Missed to note: The IF test was done at TP7 and TP6 using pomona clips i.e. brefore the preamp.
I don't have a good explanation why, but I too measured similar numbers to what Koji measured. The overall conversion gain for this board (including the +20dB gain from the daughter board) was measured to be ~5.3 V/V on the bench, and ~16000 cts/V in the CDS system (100Hz offset from the LO frequency). It would appear that the effective JMS-1-H conversion loss is <2dB. Seems fishy, but I can't find anything else obviously wrong with the circuit (e.g. a pre-amp for the RF signal that I missed, there is none).
I also attach the result of the measured noise at the outputs of the daughter board (i.e. what is digitized by the ADC), see Attachment #2. Apart from the usual forest of lines of unknown origin, there is still a significant excess above the voltage noise of the OP27, which is expected to be the dominant noise source in this configuration. Neverthelesss, considering that we have only 40dB of whitening gain, it is not expected that we see this noise directly in the digitized signal (above the ADC noise of ~1uV/rtHz). Note that the measured noise today, particularly for the Q channel, is significantly lower than before the changes were made.
Today I tried debugging the mysterious increase in REFL55 signal levels in the DRMI configuration. I focused on the demod board, because last week, I had tried routing these signals through different channels on the whitening board, and saw the same effect.
Based on my tests, everything on the Demod board seems to work as expected. I need to think more about what else could be happening here - specifically do a more direct test on the whitening board.
I did a quick check by switching the output of the REFL55 demod board to the inputs normally used by AS55 signals on the whitening board. Setting the whitening gain to +18dB for these channels had the same effect - ADC overflow galore. So looks like the whitening board isn't to blame. I will have to check the demod board out.
All connections have been restored untill further debugging later in the evening.
We could not find problems with any individual piece of the REFL55 electronics chain, from photodiode to ADC. Nevertheless, the PRMI fringes witnessed by REFL55 is ~x10 higher than ~two weeks ago, when the PRMI could be repeatably and reliably locked using REFL55 signals (ETMs misaligned).
Discussion and next steps:
Q: Koji asked me what is the problem with this apparent increased optical gain - can't we just compensate by decreasing the whitening gain?
A: I am unable to transition control of the PRMI (no ETMs) from 3f to 1f, even after reducing the whitening gain on the REFL55 channels to prevent the saturation. So I think we need to get to the bottom of whatever the problem is here.
Q: Why do we need to transfer the control of the vertex to the 1f signals at all?
A: I haven't got a plot in the elog, but from when I had the PRFPMI locked last year, the DARM noise between 100-1kHz had high coherence with the MICH control signal. I tried some feedforward to try and cancel it but never got anywhere. It isn't a quantitative statement but the 1f signals are expected to be cleaner?
Koji pointed out that the MICH signal is visible in the REFL55 channels even when the PRM is misaligned, so I'm gonna look back at the trend data to see if I can identify when this apparent increase in the signal levels occurred and if I can identify some event in the lab that caused it. We also discussed using the ratio of MICH signals in REFL and AS to better estimate the losses in the REFL path - the Faraday losses in particular are a total unknown, but in the AS path, there is less uncertainty since we know the SRM transmission quite precisely, and I guess the 6 output steering mirrors can be assumed to be R=99%.
I upgraded the old REFL199 to the new REFL55.
To do that I had to replace the old photodiode inside, switching to a 2mm one.
Electronics and optical transfer functions, non normalized are shown in the attached plot.
The details about the modifications are contained in this dedicated wiki page (Upgrade_09 / RF System / Upgraded RF Photodiodes)
I measured the optical and electrical transfer functions for REFL55 and calculated the RF transimpedance. To measure the optical transfer function, I used the light from an AM laser to simultaneously measure the transfer functions of REFL55 and a New Focus 1611 photodiode. I combined these two transfer functions to get the RF transimpedance for REFL55. I also measured the electrical transfer function by putting the RF signal from the network analyzer in the test input of the photodiode.
I put all of the plots on the wiki at http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/REFL55.
REFL55 was modified. The noise level confirmed. The PD is now ready to be installed.
Kevin's measurement report told us that something was wrong with REFL55 PD. The transimpedance looked OK, but the noise level was terrible (equivalent to the shotnoise of 14mA DC current).
Rana and I looked at the circuit, and cleaned up the circuit, by removing unnecessary 11MHz notch, 1k shunt resister, and so on.
I made a quick characterization of the PD.
The transimpedance ws measured as a function of the frequency. The resonance was tuned at 55MHz. The notch was tuned at 110MHz in order to reject the second harmonics. The transimpedance was ~540V/A at 55MHz. (For the calibration, I believed the DC transimpedance of 50V/A and 10000V/A for the DC paths of this PD and #1611, respectively, as well as the RF impedance (700V/A0 of #1611.
Output noise levels were measured with various amount of photocurrent using white light from a light bulb. The measurement was perforemed well above the noise level of the measurement instruments.
The measured output noise levels were converted into the equivalent current noise on the PD. The dark noise level agrees with the shot noise level of 1.5mA (i.e. 22pA/rtHz). In deed, the noise level went up x~1.5 when the photocurrent is ~1.4mA.
I used a matlab code written by Koji to analyse the transimpedance and current noise data of REFL55. The details are in the attached pdf file.
Resonance is at 55.28 MHz:
Q of 4.5, Transimpedance of 615 Ohms
shot noise intercept current = 1.59 mA
current noise =21 pA/rtHz
Notch at 110.78 MHz:
Q of 54.8 Transimpedance of 14.68 Ohms.
[Koji, Rana, and Kevin]
I have been trying to measure the shot noise of REFL55 by shining a light bulb on the photodiode and measuring the noise with a spectrum analyzer. The measured dark noise of REFL55 is 35 nV/rtHz. I have been able to get 4 mA of DC current on the photodiode but have not been able to see any shot noise.
I previously measured the RF transimpedance of REFL55 by simultaneously measuring the transfer functions of REFL55 and a new focus 1611 photodiode with light from an AM laser. By combining these two transfer functions I calculated that the RF transimpedance at 55 MHz is ~ 200 ohms. With this transimpedance the shot noise at 4 mA is only ~ 7 nV/rtHz and would not be detectable above the dark noise.
The value of 200 ohms for the transimpedance seems low but it agrees with Alberto's previous measurements. By modeling the photodiode circuit as an RLC circuit at resonance with the approximate values of REFL55 (a photodiode capacitance of 100 pF and resistance of 10 ohms and an inductance of 40 nH), I calculated that the transimpedance should be ~ 230 ohms at 55 MHz. Doing the same analysis for the values of REFL11 shows that the transimpedance at 11 MHz should be ~ 2100 ohms. A more careful analysis should include the notch filters but this should be approximately correct at resonance and suggests that the 200 ohm measurement is correct for the current REFL55 circuit.
RF Transimpedance of 200Ohm means the residual impedance at the resonance (R_res) of 40,
if you consider the amplifier gain (G_amp) of 10 and the voltage division by the 50Ohm termination,
this corresponds to the thermal noise level of Sqrt(4 kB T R_res)*G_amp/2 = 4nV/rtHz at the analyzer, while you observed 35nV/rtHz.
35nV/rtHz corresponds to 7nV/rtHz for the input noise of the preamp. That sounds too big if you consider the voltage noise of opamp MAX4107 that is 0.75nV/rtHz.
What is the measurement noise level of the RF analyzer?
I tried the REFL33Q for controlling MICH in the PRMI configuration (#6407)
The result was --
It was barely able to lock MICH in a short moment but didn't stay locked for more than 10 sec. Not good.
Old MZ PD (InGaAs 2mm, @29.5MHz) has been modified for REFL33.
There has been no choice for the 11MHz notch other than putting it on the RF preamp
as the notch in parellel to the diode eats the RF transimpedance at 33MHz.
I wait for judgement of Rana if the notch at the MAX4107 feedback is acceptable or not.
REFL33 is ready for the installation
Characterization results of REFL33 is found in the PDF attachment.
Resonance at 33.18MHz
Q of 6.0, transimpedance 2.14kOhm
shotnoise intercept current = 0.52mA (i.e. current noise of 13pA/rtHz)
Notch at 10.97MHz
Q of 22.34, transimpedance 16.2 Ohm
Notch at 55.60MHz
Q of 42.45, transimpedance 33.5 Ohm
The following tasks need to be done in the daytime tomorrow.
The REFL165 RF output was not reaching the Demod board. The RF cable was disconnected. I fixed that and then I put in a RF signal at 165MHz , 1.66 mVrms at the test input (100Hz off set from the 165MHz LO) and saw that the 100 Hz demodulated signal was visible in the dataviewer.
Will complete the Optical RF power -> CDS counts calibration tomorrow morning.
Kiwamu mentioned that REFL165 is not responding and its DC out seems saturated at 9V. Koji and I checked to see if changing the power supply to the PD changed its behaviour. It did not.
I then look a close look at the PD and found that the front window of the PD was not clear and transparent. There was a liquid condensation inside the window, indicating an over heating of the PD at some point. It could have arisen due to excessive incident power. The pic below shows this condensation:
I also checked the current flowing through the reverse bias voltage line. There was a voltage drop of 3V across R22 (DCC D980454-01-C) indicating a 150mA of current through the PD. This is way too much above the operating current of about 20mA. The diode must have over heated.
I pulled out the old PD out and installed a new one from stock. The pic below shows the clear window of a new PD.
After changing the PD I checked the DC output voltage while shining a torch light on to the PD. It showed an output of about 30 to 40 mV. This seemed okay because the larger 2mm photodiodes showed ~100mA DC output with the same torch.Below is the current state of the ckt board.
I will tune the PD to 165 MHz tomorrow and measure its transimpedance.
1) The REFL165 has been replaced onto the AS table.
2) When the PD interface cable is attached the PD shows a DC out put of 6mV and does not respond to a flash light. I changed the PD interface port in the LSC rack by swapping the other end of the cable with an unused (Unidentified PD) interface cable, The PD is working fine after that. There could be a problem with some binary switch state on the PD interface where the REFL165 cable was plugged in earlier.
The transfer function and current noise were measured. The location of the peak shifts with the amount of incident light power (RF or DC). The TF was measured at an incident 1064nm light power of 0.4 mW which produced a DC output voltage of 14 mV => DC photocurrent of 0.28 mA.
Many of the effects that Koji noted in the previous characterization are still present.
In addition I observed a shift of the peak towards lower frequencies as the RF power supplied to the AM Laser (Jenne Laser) is increased. This could create a dependance of the demodulation phase on incident RF power.
The plots are attached below.
To determine the amount of RF power in the AM laser beam at various RF drive levels I measured the RF power out of the Newfocus 1611 PD while driving the AM laser with a Marconi. During this measurement the DC output was 2.2V. With the DC transimpedance of 10^4 and a sensitivity of 0.8 A/W we have carrier power as 0.275 mW (-5.6 dBm). [Incidentally the measured carrier power with a power meter is about 0.55 mW. Why this discrepancy?]
Estimation of the signal strength at the REFL165 PD:
From the 40m Sensing Matrix for DRFPMI we see that the signal strength at REFL165 in CARM is about 5x10^4 W/m. Since we expect about 0.1nm of linear range in CARM length we expect about 0.05 mW of RF power. If the (DC) carrier power is about 10 mW at the photodiode (18mW is about the max we can have since the max power dissipation is 100 mW in the diode) then the RF : DC power ratio is 5x10^-3 => -23 dB
As this is lower than the power levels at which the PD transfer function was determined and where we noted the distorsion and shift of the resonance peak, it is likely that these effects may not be seen during the normal operation of the interferometer.
The shift due to the carrier power level (DC) change may still however pose a problem through a changing demodulation phase.
REFL165 removed from the table for the C(V) test
The PD was returned on the table.
The C(V) compensation path was modified and the change of the resonant freq was cancelled.
A more precise analysis comes later.
The original REFL165 had ~50MHz/A dependence on the DC photocurrent.
The resistr R21, which was 2670 Ohm contrary to the original drawing, was replaced to 532 Ohm
to increase the feedforward gain by factor of 5.
The resulting dependence is reduced to ~0.5MHz/A although it has Q reduction of ~20% at 6mA.
These transfer functions were measured between TEST IN and RF OUT while the diode was illuminated with the white light from a light bulb.
There looks some thermal effect on the resonant freq. If the white light illumination is suddenly removed, the bias compensation
is immediately removed but the resonance takes some time (~min) to come back to the original freq.
I am afraid that the light bulb gave too much heat on the surrounding PCB and lead unnecesarily high level dependence of the resonant freq on the DC current.
Or, if this thermal effect comes from the power consumption on the diode itself, we need to characterize it for aLIGO.
In order to check this, we need a test with the 1064nm illumination on the diode in stead of the light bulb.
These are the measurements for estimating the amplitude of the signal recorded in the CDS when a known amount of modulated light is incident on the photodiode.
I mounted the PD characterisation setup onto a small breadboard which could then be placed close AP table. I then placed position markers for REFL165 on the AP table before moving it onto my small breadboard. The AM laser was driven by an RF function generator (Fluke 6061A) at a frequency of 165.98866 MHz, which is 102 Hz offset from the 165MHz LO. The power level was set at -45dBm. This power level was chosen since anything higher would have saturated the AntiAliasing Whitening Filters. The counts in the CDS were converted to voltage using the ADC resolution = 20V per 2^16 counts.
When the 166MHz power is decreased by a factor of 2 the amplitude of 102Hz wave recorded in CDS goes down by sqrt(2) as expected. The RF AM power incident on the REFL165 was estimated to be 0.011mW(rms) (case #1 in the above table) using the DC power ratio and using the transimpedance of the 1611 BBPD to be 700 Ohms. This produces a 171 mV amplitude wave at 102 Hz. I then stepped down the power by factor of 2 and repeated the measurement.
(These numbers however are not agreeing with the power incident on REFL165 if we assume its transimpedance to be 12500. It will take a bit more effort to make all the numbers agree. Will try again tomorrow)
Here is a picture of the small black breadboard on which I have put together the PD characterisation setup. It would be great if we can retain this portable set up as it is, since we keep reusing it every couple of weeks. It would be convenient if we can fiber couple the path to the PD under test with a 2m long fiber. Then we will not have to remove the PD from the optical table while testing it.
To characterize the RF V to counts we need to know the state of the whitening filter board. Was the filter on or off ? What was the value of the whitening gain slider?
The filter was ON and the whiterning filter gain was 45dB
REFL165 PD has been made from the old 166MHz PD.
As the required inductance was ~10nF level, the stray inductance of the circuit pattern was significant.
So, I am not so confident with the circuit functionality before the optical transfer function test.
I will test REFL33 and REFL165 with the Jenne laser to see how they work.
This REFL165 was good in terms of RF, but I forgot to make the DC path functioning.
I will try some ideas to fix this tomorrow.
REFL165 PD was made and tested. The characterization results are in the PDF file.
Resonance at 166.12MHz
Q of 7.3, transimpedance 667Ohm (Series Resistance = Z/Q2 = 2.5Ohm)
shotnoise intercept current = 4.3mA (i.e. current noise of 36pA/rtHz)
As the circuit pattern had ~10nH level strain inductance, some technique was needed.
Now the size of the loop for the resonant circuit is comparable with the size of SOIC-8 opamp.
(Left-Top corner of the photo)
This improved the resonant gain by factor of 8.5dB at the test with TEST INPUT. (Analyzer photo)
There is no tunable component.
The resonant freq was adjusted by a parallel inductance (270nH) to the main inductor (15nH).
This is with reference to Kevin and Jenne's elogs # 3890, 4034 and 4048 .
While the electronics are working okay, there is no DC signal from the photodiode.
Since the solderings and tracks on the PCB were fine I took a close look at the exposed front face of the photodiode.
As we can see, one of the thin wires on the top surface of the photodiode is broken. We can see some wipe marks closer to the lower left edge..
Something seems to have brushed across the exposed face of the photodiode and dislodged the wire.
The new photodiode still has its protective can intact. Do we need to remove the can and expose the photodiode before istallation?
I spent some time trying to understand how touching the metal cage inside or bending the PCB board affected the photodiode response. It turned out that there was some weak soldering of one of the inductors.
Hartmut suggested a possible explanation for the way the electronics transfer function starts picking up at ~50MHz. He said that the 10KOhm resistance in series with the Test Input connector of the box might have some parasitic capacitance that at high frequency lowers the input impedance.
Although Hartmut also admitted that considering the high frequency at which the effect is observed, anything can be happening with the electronics inside of the box.
The full characterization of REFL11 is found in the PDF.
Resonance at 11.062MHz
Q of 15.5, transimpedance 4.1kOhm
shotnoise intercept current = 0.12mA (i.e. current noise of 6pA/rtHz)
Notch at 22.181MHz
Q of 28.0, transimpedance 23 Ohm
Notch at 55.589MHz
Q of 38.3, transimpedance 56 Ohm
I took REFL11 out from the AS table for a health check because it wasn't working properly.
The symptoms were :
- a big offset of ~ -3 V on the RF output. No RF signals.
- The DC output seemed to be okay. It's been sensitive to light.
I did a quick check and confirmed that +/- 5V were correctly supplied to the op-amps.
It looks that the last stage (MAX4107) is saturated for some reasons. Need more inspections.
At the moment the REFL11 RFPD is on the bench of the Jenne laser.
- Found the inductor which shunts the positive input of MAX4107 was not touching the ground.
This left the positive input level undetermined at DC. This was why MAX had been saturated.
The PCB has a cut, so it was surprising once the circuit worked.
- Resoldered the inductor to the ground. This made the circuit responding to the intensity-modulated beam.
- But the resonances and the notches were totally off, and the 200MHz oscillation has resurrected.
- Attached 40Ohm+22pF network between the neg-input of MAX and the gnd. This solved the oscillation.
- Made the tuning and the characterizations. The PD is on Kiwamu's desk and ready to go.
More to come later
I'm going to remove REFL11 demod for the noise check/circuit improvement.
First I checked the noise levels and the transfer functions of the daughterboard preamp were checked. The CH-1 of the SR785 seemed funky (I can't comprehensively tell yet how it was), so the measurement maybe unreliable.
For the replacement of AD797, I tested OP27 and TLE2027. TLE2027 is similar to OP27, but slightly faster, less noisy, and better in various aspects.
The replacement of the AD797 and whatever-film resistors with LTE2027 and thin-film Rs were straightforward for the I phase channel, while the stabilization of the Q phase channel was a struggle (no matter I used OP27 or TLE2027). It seems that the 1st stage has some kind of instability and I suffered from 3Hz comb up to ~kHz. But the scope didn't show obvious 3Hz noise.
After a quite bit of struggle, I could tame this strange noise by adjusting the feedback capacitor of the 1st stage. The final transfer functions and the noise levels were measured. (To be analyzed later)
Now the REFL11 LO cable was replaced from the soft low noise audio coax (Belden 9239) to jacketed solder-soaked coax cable (Belden 1671J - RG405 compatible). The original cable indicated the delay of -34.3deg (@11MHz, 8.64ns) and the loss of 0.189dB.
I took 80-inch 1671J cable and measured the delay to be ~40deg. The length was adjusted using this number and the resulting cable indicated the delay of -34.0deg (@11MHz, 8.57ns) and the loss of 0.117dB.
The REFL11 demod module was restored and the cabling around REFL11 and AS110 were restored, tightened, and checked.
I've removed the PD mon cables from the NI RF switch. The open ports were plugged with 50Ohm temirnators.
Attachment 1: Transfer Functions
The original circuit had a gain of ~20 and the phase delay of ~1deg at 10kHz, while the new CH-I and CH-Q have a phase delay of 3 deg and 2 deg, respectively.
Attachment 2: Output Noise Levels
The AD797 circuit had higher noise at low frequency and better noise levels at high frequency. Each TLE2027 circuit was tuned to eliminate the instability and shows a better noise level compared to the low-frequency spectrum of the AD797 version.
RXA: AD797 , all hail the op-amps ending with 27 !
Yesterday night I plugged back the REFL11 RF cable into the corresponding demodulation board.
These are the dark noise spectrum that I measured on the 11MHz and 55MHz PD prototypes I modified.
The plots take into account the 50Ohm input impedance of the spectrum analyzer (that is, the nosie is divided by 2).
With an estimated transimpedance of about 300Ohm, I would expect to have 2-3nV/rtHz at all frequencies except for the resonant frequencies of each PD. At those resonances I would expect to have ~15nV/rtHz (cfr elog entry 2760).
I have to figure out what are the sources of such noises.
A new photodiode ( Perkin and Elmer Model no. C30642GH Sl No.1526) has been installed in the place of the old photodiode. The datasheet of this model is attached.
The 68pF capacitor which was present in parallel with the photodiode has been removed. Here is a picture of the PCB ( in all its gory detail!) and the photodiode after replacement.
I also checked to see if we have a DC output from the new PD. With 375mW of 1064nm light incident we have 15mV of output. Which matches well with the typical Reponsivity of 0.8V/A reported in the datasheet and our REFL11 ckt . The schematic of the ckt is also attached here for easy reference. The various factors are
V_dc = 0.375 mW x 0.8 V/A x 10 Ohm x 5 = 15mV
The last factor is the gain of the last stage on the DC route.
When I reassembled the box I noticed that there is problem with the SMA connectors popping out of the box. The holes seem misplaced so I enlarged the holes to remove this concern.
375 mW is way too much light. We must never put more than 100 mW on any of these diodes. We don't want to blow up more diodes like we did with the WFS. The InGaAs diodes often show an excess dark noise before they finally let go and completely fail. This one may show excess during the shot noise testing.
We should ensure that the beam paths are engineered so that none of these new detectors ever sees such high light levels.
The DC path should be made to let us see a 10V from the differential EPICS readout when there is 100 mA of photocurrent (i.e. an effective 100 Ohms transimpedance):
0.1 A * 10 V/A * 5 V/V * 2V/V
The last factor of 2 is from the single to differential conversion.
If we really only get 15 mV from 375 mW, then this diode or the circuit is broken.
Suresh is saying 375mW and 0.375mW. Let's wait for his update of the actual power.
Also he is not using EPICS, there may be the factor of two missing for now.
It is 0.375 mW as in the calculation. The total diode output is just 1mW and it is divided with a 50/50 beam splitter... There are a couple of lenses along the way which may account for the ~12% loss.
I used a handheld multimeter to measure the output.
[Koji and Kevin]
I was trying to characterize the REFL11 photodiode by shining a flashlight on the photodiode and measuring the DC voltage with an oscilloscope and the RF voltage with a spectrum analyzer. At first, I had the photodiode voltage supplied incorrectly with 15V between the +15 and -15 terminals. After correcting this error, and checking that the power was supplied correctly to the board, no voltage could be seen when light was incident on the photodiode.
We looked at the REFL55 photodiode and could see ~200 mV of DC voltage when shining a light on it but could not see any signal at 55 MHz. If the value of 50 ohm DC transimpedance is correct, this should be enough to see an RF signal. Tomorrow, we will look into fixing the REFL11 photodiode.
I just wanted to remind you that the most up to date resource about the RF system upgrade, including photodiodes, is the SVN.
Because I was doing new things all the time, the wiki is not up to date. But the SVN has all I've got.
From the measurements of the 11 MHz RFPD at 11Mhz I estimated a transimpedance of about 750 Ohms. (See attached plot.)
The fit shown in the plot is: Vn = Vdn + sqrt(2*e*Idc) ; Vn=noise; Vdn=darknoise; e=electron charge; Idc=dc photocurrent
The estimate from the fit is 3-4 times off from my analsys of the circuit and from any LISO simulation. Likely at RF the contributions of the parassitic components of each element make a big difference. I'm going to improve the LISO model to account for that.
The problem of the factor of 2 in the data turned out to be not a real one. Assuming that the dark noise at resonance is just Johnson's noise from the resonant circuit transimpedance underestimates the dark noise by 100%.
Putting my hands ahead, I know I could have taken more measurements around the 3dB point, but the 40m needs the PDs soon.
Something must be wrong.
1. Physical Unit is wrong for the second term of "Vn = Vdn + Sqrt(2 e Idc)"
2. Why does the fit go below the dark noise?
3. "Dark noise 4 +/- NaN nV/rtHz" I can not accept this fitting.
Also apparently the data points are not enough.
1) True. My bad. In my elog entry (but not in my fit code) I forgot the impedance Z= 750Ohm (as in the fit) of the resonant circuit in front of the square root: Vn = Vdn + Z * sqrt( 2 e Idc )
2) That is exactly the point I was raising! The measured dark noise at resonance is 2x what I expect.
I also admitted that the data points were few, especially around the 3dB point.
Today I'm going to repeat the measurement with a new setup that lets me tune the light intensity more finely.
Here's another measurement of the noise of the REFL11 PD.
This time I made the fit constraining the Dark Noise. I realized that it didn't make much sense leaving it as a free coefficient: the dark noise is what it is.
Result: the transimpedance of REFL11at 11 MHz is about 4000 Ohm.
Data looks perfect ... but the fitting was wrong.
Vn = Vdn + Z * sqrt( 2 e Idc ) ==> WRONG!!!
Dark noise and shot noise are not correlated. You need to take a quadratic sum!!!
Vn^2 = Vdn^2 + Z^2 *(2 e Idc)
And I was confused whether you need 2 in the sqrt, or not. Can you explain it?
Note that you are looking at the raw RF output of the PD and not using the demodulated output...
Also you should be able to fit Vdn. You should put your dark noise measurement at 10nA or 100nA and then make the fitting.
# gnd n22
# | |
# Rip Rw2
# | | |\
# nt- Rsi-n2- - - C2 - n3 - - - - | \
# | | | | |4106>-- n5 - Rs -- no
# iinput Rd L1 L2 R24 n6- | / | |
# |- nin- | | | | | |/ | Rload
# Cd n7 R22 gnd | | |
# | | | | - - - R8 - - gnd
# gnd R1 gnd R7
# | |
# gnd gnd