1

Abstract— Breast cancer is one of the leading causes of death

among women. Earlier detection of breast cancer improves the

chances of a patient full recovery. The nuclear medicine imaging

technique known as Positron Emission Tomography (PET)

allows earlier detection of a breast tumor and gives an indication

about the nature of that tumor (benign or malign) . The PETs

detector is composed of a scintillation crystal which convert γ –

rays into photons in the visible light spectrum, an optical

photodetector which converts the visible light photons into an

electrical current and a transimpedance amplifier (TIA) which

convert that current into a voltage.

The development of a new kind of photo-detectors, the silicon

photomultiplier (SIPM), arise the need to investigate a TIA

adapted to the electrical characteristics of these detectors.

In this thesis is presented a short description of SIPMs, as well

as their simplified electrical model. The two common

configurations of TIAs, the feedback TIA and the common gate

TIA, are analyzed and it is concluded that these configurations

are not adequate for SIPMs. This led to the study of the regulated

common gate TIA (RCG TIA).

A test circuit comprised of a RCG TIA was designed in UMC

130 nm technology with a 1.2 V supply voltage. The test circuit

was manufactured and experimentally evaluated. The maximum

voltage (Vom) measured at the circuit output was of 301 mV, with

a rise time (tm) of 40 ns; the RMS noise value (Vno_rms) measured

was of 1.7 mV with a power dissipation of 1.17 mW.

IndexTerms — Siliconphotomultipliers (SIPMs), Transimpedance

amplifiers (TIA), Regulated common gate Transimpedance

amplifier (RCG TIA), Positron emission tomography (PET).

I. INTRODUCTION

Breast cancer is one of the leading causes of death among

women [1]. Earlier detection of breast cancer improves the

chances of a patient full recovery. The standard method for

earlier detection of breast cancer, the mammography has some

shortcomings such as a low effectiveness in some cases and

the inability to determine the degree of malignancy present in

a tumor. The nuclear medicine imaging technique known as

Positron Emission Tomography (PET) allows earlier detection

of a breast tumor and gives an indication about the nature of

that tumor (benign or malign). PET is based on the fact that

cancer cells have an accelerated metabolism, needing a greater

quantity of glucose for your metabolic processes. The patient

is injected with glucose molecules identified by a radioactive

marker, Fluorodeoxyglucose (18F-FDG), and thus it is

possible to identify the areas with the greatest concentration of

glucose and consequently the cancerous cells. The PETs

detector is composed of a scintillation crystal which convert

γ – rays into photons in the visible light spectrum, an optical

photodetector which converts the visible light photons into an

electrical current and a transimpedance amplifier (TIA) which

convert that current into a voltage,Fig. 1.

Fig.1 – PET Detector

The development of a new kind of photo-detectors, the

silicon photomultiplier (SIPM), with a gain of order of

magnitude 106 and bias voltages between 25 V and 50 V

making this sensors more interesting than avalanche

photodiodes (APDs), which has a gain between 100 and 50

and bias voltage between 100 V and 500V [2]. On the other

hand the SIPMs has a parasitic capacitance much greater than

APDs (it can reaches to 30 times greater). This high parasite

capacitance, together with high gain of SIPMs brings new

challenges in selecting and sizing of TIA, particularly in terms

of input impedance, bandwidth and noise circuit. The goal of

this dissertation is investigate a TIA which complies with the

specifications for Pet mammography systems [3], when we

have a SIPM in input instead a APD.

In section II is presented the principle of operation for the

SIPMs as well as their simplified electrical model.

In section III is analyzed the two basic configuration of

TIA, feedback TIA and common gate TIA (CG TIA) and the

regulated common gate TIA (RCG TIA) is investigate.

In section IV is presented the several phases of project of

RCG TIA.

In section V is described the choices made in the

preparation of printed board circuit (PCB) and the

experimental results are presented.

In section VI is presented the conclusion of work developed

and the perspectives for future work.

In appendix is presented the relationship between the rms

value of output noise and the power spectral density of her

noise source for 2-ª order systems with one zero and two

poles.

II. SILICON PHOTOMULTIPLIERS

Silicon Photomultipliers, SIPMs, are a new kind of light

detectors. They are a set of avalanche photodiodes, APDs, join

in parallel and each one joined to a resistor, known as

quenching resistor [4 - 6]. One Silicon Photomultiplier are

represented in Fig. 2.

The RCG TIA for PET applications

Pedro.S. Ferreira, MEEC student, IST

2

Fig. 2 – SIPM.

The APDs are a p – n junction which is polarized with a

voltage few volts higher than a breakdown voltage, [5]. That

voltage generates a electrical field very strong. If a photon hit

in a lattice, it will able to create a electron – hole pair. That

pair is accelerated and collide with lattice, created again a

electron – hole pair. This process, known as avalanche [7],

creates a current electrical. The avalanche effect will be kept

until the bias voltage to be less than breakdown voltage, due to

current which flow through the serial resistive [7]. The several

currents APDs are added, created a current which rise in few

nanoseconds for values dozens to hundreds of μA.. Thereafter

this current falls nearly with a exponential shape. After the

quenching of avalanche effect, the inverse bias voltage rises

above the breakdown voltage, being readied to detect another

photon [7].

In literature are presented some electrical models for SIPM,

[4 - 6]. These models are complex but in this work is used the

ordinary model which is represented in Fig. 3.

Fig. 3 – SIPM model.

This model is composed by a current source id on parallel

with a capacitor Cd. In this work, the max value of current is

25 μA and 300 pF for the capacitor [8]. The input resistor of

electronic circuit joined to SIPM, change the proportionality

between the number of APDs which shoot and the current

intensity give by SIPM [6]. In addition the input resistor

anticipates the quenching time of avalanche effect.

III. TRANSIMPEDANCE AMPLIFIERS

A. Specifications of TIA

The input signal of TIA is the pulse current provide by

SIPM. The current pulse has the shape of Fig. 4.

Fig. 4 – Shape of current pulse of SIPM.

The maximum current is Idm = 25 μA and it has a decay

constant τd = 40 ns. The shape of output voltage is represented

in Fig. 5. The maximum output voltage Vom must be at least

Fig. 5 – Shape of output voltage of TIA.

250 mV and the peaking time, tm, must be lower or equal to 40

ns. Vom must vary linearity with Idm . The noise at output of

amplifier must be the lower possible. In Table I are

summarized the specifications of TIA.

TABLE I – SPECIFICATIONS FOR PROJECT OF TIA

Idm 25 uA

τd 40 ns

Vom >250 mV

tm <= 40 ns

Power <= 1 mW

Output noise Minimum

B. Feedback Tia

The feedback TIA [9] is a basic configuration of

transimpedance amplifier often used. This amplifier is

composed by an operacional amplifier, OA, feedback by a

resistor Rf in parallel with a capacitor Cf. The capacitor Cf

increases the stability of circuit and allows that the shape of

output signal to be adequated. The feedback TIA is

represented in 6.

Fig. 6 – Feedback TIA.

If the OA is a ideal amplifier, the transimpedance function

is

3

(1)

In this case, the transimpedance function depends only on the

feedback impedance. That approximation for OA is

inadequate because the frequency of first pole of OA can not

be very higher than the other poles of circuit [10]. Thus, it

assume that the OA has a dominant pole with time constant τa,

being the voltage gain equal to

(2)

where A0 is the gain at low frequencies.

And the gain bandwich product of OA is

(3)

The transimpedance functon, assumed that the OA has a

dominant pole is [10]

(4)

(4a)

(4b)

(4c)

4 is valid if equation (4a) to equation (4c) are satisfied [10]

τ1 e τ2 are the two poles of transimpedance function. In this

work assume that poles are coincident because it is very

difficult to have one very distance of other. This poles are

connected through equation (4d) and equation (4e)

(4d)

(4e)

From equation (4e) and assumes that τ1 = τ2 = 10 ns,

Cd = 300 pF, and Rf = 20 kΩ, it gets B = 60 GHz. This value

for B is impracticable.

The main noise source this circuit is the input transistor of

OA. Her spectral density is

(5)

where gm_in is the input transistor`s transcondutance The input

noise can be minimize increases the value of gm_in, by other

words increased the width or the bias current of input

transistor.

The noise function due to noise source vna is [10]

(6)

(7)

and τ1 and τ2 satisfy (4d) and.(4e).

Since τZ >>τ1τ2 it can be applied (A.1). Replaced by (5) in

(A.1), it obtains

(8)

From equation (8) it concludes that for minimize the rms

output voltage, it is necessary maximize the value of gm_in.

C. Common Gate TIA

Besides the Feedback TIA, another circuit which is often

used is the Common Gate TIA (CG TIA). The CG TIA [11] is

represented in Fig. 7.

Fig. 7 - CG TIA.

Where VB and IB are respectively the polarize voltage and

polarize current of transistor M1.

The input impedance of CG TIA is [11]

(9)

in equation (9) is not considered the body effect of transistor

M1.

The transimpedance function is equal to [10]

(10)

4

with

(10a)

(10b)

Thought the equation (10a) and taking in count that τ1 = 10

ns and Cd = 300 pf, it gets gm1= 3 mS. This value for gm1 is too

high because it needs a polarize current excessive, about 3 mS

if VGS1 – Vt1 = 100 mV. This value for polarize current makes

that the value of resistor RX decreased and consequently the

gain of transimpedance function also. Hence, this

transimpedance amplifier needs a second floor of

amplification.

The main noise sources of the circuit are the transistor M1,

In1 and a current source IB1, InB [10]. Their spectral densities

are respectively

(11)

and

(12)

The because of noise source InB is express by [10]

(13)

The value of rms output noise will be reduced, if the value of

gmB .is decreased. This is achieved increasing the value of

overdrive voltage of current source transistor.

The because of noise source In1 is express by [10]

(14)

the equation (14) is valid if , wherein τZ = R0B Cd;

The value of rms noise output is decreased, increasing the

value of gm1. This value is restricted by value of τ1, as it can be

seen in equation (10a).

D. Regulated common gate TIA

The circuit regulated commom gate TIA (RCG TIA) [12 -

13] is represented in Fig. 8

Fig. 8 - RCG TIA.

As can be observed in Fig.8 the RCG TIA is composed by

the CG TIA, adding to it, a common source transistor M2 with

active load IB2, that compose an amplifier with gain A, making

a close network between the gate and the source of common

gate transistor.

In this paper, it assumes that the current source IB2 is a simple

current mirror which is composed by a transistor with

transcondutance gmB2

The gain A is equal to

(15)

The input impedance, Zi, is [10]

(16)

equation (16) is valid, if it satisfies the equations from (16a) to

(16c).

(16a)

(16b)

(16c)

The input impedance of RCG TIA is A times higher than the

CG TIA. The value of A can reached to 100. The fact of input

impedance of RCG TIA does not depend only of parameter

gm1 as it happens with the CG TIA allows having a current in

common gate transistor smaller and therefore a value for RX

higher.

The transimpedance function of RCG TIA is given by [10]

(17)

wherein the time constant of the first pole is

5

(18)

and the time constant of the second pole is

(19)

From noise analyses, it is concluded that the resistor RX has

a little contribution to output noise because her value has a

order of magnitude of douzens of kΩ. And it is concluded that

the transistor M1 has a contribution for output noise negligible

because the output rms noise is inversely proportional to A2.

Finally it concluded that main noise sources of the circuit are

the current source IB2 and the transistor M2. Then it going to

be analyzed each one of main souces.

Noise source INB2

INB2 is the electrical model to noise generated in M2

The spectral density of InB2 is

(20)

Her noise function is [10]

(21)

where

(22)

and τ1 and τ2 are defined by equations (18) and (19).

Through the equation (21) and applying the appendix

(A.2), we obtain the rms value of output noise

(23)

Replacing by equation (20) in equation (23) and

assuming that τZ >> τ1 τ2, it reaches to

(23a)

The rms output noise is minimized if the quotient

between gmB2 e (gm2)2 is minimized.

Example: If RX =20 kΩ, Cd = 300 pF, gm2 = 6 mS,

gmB2 = 2 mS and τ1 = τ2 = 10 ns it has Vno_rms = 2 mV.

Noise source In2

In2 is the thermal electrical noise for the transistor M2.

The spectral density of In2 is

(24)

The noise source In2 has the same position of noise

source InB2 on model weak signals, therefore her noise

function is the same and given by equation (21).

Replacing by equation (24) in equation (23),

where is , and assuming that τZ >> τ1 τ2, it reaches

to

(25)

The value of can be decrease, increasing the

value of gm2. Another option will be decrease the value of

RX but her value is restricted by steady point of circuit

and by amplitude of output voltage.

Example: If RX =20 kΩ, Cd = 300 pF, gm2 = 6 mS e τ1 =

τ2 = 10 ns, it has = 3,5 mV.

The noise source In2 represents nearly 64 % of the total

ouput noise and InB2 represents abo 36 %.

IV. PROJECT OF RCG TIA

A. Simulation of circuit

In Fig. 9 is showed the schema of RCG TIA.

Fig.9 – Schema of RCG circui t

In sizing of circuit (see table II) was considered the

following options:

The MP1 and MP2 transistors must be in saturation

region and they should have ro much greater than the

6

ro of MN2 transistor, so that equation (15) is going to

be equal to . For these transistors

the Vgs –Vt should be the greater possible, to

minimize yours contributions to Vno rms but keeping

the MN2 transistor in saturation region;

The value of gm_MN2 should be the greater possible to

minimize the contribution of MN2 to Vno rms. For

such, the MP2 transistor should supply the maximum

current possible and the MN2 needs to have a

Vgs –Vt the lowest possible;

The gain A should be about 100 and gm_MN3 needs to

have a value such that the input impedance be enough

lower to get the goal values of tp and Vom;

The pole frequency of regulation amplifier must be

such that the stability of circuit be greater or equal to

60º;

The value for Rx = R1 + R0 is set by steady point

needed to the amplitude of output signal, without

transistor MN3goes out of saturation region. R1 and

R0 are the type of non salicide HR poly resistor

because this technology allows getting the resistor

values higher, for the same values of W and L. The

value of CX = C1 is determined by equation (19),

wherein

τ2 = 10 ns.

TABLE III – THE COMPONENTS SIZING OF RCG TIA

Component W (μm) L (μm) Fingers

MN0 40 1 20

MN1 8 1 4

MN2 220 1,3 20

MN3 3,4 0,240 2

MP0 420 5 20

MP1 420 5 20

R0 1,5 16 -

R1 2 20 -

C1 26,5 15,41 -

Following RCG TIA puts a buffer to isolate her output of

probe’ impedance of oscilloscopic.

Fig. 10 - The output voltage of buffer

In Fig. 10 observes that the Vom = 330 mV and

tp = 40 ns. The circuit power is 1.18 mW. This value exceeds

118 W, (roughly corresponds to a deviation of 10 %) the value

specified for this parameter.

Fig. 11 – Module of input impedance

The module of input impedance (Fig. 11) is 26 Ω until

1 MHz and from there reaches a maximum of 35 Ω at a

frequency of 15.9 Mhz. This rise of input impedance is due to

decreasing of effect of gain of the regulation amplifier, due to

its pole.

Fig. 12 –Frequency response of transimpedance function

The Bode diagrams of transimpedance functions are

represented in Fig.12. The amplitude has a value of 86 dbΩ at

low frequencies, which is equal to 20,6 kΩ, the bandwidth to

3dB is 16,22 MHz which corresponds approximately to the

frequency of the pole due to RX and CX. The function of

transimpedance presents 4 poles, since your module drops 75

db in a decade and the phase falls approximately 330º. This

differs from what was presented in section III.D, where it was

considered that the function of transimpedance had only two

real poles. The existence of two additional poles makes the

amplifier having a gain bandwidth product, GBW, shorter and

GBW = 289.3 MHz.

7

In Fig. 13 is represented the noise spectrum of the circuit

obtained by simulation

Fig.13 – Noise of the circuit in function of frequency

The overall noise of the circuit is Vno_rms = 3 mV, which is an

acceptable value, since it is about 100 times smaller than Vom.

This value is approximately half the total noise obtained

theoretically, 5.5 mV. This difference is due to the fact that the

zero of the function of noise to be a frequency (413 kHz)

higher than the theoretical to the main contributions of noise

(1/(2πRo_MN1Cd) 3 kHz) and also due to the existence of 4

poles instead of the two real poles considered in theory.

Table IV represents the contributions of several components

to the overall noise of the circuit..

TABLE IV - CONTRIBUTION OF EACH COMPONENT FOR THE OVERALL NOISE OF

THE CIRCUIT

Component Type

of noise

Contribution

to the overall

noise (V2)

Contribution

to the total

noise (%)

MN2 Thermal 67,2

MP1 Thermal 24,9

MP0 Thermal 6,3

MN3 Flicker 0,5

As it was conclude in section III.D the transistor NM2 has the

greater contribution to the overall noise of the circuit, 67.2 %.

This transistor and MP1 are responsible virtually by overall

noise of the circuit, 92.1 %. As was expected the noise is

thermal noise, according to the indication of the simulator

(Table IV).

The circuit was subjected to-corners testing, in which the

transistors are simulated in conditions:

tt – typical;

ss - transistors n slow and transistors p slow;

snfp, - transistors n slow and transistors p fast;

fnsp - transistors n fast and transistors p slow;

ff - transistors n fast and transistors p fast;

The capacitors and resistors may have maximum, typical and

minimum values. It is considered that the temperature is 25°

and that the power supply voltage remains constant.

Vom presents a value always above 250 mV, thus fulfilling the

specifications for this parameter. Vno_rms does not exceed 3.5

mV, which is an acceptable value since Vno_rms is

approximately 100 times lower than Vom. For the majority of-

corners testing the value of tm is below 44 ns (value 10 %

above the initial specification, 40 ns); this only does not

happens when the transistors p and n are slow and the

capacities and resistors are not minimums. The corners testing

have a little influence in linearity of circuit.

B. Layout of circuit

The layout of the circuit is shown in Figs. and X. The layout

was submitted to the program DRC (design rules check) and

the program LVS (Layout vs. schematic). The layout passed

successfully these checks

Fig. 14 - Layout of RCG TIA with pads and diodes for protection

against electrostatic discharge (ESD).

Fig 15 – Zoom of the layout of the RCG TIA.

In the implementation of the layout of circuit were made the

following options:

Instead of conventional pads we used rf pads because

the RF pads has a capacity of approximately 300 fF

while the conventional has approximately 2 pF;

We applied the common centroid technique to current

mirrors, so that the current mirroring to be the most

perfect possible [14];

We placed guard rings around all of the components.

This is especially important in the case of the

transistor MN2 which is what contributes more

significantly to the output noise [14];

In interconnections between the various components,

8

we have been used the metals from the fifth to the

eighth layer, with the goal of minimizing the parasite

capacities to the substrate. In connection with the

pads we used the metal of the last layer, because it is

what has the least resistance and the least capacity;

The transistors MP0 and MP1, deployed with the

common centroid technique occupy an area

considerable. Therefore the connection of Vdd1 to

the ends of the transistors on the centroid is long,

which means that there is a significant number of

squares, i.e. the resistance may not be negligible and

consequently, the drop voltage also does not. To

resolve this question, we used two metals with a

width of 1 μm connected in parallel. The same was

done on the connection of MP1 to MN2.

After put the pads is formed an empty zone that we

were filled with three capacitors of 10 pF connected

in parallel between the gate and the source of

transistor MP0. The target of these capacitors is filter

the noise in current which polarizes MP0;

We used diodes with dimensions minimum to make

of ESD protection.

C. Pos – Layout simulation

The simulation of circuit included the parasites resistors and

parasites capacitors were performed. The output voltage has

the same shape of Fig. 8 and we got Vom = 324 mV and

tm = 39,6 ns. These values are identical which we obtain in

section III.A.

TABLE V - MAIN CONTRIBUTIONS TO THE TOTAL NOISE OF THE CIRCUIT.

Component Type

of noise

Contribution

to the overall

noise (V2)

Contribution

to the total

noise (%)

NN2 Thermal 46,6

Iin_line Thermal 27,7

MP1 Thermal 17,3

MP0 Flicker 1,8

We got Vno_rms = 3.2 mV. It is confirmed that the transistor

NM2 has a largest contribution to the noise, but now its

contribution is 46.6%, instead of 67.2 %. This is due to the

fact that we put put a dense guard ring around this transistor,

which filtered some noise generated. There is a important new

contribution to the noise that is the resistance of the line that

carries the input signal.

V. EXPERIMENTAL RESULTS

A. Printed circuit board

The printed circuit board ,PCB, was designed with the

software tool EAGLE 5.11, being the footprints of various

components drawn from the respective catalogs. The circuit

was implemented on a board with two layers with a thickness

of 0.8 mm. The top layer serves for the placing of the various

elements of the circuit and the connections between them,

while the lower layer is used as ground plain and to

connections that could not be placed on the top layer.

In the preparation of PCB has taken the following options:

The length of input signal line must be lower that

2,3 cm and the length of output signal must be

lower 54cm for that lines behave as lines of

concentrates parameters.

The generation of power supply voltages (1.2 V and

3.3 V) is made by two voltage regulators (Reg 1 to

1.2 V and Reg 2 to 3.3 V), each one linked to a

resistive divider, see Fig. 16. The voltage regulator

chosen was the TPS 71701DCKT from Texas

Instruments [15] because it presented a low noise

Power supply rejection ratio PSRR = 67 dB at 100

kHz. For these regulators to be stable, it necessary

to connect a capacitor of 1 μF (C5 to 1.2 V and C2

to 3.3 V, see Fig. 16) at output.

The capacitor C5 and C2 together with the

capacitors (C4 = C1 = 0.1 μF, see Fig. 16) work as

bypass capacitors, making lower the impedance

between the power lines and the ground plain,

filtering out the noise of middle and high

frequency. The bypass capacitors must be placed as

close as possible to the output pin of the regulators.

To monitor the bias currents Ib2, Ibuf, Ib1 resistors

are used respectively R1 = 680 Ω, 500 Ω and R2 =

R3 = 1.8 kΩ,. The values of these resistors allow

Ib2, IBUF and Ib1 do not exceed the maximum

values that lines support. Rvar1 = 2 kΩ,

Rvar2 = 500 Ω, Rvar3 = 5 kΩ.

Fig. 16 - Layout of PCB test.

In Fig. 16 is represented a layout of PCB with the software

tool EAGLE and Figs. 18 and 19 show respectively the top

and bottom of PCB with the components .

9

Fig. 17 – Placement of lines around the integrated circuit.

The placement of lines around the integrated circuit was

made in such a way to minimize the length of bond wires and

consequently their parasites inductances, see Fig. 17. The

space between lines is ,Dp = 0.2 mm and its width is Lp = 0.3

mm.

Fig. 18 – Top of PCB with the components.

Fig. 19 – Bottom of PCB with the components.

B. Experimental results

The test of TIA with SIPM requires the use of components

and techniques that are not available. Then we were going to

simulate the current pulse of SIPM. For this, we apply a

voltage step with amplitude Vim to a capacitor Ca = 1pF in

series with a capacitor Cd = 300 pF. The capacitor Ca was

integrated together with the RCG TIA. In Fig. 20 is shown the

linearity of RCG TIA.

Fig. 20 – Linearity of RCG TIA.

From the observation of Fig. 20 was concluded that the

RCG TIA is approximately linear until Vim = 360 mV (this

value corresponds to a SIPM charge equal to 360 fC).

Fig.21 – Input and output signals of buffer.

The Fig. 21 shows the buffer output when Vim = 360 mV,

Vom = 301 mV and tm = 40 ns. The value of Vno_rms may be

calculated though the definition of rms value. So is acquired a

set of 5 samples, each one with 10000 points of transient

output signal of buffer. To obtain Vno_rms = 1,7 mV which is

176 times higher than Vom.

VI. CONCLUSIONS AND FUTURE WORK

A. Conclusions

The feedback TIA cannot be used with SIPMs with high

capacities in input, since to comply the specifications, it is

necessary a gain bandwidth product of 60 GHz to operational

amplifier, which is impractical.

The CG TIA cannot be used with SIPMs because to obtain a

low input impedance is necessary a bias current of common

10

gate transistor of 3mA, this mean an excessive power and a

reduction important of transimpedance function at low

frequencies.

The main advantage of RCG TIA is obtained an input

impedance lower, about one hundred lower than CG

impedance. In the circuit projected the input impedance

changes between 26 Ω and 35 Ω.

The transimpedance function of circuit has a value of

86 dbΩ at low frequencies (RX = 20,6 kΩ, see Fig. 12). The

bandwidth of 3 db is equal to 16,7 MHz, which is

approximately set by the time constant CX RX (Fig. 12).

Unlike what it was considered in theory, the transimpedance

function has four poles, because the amplitude bode diagram

falls 75 db in a decade and the phase diagram reaches near to

330º.

In addition, the zero of experimental noise function is a

frequency higher than the theoretical. As a result, the total

noise of the circuit is approximately half that obtained

theoretically. The regulated transistor and the resistance of the

line of input signal are that has a greater contribution to the

overall noise of circuit, especially the transistor which is

between the source and the gate of the common gate transistor

that contributes at least 50%.

The RCG TIA was designed in UMC 130nm technology for

a supply voltage of 1.2 V and it has got Vom = 301 mV, tm = 40

ns and Vno_rms = 1.7 mV for Vim = 360 mV (Fig. 21). The

power of circuit is 1.17 mW. The circuit meets the

specifications defined initially for Vom, tm, Vno_rms, but

exceeding slightly the total power required. Vno_rms is

approximately 176 times greater than the Vom, this value is

acceptable. The total output noise is half than simulate

because the GBW is lower than expected. The circuit is liner

until Vim = 360 mV, in other words for SIPMs with charges

lower or equal to 360 fC.

B. Future Work

We propose the following topics as object of investigation in

future:

Analyze the effect of pole of regulation floor, in

transimpedance function and input impedance of

circuit;

With base the RCG TIA, project a reconfigurable

circuit which provides amplifier the signal of SIPMs

with different capacities and current peaks.

Study the TIA for optical communications presented

in [16]. This TIA has interesting issues, as a

bandwidth greater than RCG TIA and also the overall

noise lower;

APPENDIX

We consider a linear time – invariant system with a noise

source x(t), whose power spectral density is . y(t) is the

system output noise made by x(t), with respectively power

spectral density and rms and

. and

are

connected though the noise function N(s). Though N(s)

establishes a relationship between the and

. If N(s)

is a second order function equal to

A.1

then, the value of is

A.2

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