# Current to Voltage Feedback Capacitance for SiPM

I'm having an issue with my Silicon Photomultiplier (SiPM) feedback circuit. The output is not behaving as expected. My board schematic is below:

simulate this circuit – Schematic created using CircuitLab

I apologize for the layout of the schematic, but this was the best way I could model my board. When designing it, people say that putting two SiPMs in one channel is a bad idea, much less having 4 SiPMs on one board in the layout shown, but we decided to go for it and see how it goes. The board has already been made, so there's no going back. I'm trying to work with what I got, so please keep that in mind. Also, please understand that the feedback resistance is the same per channel; it's just that we face different issues depending on the value. The resistance for both channels is either 49.9 ohms or 470 ohms.

Initially, we had some crosstalk due to bad board design, but by adding in the coupling capacitors, C1 and C2, we were able to reduce it to a tolerable amount. Our issue is with the output. Depending on the feedback resistance, there are some issues that I am trying to address. Our testing procedure induces the SiPMs on one channel while leaving the other channel alone. Please see the figures below and their description:

Figure 3 above shows the output results of both channels with the feedback resistance at 470 ohms. The purple signal shows the active channel while the green signal shows the inactive channel. The blue signal is the trigger signal. We observe some crosstalk from the green signal, but given the layout, this is unavoidable, so we are adjusting values of C1 and C2 to keep it under control but that's not so much of an issue right now. We observe some oscillation on both channel outputs, but we believe that this is due to impedance mismatch and reflectance, with the coaxial output being at 50 ohms and the feedback resistance at 470 ohms. My question here: Is there a way to keep the signal amplitude high like the purple signal while matching the impedance of the coaxial cable so as to eliminate or reduce the oscillation?

Similarly, Figure 4 shows the output results of both channels with the feedback resistance at 50 ohms. Purple is the active signal, green is the inactive signal, and blue is the trigger signal. Now, with the feedback resistance at 49.9 ohms, we have less oscillation than 470 ohms, but there's still some observable oscillation. Our issue with this variant is the smaller amplitude as well as the double peaks in the active channel. I'm not sure why this double peak is occurring, but is there anything that can be done about it? I was thinking that we might have to increase the feedback capacitance to hold the voltage given that we're working with 2 SiPMs. Also, this kind of ties back to Figure 3, but is there anything that can be done about the amplitude while avoiding reflectance? If we increase the feedback resistance, the gain would be higher, but how can we increase it without causing impedance mismatch?

EDIT: For reference, below is an image of the board with a feedback resistance of 470 ohms, but C1 and C2 are not present. This image highlights the initial crosstalk issue that we had, where the green signal is the active channel, the blue signal is the inactive channel, and the purple channel is the trigger pulse. Even though it is inactive, the blue signal seems to be active with a negative signal due to response from the active channel. This is the crosstalk issue that we faced.

The next image below shows the results of adding only C1 (at 3 pF) while not adding C2. Green is the trigger, and the signals are self-explanatory. The channel with C1 shows a positive signal when triggered, but the channel without the capacitor in blue shows some action, but this clearly shows that the addition of C1 helps with what we thought to be the crosstalk issue.

EDIT: I discussed it with the team that was doing the testing, getting information on how they are testing the boards exactly to see if there might be any problems with how they are testing it. The testing rig consists of a laser pulser connected to a fiber optic cable, and the boards are inside a feed-through chamber to block out ambient light. The fiber shines on a single SiPMT, with no light going to the other 3. There are 2 MMCX to BNC cables that connect the board to the outside of the chamber, and there are another 2 BNC cables going to the oscilloscope from the chamber. The MMCX to BNC cables are around 0.5 ft long while the BNC to BNC cables are about 2.5 feet long.

EDIT: I've included a image of the board layout to show you what I'm working with. I apologize for the quality of the image, but this is the best capture that I can provide. It's a six-layer rectangular board with 4 inner copper layers and being 50 mm by 10 mm in size (1.968 in by 0.394 in). Red is the top layer, yellow is inner layer 1, pink is inner layer 2, light blue is inner layer 3, dark blue is inner layer 4, and green is the bottom layer. Despite how it looks, all layers are ground planes. I just turned off the plane fill to show the traces. Having the board with the planes filled in makes it really difficult to show the multi-layered traces. Also, all of the trace widths are 0.5 mm wide. To be honest, the board layout is just slightly different than what is shown in the schematic. The board was designed so that you can have four individual channels with one SiPMT per channel, or you can have two channels with two SiPMTs each. This is accomplished by just shorting two pads together which connect the cathodes of the SiPMTs together to one channel. I would also appreciate some constructive criticism of the board. I'm still inexperienced with the intricacies of PCB layout design, so any advice that I can use for the next design would be most helpful.

• The 470 ohm feedback resistor has nothing to do with whether there are reflections at the output. – The Photon Aug 11 '17 at 16:05

If you cannot live with the crosstalk, you must redesign the board.

You have stated, "The board has already been made, so there's no going back."

That is too bad. It won't work with any tweak you can make to the component values.

You have stated, "I'm trying to work with what I got, so please keep that in mind."

I am keeping it in mind. That won't make the board work. It is not going to work. You need to suck it up and do what is necessary, even though it hurts.

On the one hand, you have stated that you just make and assemble the boards. On the other hand, you apparently have responsibility for the design of the circuit and layout of the board. Unfortunately, you are very ignorant of how to design a circuit, and you have gotten in way over your head. Among other things, this has lead you to commit to a design which was not tested before going into production. Now it's in production and it doesn't work. I'm not trying to be harsh here, but in this case it sucks to be you. You are out of your depth.

I'll start with what I believe is the underlying problem. You have not shown the pcb layout, and I'll bet that that is your culprit. Putting on my psychic hat, I predict that you do not use ground plane construction. Your ground trace is narrow (less than 0.1 inch) and snakes around the board to make connections. Am I right? What you're seeing is called "ground bounce", also called ground loops (in a general sense).

There are two possible solutions, one short-term, and the other long-term.

The short-term solution is to re-layout the board. When you do this,

a) use a ground plane.

b) place your power/ground connector between the two channels

c) place at least a 0.1 uF ceramic at the + and - power pins of EACH op amp, as close as you can. For high-speed, high-current op amps like you're using, a single set of decouplers is asking for trouble. It does not seem to have bitten you in the ass this time, but you need to start using good practice.

Now, as to design.

a) GET RID OF THOSE INPUT CAPS. The fact that you have inserted them and do not understand the consequences of that action demonstrate that you have no clue how the TIA circuit works. You are just cutting and pasting from another source. I have no idea who or what SenseL is, and I don't much care.

b) Feedback resistors should be larger rather than smaller. With your 50 ohm output termination and a 50 ohm load at the scope (although you have not actually stated that the "test team" understands the need for a termination at the scope if you're really worried about reflections - more likely they figure that with these waveforms they don't need to worry about it, and they are right) the minimum load on the op amp is 100 ohms, and that is the data sheet spec. Adding a 50 ohm feedback resistor increases the effective load from 100 ohms to 33, and that is asking for trouble. Stick with the 500 ohms. It is possible that this board is intended to be used as series-terminated rather than double-terminated. If so, and if you are willing to live with the implications, fine, and you can ignore this recommendation.

c) Optimal value of the feedback capacitor is almost certainly not 3 pF, particularly with the addition of a second SiPD. See Process.

d) As analogsystemsrf has commented, a single bias supply with that filter network is a bad idea if you are worried about cross talk.

Now, with pcb and circuit design at least partially addressed, let's talk Process.

First, as stated, you are completely out of your depth. You need to find someone who (no personal offense intended) has clue. You don't.

Second, you (and whoever your supervisor is) need to learn that assuming a design will work the first time is insane. To say, as you have done, that "we decided to go for it and see how it goes.", and then to say that "the board has already been made, there's nothing I can really do about the layout" means that "see how it goes" really means "commit to producing it in the hopes that it will work". And it doesn't work. And it won't work. To put it another way, you have seen how it goes, you don't like what you see, and are frantically trying to slap a coat of paint on it to change how it looks. Sorry. That is not going to help.

Unless you have a great deal of experience, and you are not breaking new ground in your circuit, you should assume that the first time never works completely. It's like sex. "Sex is perfectly natural, but it's not naturally perfect."

I suspect that you will respond that you CAN'T redo the board, and you may even give more details about why. That does not change the fact that it's not going to work as it stands, no matter what component changes you make. Your crosstalk is built in to your current layout. If you cannot live with it, you must change the layout.

END EDIT.

Your problem is simple - you added C1 and C2. The input capacitance to the op amps causes them to oscillate.

The idea that the oscillation is caused by impedance mismatch is wrong on at least 3 counts.

1) You have 49.9 ohm series terminations on the outputs.

2) Your oscillation periods are too great unless you are driving about 70 feet of cable for the 50 ohm feedback and 200 feet for the 500 ohm case, and

3) Most importantly, the oscillation frequency changed when you changed the feedback resistor. Well, unless you ALSO happened to shorten your scope cables at the same time you reduced the resistor.

If you doubt this, stop using your scope as a direct input device. Use a 10x probe and look directly at the op amp outputs with no cable attached.

Your solution is "simple" - that is, it's simple but you may not like the consequences - increase your feedback capacitors. This will eliminate the oscillation at the expense of slowing down your response.

Well, there is an alternative - get rid of those caps. I have no idea what you mean by "crosstalk", so I can't help you with whatever problem you addressed with the caps, but they are the root of your current difficulty.

Also, for what it's worth, you do not show your power supply connections to the op amps. Since you don't, there is no way to be sure that your op amps are properly decoupled. Maybe they are, maybe they arent', and if they aren't that is only going to make the situation worse.

Also, I have to ask - have you provided a 50 ohm termination at the scope? You don't say, and with the waveforms shown there will be no obvious effect if you're using a 1 meter cable, but I just thought I'd check.

Finally (and this will be of no help to you in this instance, since you've settled on using your inappropriate circuit) using a TIA (transimpedance amplifier) with these devices is just silly. You use TIAs when you want both high gain and high speed. Outputs of 100 mV with a 50 ohm feedback resistor indicate that your PDs are putting out about 2 mA. Converting this current level to volt-level signals is emphatically not a high-gain situation. You'd have been better off with simple resistor sensing followed by a buffer/combiner stage. If you look at the OPA656 data sheet, a simple gain of 2 non-inverting amplifier will work with 10 nsec rise and fall times. Do that for each SiPM and follow with an inverting summer with gain of your choice.

• Thanks for the comment. I apologize for not including the power pins on the OpAmps. I changed that in the schematic. I hope that the images I added show our 'crosstalk' issue. The TIA was the recommended circuit by SensL. It worked for our needs the last three times we did this circuit (with one SiPM), so we wanted to see what if we had two instead. As for your other questions regarding scope termination and cable length, I'm not actually doing the testing. That's being done at another location elsewhere; I just make and assemble the boards. I'll see what I can do then with your suggestions. – user101402 Jul 3 '17 at 14:47
• Additionally, if we increase the feedback capacitance, we could always adjust the feedback resistance as well in order to increase the speed, correct? Going from 470 ohms to 50 ohms would definitely increase the speed, but going from 3 to 6 pF with 50 ohms shouldn't make too much of a difference in the rise time, though the issue with small amplitude is still a factor. – user101402 Jul 3 '17 at 15:26
• @user101402 - See edit. – WhatRoughBeast Jul 4 '17 at 13:20
• After much discussion with the team, we are looking primarily for high speeds and high gain, though gain is not as important as speed. Given this, what can we do in order to increase the speed? – user101402 Aug 11 '17 at 16:51
• @user101402 - Does this mean that you've decided to re-layout the board? And what happened to your cross-talk problems? – WhatRoughBeast Aug 11 '17 at 19:30

To explore with the crosstalk, lets NOT SHARE the -30 volt bias. Duplicate (or quadruplicate) the R2/C5 and tie the GND end of C5 to VIN+ of each opamp. Ensure you use the isolation resistor(R2 at 50 ohms) to minimize the crosstalk.

Also use solder-wick (copper braid, many tiny strands) to tie the GND end of C1 and C2 to their respective opamp's VIN+.

• Thanks for your reply. Unfortunately, as the board has already been made, there's nothing I can really do about the layout, so I can't replicate the R2/C5 filter. Why would the isolation resistor, R2, minimize the crosstalk? Also, why is it ncecessary to tie the GND end of C1 and C2 to VIN+? Also, the reason I used 49.9 ohms rather than 50 ohms was that it was cheaper to use 49.9 ohms given that I am working with the 0402 SMD size. – user101402 Jul 3 '17 at 19:06
• Also, why not share the -30V bias? I need to provide a negative bias at the anode of the SiPMs, and since there's only one source, we would have to share it. How would you recommend going about it? – user101402 Jul 5 '17 at 16:13
• +1 to this. The cross-talk most likely comes from the -30 V supply sagging when signal is present. Definitely OP needs to fix this before worrying about radiative coupling between traces. – The Photon Aug 11 '17 at 16:03

we believe that this is due to impedance mismatch and reflectance, with the coaxial output being at 50 ohms and the feedback resistance at 470 ohms. My question here: Is there a way to keep the signal amplitude high like the purple signal while matching the impedance of the coaxial cable so as to eliminate or reduce the oscillation?

The feedback resistor value doesn't much affect the output impedance of the amplifier circuit, so it doesn't affect the transmission line reflections between the output cable and the amplifier.

Given your 49.9 ohm series output terminations, you should not be having any problems with transmission line reflections.

More likely causes of your problems are

• The op-amp sees the coaxial cable as a capacitive load, and the 49.9 ohm in series is not sufficiently decoupling that load. This can reduce the phase margin of the amplifier circuit and lead to ringing of the output.

• You are trying to make a transimpedance amplifier with 110 MHz bandwidth using an op-amp with 230 MHz GBW product. In my experience, a fairly wide (decade or more) buffer is needed between the closed loop bandwidth and the op-amp's GBW to get good results --- unfortunately I am not remembering the exact mechanism for this requirement.

Confirming or rejecting either of these hypothetical root causes for your problem would require some more detailed analysis than I am able to do right now.

I agree with the answer by analogsystemsrf that cross-talk most likely comes through the output impedance of the -30 V power supply rather than from PCB layout issues.

• Thanks for your answer. How did you get the 110 MHz bandwidth from the feedback circuit? Also, since the bandwidth is much smaller than the GBW, the amplifier should be suitable for the job? Increasing the bandwidth by reducing the feedback elements seems like opening the floodgates for trouble. – user101402 Aug 11 '17 at 16:47
• $1/(2\pi (470\ \Omega)(3\ {\rm pF}))\approx 110\ {\rm MHz}$. Like I said, in my experience you want (not sure about need) at least a decade between the closed loop bandwidth and GBW. 110 to 230 MHz is less than a decade. – The Photon Aug 11 '17 at 16:53
• Say we double the capacitor to 6 pF. Doing so would give a bandwidth of 56.4 MHz, which would be make the difference between the bandwidth and the GBW better (though not yet a decade), but that would affect the rise time. Speed is the important factor here. – user101402 Aug 11 '17 at 18:30
• @user101402, I don't know what the solution is. Making a 100 MHz TIA from an op-amp is not an easy problem. – The Photon Aug 11 '17 at 20:01

Nice to meet you again on this forum!

Did you layout this board? I hope not. Anyway, the others gave excellent advice, I'll add my own:

Your opamp is pretty fast. It needs good local power supply decoupling.

Routing power using long traces from decoupling caps at the other end of the board won't work well.

Either you use supply planes, or you give each opamp its own pair of decoupling caps.

If you do not use planes, one cap per opamp per supply is enough. Two caps will ring and screw your settling time. Get the highest capacitance available in the package that will fit with X7R dielectric. And add some resistors of appropriate value between the main supply and the caps to prevent them from ringing with each other.