the rcg tia for pet applications - ulisboa · the circuit regulated commom gate tia (rcg tia) [12 -...
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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
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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.
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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,
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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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