Compensation capacitor for transimpedance amplifier

[DanInvents]

Hi!

I'm currently doing some back-of-the-envelope calculations to design a radiation detector based on PIN photodiodes. I found an application note from Maxim where they describe how to do that with a MAX4477 op.amp. The MAX4477 has a GBP of 10 MHz and the first stage of amplification is a simple transimpedance amplifier with a 10M resistor and a 4.7 pF compensation capacitor.

Crunching in the numbers I get, based on the resistor and capacitor value, a cut off frequency of about 3 kHz. Interestingly, they show a graph where they claim that they can detect radiation pulses that are 5 microseconds long. According to my understanding this suggests a bandwidth of 200 kHz. I know that by cascading amplifiers their effective GBP is increased but how is it possible that the radiation pulse makes it beyond the first stage?

I would also like to understand what is the purpose of the first stage. With a gain of 10M the first stage would be operating at unity gain right? Is the purpose to buffer the photodiode?

Here is the application note:

https://www.maximintegrated.com/en/design/technical-documents/app-notes/2/2236.html

Daniel

[RoGeorge]

The first stage is the transimpedance amplifier, meaning an amplifier for which the output voltage is proportional with the input current.  It turns amps into volts.

Intuitively, it works like this:
- in an ideal opamp, no current flows in/out of the input pins in+ and in- of the opamp
- an opamp with negative feedback will do its best to keep zero volts difference between its in+ and in+ pins
- the PIN diode with all the resistors and input capacitors on the leftside produces current pulses (not voltage)

Now, if you tie in+ pin of the opamp to GND, then the opamp (here IC1a in Fig.1 from the gamma detector) will vary its output so to keep its  in- pin also at zero volts.  However, the current in/out of any input pin is zero, so all the current pushed by the PIN diode will go through the feedback resistor R2 (and through the capacitor C1, too).

For, let's say 1uA coming from the PIN photodiode, the voltage drop on the R2 will be 1uA*10M=10V (if we neglect C1).  Because one terminal of the R2 is at zero volts (in- must be zero, because in+ is tied at GND), then the other terminal of R2 (which is also the output of the first amplifier) will show 10V.

That's how a transimpedance amplifier works, in principle, and that's how IC1a works, too.



About the AC response of IC1a, the cutting frequency is indeed about 3.4kHz (https://www.ti.com/lit/an/sboa268a/sboa268a.pdf), but the roll off of a first order low pass filter is only 20dB/decade, so at 34kHz it will still amplify, just that it will amplify 10 times less than at DC.  However, the output voltage from the first opamp might be still enough, considering that after the first opamp there are 3 more op amps (working as voltage amplifiers) further amplifying the signal 1000 times (60 dB all 3 together).

If, say the diode produces 1uA, then the output will be 10V at DC and roughly about 1V at 34kHz, and the LTspice simulation shows about 1Vpp for 5us pulses of 1uA.

[Terry Bites]

Its a not quite a TIA, its a charge sensitive amplifier.  See https://physicsopenlab.org/2017/09/27/charge-sensitive-preamplifier/

[DanInvents]

Wow! Thank you for such quick and thorough responses.  Thank you for supporting your knowledge with simulations and for commenting on the existence of the charge amplifier. I had never heard that charge amplifiers existed but the working principle makes sense. So much left to learn

[RoGeorge]

I had never heard that charge amplifiers existed

That's because there is no such thing, but physicists are legendarily bad at naming.  Well, at least this "charge sensitive amplifier" was not named after a color. 
( https://en.wikipedia.org/wiki/Color_charge )

Though, note the one in the blog is called a "charge sensitive amplifier", which is more about its goal in the given setup than about its class as an opamp amplifier, and unrelated with how that opamp works.  Also, incorrect because that amplifier is sensitive to current, not to charge.  It's the surrounding devices and timing that turns charge into current so it can be amplified by the opamp.

Also "charge amplifier" would be incorrect to describe a transimpedance amplifier.  You do not put 1 microcoulomb at input and get 10 microcoulombs at output.  That amplifier does not respond to the amount of charge (Coulombs), it needs a current to work, and in the end the output voltage is not proportional with the input charge (Coulombs), but with the input current (Amperes).  Note the output is not Coulombs, but Volts.

Charge and Current are not the same, and they can not be used interchangeably.

Both the op amp from the PhysicsOpenLab blog link and the IC1a from the Maxim's AN-2236 are transimpedance amplifiers.  The one from the blog is indirectly used to measure charge.  You would use yours to detect radiation, but it would be misleading to call IC1a a "radiation amplifier", wouldn't it?  However, we can say that in your setup the IC1a is a "radiation sensitive [transimpedance] amplifier".

Now, if we mangle the too complicated word transimpedance, and throw a nice acronym at it, ours will become an RSA.  If I were to be a physicist, I'll call it a "prism amplifier" because light rays combined with the triangle shape of the opamp reminds me of a prism.  I guess "rainbow amplifier" would be too much.  "Prism Amplifier" sounds perfect to me, or we may also call it "Illuminati amplifier". 

[tggzzz]

You can use current-measuring devices to measure charge; I remember doing it as a kid with a "ballistic galvanometer".https://en.wikipedia.org/wiki/Ballistic_galvanometer

The basic principle is based on charge being the integral of current over time. If the charge flows for a short time compared with the meter's response time, then the maximum response is proportional to the charge.

[RoGeorge]

Don't mind me, I was just fun-ranting there. 

To be pedantic, I think it's not OK to say we measure charge by measuring current, because to measure something (by definition) means to compare it with a standard unit.  To find the charge by current integration we will need two standard units to compare against, one comparison against the 1 Ampere current unit, and the other comparison against the 1 second unit of time.  So I'll prefer to say we deduced/calculated the charge by integration, which is different then a direct comparison against a standard 1 Coulomb unit of charge.

The integration of current method to deduce the charge has a lot of tacit assumptions embedded in it, assumptions that might or might not hold, while a direct comparison would be more straightforward in the sense that will let less room for conceptual errors.  This doesn't necessarily means that a direct comparison will be the way to go when measuring charges in practice.

For something well established like charges and current, all the above looks like nonsense philosophical rambling, but if it were to be about measuring some other completely new "something", which obeys to less understood or not yet known laws of physics, then it would make sense to prefer a direct comparison.

[tggzzz]

Don't mind me, I was just fun-ranting there. 

To be pedantic, I think it's not OK to say we measure charge by measuring current, because to measure something (by definition) means to compare it with a standard unit.  To find the charge by current integration we will need two standard units to compare against, one comparison against the 1 Ampere current unit, and the other comparison against the 1 second unit of time.  So I'll prefer to say we deduced/calculated the charge by integration, which is different then a direct comparison against a standard 1 Coulomb unit of charge.

The integration of current method to deduce the charge has a lot of tacit assumptions embedded in it, assumptions that might or might not hold, while a direct comparison would be more straightforward in the sense that will let less room for conceptual errors.  This doesn't necessarily means that a direct comparison will be the way to go when measuring charges in practice.

For something well established like charges and current, all the above looks like nonsense philosophical rambling, but if it were to be about measuring some other completely new "something", which obeys to less understood or not yet known laws of physics, then it would make sense to prefer a direct comparison.

Measurements are relative; you are choosing one base but others are equally valid. Me? I measure capacitance in Jars, https://en.m.wikipedia.org/wiki/Jar_(unit)

All measurements are imprecise and depend on presumptions. The degree of imprecision must be assessed and compared to the requirements. Sometimes the integration of current to deduce charge is sufficient. Sometimes measuring voltage to deduce time (and vice versa, and et cetera) is sufficient.

[DanInvents]

I do hold a Bachelor's and Master's degree in Physics and I concur with the opinion that physicists are legendarily bad at naming 🤣.

Coming back to the topic of transimpedance amplifiers. Do you have any experience using discrete JFETs as the front end of said amplifiers? I read about such an approach in The Art of Electronics and I also found an application note describing the approach.

https://www.analog.com/en/technical-articles/1mw-transimpedance-amplifier-achieves-near-theoretical-noise-performance.html

Unfortunately low-noise JFETs seem to be rare and expensive.

[RoGeorge]

Do you have any experience using discrete JFETs as the front end of said amplifiers?

Not really.  From the OP and this former question I assume you want to measure some very faint light, where noise is a big problem.  In case you don't have the low noise parts you need, there might be other workarounds:
- cooling the first stage of the amplifier might be easier than procuring rare/expensive parts (for example with a Peltier element, or by placing the amplifier in the freezer if the setup allows that)
- if the light to measure can be externally chopped (either electronic or with a mechanically rotating shutter disc), then a lock-in amplifier can be used to recover even the faintest signals out of noise.  A lock-in amplifier can be improvised pretty easy, and the benefits from even the simplest LIA are spectacular (shameless plug:  my LIA improvised from an oscilloscope with trace averaging mode, note how clean the 3rd screen capture is - because of the synchronous averaging - in comparison with the noisy first one)
- if we talk single photons detector, maybe a photomultiplier might be the way to go, maybe something else

What do you want to measure with the device?

If you can disclose the end application, that would be of great help in narrowing down a solution, and somebody might chip in with a known working one that fits well.  If not, at least set the must have performance (with numbers), if it's for one shot or continuous beam, etc.



Later edit:
I forgot to tell there are also some models of photodiode+amplifier on the same chip, random search examples:
http://www.centronic.co.uk/products/6/photodiodes-with-integrated-amplifiers
https://www.osioptoelectronics.com/standard-products/silicon-photodiodes/photodiode-amplifier-hybrids/photodiode-amplifier-hybrids-overview.aspx
https://www.pacer-usa.com/components/specialist-detectors/integratedmodules/

[dietert1]

One can build a transimpedance amplifier with resistive or capacitive feedback, or both . like above. In the schematic above the output voltage will be large and proportional to photodiode current at low freuencies or DC. With short input current pulses the capacitive feedback dominates and output voltage will be small and proportional to injected charge.
Building low noise transimpedance amplifiers is a known problem. You can find literature on the web. As far as i remember there should be a resistor between the pin diode and the amplifier negative input in order to limit noise gain at high frequencies.

Regards, Dieter

[RoGeorge]

This paper shows some low noise design tricks Photodiode Front Ends - PHILIP C. D. HOBBS, and from the same author:

- paper PHILLIP C. D. HOBBS, "REACHING THE SHOT NOISE LIMIT FOR $10"
Optics & Photonics News 2(4), 17-23 (1991) https://opg.optica.org/opn/abstract.cfm?URI=opn-2-4-17
DOI: 10.1364/OPN.2.4.000017

- book "BUILDING ELECTRO-OPTICAL SYSTEMS - MAKING IT ALL WORK" by Philip C. D. Hobbs
2nd Edition, 800+ pages, WILEY 2009
ISBN 978-0-470-40229-0

Also noise related, I found this 6 minutes "LTspice: Noise Simulations" 101 very useful:
https://www.analog.com/en/education/education-library/videos/video-series/ltspice-ac-noise-analysis-tutorial.html

Later edit:
-------------
Bob Pease had a look at TIA and its compensation capacitor in "What’s All This Transimpedance Amplifier Stuff, Anyhow?"
https://www.electronicdesign.com/technologies/analog/article/21801223/whats-all-this-transimpedance-amplifier-stuff-anyhow-part-1

[DanInvents]

Do you have any experience using discrete JFETs as the front end of said amplifiers?

What do you want to measure with the device?

If you can disclose the end application, that would be of great help in narrowing down a solution, and somebody might chip in with a known working one that fits well.  If not, at least set the must have performance (with numbers), if it's for one shot or continuous beam, etc.

This is a hobby project, I would like to build a compact and inexpensive radiation detector to monitor environmental radiation. In the past I have used Geiger-Müller tubes, those feature higher sensitivity than silicon photodiodes but the problem is that they are bulky, fragile, increasingly rare, and require high voltage. For the sake of fun I have thought about using an array of photodiodes that could be individually monitored to detect radiation. Then a microcontroller would record the pulses to a micro-SD card. I have also thought about using sample-and-hold circuitry combined with ADCs to make a "poor man's" spectrometer.

So far the project is in the ideation phase but the guiding stars for the project would be: as inexpensive, as compact, and as few components as possible.

[RoGeorge]

That's a fun project!   

No idea how sensitive a PIN diode can be as a background radiation detector.  My guess is for such a project the input stage of the amplifier doesn't need to be particularly noiseless.  Pretty much any TIA would do it, including those made out of discrete jellybean transistors (so to keep the price down).

Physics is a hobby of mine, and absolutely love any related experiments.  Regarding radiation detection, seen some blogs were a very simple open-air ionization camera was used as detector (e.g. http://techlib.com/science/ion.html ).

I guess any webcam should work as a radiation detector, too, or maybe a CCD sensor from a former photo camera, for larger area and less noise, but I didn't try.