The real time calibration system is not correct in high frequency.
The attachment are the plot of two free running noise. Blue curve is the plot of noise calibrated with OLTF. Green one is the just fft analysed signal of the real time calibration system output. You can see the ripple in high frequency region in green curve. That is because the anti-aliasing filter and digital anti-aliasing filter. I assume the sensitivity of MI as constant but Rana mentioned that we should take these filters into account.
modeled OLTF and sensitivity H
I put the AA filter and DAA filter effects into matlab calibration script. The attachment 2 is the modeled sensitivity of the MICH. You can find each filter properties in elog#8555 (analog AA filter) and in elog#3961. I estimate the H gain by measuring the fringe. The attachment 3 is the plot of fringe and I averaged with green points. The actual number is 3.48e7 count/m.
attachment 2: the sensitivitiy of MICH
attachment 3: fringe of the MICH
I modeled OLTF with this H and the fitted into the measurement data. That is in attachment 4. In this OLTF I also included the DAI filter and AI filter, and ' sample and hold circuit' of DAC TF . These are mentioned in two references. Additionally I added the time delay 309.6 us. Yuta mentioned that in C1SUS has 125us time delay. In MICH control we have also C1LSC , so I think this time delay is reasonable. I compensated the error signal with these OLTF and MICH sensitivity.
attachment 4: OLTF of the MICH control
You can see that the ripple is gone in blue curve and after 5 kHz the curve is flat.
Next step
I'm trying to put the inverted AA filter and DAA filter in C1CAL_INCV servo. But the ploblem is the difference of sampling frequency, so I couldn't fix yet. One possibility is putting approximated filter. I hope I will find some good way to design these filters.
Other thing
I esitimated the FPMI noise propagated from the residual noise of IR PDH control of both ARMS. I will summarize and write these staff in this afternoon. |