Correction to previous post

On the last noise measurement of the CARM RFPD, we found that the input impedance of the Moku:Lab used in the measurement was set to $50\,\mathrm{\Omega}$.
As a result, the measured voltage was reduced by a factor of two compared to a high-impedance input, and the analysis was done without its correction.

In this post, we apply the factor-of-two correction and reanalyze the data, and present the updated results.

Details:

Figure 1 shows the demodulated noise spectra taken at different PD input powers (the amplification by the SR560 and 1/2 by Moku 50Ω input impedance have been corrected).
To extract the noise-floor values for each input power, we computed the mean and standard error over the frequency band from 50 kHz to 100 kHz for each spectrum.
This frequency region was selected to avoid the peak near 40 kHz.

Figure 2 shows the power dependence of the obtained noise-floor values.
The data were fitted using the following model to extract the power dependence of the PD dark noise and shot noise:

Fitting model:

$\delta V_\mathrm{RFPDnoise} = \sqrt{\delta V_\mathrm{dark}^2+\delta V_\mathrm{shot}^2}$

$\delta V_\mathrm{dark}$: Dark noise of RFPD$$

$\delta V_\mathrm{shot} \equiv R\sqrt{2e\alpha}\times\sqrt{P_\mathrm{in}}$: Shot noise after RFPD demodulation

$R$: effective transimpedance including demodulation

$e$: elementary charge

$\alpha$: responsibility

$P_\mathrm{in}$: input power to RFPD

Result of fitting:

$V_{dark}=7.92(2)\times {10}^{-8}V/\sqrt{Hz}$
$R\sqrt{2e\alpha}=4.54(2)\times10^{-8}\,\mathrm{V/\sqrt{Hz\,mW}} =1.436(5)\times10^{-6}\,\mathrm{V/\sqrt{Hz\,W}}$

Assuming $\alpha=0.77\,\mathrm{A/W}$, the effective transimpedance $R$ and the power-to-voltage conversion efficiency including demodulation $R\alpha$ are

$R=2.84(1)\times10^3\,\mathrm{\Omega}$
$R\alpha=2.271(8)\times10^3\,\mathrm{V/W}$