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Message ID: 2297     Entry time: Mon Jan 28 10:56:49 2019
 Author: awade and anchal Type: DailyProgress Category: NoiseBudget Subject: Noisebudget with Resonant Beat Note Photo Detector - Touching new lows

### Shot Noise of Photocurrent:

• Assuming 0.5 mW power is falling on the wideband beat note photodetector New Focus 1811-FC, with 40 kV/A of transimpedance $Z_{TI}$ and 0.75 A/W  responsivity $\mathrm{R}$ , shot noise of the photocurrent itself is:
\begin{aligned} S_V^{Shot Noise} &= (2 e P_{inc} \mathrm{R}) Z_{TI}^2 \\&= (2\times1.6\times10^{-19} C\times0.5\times10^{-3}\,W\times0.75\, \frac{A}{W})\times (40\times10^3\,\frac{V}{A})^2 \\&= 1.92\times10^{-13}\,\frac{V^2}{Hz} \end{aligned}
• Edit anchal Tue Jan 29 18:33:55 2019
This shot noise would be present as both amplitude and phase noise in the incoming BN signal. Amplitude noise affects negligible (through slight changes in open loop gain) to the PLL loop but phase noise directly affects the measured frequency noise. Effective phase noise contribution from shot noise is (here $V_{BNpkpk}$ is peak to peak amplitude of Beat Note signal):
\begin{aligned} \sqrt{S_\phi^{ShotNoise}}&=\frac{\sqrt{S_V^{ShotNoise}}}{V_{BNpkpk}}\pi\\ &= \frac{\sqrt{1.92\times10{-13}\frac{V^2}{Hz}}}{2\times0.5\times10^{-3}\,W\times0.75\frac{A}{W}\times40\times10^3\frac{V}{A}}\pi\\ &=4.589\times10^{-8}\frac{rad}{\sqrt{Hz}} \end{aligned}
• The phase noise is perceived as frequency noise as follow:
\begin{aligned} \sqrt{S_f^{ShotNoise}} &= f\sqrt{S_\phi^{ShotNoise}} \end{aligned}
• So, the noise due to shot noise of photocurrent will remain below $10 mHz/\sqrt{Hz}$ up to 217.93 kHz. So below written statements with red background were incorrect.
• This means the contribution of shot noise of photocurrent in the beat note noise ASD at amplifier gain of 200 and actuation slope of 1 kHz/V is:
\begin{aligned} \sqrt{S_{BNf}^{ShotNoise}} &= \sqrt{S_V^{ShotNoise}}\times200\,\frac{V}{V}\times 1\times10^3\frac{Hz}{V}\\ &= 87.64 \frac{mHz}{\sqrt{Hz}} \end{aligned}
• So a major portion of the noise floor recorded in Jan 24th measurement is actually due to photocurrent shot noise at the beat note detector.
• So our limiting factor is SNR of the beat note detector.

### Noise budget with Resonant BNPD:

On Friday, awade ran beat note measurement with resonant beat note photodetector to see how low we can get with improved SNR of this resonant detector. The method is the same as (PSL:2272) with 1000 measurements. The new noise budget is attached.

• Results are little better than using the wideband New Focus 1811-FC.

• Noise floor between 100-1000 Hz is about $90 mHz/\sqrt{Hz}}$ and above 1kHz it is $70 mHz/\sqrt{Hz}}$.

• The bumps at 150-160 Hz, 300 Hz, 800 Hz, and 900 Hz are still present. So their origin is something else in the experiment.

Edit Tue Aug 13 17:08:46 2019 anchal:

The PLL Readout noise added on this plot was erroneous and I can't find where it came from either. So the noisebudget attached is wrong! I was a dumbo then.

 Attachment 1: BeatNoteJan25_2019_Iris.zip  1.782 MB
 Attachment 2: 20190128_105844noiseBudget.pdf  945 kB
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