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Thu Dec 19 19:45:12 2013
X-Arm Green PDH Loop Stuff
With the fixed servo box, I remeasured the OLTF, the servo, and the low pass filter between the mixer output and servo input. Dividing the OLTF by the servo and LPF transfer functions should just leave the the [laser PZT->cavity->PD] transfer function, which should have the shape of the cavity pole plus any delay in the loop, up until the PZT is no longer linear / the measurement has bad SNR.
I'm missing a few pieces of the loop. While I know the PD gain in V/W, I don't know how much power is in the sideband, which affects the slope of the PDH error function. Also, I've found old ELOG posts mentioning either 1 or 5MHz/V being the NPRO PZT response, but am not sure how to determine what it actually is. These are essentially just scalars though, so finding the reason for low phase margin doesn't depend on them.
Here are the TFs I've measured ("residual" refers to OLTF/(servo*LPF)):
The teal "residual" TF presumably owes its shape to the cavity pole + the time delay around the loop. Messing around with the data, the shape fits very well to a real pole at 27kHz and a ~3usec delay. I have no real way to back that up as the unique truth behind it, however. Is there a good way to measure the delay? Without assuming any delay, the shape is best fit by a real pole at 26kHz and some funky complex zeros.
Another thing to look at is the CLG implied by the measurement of the OLTF, given by 1/(1-G). I plotted this quantity for the measured loop, and also for G/2 and 3G/2 to get an idea for how it changes as you turn the servo gain knob. I measured with the knob at 4.0. There seems to be quite a bit of gain peaking!
Also, I drew up a simple block diagram sort of thing to show how everything is connecting down at the green electronics rack at the end of the X arm (while totally glossing over the optical elements involved). This hopefully helps anyone who wants to inspect/take apart/massacre the setup.