  This can be done by effectively nesting the PZT loop into the round trip gain in a way similar to that described in Josh Smith's Thesis section 2.6.2.  Finding the actuation signal should be similar to finding the PLL actuation signal, at this point in the loop it is the G/(1-G)/A copy of the sensor noise.  In the high gain regime the applied EOM control signal should just be the laser frequency  divided by the EOM frequency slope. Of course you can compute for G_EOM OLG to get a true value with a bunch of algebra.

Quote:

I added some more graphs to our FSS analysis.

• I modeled AD602 variable gain amplifier with a circuit similar to how it actually works internally. The resultant circuit now has a right input resistance of 100 Ohm and capacitance of 2 pF. It is slightly noisier than AD602.
• I calculated the total suppression function and suppressed laser frequency noise.
• I did a parametric analysis by varying the PZT gain and obtained a range of cross over frequencies and phase margin we can attain.
• Everything looked awesome so far, but the real problem is EOM railing.
• So I calculated that if the said suppression is achieved, what is the actuation signal that is sent to EOM.
• The last plot is the spectral density of this actuation signal. Since $V_{\pi}=209.44\, V$only, we clearly are going to rail the EOM and the said suppression will never actually happen.
• We need to shift actuation region of EOM to even higher frequencies so that it doesn't rail. But at the same time, we need to keep the crossover frequency and phase margin of crossover decent. And to top it off, we need to do all this making sure we get at least $10^5$ suppression at 100 Hz.
• So from here, I guess we need to work on shifting the poles and zeros and tune in the gain values right to get point.
• I'm not 100% sure about this analysis, please let me know if I am doing something wrong here. The latest notebook and pdf are on git.
 Quote: I'm attaching the first results of the transfer function from liso model of complete TTFSS box. I've also attached the jupyter notebook with some important formulas used. Both files are present in git/cit_ctnlab/ctn_electronics/TTFSS_lisomodel/ git repo. I'm just posting results for the analysis I did so far. I'll be able to make better inferences with some more work I intend to do tomorrow. Edit: Wed Feb 6 16:59:59 2019 The updated plot is at git. Added analysis of variation of crossover frequency and phase margin with changing Fast gain.

 Attachment 1: EOM_Vrms_FunctionOfLowerFrequencyBoundOfTF.pdf  50 kB
 Attachment 2: TTFSS_lisomodel_FSS_Mod_Analysis.ipynb.zip  851 kB
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