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Analog Front End
02/07/2024 at 06:04 • 0 commentsSiPM pulses have fairly large amplitudes so don’t need a lot of amplification, but they have fast rise-times below a few ns and decay times in the range of hundreds of ns. The figure below is an example pulse provided in the Broadcom AFBR-S4N44P014M datasheet.
The easiest way to digitize its amplitude with a slow ADC would be using a very fast peak detector that can handle the high frequency content of the rising edge. But this wouldn’t be very low power as the peak detector has to be constantly enabled to catch pulses, and fast op-amps draw high current. My approach is to “round off” the pulses using RC integrators to slow them down, and then triggering on this slow version of the pulse to enable a peak detector before this pulse reaches its maximum. While this sounds easy, it was my first attempt at some analog design so I ended up spending a few days simulating it in PSpice for TI. This is the schematic I ended up with in the simulation, with components grouped into functional blocks that are described below.
SiPM
I simulate the SiPM as a current source that produces a pulse with a shape that approximates what I measured on the oscilloscope. The limited bandwidth of my measurement setup made the rising edge less steep so I generate a pulse with a 15ns rise time and 300ns fall time. The current amplitude is chosen to provide some hundreds of millivolts on a 50 Ohm resistor.
Raise zero signal a little above GND
This is just a resistor from 3.3V to inject a small DC offset into the measurement. The op-amp outputs in the system don’t go down to 0V, but have a minimum output voltage of 100mV or so. So this is a very simple solution to cope with that. It does cost a little though – the ADC input DOES go to 0V, so I lose a little bit of ADC range.
2 stages of RC integrators and another stage after the first op-amp
These round off the sharp input pulse to much slower pulses. There are two tradeoffs though. One is that you lose amplitude, but you can easily recover that using subsequent amplification stages. The second tradeoff is that in high count-rate applications you can get pulse pile-up, where the detector provides another short current pulse before the integrator output reached down to zero -- and that makes your measurement wrong. Serious analog processing uses a series of CR differentiators and RC integrators together with pole-zero compensation networks to create nearly gaussian pulses.
Amplify pulses to ADC range
The LMV793 is a decompensated op-amp. This means it’s much faster than op-amps with similar power requirements, but it’s not unity-gain stable. It only works at high amplification, in the LMV793’s case more than 10x. This is the only place in the circuit that allows for some flexibility in setting the gain, apart from the bias voltage on the SiPM. Thus this gain is set to match the gamma spectrum range to the ADC range. As this op-amp needs to be constantly powered it will significantly contribute to the total system power draw -- the LMV793 is spec'd to draw at most 1.65mA so it should fit in my power budget.
Peak detector with reset
This is just half of the peak detector circuit. Another unity gain buffer follows, but for this simulation it’s unnecessary. The 100 Ohm series resistor is there to make the op-amp happy driving a capacitive load. The OPA357 has an enable input (not used in this schematic) that can turn the op-amp on in 100ns. So as long as the trigger pulse is generated well in advance the peak detector should consume no power until it’s actually needed. And then after reading the stored value it can be shut down until the next pulse. This section of the simulation also contains a pulsed source that periodically resets the peak detector such that I can simulate several pulses.
Most peak detector designs use identical op-amps for both the ideal diode as well as the unity gain buffer (that is not included in this schematic). This allows those designs to use fancier feedback loops that minimize capacitor discharge or improve response to short peaks. However I decided to keep the loop simple because I was afraid of circuit behaviour when enabling both op-amps and then expecting a valid result in a few hundred ns. Keeping separate feedback loops for the ideal diode and the voltage follower allows one to treat them independently. Additionally the voltage follower can now be a much slower op-amp that even when active will draw very little power contributing a little to making a low power design. I decided for a TLR341G for this.
I used two great resources for understanding what I'm doing while designing this section:
EEVblog's video on peak detector circuits
Section 4.5.1 from The Art of Electronics, 3rd Edition
PSpice for TI simulation
To validate all of this I ran some simulations with different pulse amplitudes to confirm the system behaves linearly. Below is the schematic with the color-coded probe points, as well as the simulation results.
Conclusions
Not included in this simulation is the trigger section. A comparator triggers on the LMV793 output and enables the peak detector. Simulations shows that there are several hundred ns between the LMV793 output rising above a set threshold and the peak detector input reaching its maximum, thanks to the additional RC integrator in between the two. So this whole thing should work.
These integrators do pose a limit on how closely spaced pulses can be. One can see the peak detector input returns to baseline in ~15us so this will not properly handle very high count rates. I expect ~20 kCPS (to account for statistical fluctuations) should be doable without messing up the energy resolution.
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SiPM bias power supply
01/25/2024 at 05:28 • 0 commentsThe CosmicPi project uses a very nice chip for biasing SiPMs, the MAX1932. It can be configured to output as much as 90V for powering SiPMs, and you can set the voltage within a programmable range using SPI. It’s not cheap, but it’s very cool.
The jumpers (O1 and O2) allow two output ranges: 25.5V..30.5V for Onsemi SiPMs, or 36.5V..48.5V for Broadcom ones.
The board works great for powering the SiPMs, but draws a bit more current than I'd be happy with, at ~9mA while supplying 31V. I certainly did not help with the feedback resistors that can draw up to 150uA @ 31V. Adding reverse current through diode, switching efficiency (0.5 hinted in the datasheet), and the 1mA operating supply current I'd expect about 4mA. Interestingly even with the chip in shutdown (DAC = 0x00) I'm seeing ~3mA being drawn.
But it's definitely good enough to allow me to develop the analog front-end for the SiPM which plugs into the horizontal headers on the PCB.
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Silicon photomultiplier
01/21/2024 at 08:50 • 0 commentsPhysics overview
To convert the small number of optical photons into an electric signal a photodiode is not ideal. Short of using a photomultiplier tube (PMT) the best option is a silicon photomultiplier (SiPM). These are arrays of thousands of cells, with each cell being sensitive to a single photon. When a photon is absorbed by a cell it supplies a small pulse of current. If more photons hit the same cell at the same time, you won’t see any difference – the cell either fired or it didn’t. But since scintillators produce such a small number of photons it’s very likely that each one will strike a different cell. All these small pulses of current are added up and you get a signal that is proportional to the number of cells that fired.
Each cell is a small photodiode that is built to be operated above its breakdown voltage. That makes them super unstable, and once a photon is absorbed, the diode breaks down generating that pulse of current. The cell has a series quenching resistor that causes the voltage across the cell to drop during breakdown ending the pulse and effectively resetting the cell.
Since cells are so unstable, they also fire randomly, due to thermally-generated carriers. This leads to a “dark count rate” of the order of millions of counts per second but as these pulses don’t overlap you only see them as an increased noise floor.
Detector assembly
To make the most out of the small number of scintillation photons the optical coupling between scintillator and SiPM has to be as good as possible. Changes in the index of refraction, as can be generated by small pockets of air at the interface between the two, can cause photons to be reflected away from the detector. This is only made worse if the optical contact is uneven across the detector surface. A common solution to this problem is optical grease, having a known index of refraction, that can be applied similarly to how thermal paste is used on CPUs to improve thermal conductivity.
Because of light leakage through the PCB I had to wrap the assembled detector in black electrical tape.
Pomelo
I used the Broadcom AFBR-S4N44P014M 4mm x 4mm (ish) SiPM since it’s fairly low-cost and comes in a reasonable package for soldering with a heat gun. It needs to be operated between 38V and 48V.
Testing the fully assembled detector (wrapped scintillator, case, SiPM, power supply) with a digitizer at work I could get a feel for the expected performance before I started agonizing over my own readout electronics.
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Scintillator
01/18/2024 at 05:30 • 0 commentsPhysics overview
When a high energy photon (a gamma ray) is absorbed by a scintillator some visible photons are emitted. These visible photons have a fairly fixed wavelength, but the number of photons is proportional to the energy of the gamma ray. This number is in the range of tens of photons per keV, so for a 662 keV gamma ray coming from Cs137 hitting a CsI(Tl) scintillator you get ~36000 optical photons. For a 59 keV gamma ray from Am241 you only get about 3000. This is a statistical process so the numbers vary, giving rise to limited detector resolution – the full energy peak of a monoenergetic gamma ray will appear as a broad distribution in the detector. The optical photons are emitted in all directions from the point of interaction in the crystal, and there may be multiple such points (e.g. if the gamma ray suffers Compton scattering within the scintillator and the resulting lower energy gamma ray is also absorbed).
Important properties of scintillators are light yield (optical photons per keV), density, and atomic composition. High density materials containing elements with a high atomic number are preferred as they have a higher probability that the gamma ray will interact with the scintillator and not let any of the deposited energy escape the scintillator.
Detector assembly
Since the scintillator emits a pretty small number of photons and they can originate anywhere in its volume, it is important to try to reflect as many of these as possible towards the detector. This can be done either with specular (mirror-like) as well as diffuse (matte) reflection. It’s very common to wrap the scintillator in plumber’s tape (Teflon).
Also because of the small number of optical photons you’ll want to keep any stray light from entering the detector as this will completely overwhelm the scintillation photons. You’ll sometimes see people in labs placing several layers of dark heavy clothes over detectors when these are not light-tight by design.
Pomelo
I used a 4mm x 4mm x 10mm GAGG(Ce) crystal wrapped in Teflon tape and placed in a black 3D printed holder. I was hoping the PCB would provide enough light-tightness on the bottom but some light ended up coming through the PCB material around traces that did not have copper pour behind them. The picture on the right shows an extreme case with a flashlight shining through the PCB. Enough photons to disturb the measurement came through even in ambient lighting conditions.