Summary:

The RF transimpedance of the PMC PDH RFPD was measured, and found to be 1.03 kV/A. 

Details:

With the new fiber coupled PDFR system, it was very easy to measure the response of this PD in-situ 🎉 . The usual transfer function measurement scheme was used, with the AG4395 RF out modulating the pump current of the diode laser, and the measured transfer function being the ratio of the response of the test PD to the reference PD.

I assume that the amount of light incident on the reference NF1611 photodiode and the test photodiode were equal - I don't know what the DC transimpedance of the PMC REFL photodiode is (can't find a schematic), but the DC voltage at the DC monitor point was 16.4 mV (c.f. -2.04 V for the NF1611). The assumption shouldn't be too crazy because assuming the reference PD has an RF transimpedance of 700 V/A (flat in the frequency range scanned), we get a reasonable shape for the PMC REFL photodiode's transimpedance.

The fitted parameters are overlaid in Attachment #1. The 2f notch is slightly mistuned it would appear, the ratio of transimpedance at f1/2*f1 is only ~10. The source files have been uploaded to the wiki.

Knowing this, the measured PDH discriminant of 0.064 GV/m is quite reasonable:

• expected optical gain from modulation depth assuming a critically coupled cavity is 0.089 GW/m.
• Assume 0.7 A/W responsivity for InGaAs.
• Account for the fact that only 0.8 % of the reflected light reaches the PMC photodiode because of the pickoff window.
• Account for a conversion loss of 4.5 dB in the mixer.
• Account for the voltage division by a factor of 2 at the output of the BLP-1.9 filter due to the parallel 50 ohm termination.
• Then, the expected PDH discriminant is 0.089e9 W/m * 0.7 A/W * 0.8e-2 * 1.03kV/A * 10^(-4.5/20) * 0.5 ~ 0.15 GV/m. This is now within a factor of ~2 of the measured value, and I assume the total errors in all the above assumed parameters (plus the cable transmission loss from the photodiode to the 1X1 rack) can easily add up to this. 

So why is this value so different from what Koji measured in 2015? Because the monitor point is different. I am monitoring the discriminant immediately after the mixer, whereas Koji was using the front panel monitor. The latter already amplifies the signal by a factor of x101 (see U2 in schematic). 

Conclusion:

I still haven't found anything that is obviously wrong in this system (apart from the slight nonlinearity in the VGA stage gain steps), which would explain why the PMC servo gain has to be lower now than 2018 in order to realize the same loop UGF.