J. Kissel, K. Izumi, C. Cahillane Evan and Kiwmau wished to get a better answer than my supremely bold claim of being able to ALS DIFF VCO's pole and zero to 1% and 1 [deg] (LHO aLOG 20542). As such, they remeasured the ALS DIFF PLL OLGTF with no boosts, as had been done before, but this time with the PLL Common gain reduced to -32 dB([V/V]) instead of the nominal 26 dB([V/V]). In this way, they reduce the overall loop suppression, in hopes to alleaviate the non-linear distortion we had been plagued by before. The message -- they were right. The new OLGTF, with all other parameters the same, shows that the "nominal" z:p = 40:1.6 [Hz] pair fits the data better than my previously claimed z:p = 40:1.05 [Hz]. However, naturally, there is still confusion. The new *magntiude* residual shows what looks to be a descrepant pole-zero pair around 100 to 500 Hz, but there's no such affect in the phase. Recall that the frequency dependence in the model is simple -- a pole a DC for the phase-frequency descriminator, the z:p pair for the VCO, a time delay, and a single 450 kHz pole. Nothing around 100 - 500 Hz. What do we suspect? More non-linearity. Great. More to think on. We'll measure the PLL controller in the -32dB gain setting tomorrow to make sure it's what we hope -- non-linearity at the negative-edge of the gain setting for this box, that we can just measure and divide out.
Since we propagate the uncertainty in the estimation of the poles and zeros to the entire diff calibration, we needed to do a quantitative fitting. So we did it using LISO. Here is the resultant plot:
The below are the raw output from LISO. We will propagate these errors throughout the ALS Diff calibration.
########## fitting results ###############
It seems that parameter 'delay' has only a little influence on the fit.
Suggestion: disable the 'param delay' instruction.
Correlation matrix (using fast derivatives)
pole1:f zero0:f factor delay
pole1:f 1
zero0:f 0.435 1
factor -0.909 -0.104 1
delay -0.00739 -0.022 1.01e-11 1
Best parameter estimates:
pole1:f = 1.5812454061 +- 8.509m (0.538%)
zero0:f = 40.8398688169 +- 114.7m (0.281%)
factor = 1.8947798127M +- 8.898k (0.47%)
delay = 1.2910415204u +- 84.71n (6.56%)
Final chi^2=1.87823
The fitting code can be found in SVN at
aligocalibration/trunk/Runs/ER8/H1/Scripts/ALSDiff/fit_diff_pll_olgtf_20150824.fil