For a series resistance of 4.5 kohm, we are suffering from the noise-gain amplified voltage noise of the Op27 (2*3.2nV/rtHz), and the Johnson noise of the two 1 kohm input and feedback resistances. As a result, the current noise is ~2.7 pA/rtHz, instead of the 1.9 pA/rtHz we expect from just the Johnson noise of the series resistance. For the present EX coil driver configuration of 2.25 kohm, the Op27 voltage noise is actually the dominant noise source. Since we are modeling small amounts (<1dB) of measurable squeezing, such factors are important I think.
[Attachment #1] --- Sketch of the fast signal path in the coil driver board, with resistors labelled as in the following LISO model plots. Note that as long as the resistance of the coil itself << the series resistance of the coil driver fast and slow paths, we can just add their individual current noise contributions, hence why I have chosen to model only this section of the overall network.
[Attachment #2] --- Noise breakdown per LISO model with top 5 noises for choice of Rseries = 2.25 kohm. The Johnson noise contributions of Rin and Rf exactly overlap, making the color of the resulting line a bit confusing, due to the unfortunate order of the matplotlib default color cycler. I don't want to make a custom plot, so I am leaving it like this.
[Attachment #3] --- Noise breakdown per LISO model with top 5 noises for choice of Rseries = 4.5 kohm. Same comments about color of trace representing Johnson noise of Rin and Rf.
Possible mitigation strategies:
- Use an OpAmp with lower voltage noise. I will look up some candidates. LT1028/LT1128? LISO library warns of a 400 kHz noise peak though...
- Use lower Rin and Rf. The values of these are set by the current driving capability of the immediately preceeding stage, which is the output OpAmp of the De-Whitening board, which I believe is a TLE2027. These can source/sink 50 mA according to the datasheet . So for +/-10V, we could go to 400 ohm Ri and Rf, source/sink a maximum of 25mA, and reduce the Johnson noise contribution by 40%.
I've chosen to ignore the noise contribution of the high current buffer IC that is inside the feedback loop. Actually, it may be interesting to compare the noise measurements (on the electronics bench) of the circuit as drawn in Attachment #1, without and with the high current buffer, to see if there is any difference.
This study also informs about what level of electronics noise is tolerable from the De-Whitening stage (aim for ~factor of 5 below the Rseries Johnson noise).
Finally, in doing this model, I understand that the observation the voltage noise of the coil driver apparently decreased after increasing the series resistance, as reported in my previous elog. This is due to the network formed by the fast and slow paths (during the measurement, the series resistance in the slow path makes a voltage divider to ground), and is consistent with LISO modeling. If we really want to measure the noise of the fast path alone, we will have to isolate it by removing the series resistance of the slow bias path.
Comment about LISO breakdown plots: for the OpAmp noises, the index "0" corresponds to the Voltage noise, "1" and "2" correspond to the current noise from the "+" and "-" inputs of the OpAmp respectively. In future plots, I'll re-parse these...
I will upload more details + photos + data + schematic + LISO model breakdown tomorrow to a DCC page.