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Message ID: 2324     Entry time: Wed Apr 10 13:10:45 2019     In reply to: 2318
 Author: awade Type: DailyProgress Category: WOPO Subject: Rebuild of WOPO homodyne detectors using AD829

This post details the rebuild I made of the transimpedance amplifiers (TIA) for the homodyne detectors.  My previous iteration of this design failed to take into account the output swing limitations and current draw limitations at the output of the op amp.  It turns out that the OP27 was not the best choice here.  On the face of it its GBP and input referred noise were fine for a ~ 1 MHz detection.  However, operating the chip with 5V output voltage (to get 10 dB shot noise clearance from thermal noise) and with output impedance on order of 150 Ω meant that the frequency response was not as expected (see ATF:2316).

A better choice is something like AD829 which is designed for driving signals directly into 50Ω terminated outputs.  The updated design is illustrated below.

Here the transimpedance gain has been lowered to 2 kΩ to lower the relative input referred noise contributed by the AD829's slightly higher current noise.  Here the optical power can be increased to give the same effective output signal.  In this case increase optical power and lowering gain keeps the thermal noise clearance below shot noise constant but improves the clearance of the AD829 input current noise.

## Scaling of thermal noise relative to shot noise given DC output voltage

For reference the thermal noise of the TIA is given by the Johnson noise

$\delta n_\mathrm{thR} = \sqrt{\frac{4k_BT}{R_\textrm{fb}}}$

where k_B is the  Boltzmann's constant, T is the temperature (300K) and Rfb is the feedback resistor value.  Also here the shot noise is

$\delta n_\mathrm{SN} = \sqrt{2 e^- \mathcal{R}P_\textrm{PD}}$

Where e is the charge on an electron (1.602e-19 C), R is the photodiode responsivity (~0.8 A/W), and P_PD is the power on the photodetectors (0.5-5 mW).  Keeping in mind that there is a maximum voltage swing (V_max) on the output of the op amp, this comes from its current driving capability into a given load, then the feedback resistance (TIA gain) is limited to

$R_\textrm{fb} = \frac{V_\textrm{Max}}{\mathcal{R} P_\textrm{PD}}$

The noise clearance, given a maximum output voltage, is then given by the ratio

$NR = \frac{\delta n_\mathrm{SN}}{\delta n_\mathrm{thR}} = \sqrt{\frac{e^-V_\textrm{Max}}{2kT}}$

Power on the photodiode and responsivity cancel out for the noise clearance.  Assuming we are not optical power limited then the thermal noise ratio (clearance below shot noise) is wholly determined by V_Max and the physical constants e, k_B and T.  For room temperature (300 K) this reduces to the rule of thumb

$NR \sim 4.4 \sqrt{V_\textrm{Max}}$

Keeping the V_max to within 3 V means that we will get a thermal noise clearance factor of 7.6 below shot noise (8.8 dB). V_max of 5.2 volts will give 10 dB clearance. Ok I guess.

Koji suggested the AD829 as a replacement to OP27.  AD829 has applications in driving 50 Ω/75 Ω loads in video applications and has some nice noise characteristics.  The bottom line is that it has 1.7 nV/√Hz input voltage noise, 1.5 pA/√Hz input current noise, can do a ±3 V voltage swing into 150 Ω load (DC coupled), and is fast (600 MHz uncompensated, with 230 V/µs slew).  There are some quirks.  AD829 seems have have a weird 80 MHz feature that causes oscillations if not compensated properly.  I did a bit of modeling in LISO and then just decided to build it once I found that ~2 kΩ gain was about right for ensuring that the dark noise wasn't dominated by the op amp current noise.

Because I was building on proto-board I wanted to ensure that there was as little parasitic capacitance as possible.  I built the whole amplifier + PD onto a single SOIC-14 to 0.1 pitch adaptor (Adafruit SMT Breakout PCB for SOIC-14, Part No. 1210), pictured below.  The small footprint and short trace lengths between critical pins means that there is a lower chance of parasitic impedance causing instability or impact on bandwidth.

The feedback resistor (2 kΩ) and feedback compensating capacitor (15 pF ceramic + 3 pF nominal pin parasitic) were soldered directly to the reverse side where the TSSOP-14 pins were connected through vias to the top side.  This minimized the path length of this electrical signal.  I scratched off pads that were unused in case they shorted or were a source of crosstalk.  The photodiode mount pin was soldered directly to the edge of the board to minimize distance.  The power bypassing capacitors were SMT 100 nF ceramics (5%) that were soldered directly to the SMT breakout with the shortest path to ground on that board (see pictured).  The other photodiode pin was soldered to +5 V (-5V) supply pin in unit A (unit B).  The opposite biasing makes subtracting the signals using a summing circuit easier but may affect the overall TF response. There is no power regulation, I'm planning to use batteries to power these circuits.

In my initial tests I had no compensating capacitor attached to pin 5.  I inserted a 40 pF ceramic capacitor in place of the photodiode and looked at the AD829 output pin with a high impedance probe on an oscilloscope.  I immediately saw 80 MHz oscillations.  I don't really need a super high bandwidth so I went strait to the maximum recommended choice for pin5 compensating capacitor of 68 pF.  This makes AD829 unity gain stable with 66 MHz bandwidth (slew 16V/µs) but is more than enough for my needs.  This killed the high frequency RF ringing junk. Maybe less capacitance here would have worked, but this performance is enough for my needs and gives some certainty about the op amps stability (ignoring input capacitance compensation).

At the output I added 100 Ω of series resistance to limit the loading on the op amp and current draw when 50 Ω terminated.  With 50 Ω terminating impedance this makes a 150 Ω to ground.  Providing the output DC swing is kept within 3V the op amp should behave as expected.

The whole thing fits together very nicely on a single SMT breakout board. Making it compact will hopefully avoid any issues with stray capacitance messing up the performance.  I have then mounted this on a larger proto board for ease of installing in the experiment. Paths to the output SMA output are thin wire and not routed through the underlying board. Only power and ground is routed through the board, all other pins to the op amp disconnected.

## Transfer function PD

I measured the signal transfer function of the above TIA units using the Jenne rig at the 40 m.  It took me a number of tries: I made the mistake of loading the DC port of the NF 1611 detector with 50 ohms (which resulted in too much current draw and affected the LF response of the witness detector); there were also some issues with the polarization/positioning onto the beam splitter there that made it not 50:50 (it was 69:33 ), I moved the fiber launch a bit to get the splitting right and retook measurements after that; also I initially had the current set too high on the laser current driver which I think was saturating its response.  I'll skip over the details and just present the final measurement. I've included a zip in the attachments with the data that logs some more of the details of my failed attempts.

I used the same calibration as used in PSL:2247.  Here the laser diode current was set to 25.0 mA, which is 1.51 mW of 1064 nm, and the AC excitation into the laser was set to -21 dBm (19.9 mV rms).  Power on the witness detector was measured to be 0.79 mW and that on the PD under test was 0.75 mW (as measured with a power meter).  Units of measurement were linear magnitude and phase in degrees. DC voltages were measured with 1 MΩ impedance.

Unit A: using 25 mA current into laser and -21 dBm sweep I get DC on PD of 1.20 V (into 1 MΩ) and a DC voltage of NF1611 detector of -2.13 V (into 1 MΩ).

Unit B: using 25 mA current into laser and -21 dBm sweep I get DC on PD of 1.07 V (into 1 MΩ) and a DC voltage of NF1611 detector of -2.12 V (into 1 MΩ).

The calibrated TIA current to voltage gain is plotted below:

A notebook detailing all the attempts is attached below.

 Quote: This set of measurments turned out to be bad. The OP27 (±15V supplies) with 50 Ω series at the output + 50 Ω load impedance seemed to be saturated.
 Attachment 1: BasicSchematic_TranImpPD_AD829.pdf  35 kB  Uploaded Wed Apr 10 14:51:49 2019
 Attachment 4: WOPO_HDPD_AD829_2kohmTranImpGain_UnitAandBandLISO.pdf  90 kB  Uploaded Tue Apr 30 12:13:14 2019
 Attachment 5: 20190405_TFHDPDs_AD829Design_LargeBoard.zip  179 kB  Uploaded Tue Apr 30 12:30:18 2019
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