# Pre-amplifier noise dependence on feedback capacitance and shaping time

#### LordOfThunder

Joined Jun 27, 2018
53
Hello.
This is my first post, so I would like to say hi to everybody!

I am an Experimental Particle Physics Ph.D. student but I have a background in Theoretical Primordial Cosmology. So I am pretty new to the field.
Anyway, I am here because I am trying to understand the inner functioning of an ASIC that we are currently using in our experiment. The ASIC is named SPIROC and is developed by the Omega company. The experiment I am collaborating to is called T2K (but it isn't relevant for the present discussion)
Despite SPIROC being almost 10 years old, it is still under active development. This is one of the reasons, as you can see from the linked webpage, why any manual or official documentation doesn't exist. Believe me or not, all the physicists who I know that use or have used SPIROC, learned about it by word of mouth, so they basically only know how to operate it but have little knowledge of its inner functioning or its most subtle properties.

Anyhow, by searching online I stumbled upon various articles dealing with SPIROC and now I am reading through them and trying to put all the pieces together. But there is a part of an article that goes against what I have learned about pre-amplifiers until now. So here I am. I will tell you what doesn't make sense about that article and I hope that here there is someone who could kindly tell me if I am wrong in doubting the article authors or if their result is indeed strange.

As far as the present discussion is concerned, I am just focusing on the pre-amplifier stage of SPIROC (that is always used to read Si Photon Detectors). In particular on the dependence of the pre-amplifier noise on the feedback capacitance and on the shaping time.

As I said On page 6 and 7 there are two figures that I don't quite understand. I will analyze them one at a time ...

The first figure is this (page 6 figure 3):

In the article, it is specified that the expected dependence of the noise on the feedback capacitance is 1/Cgain, where Cgain is the feedback capacitance.
Now, in every other reference literature that I consulted, it is written that the noise (equivalent noise charge) is always increasing with increasing input capacitance (including the feedback capacitance). For example, here it is shown that any kind of electrical noise grows almost linearly with the input capacitance of the pre-amplifier, as also shown in this graph:

Going on to the second picture from the article, it is shown the dependence of the noise on the shaping time of the linear amplifier.
The shaped signal is a semi-gaussian obtained through a CR-(RC)^2 equivalent circuit. The shaping time can be trimmed from 25ns to 175ns.

In the famous book by Knoll it is shown that the dependence on the shaping time should have a minimum and not be monotonic:

Thank you for reading this long post. I really thank in advance whoever would help me clear my doubts.

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#### bogosort

Joined Sep 24, 2011
622
Hello.
This is my first post, so I would like to say hi to everybody!
Hi, welcome to AAC!

In the article, it is specified that the expected dependence of the noise on the feedback capacitance is 1/Cgain, where Cgain is the feedback capacitance.
Now, in every other reference literature that I consulted, it is written that the noise (equivalent noise charge) is always increasing with increasing input capacitance (including the feedback capacitance).
I'm not familiar with the noise analysis of particle detectors, but could it be that the discrepancy is simply a case of measuring two different parameters? The SPIROC graph seems to be describing output noise (in voltage) as a function of the feedback capacitor, while the other reference characterizes the noise charge (in rms electrons) with respect to the detector capacitor.

Going on to the second picture from the article, it is shown the dependence of the noise on the shaping time of the linear amplifier.
The shaped signal is a semi-gaussian obtained through a CR-(RC)^2 equivalent circuit.

In the famous book by Knoll it is shown that the dependence on the shaping time should have a minimum and not be monotonic:
My interpretation of Figure 17.26 is that in this shaper, both the series and parallel noise contributions are monotonic, while the hyperbolic curve between them represents equivalent noise charge. The shaper noise graph from the SPIROC seems to be showing the parallel source, which is shot noise. Since the integrator in the shaper "counts electrons", it makes sense that the shot noise increases with shaping time.

#### LordOfThunder

Joined Jun 27, 2018
53
I'm not familiar with the noise analysis of particle detectors, but could it be that the discrepancy is simply a case of measuring two different parameters? The SPIROC graph seems to be describing output noise (in voltage) as a function of the feedback capacitor, while the other reference characterizes the noise charge (in rms electrons) with respect to the detector capacitor.
Yes of course, probably it is as you say. But the noise in voltage and the noise charge shouldn't be somewhat directly proportional?
Moreover always in the same reference article it is written (after equation (4)) that the total capacitance of the detector plus pre-amplifier at the preamplifier input is $$C_T = C_d + C_i + C_f + C_s$$, sum of the detector ($$C_d$$). the input transistor ($$C_i$$), the feedback ($$C_f$$) and stray ($$C_s$$) capacitances. And then every kind of noise calculated in that article is proportional to $$C_T$$. So the noise should be directly proportional (or at least increasing) to the feedback capacitance, or I am missing something?

My interpretation of Figure 17.26 is that in this shaper, both the series and parallel noise contributions are monotonic, while the hyperbolic curve between them represents equivalent noise charge. The shaper noise graph from the SPIROC seems to be showing the parallel source, which is shot noise. Since the integrator in the shaper "counts electrons", it makes sense that the shot noise increases with shaping time.
So you are saying that the series noise in SPIROC seems negligible for every value of the shaping time. Ok I can believe that.

#### bogosort

Joined Sep 24, 2011
622
Yes of course, probably it is as you say. But the noise in voltage and the noise charge shouldn't be somewhat directly proportional?
Moreover always in the same reference article it is written (after equation (4)) that the total capacitance of the detector plus pre-amplifier at the preamplifier input is $$C_T = C_d + C_i + C_f + C_s$$, sum of the detector ($$C_d$$). the input transistor ($$C_i$$), the feedback ($$C_f$$) and stray ($$C_s$$) capacitances. And then every kind of noise calculated in that article is proportional to $$C_T$$. So the noise should be directly proportional (or at least increasing) to the feedback capacitance, or I am missing something?
I can't freely access the reference article, but consider this paper: http://www-physics.lbl.gov/~spieler/SLAC_Lectures/PDF/Sem-Det-II.pdf

On page 4, the gain of a charge-sensitive amplifier, such as the preamp in SPIROC, is shown to be $$\small{A_Q \approx 1/C_f}$$. Figure 3 from the SPIROC paper was measured with the input grounded, i.e., the only source of noise is the chip's own electronics. Because the circuit gain is inversely proportional to $$\small{C_f}$$, and since self-noise is proportional to gain, we would expect noise as a function of feedback capacitance to have the same shape as Figure 3. In other words, with the ASIC's input grounded the total capacitance $$\small{C_T}$$ is dominated by $$\small{C_f}$$, and so noise should fall with increasing feedback capacitance.

Notice Figure 9 in the SPIROC paper. The data in this graph were taken with the ASIC's input connected through a coupling capacitor to a pulse generator, simulating actual measurements. Here $$\small{C_f}$$ is constant and no longer dominates $$\small{C_T}$$; consequently, the noise graph has the expected rise with increasing $$\small{C_T}$$.

In summary, I believe the SPIROC noise is indeed dependent on total capacitance. But with the input grounded, $$\small{C_T \approx C_f }$$, and so Figure 3 didn't match your expectation.

#### LordOfThunder

Joined Jun 27, 2018
53
I can't freely access the reference article, but consider this paper: http://www-physics.lbl.gov/~spieler/SLAC_Lectures/PDF/Sem-Det-II.pdf

On page 4, the gain of a charge-sensitive amplifier, such as the preamp in SPIROC, is shown to be $$\small{A_Q \approx 1/C_f}$$. Figure 3 from the SPIROC paper was measured with the input grounded, i.e., the only source of noise is the chip's own electronics. Because the circuit gain is inversely proportional to $$\small{C_f}$$, and since self-noise is proportional to gain, we would expect noise as a function of feedback capacitance to have the same shape as Figure 3. In other words, with the ASIC's input grounded the total capacitance $$\small{C_T}$$ is dominated by $$\small{C_f}$$, and so noise should fall with increasing feedback capacitance.

Notice Figure 9 in the SPIROC paper. The data in this graph were taken with the ASIC's input connected through a coupling capacitor to a pulse generator, simulating actual measurements. Here $$\small{C_f}$$ is constant and no longer dominates $$\small{C_T}$$; consequently, the noise graph has the expected rise with increasing $$\small{C_T}$$.

In summary, I believe the SPIROC noise is indeed dependent on total capacitance. But with the input grounded, $$\small{C_T \approx C_f }$$, and so Figure 3 didn't match your expectation.
Thank you very much for spending the time to look for a reference. Now I have understood perfectly the configuration and that behavior.
I would be happy to offer you a beer in someway.

#### bogosort

Joined Sep 24, 2011
622
Thank you very much for spending the time to look for a reference. Now I have understood perfectly the configuration and that behavior.
I would be happy to offer you a beer in someway.
Cheers! Best of luck with your research.