[Koji, Gautam]

Summary:

As I suspected, when the SR560 is operated in 1 Hz, first order LPF mode, the (electronic) transfer function has a zero at ~5kHz (!!!).

Details:

This is what allowed the PLL to be locked with this setting with UGF of ~30kHz. On the evidence of Attachment #3, there is also some flattening of the electrical TF at low frequencies when the SR560 is driving the NPRO PZT. I'm pretty sure the flattening is not a data download error but since this issue needs further investigation anyway, I'm not reading too much into it. I fit the model with LISO but since we don't have low frequency (~1Hz) data, the fit isn't great, so I'm excluding it from the plots.

We also did some PLL loop characterization. We decided that the higher output range (10Vp bs 10Vpp for the SR560) of the LB1005 controller means it is a better option for the PLL. The lock state can also be triggered remotely. It was locked with UGF ~ 60kHz, PM ~45deg.

We also measured the actuation coefficient of the NPRO laser PZT to be 4.89 +/- 0.02 MHz/V. Quoted error is (1-sigma) from the fit of the linear part of the measured transfer function to a single pole at DC with unknown gain. I used the "clean" part of the measurement that extends to lower frequencies for the fit, as can be seen from the residuals plot. Good to know that even though the LDs are dying, the PZT is still going strong :D.

Remaining loop characterization (i.e. verification of correct scaling of in loop suppression with loop gain etc.) is left to Jon.

Measurement schemes:

1. OLG (Attachment #1) was measured using the usual IN1/IN2 technique.
2. PZT calibration (Attachment #2) was measured by injecting an excitation at the PLL control point.
   • The ratio of the PLL error point (Volts) to Excitation (Volts) was measured using the SR785.
   • The error point was calibrated by looking at the PLL open loop Vpp (corresponds to pi radians of phase shift).
   • Dividing the fitted gain of the phase->Frequency conversion by the error point calibration, we get the PZT actuation coefficient. 

Some other remarks:

1. In the swept-sine mode, the SR785 measures transfer functions by taking the ratio of complex FFT values of its inputs at the drive frequency. So the phase in particular is a good indicator of whether the measurement is coherent or not.
2. In all these measurements, the PLL gain is huge at low frequencies, and hence, the excitation is completely squished on propagating through the loop. E.g. a 10mV excitation is suppressed by a factor of ~60dB = 1000 to 10uV, and if the analyzer autoRange is set to UpOnly, it is easy to see how this is drowned at the IN1 input. This is why the measurements lose coherence below ~1 kHz.
3. It is easy to imagine implementing an EPICS servo that offloads the DC part of the LB box control signal to the SLOW frequency input on the Lightwave controller. This would presumably allow us to extend the lock timescales. We can also easily implement a PLL autolocker.
4. Preliminary investigation of the SR560 situation suggests that individual filter stages can only achieve a maximum stopband attenuation of 60dB relative to the passband. When we cascade two stages together, 120dB seems possible...