Master Thesis

1. Pulse Preamplifiers for CTA
Camera Photodetectors
PROYECTO FIN DE CARRERA
Ignacio Diéguez Estremera
Departamento de Física Aplicada III (Electricidad y Electrónica)
Facultad de Ciencias Físicas
Universidad Complutense de Madrid
Septiembre 2011

2. Pulse Preamplifiers for
CTA Camera
Photodetectors
Proyecto de Ingeniería Electrónica
Dirigido por los Doctores
D. José Miguel Miranda Pantoja y D. Pedro Antoranz
Canales
Departamento de Física Aplicada III (Electricidad y
Electrónica)
Facultad de Ciencias Físicas
Universidad Complutense de Madrid
Septiembre 2011

4. A Ana, a mis padres y a mis hermanos.

5. Agradecimientos
Aunque este trabajo está redactado en inglés, me voy a tomar la licencia de
escribir estos párrafos en castellano.
En primer lugar quiero dar las gracias a José Miguel y a Pedro por
haberme dado la oportunidad de hacer el proyecto con ellos durante dos
cursos. La experiencia adquirida con vosotros en el laboratorio no tiene
precio.
Por supuesto, agradecer a José Manuel todos sus sabios consejos y lec-
ciones con la instrumentación. Siempre has dejado tus quehaceres para
echarme una mano con cualquier duda.
A Ana agradecerle todo. Sin tí, nunca habría llegado a este punto.
Muchas gracias por la paciencia infinita que has demostrado tener conmigo.
A mis padres, por darme la mejor herencia que se puede dar. Gracias a
vosotros soy quien soy.
No me puedo olvidar de pedir disculpas (con cariño y humor) a Pili,
Eduardo y Elena por la paliza de varios años que ha supuesto ésto. Siempre
me habeis cuidado fenomenal.
A mis amigos, muchas gracias por los grandes momentos. Aunque es-
temos lejos, cada uno en un país, ciudad, pueblo o barrio distinto, siempre
estais cerca.
Finalmente, quiero dar las gracias a Gus, nuestro perro labrador, por ser
como es.
v

6. Abstract
The Cherenkov light pulses coming from gamma ray induced atmospheric
showers are extremely weak and short, thus setting very demanding re-
quirements in terms of sensibility and bandwidth to the photodetectors
and preamplifiers in the camera. For bandwidth and integration reasons,
the transimpedance preamplifier of MAGIC (Major Atmospheric Gamma-
ray Imaging Cherenkov telescope) was replaced by a MMIC (Monolithic Mi-
crowave Integrated Circuit) amplifier in MAGIC II. Today, integrated tran-
simpedance preamplifiers are being developed for the CTA (Cherenkov Tele-
scope Array), but apparently, the benefits of using transimpedance amplifi-
cation are not clear.
In this master thesis, the benefits and drawbacks of both approaches are
analysed and preamplifier prototypes meeting most of the CTA specifications
are designed, implemented and tested using only open source CAD (Com-
puter Aided Design) software. The superiority of the transimpedance ampli-
fiers for CTA is shown.
vi

7. Contents
Agradecimientos v
Abstract vii
1 Introduction 1
1.1 Thesis objetive and structure . . . . . . . . . . . . . . . . . . 2
1.2 Modern observational astronomy . . . . . . . . . . . . . . . . 3
1.3 Gamma ray astronomy . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Photodetectors used in IACTs . . . . . . . . . . . . . . . . . . 7
1.5 Open Source CAD . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Front-end Electronics 15
2.1 General overview . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Preamplification approaches . . . . . . . . . . . . . . . . . . . 16
2.3 Specifications of the front-end . . . . . . . . . . . . . . . . . . 23
2.4 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 MMIC Amplifier Design 29
3.1 Selection of the MMIC . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Design of the prototypes . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Prototype 1 . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Prototype 2 . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.3.1 Prototype 1 . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2 Prototype 2 . . . . . . . . . . . . . . . . . . . . . . . . 37
vii

8. Index viii
4 Transimpedance Amplifier Design 43
4.1 Basic feedback concepts . . . . . . . . . . . . . . . . . . . . . 43
4.2 Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 Selection of the transistor . . . . . . . . . . . . . . . . . . . . 46
4.4 Small signal models and distortion . . . . . . . . . . . . . . . 47
4.5 Design of the prototypes . . . . . . . . . . . . . . . . . . . . . 49
4.5.1 Systematic design procedure . . . . . . . . . . . . . . . 49
4.5.2 Checking device parameters . . . . . . . . . . . . . . . 51
4.5.3 Design of the feedback network . . . . . . . . . . . . . 51
4.5.4 Design of the first nullor stage: noise . . . . . . . . . . 53
4.5.5 Design of the last stage: distortion . . . . . . . . . . . 56
4.5.6 Bandwidth and stability . . . . . . . . . . . . . . . . . 58
4.5.7 Bias circuit and output matching . . . . . . . . . . . . 62
4.5.8 Prototype 1 . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5.9 Prototype 2 . . . . . . . . . . . . . . . . . . . . . . . . 64
4.6 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.6.1 Prototype 1 . . . . . . . . . . . . . . . . . . . . . . . . 66
4.6.2 Prototype 2 . . . . . . . . . . . . . . . . . . . . . . . . 68
5 Implementation of the Prototypes 77
5.1 Printed circuit board technology overview . . . . . . . . . . . 77
5.2 MMIC prototypes . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3 Transimpedance prototypes . . . . . . . . . . . . . . . . . . . 79
5.4 GAPD biasing circuits . . . . . . . . . . . . . . . . . . . . . . 79
6 Measurements and Tests 83
6.1 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Test setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2.1 Measuring S-parameters . . . . . . . . . . . . . . . . . 85
6.2.2 Measuring the noise figure . . . . . . . . . . . . . . . . 86
6.2.3 Measurements with the GAPD . . . . . . . . . . . . . 87
6.2.4 Measuring the dynamic range . . . . . . . . . . . . . . 89

9. Index ix
7 Experimental results and discussion 91
7.1 S-parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Noise figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.3 Dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.4 Pulse shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.5 Photon counting . . . . . . . . . . . . . . . . . . . . . . . . . 96
8 Conclusions and Future Work 101
8.1 Prototype specification . . . . . . . . . . . . . . . . . . . . . . 101
8.2 Accomplishments . . . . . . . . . . . . . . . . . . . . . . . . . 101
8.3 MMIC vs Transimpedance . . . . . . . . . . . . . . . . . . . . 103
8.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Bibliography 105
List of Acronyms 107
Bill of Materials 111
Layouts 113
SPICE Models 123

10. List of Figures
1.1 Jansky’s Antenna, image courtesy of NRAO/AUI. . . . . . . . 4
1.2 Electromagnetic spectrum, image courtesy of Wikipedia. . . . 5
1.3 MAGIC gamma ray telescope, located in Roque de los Mucha-
chos, La Palma (Spain), image courtesy of http://magic.
mppmu.mpg.de. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 CTA computer generated graphic, image courtesy of www.
cta-observatory.org. . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Schematic of a PMT (Photo Multiplier Tube) coupled to a
scintillator, image courtesy of Wikipedia. . . . . . . . . . . . . 8
1.6 GAPD (Geiger mode Avalanche Photo Diode) cross section,
image courtesy of Wikipedia. . . . . . . . . . . . . . . . . . . 10
2.1 Stages of the front-end. . . . . . . . . . . . . . . . . . . . . . 16
2.2 Circuit topologies for voltage and transimpedance approaches
using a GAPD. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Simplified photodetector model connected to voltage and tran-
simpedance amplifiers. . . . . . . . . . . . . . . . . . . . . . 19
2.4 Simulated response of the BGA614 MMIC amplifier (in blue)
and the transimpedance amplifier (in red) to a square current
pulse with amplitude 100 µA, rise time 500 ps, pulse width 4
ns from a photodetector model with Cj = 35 pF and Rshunt =
10 KΩ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Noisy two port network modelled as a noiseless network with
input referred noise generators. . . . . . . . . . . . . . . . . . 22
x

11. List of Figures xi
2.6 Transimpedance amplifier and solid state photodetector with
current noise generators. ithermal is the thermal noise gener-
ated in the resistive semiconductor material of the photode-
tector; iamp is the EINC (Equivalent Input Noise Current)
generator of the amplifier; inf is thermal noise generated by
the feedback resistor Rf . . . . . . . . . . . . . . . . . . . . . . 23
2.7 Photograph of the NECTAr (New Electronics for the Cherenkov
Telescope Array) prototype board, image courtesy of [16]. . . 27
2.8 The DRAGON-Japan prototype, image courtesy of [9]. . . . 28
3.1 Simplified circuit of the BGA614, image courtesy of Infineon. 31
3.2 Schematic of prototype 1 without parasitics. . . . . . . . . . . 32
3.3 A component’s real life behaviour at high frequencies, image
courtesy of [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 Schematic of prototype 2 without parasitics. . . . . . . . . . . 34
3.5 QUCS (Quite Universal Circuit Simulator ) schematic for fre-
quency domain simulations of prototype 1 with parasitics. . . 35
3.6 Simulated S11 and S22 of prototype 1. Modulus in dB (left)
and Smith chart (right). . . . . . . . . . . . . . . . . . . . . . 36
3.7 Simulated S21 (modulus in dB) of prototype 1. . . . . . . . . 37
3.8 Simulated stability parameters µ and µ (left) and stability
circles (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.9 Simulated noise figure of prototype 1. . . . . . . . . . . . . . . 38
3.10 QUCS schematic for frequency domain simulations of proto-
type 2 with parasitics and coplanar transmission line sections. 39
3.11 Simulated S11 and S22 of prototype 2. Modulus in dB (left)
and Smith chart (right). . . . . . . . . . . . . . . . . . . . . . 40
3.12 Simulated S21 (modulus in dB) of prototype 2. . . . . . . . . 40
3.13 Simulated stability parameters µ and µ (left) and stability
circles (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.14 Simulated transimpedance gain of prototype 2 for different
photodetector capacitances. . . . . . . . . . . . . . . . . . . . 41
3.15 Simulated noise figure of prototype 2. . . . . . . . . . . . . . . 42

12. List of Figures xii
4.1 Ideal feedback configuration. . . . . . . . . . . . . . . . . . . . 44
4.2 Shunt-shunt feedback configuration. . . . . . . . . . . . . . . . 45
4.3 Simplified Hybrid-Pi small signal model of the BJT (Bipolar
Junction Transistor ). . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Large signal plots of the BFP420 BJT transistor. . . . . . . 52
4.5 The nullor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.6 Transforms on the noise generators that affect the noise per-
formance. ven and ien are the equivalent input referred noise
generators of the first stage of the nullor implementation. . . 54
4.7 Influence of photodetector’s capacitance on noise current. . . 57
4.8 Small signal model with test signal ix used to calculate the
low frequency return-ratio of the amplifier. . . . . . . . . . . . 60
4.9 Final configuration of the amplifier in two CE-CC stages. . . 62
4.10 Prototype 1 with bias network, coupling capacitors, and out-
put matching resistor. . . . . . . . . . . . . . . . . . . . . . . 63
4.11 Prototype 2 with bias network, coupling capacitors and out-
put matching resistor. . . . . . . . . . . . . . . . . . . . . . . 64
4.12 Prototype 1 with parasitics for SPICE (Simulation Program
with Integrated Circuit Emphasis) simulations. . . . . . . . . . 66
4.13 Protototype 1 schematic with parasitics for AC and transtient
simulations with QUCS. . . . . . . . . . . . . . . . . . . . . . 68
4.14 Influence of photodetector capacitance on the transimpedance
bandwidth of prototype 1. CS = 0 pF, 35 pF and 320 pF. Tran-
simpedance gain is plotted in dB. . . . . . . . . . . . . . . . 69
4.15 Protototype 1 schematic with parasitics and coplanar lines for
S-parameter simulations with QUCS. . . . . . . . . . . . . . . 70
4.16 Simulated S11 and S22 of prototype 1. Modulus in dB (left)
and Smith chart (right). . . . . . . . . . . . . . . . . . . . . . 70
4.17 Simulated S21 of prototype 1. . . . . . . . . . . . . . . . . . . 71
4.18 Simulated noise parameters of prototype 1. . . . . . . . . . . 71
4.19 Prototype 2 with parasitics for SPICE simulations. . . . . . . 72
4.20 Protototype 2 schematic with parasitics and coplanar lines for
S-parameter simulations with QUCS. . . . . . . . . . . . . . . 72

13. List of Figures xiii
4.21 Simulated S11 and S22 of prototype 2. Modulus in dB (left)
and Smith chart (right). . . . . . . . . . . . . . . . . . . . . . 74
4.22 Simulated S21 of prototype 2. . . . . . . . . . . . . . . . . . . 74
4.23 Influence of photodetector capacitance on the transimpedance
bandwidth of prototype 2. CS = 0 pF, 5 pF, 35 pF and 320 pF.
Transimpedance gain is plotted in dB. . . . . . . . . . . . . . 75
4.24 Simulated noise parameters of prototype 2. . . . . . . . . . . 75
5.1 Coplanar transmission line, image courtesy of http://wcalc.
sourceforge.net/coplanar.html. . . . . . . . . . . . . . . . 78
5.2 The BGA614 prototype 2 layout. The size of the board is 30
mm × 40 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.3 The transimpedance prototype 1 layout. The size of the board
is 45mm × 40 mm. . . . . . . . . . . . . . . . . . . . . . . . 81
5.4 The transimpedance prototype 2 layout. The size of the board
is 42mm × 40 mm. . . . . . . . . . . . . . . . . . . . . . . . 82
5.5 GAPD bias circuits. . . . . . . . . . . . . . . . . . . . . . . . 82
6.1 HP87020C network analyser with HP85020D 3.5 mm calibra-
tion kit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2 Agilent Infinium DSO81204B oscilloscope. . . . . . . . . . . . 84
6.3 Noise measurement setup, image courtesy of Agilent. . . . . . 87
6.4 Connection of the GAPD to the transimpedance amplifier. . . 88
6.5 Shielded black box. . . . . . . . . . . . . . . . . . . . . . . . 88
6.6 Setup for pulse shape and single photon counting measurements. 88
7.1 Measured (circles) and simulated (solid line) scattering pa-
rameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2 Measured noise figure. The peaking at 900 MHz is due to
mobile networks interference. . . . . . . . . . . . . . . . . . . 93
7.3 Measured dynamic range of the transimpedance prototype 1
with Rf = 300 Ω. . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 Measured dynamic range of the transimpedance prototype 1
with Rf = 1500 Ω. . . . . . . . . . . . . . . . . . . . . . . . . 96

14. List of Figures xiv
7.5 Simulated dynamic range of the transimpedance prototype 2
with Rf = 1000 Ω. . . . . . . . . . . . . . . . . . . . . . . . . 97
7.6 Dynamic range of the BGA614 prototype 2. . . . . . . . . . . 98
7.7 Output pulse shape. . . . . . . . . . . . . . . . . . . . . . . . 99
7.8 Photon counting measurements. . . . . . . . . . . . . . . . . 100

15. List of Tables
2.1 Set of specifications for the preamplifier. . . . . . . . . . . . . 24
2.2 Estimated minimum and maximum current and voltage peaks.
The voltage peak is calculated assuming a 50 Ω load. . . . . . 25
4.1 Basic feedback configurations. . . . . . . . . . . . . . . . . . . 45
4.2 Estimated total noise current integrated in the band 100 Khz
- 750 MHz and SNR for different photodetector capacitances. 56
4.3 Small signal parameters obtained with ngspice. . . . . . . . . 67
4.4 Prototype 1 total current and voltage noise integrated in the
band 100 Khz - 750 MHz simulated with ngspice for different
photodetector capacitance. . . . . . . . . . . . . . . . . . . . . 67
4.5 Prototype 2 small signal parameters obtained with ngspice. . 73
4.6 Prototype 2 total current and voltage noise integrated in the
band 100 Khz - 550 MHz simulated with ngspice for different
photodetector capacitance. . . . . . . . . . . . . . . . . . . . . 73
5.1 Parameters of the FR4 substrate. r is the dielectric constant,
τ is the metal thickness and h is the dielectric thickness. . . . 77
6.1 Measure settings for the network analysers. The rest of pa-
rameters are left to its default value. . . . . . . . . . . . . . . 86
6.2 Measure settings for the noise figure analyser. The rest of
parameters are left to its default value. . . . . . . . . . . . . . 86
7.1 Pulse shape time measurements. . . . . . . . . . . . . . . . . 99
xv

16. List of Tables xvi
8.1 BGA614 prototype specification. . . . . . . . . . . . . . . . . 102
8.2 TIA prototype specification. . . . . . . . . . . . . . . . . . . . 102

17. Chapter 1
Introduction
Some idea of the vastness of the
Universe may be gained by considering a
model in which everything has been
scaled down by a factor of a billion. In
this model the Earth would have the
dimensions of a grape. The Moon would
resemble a grapeseed 40cm away while
the Sun would a 1.4-meter diameter
sphere at a distance of 150 meters.
Neptune would be more than 4 km away.
On this one-billionth scale, the nearest
star would be at a distance of 40,000 km
- more than the actual diameter of the
Earth. One would have to travel five
thousand times farther yet to reach the
center of the Milky Way Galaxy, another
80 times farther to reach the next nearest
spiral galaxy, and another several
thousand times farther still to reach the
limits of the known Universe.
Gareth Wynn-Williams
Summary: This chapter introduces the reader to gamma ray astron-
omy, presents the most remarkable gamma ray telescopes and discusses
1

18. 1.1. Thesis objetive and structure 2
the photodetectors used in IACT (Imaging Atmospheric Cherenkov
Technique) experiments.
1.1 Thesis objetive and structure
The primary objective of this thesis is the design, implementation and test of
broadband, low noise and high dynamic range signal conditioning electron-
ics for the CTA (Cherenkov Telescope Array). The prototypes developed
are going to be tested with state of the art GAPD (Geiger mode Avalanche
Photo Diode). In this thesis, two design alternatives will be proposed, tran-
simpedance amplifier and 50 Ω input impedance MMIC (Monolithic Mi-
crowave Integrated Circuit) amplifier, and the advantages and drawbacks of
these two approaches will be analysed.
This thesis also aims to provide a proof of concept of the viability of
the engineering of electronic circuits using open source tools. The benefits
and drawbacks of this approach against licensed commercial software will be
discussed.
The work has been divided in eight chapters. Chapter 1 introduces the
reader to gamma ray astronomy, presents the most remarkable gamma ray
telescopes and discusses the photodetectors used in IACT (Imaging Atmo-
spheric Cherenkov Technique) experiments.
Chapter 2 introduces the front-end electronics and makes an analysis of
the approaches used to amplify the signals generated by the photodetectors.
It also reviews the specifications of the front-end that have been agreed by
the CTA collaboration and describes the state of the art of the front-ends
for CTA.
In Chapter 3, the design of two prototypes based on the BGA614 MMIC
is described. This chapter also includes all the simulations performed with
QUCS to validate the designs before implementation.
Chapter 4 deals with the design of transimpedance preamplifier proto-
types. Firstly, negative feedback is introduced. Then, the rationale of the
need of the design and the selection of the appropriate transistor is discussed.
Finally, the design is developed and the simulations are presented.

19. 1.2. Modern observational astronomy 3
Chapter 5 describes the implementation details of the prototypes. The
technology used for the PCB (Printed Circuit Board ) will be introduced and
the created boards will be shown.
Chapter 6 describes the setups used to test and measure the implemented
prototypes. A review of the instrumentation available in the laboratory is
done.
In Chapter 7, the experimental measurements and tests on the imple-
mented prototypes are presented and discussed.
Finally, in Chapter 8, the obtained results are analysed and compared.
The future work is also described.
1.2 Modern observational astronomy
The outer space has fascinated the human kind since the ancient times. For
many years, the observation of the cosmos has been limited to the optical
window, mainly because our eyes are the only “antenna” we naturally have
to detect the electromagnetic energy radiated by celestial bodies. Optical
telescopes have aided us in the exploration of outer space, but with the
limitation of exploring a very narrow band of the entire electromagnetic
spectrum.
In 1865, the great scottish physicist James Clerk Maxwell published the
famous equations that carry his name, unifying the laws of electricity and
magnetism into a set of four succinct equations1 . More than two decades af-
ter, in 1888, Heinrich Hertz proved the existence of electromagnetic waves by
creating them artificially, and in the beginning of the 20th century, Guglielmo
Marconi layed the foundations of radio communications. But it was not until
1931 when Karl G. Jansky, a radio engineer working for the Bell Telephone
Laboratories in Holmdel, New Jersey, in a attempt to study the interference
caused by thunderstorms in the transoceanic radio link, accidentally discov-
ered a strange RF (Radio Frequency) source, which he later proved to be
extraterrestial by correlating the received power to the the earth’s rotation
1
A special mention to Oliver Heaviside must be made for his work done in simplifying
the original set of 13 equations into a set of 4 equations in differential form as we know
them today.

20. 1.3. Gamma ray astronomy 4
[10, chap. 1].
Figure 1.1: Jansky’s Antenna, image courtesy of NRAO/AUI.
Jansky’s discovery was to become the dawn of a new era in Astronomy.
From now on, it was known that celestial bodies radiate electromagnetic
energy along specific bands of the spectrum (including visible light). After
the Second World War, radio astronomy developed quickly and firmly. This
eye-opening to the space has provided a lot of information which wasn’t
available in the optical window for many centuries, and has led to a significant
advance in our understanding of the Universe.
1.3 Gamma ray astronomy
Gamma ray astronomy is the study of gamma radiation emitted by extrater-
restrial bodies. Gamma radiation is located at the top of the radiation
spectrum, with wavelengths in the order of 10−12 m and energies of 106 eV
and higher (see figure 1.2).
High energy gamma rays, with energies ranging from GeV to TeV cannot
be generated by thermal emission from hot celestial bodies. The energy of
thermal radiation reflects the temperature of the emitting body. Apart from
the Big Bang, there hasn’t been such a hot body in the known Universe.

21. 1.3. Gamma ray astronomy 5
Figure 1.2: Electromagnetic spectrum, image courtesy of Wikipedia.
Thus, gamma ray astronomy is the window within the electromagnetic spec-
trum to probe the non thermal Universe. Gamma rays can be generated
when highly relativistic particles, accelerated for example in the gigantic
shock waves of stellar explosions, collide with ambient gas, or interact with
photons and magnetic fields. The flux and energy of the gamma rays reflects
the flux and spectrum of the high-energy particles. They can therefore be
used to trace these cosmic rays and electrons in distant regions of our own
Galaxy or even in the other galaxies. Gamma rays can also be produced
by decays of heavy particles such as hypothetical dark matter particles or
cosmic strings, both of which might be relics of the Big Bang. Gamma rays
therefore provide a window on the discovery of the nature and constituents
of dark matter [1, chap.2].
Fortunately for us and all the living creatures in our planet, the Earth’s
atmosphere blocks most of the gamma radiation coming from outer space.
Unfortunately for astrophysicists, gamma rays cannot be directly detected
from the ground. In the 60’s, with the development of the space technology,
satellites became a feasible tool for the detection of gamma rays. Some ex-
amples of these satellites can be found in [2, chap. 1.2], such as the Explorer
XI, which in 1961 discovered the first gamma rays outside the atmosphere.
The satellites of the Vella Network, initially designed to detect illegal nuclear
tests, detected in 1967 the first gamma ray burst in history. Modern space

22. 1.3. Gamma ray astronomy 6
gamma ray telescopes include EGRET (Energetic Gamma Ray Experiment
Telescope), an instrument aboard the American satellite Compton Gamma
Ray Observatory, and the Fermi Gamma-ray Space Telescope, launched in
June 2008.
The other major technique used to detect gamma rays are the ground
based telescopes, see figure 1.3. The ground based telescopes detect gamma
radiation indirectly, by means of the Cherenkov light produced by air show-
ers. When a very high energy gamma ray enters the atmosphere, it inter-
acts with atmospheric nuclei and generates a shower of secondary electrons,
positrons and photons. These charged particles move in the atmosphere at
speeds beyond the speed of light in the gas, which gives place to the emis-
sion of Cherenkov light, illuminating a circle with a diameter of about 250m
on the ground [1, chap 2.1.3]. This light is captured by the ground based
telescopes’ camera pixels and is used to image the shower. Reconstructing
the shower axis in space and tracing it back onto the sky allows the celes-
tial origin of the gamma ray to be determined. This is known as IACT.
This tecnique allows the detection of VHE (Very High Energy) gamma rays,
which would require prohitively large effective detection area in the space
telescopes [1, chap. 3]. The latest generation of IACT gamma ray telescopes
include H.E.S.S, MAGIC, VERITAS, Cangaroo II and MILAGRO.
The CTA proyect is to become the cutting-edge gamma ray telescope
array. It combines the experience of virtually all groups world-wide working
with atmospheric Cherenkov telescopes to provide a never seen energy range
from about 100GeV to several TeV, angular resolutions in the arc-minute
range, which is about 5 times better than the typical values for current in-
struments, excellent temporal resolution and full sky coverage from multiple
observatory sites [1, chap. 3]. In figure 1.4, a computer generated graphic
with a possible arrangement of one of the telescope array is shown.
CTA will also be the first observatory open to the astrophysics and par-
ticle physics community. The generated data will be made publicly available
through Virtual Observatory Tools in order to make the access and analysis
to data much easier [1, chap. 3].

23. 1.4. Photodetectors used in IACTs 7
Figure 1.3: MAGIC gamma ray telescope, located in Roque de los Mucha-
chos, La Palma (Spain), image courtesy of http://magic.mppmu.mpg.de.
Figure 1.4: CTA computer generated graphic, image courtesy of www.
cta-observatory.org.
1.4 Photodetectors used in IACTs
A photodetector is a transducer that converts light energy into an electrical
current. In this section, the photodetectors mostly used in IACT experiments
will be introduced and compared. Special attention will be put in the GAPD
for being a serious, semiconductor replacement of the PMT.
The PMT is a vacuum tube consisting of an input window, a photo-
cathode with a low work function and an electron multiplier sealed into an
evacuated glass tube (see figure 1.5). Light which enters a photomultiplier

24. 1.4. Photodetectors used in IACTs 8
tube is detected and produces an output signal through the following pro-
cesses [6, chap. 2]:
• Light passes through the input window.
• Excites the electrons in the photocathode, which has a low work func-
tion, so that photoelectrons are emitted into the vacuum because of
the photoelectric effect.
• Photoelectrons are accelerated by the strong electric field present by
the polarisation of the PMT with up to 1 ∼ 2kV , and focused by
the focusing electrode onto the first dynode where they are multiplied
by means of secondary electron emission. This secondary emission is
repeated at each of the successive dynodes.
• The multiplied secondary electrons emitted from the last dynode are
finally collected by the anode in the form of an electric current.
The electron multiplication process gives the PMT an internal gain of
106 ∼ 107 , which makes them suitable for single photon counting.
Figure 1.5: Schematic of a PMT coupled to a scintillator, image courtesy of
Wikipedia.
One of the most important features of PMTs is the QE (Quantum Ef-
ficiency), which is the ratio of the number of generated electrons in the
photocathode to the number of incident photons. The closer to 1, the bet-
ter its perfomance as a detector. PMTs can be designed to peak this effi-
ciency in the blue region of the spectrum, to match the characteristics of the
Cherenkov light [2, chap. 3].

25. 1.4. Photodetectors used in IACTs 9
Being the PMT a mature and well known technology, it has been used
in most of the IACT experiments and it has become the favourite canditate
photodetector to be used in the CTA project.
The HPD (Hybrid Photon Detector ) combines the advantages of PMT
and solid state devices. It consists in a vacuum tube with a high QE photo-
cathode which is biased at voltages of several kV. The generated photoelec-
trons are accelerated by an electric field and focused on an APD (Avalanche
Photo Diode). This way, two stages of amplification are applied: the first
due to acceleration and impact on the semiconductor, and the second due
to the avalanche in the diode. Combined multiplication factors of 5 · 104
can be achieved. These devices have much better energy resolution, sensi-
tivity and QE than PMTs. The detection area is much bigger than that of
solid state devices. The main drawbacks are the ageing of the photocathode,
high rates of afterpulses, dark counts, temperature dependence or handling
of high voltages [2, chap. 3].
Finally, the GAPD has been developed during recent years and has be-
come a serious alternative to PMTs. A GAPD is an APD which has been
biased above its avalanche breakdown voltage, see figure 1.6. This way, a
single photon impinging the space charge region of the pn junction will gen-
erate a hole-electron pair that will trigger a huge avalanche, thus creating a
current pulse that can be detected when properly amplified. An integrated
quenching resistor collapses the breakdown by lowering the voltage at the
n terminal during the breakdown. These devices are commercialised in the
form of a matrix consisting in N × M individual cells. Each cell detects a
single photon. When n photons arrive, n of the N · M cells are very likely
to produce an avalanche. The resulting output current is the sum of the in-
dividual currents of the triggered cells. It is inmediate to see that the upper
limit of detected photons is N · M .
The most critical figures of merit which should be optimised in a GAPD
in order to make it suitable for the application pursued in this work are listed
below [14],
• Gain: GAPDs produce a current pulse when any of the cells goes to
breakdown. The amplitude Ai is proportional to the capacitance of

26. 1.4. Photodetectors used in IACTs 10
Figure 1.6: GAPD cross section, image courtesy of Wikipedia.
the cells times the overvoltage, Ai ≈ C(V − Vb ), being V the operating
bias voltage and Vb the breakdown voltage. When many cells are fired
at the same time, the output is the sum of the individual pulses.
• Dark counts: A breakdown can be triggered by an incoming photon
or by any generation of free carriers. The latter produces dark counts
with a rate of 100 KHz to several MHz per mm2 at 25o C. Carriers
in the conduction band may be generated by the electric field or by
thermal agitation. Thermally generated carriers can be reduced by
cooling the device. Another possibility is to operate the GAPD at a
lower bias voltage resulting in a smaller electric field and thereby lower
gain. The dark counts can be reduced in the production process by
minimizing the number of recombination centres, the impurities and
the crystal defects.
• Optical crosstalk : In an avalanche breakdown there are in average 3
photons emitted per 105 carriers with a photon energy higher than 1.14
eV, the bandgap of silicon. When these photons travel to a neighbour-
ing cell, they can trigger a breakdown there. The optical crosstalk is
an stochastic process and introduces an excess noise factor like in a
normal APD or PMT.
• Afterpulsing: Carrier trapping and delayed release causes afterpulses
during a period of several µ-seconds after the breakdown.

27. 1.5. Open Source CAD 11
• Photon detection efficiency: The PDE (Photon Detection Efficiency) is
the product of the QE of the active area, a geometric factor which is
the ratio of sensitive to total area and the probability that an incoming
photon triggers a breakdown Ptrigger , so P DE = QE · · Ptrigger .
• Recovery time: The time needed to recharge a cell after a breakdown
has been quenched depends mostly on the cell size due to its capaci-
tance and the individual resistor (RC).
• Timing: The active layers of silicon are very thin (2-4 µm), so the
avalanche breakdown process is fast and the signal amplitude is big.
Therefore, very good timing properties even for single photons can be
expected.
There are more features that make GAPDs promising [14]:
• GAPDs work at low bias voltages (50 V ∼ 70 V).
• have low power consumption (< 50 µW/mm2 ).
• are insensitive to magnetic fields up to 15 T.
• are compact and rugged.
• tolerate accidental illumination.
The main drawbacks that are limiting their use in IACT experiments are
the small detection area available and the high dark count rate.
1.5 Open Source CAD
Nowadays, the use of CAD software is a must in every engineering discipline,
and Electronic Engineering is not an exception. Simulation of the designs
is a mandatory phase of a project, as it provides invaluable insight on the
performance of the design before its implementation. Simulation CAD tools
in Electronic Engineering involve one or more of the following types [15,
chap. 11]:

28. 1.5. Open Source CAD 12
• SPICE, originally developed at the Electronics Research Laboratory
of the Berkeley University, is a general purpose analog circuit simu-
lator. It takes a text based netlist, which describes the circuit to be
simulated and solves the system of non-linear differential equations for
currents and voltages. SPICE also provides models for semiconductor
devices which have become a standard both in industry and academic
environments. The following analyses are typically supported by any
SPICE implementation:
– AC analysis: which performs an ac sweep in a selected frequency
band and simulates the frequency response of the circuit. The
non-linear devices, such as diodes or transistors, are linearised on
its bias operating point and a small signal model is used.
– DC analysis: calculates the DC quiescent point of non-linear de-
vices.
– Transient analysis: calculates the current and voltage in every
node and branch of the circuit as a function of time by obtaining
the time domain large signal solution of non-linear differential
equations that arise from the circuit schematic.
– Noise analysis: calculates the noise sources of each noisy element
in the circuit. It also adds all the uncorrelated noise sources to
obtain the equivalent input and output noise sources.
– Distortion analysis: using Volterra series.
The most common licensed SPICE implementation used today is Or-
cad PSpice from Cadence. In this thesis, an alternative open source
implementation called ngspice has been used. This tool is part of
gEDA (Gnu EDA), an open source EDA (Electronic Design Automa-
tion) suite which includes schematic capture, SPICE simulation and
advanced PCB layout.
• Linear simulators. These simulators are the dominant program types
used in the RF and microwave world today. Linear simulators work
by exploting S-parameter models for both active and passive devices.

29. 1.5. Open Source CAD 13
These simulators are therefore more suitable for accurately simulating
in high frequencies than SPICE based simulators.
Some licensed software in this category include APLAC, which is an
excellent simulator for high frequency circuits, or the superb and com-
plete Agilent ADS and AWR Microwave Office. These packages offer
support for the entire design flow, including schematic capture, simu-
lation (linear, harmonic balance and 2D electromagnetic simulation),
PCB layout integrated with the schematic, and many other function-
ality.
In this thesis, the excellent simulator QUCS has been used. Its inter-
face is similar to Agilent ADS, and although it is not comparable to
ADS, it can very well compare to APLAC. QUCS is capable of the
following:
– AC, DC, S-Parameter, harmonic balance, noise, digital and para-
metric simulations.
– Support for VHDL, Verilog-AMS and SPICE netlists.
– Attenuator design tool, Smith chart tool for noise and power
matching, filter synthesis tool, optimizer and transmission line
calculator.
In the future, the following capabilities will be implemented:
– Layout editor for PCB and chip.
– Monte Carlo simulation (device mismatch and process mismatch)
based on real technology data.
– Automated data aquisition from measumerent equipment.
– Electromagnetic field simulator, which is very useful for simulat-
ing arbitrary planar structures (microstrip antennas, distributed
filters, couplers, etc.) and obtain their scattering parameters.
– Transient simulation using convolution for devices defined in the
frequency domain.

30. 1.5. Open Source CAD 14
• Electromagnetic simulators: most of the planar electromagnetic anal-
ysis software employs the Method of Moments to linearly simulate mi-
crostrip, stripline or arbitrary 2D metallic and dielectric structure at
RF and microwave frequencies. This category of simulators is able
to accurately display the gain and return loss of distributed filters,
microstrip antennas, transmission lines and more, in addition to pre-
senting the actual current flow and current density running through
these mettalic structures.
Two examples of electromagnetic simulators are the licensed commer-
cial software Sonnet Suite and Moment, which is included in Agilent
ADS. The open source software QUCS will include its own electromag-
netic simulator in the future.
CAD software is also an invaluable tool to implement the routing of
the circuit, either in an integrated circuit or a PCB. In the field of PCB
design licensed software, there is Cadence Allegro, Eagle, Protel and
many others. In this thesis, we will use the software PCB, which is part
of the gEDA suite. PCB is a powerful tool that supports autorouting,
DRC checks and up to 16 layers in a single board. There is a great
community behind, both for support and footprint libraries.
To perform some numerical computation and to generate some of the
plots, the package Octave has been used. Octave is an open source nu-
merical computation tool which is very similar to Matlab. Its syntax is
almost identical and has many toolboxes available. Its main drawback
is that it lacks of a functional Simulink equivalent, but this is not an
issue for the purpose of this work.

31. Chapter 2
Front-end Electronics
Summary: This chapter introduces the reader to the front-end elec-
tronics and makes an analysis of the approaches used to amplify the
signals generated by the photodetectors. It also reviews the specifica-
tions of the front-end that have been agreed by the CTA collaboration
and describes the state of the art of the front-ends for CTA.
2.1 General overview
Photodetectors such as PMTs and GAPDs convert light signals into electrical
signals in the form of current. Detection of Cherenkov light showers results in
extremely weak current pulses from the photodetectors. This current must be
amplified, conditioned and digitised for storing and further processing of the
pulses. The complete chain, including preamplification, pulse conditioning
and digitisation is called the front-end electronics. A diagram of the front-
end can be seen in figure 2.1.
The preamplifier is the first amplification stage after the photodetector.
The performance of this first stage is critical. If more amplification is needed,
additional amplifier stages can be added. The pulse conditioning and shaping
stage comprises any signal proccesing, such as filtering, pulse shortening,
buffering or converting to differential output that may be needed to drive
the digitiser. The digitiser includes the sampler and the ADC (Analog to
15

32. 2.2. Preamplification approaches 16
photo
detector Digitizer
preamplifier signal conditioning
Figure 2.1: Stages of the front-end.
Digital Converter ). In most modern Cherenkov telescopes, the sampler is
implemented with a switched capacitor array.
The complete chain must minimise signal distortion and must be able to
resolve one single photoelectron up to a few thousand without truncation.
These requirements translate into very demanding specifications on the pho-
todetectors and the front-end electronics: high bandwidth, low noise, low
power, high linearity and very high dynamic range.
2.2 Preamplification approaches
The current pulse from the photodetectors must be converted into a voltage
pulse at some point of the amplification stages. This is usually done at the
preamplification stage using the following three approaches:
• Voltage amplification: the current is converted into a voltage at the
input impedance of a voltage amplifier by means of the Ohm Law
vin = iin ·Zin (jω). Given the frequency dependent gain of the amplifier,
G(jω), the output voltage is given by the following equation:
vout = G(jω) · iin · Zin (jω) (2.1)
• Transimpedance amplification: the current pulse is fed into a tran-
simpedance amplifier which outputs a voltage pulse proportional to
the input current. Given the frequency dependent transimpedance gain
of the amplifier, Ω(jω), the output voltage is given by the following
equation:
vout = Ω(jω) · iin (2.2)

33. 2.2. Preamplification approaches 17
• Charge amplification: the output voltage is proportional to the time
integral of the input current, which is the charge transferred by the
photodetector to the amplifier. The integrating element is a feedback
capacitor, which makes this type of preamplifiers not fast enough to
meet the CTA specifications.
Figure 2.2 shows the circuit topology of the two preamplification ap-
proaches for a GAPD. The biasing circuit of the GAPD is also shown.
Vcc
Vcc
Rbias
Rbias Rf
Rload
50 ohm Rload
(a) Voltage preamplifier topology. (b) Transimpedance preamplifier topology.
Figure 2.2: Circuit topologies for voltage and transimpedance approaches
using a GAPD.
When using a voltage amplifier, figure 2.2a, the GAPD is connected to
the amplifier through a 50 Ω resistor. This resistor is only used for impedance
matching, and it lowers the effective impedance of the voltage amplifier to
Rin || 50 Ω. Thus, if the amplifier is close enough to the GAPD, the resistor
can be removed.
The GAPD is connected directly to the input of the transimpedance
amplifier, see figure 2.2b. This class of amplifiers have a low input impedance,
usually 10 ∼ 20 Ω. In order to avoid signal reflections due to the impedance
mismatch, the preamplifier should be as close as possible to the GAPD.

34. 2.2. Preamplification approaches 18
Let us consider a model of a solid state photodetector as an ideal current
source with a shunt capacitance. The capacitance models the junction ca-
pacitance of the reverse biased pn junction and any capacitive impedance at
the input of the preamplifier. This model is extremely simple and neglects
the series and shunt resistance, but it fits our purposes for the moment.
When the photodetector is connected to a load, the load resistance forms
a shunt RC circuit with the capacitance of the photodetector. This is shown
in figure 2.3. In the following analysis, we will show that this shunt RC
circuit introduces a pole into the photodetector-amplifier system that can
limit its frequency response.
In figure 2.3a, the photodetector is connected to a voltage amplifier with
input resistance Rin and voltage gain G(jω). It can be shown that the first
order transfer function relating the output voltage to the input current is
given by:
vout G(jω) · Rin
= (2.3)
iin 1 + jωRin Cj
1
The transfer function 2.3 introduces a pole at ω0 = Rin Cj . This pole
shows that no matter how broadband and fast your voltage amplifier is,
the frequency response is probably dominated by this lower frequency pole.
Given a photodetectors with a junction capacitance Cj , the only way to push
the pole to higher frequencies is to lower the amplifier’s input resistance Rin .
Unfortunately, this will also lower the overall gain and limit its sensitivity.
On the other hand, in figure 2.3b, the photodetector is connected to
a transimpedance amplifier, with an open-loop gain G(jω) and a tran-
simpedance gain fixed by the feedback resistance, Ω(jω) ≈ −Rf , since
G(jω) >> 1. All the current iin flows through the feedback resistance and
the shunt capacitor, so the following equations apply:
− iin = irf + icap (2.4)
1 − G(jω)
vin − vout = irf Rf =⇒ vout = irf Rf (2.5)
G(jω)
jωCj vout
icap = (2.6)
G(jω)
For frequencies lower than the cut-off frequency, we can approximate
1−G
G ≈ −1.

35. 2.2. Preamplification approaches 19
Combining the equations we end up with the following tranfer function:
vout Rf
= − jωR Cj (2.7)
iin f
G(jω) − 1
G
The transfer function 2.7 introduces a pole at ω0 = Rf Cj . This shows that
the transimpedance feedback amplifier shifts the pole to higher frequencies
by a factor of G, so the bandwidth of the system is considerably improved.
G(jw) +
iin Cj Rin vout
-
(a) Photodetector model connected to voltage amplifier with input
resistance Rin .
Rf
G(jw) +
iin Cj vout
-
(b) Photodetector model connected to transimpedance amplifier.
Figure 2.3: Simplified photodetector model connected to voltage and tran-
simpedance amplifiers.
In figure 2.4, the output of the pulse response with the simplified pho-
todiode model of the two prototypes developed in this thesis is shown. The
simulation has been done with QUCS. The photodiode model used in the
simulation includes a pulse current source with an amplitude of 100 uA, rise
time of 500 ps and pulse width of 4 ns; shunt junction capacitance Cj = 35pF
and a shunt resistance Rshunt = 10KΩ. This capacitance is a typical value
for GAPDs from Hamamatsu.
The effect of the bandwidth limitation due to the photodetector capac-
itance can be seen in figure 2.4. Although both prototypes have about the

36. 2.2. Preamplification approaches 20
BGA614 output
0.02 Transimpedance output
0.015
Output voltage (V)
0.01
0.005
0
0 2e-09 4e-09 6e-09 8e-09 1e-08
time (s)
Figure 2.4: Simulated response of the BGA614 MMIC amplifier (in blue)
and the transimpedance amplifier (in red) to a square current pulse with
amplitude 100 µA, rise time 500 ps, pulse width 4 ns from a photodetector
model with Cj = 35 pF and Rshunt = 10 KΩ.
same bandwidth, the response of the MMIC preamplifier1 is much slower
than that of the transimpedance preamplifier the gain is not the same for
both prototypes, but this fact is not relevant for the moment.
The advantage of using a transimpedance preamplifier is clearly seen
in the following noise analysis. The study of noise is important because
it represents the lower limit of the size of the signal that can be detected
by a circuit. Noise is a random phenomena, so the language and tools of
statistics are used to describe it. A noisy signal is modelled as a random
variable of which the interesting parameter is its variance. If we measure
a constant current flowing through a conductor using an ideal amperimeter
we will notice that the current is not perfectly constant but it has slight
fluctuations. These fluctuations are generally specified in terms of its mean
square variation about the average value [4, chap. 11]:
1
Formally, the MMIC amplifies power, not voltage, but at frequencies below 1 GHz we
can consider it as a voltage amplifier with an input impedance of 50Ω.

37. 2.2. Preamplification approaches 21
1 T
i2 = (I − Iavg )2 = lim (I − Iavg )2 dt (2.8)
T →∞ T 0
For the purpose of analysis, we will only take into account thermal noise.
Other sources of noise in photodetectors, such as flicker noise or shot noise
will be ignored, as they affect both preamplifier configurations and will only
add mathematical complexity to the analysis. Thermal or Johnson noise is
generated by any resistive material due to the thermal random motion of its
carriers. A resistor R generates thermal noise with a mean square variation
given by:
v 2 = 4kT R f (2.9)
1
i2 = 4kT f (2.10)
R
where k is the Boltzmann’s constant, T is the temperature in Kelvin and
f is a narrow frequency band in Hz. The current spectral noise density is
i2
therefore given by f and has units of A2 /Hz.
Every two port network generates noise. Even when there is no signal
present at the input, there is a noise signal at the output. Noise generated
by a two port network is specified in terms of an equivalent noise voltage
and an equivalent noise current, which is usually referred to the input, so
they are named EINV (Equivalent Input Noise Voltage) and EINC. Figure
2.5 shows a noisy two port network modelled as a noiseless network with the
equivalent noise generators at the input. These ficticious noise generators
are the generators that should be present at the input of the ideal noisyless
two port network to obtain the equivalent noise signal at the output.
At microwave frequencies, where power signals are used instead of volt-
ages and currents, the NF (Noise Figure) is used to specify the noise perfor-
mance of a n-port network. It is defined as the ratio of the input SNR (Signal
to Noise Ratio) to the output SNR:
SN Rin
NF = (2.11)
SN Rout
In decibels:

38. 2.2. Preamplification approaches 22
einv i2
+
−
Noisyless
einc v2
two port
Figure 2.5: Noisy two port network modelled as a noiseless network with
input referred noise generators.
SN Rin
N FdB = 10 · log (2.12)
SN Rout
Now that the basic noise concepts have been introduced, we proceed to
analyse the noise performance of voltage amplification versus transimpedance
amplification for a solid state photodetector. Figure 2.6 shows a tran-
simpedance amplifier connected to a solid state photodetector. The equiva-
lent current noise generators are also shown. Note that the sign of the current
generators is ignored because they are uncorrelated, so the phase information
is not relevant. The total noise current at the input of the transimpedance
amplifier is given by:
1 1
i2 = i2
n
2 2 2
amp + ithermal + inf = iamp + 4kT f + 4kT f (2.13)
Rs Rf
From equation 2.13, it is clear that the sensitivity of the transimpedance
amplifier can only be improved by incrementing the feedback resistance Rf ,
thus minimizing the current noise contribution of the feedback resistor. This
also increments the transimpedance gain. It can be seen in equation 2.7
that, ideally, the bandwith of the system is not compromised because the
increment of Rf is compensated by the the open-loop gain G(jω).
On the other hand, using voltage amplification, the sensitivity can be
improved by incrementing the conversion resistance (figure 2.2a), but unfor-
tunately, the bandwidth and noise of the system will be compromised. Using
this amplification approach, sensitivity is traded for bandwidth and noise.
Finally, the high dynamic range required for the CTA front-end results
in a huge voltage drop in the input impedance of the voltage amplifier.

39. 2.3. Specifications of the front-end 23
The transimpedance amplifier’s low input impedance is able to support such
dynamic ranges.
inf
Rf
ithermal iamp
Figure 2.6: Transimpedance amplifier and solid state photodetector with cur-
rent noise generators. ithermal is the thermal noise generated in the resistive
semiconductor material of the photodetector; iamp is the EINC generator of
the amplifier; inf is thermal noise generated by the feedback resistor Rf .
2.3 Specifications of the front-end
CTA will be a cutting-edge Cherenkov telescope providing an extremely wide
energy range and sensitivity. The specifications have been extracted from
various documents in www.cta-observatory.org and have been summarised
in table 2.1.
The response of the photodetector to 1 phe must be known for a complete
understanding of the specifications. In general, we can estimate the current
peak response of a photodetector operating at a gain Gp by obtaining the
charge Q delivered due to 1 phe in the time period τ using a triangular
approximation of the pulse:
ipeak ipeak · τ
Q= t · dt = (2.14)
τ τ 2

40. 2.3. Specifications of the front-end 24
Table 2.1: Set of specifications for the preamplifier.
Broad band- ∼ 400 MHz The electronics must provide a bandwidth
width matched to the length of the Cherenkov pulses
of a few nanoseconds. The signal charge is
obtained by integration over a time window
of minimum duration to decrease the effect
of the NSB (Night Sky Background ). To use
the shortest possible time window, the ana-
log pulse duration must be kept as short as
possible. This means that the analog band-
width must be large enough not to widen the
photodetector pulses.
High dynamic ∼ 3000 phe (Photoelec- The high energy range above 10 TeV produce
range trons) strong light showers, so the photodetector and
the electronics must have a very high dynamic
range to be able to detect the light pulse with-
out clipping.
√
Low noise ∼ 10 pA/ Hz Operating the photodetectors at a lower gain
(∝ 104 ) lengthens the life time (for PMTs)
and decreases the dark counts (for GAPDs).
The electronics must be able to detect single
photoelectrons, so the noise level must be be-
low the signal delivered by the photodetector
for a single photon response. The required
signal to noise ratio is SN R ≈ 5 ∼ 10.
Linearity <3% The response must be proportional to the
number of incident photons, so highly lin-
ear photodetectors and electronics are needed.
Nonlinearities can be tolerated if they can be
accurately corrected for in the calibration pro-
cedure.
Low power < 150 mW/channel The CTA consortium is planning to use up
to ∼ 105 sensor channels. The front-end elec-
tronics must be integrated in the camera clus-
ter.
Low cost

41. 2.4. State of the art 25
Q = Gp · e (2.15)
Where e = 1.602 · 10−19 C is the electron charge in coulombs.
Solving for ipeak , we obtain:
2Gp · e
ipeak = (2.16)
τ
In table 2.3, the minimum and maximum ratings are shown. This data
gives us an estimation of the magnitude of the signals the front-end will have
to cope with.
Table 2.2: Estimated minimum and maximum current and voltage peaks.
The voltage peak is calculated assuming a 50 Ω load.
Gain Pulse width Min ipeak Min vpeak Max ipeak Max vpeak
4· 104 3 ns 4.6 µA 0.23 mV 13.8 mA 0.69 V
7.5 · 105 40 ns 7 µA 0.35 mV 21 mA 1.05 V
2.4 State of the art
There are numerous groups working on prototypes for the front-end of CTA.
These state of the art prototypes include the preamplification, signal condi-
tioning and digitisation. This section compiles a non-exhaustive list of the
most promising prototypes and analyses the main benefits of each of them.
The first prototype to be analysed is developed by the NECTAr collab-
oration, which involves the following groups:
• LPNHE, IN2P3/CNRS Universites Paris VI & IN2P3/CNRS, Paris,
France.
• IRFU, CEA/DSM, Saclay, Gif-sur-Yvette, France.
• LUPM, Universite Montpellier II & IN2P3/CNRS, Paris, France.

42. 2.4. State of the art 26
• ICC-UB, Universitat de Barcelona, Barcelona, Spain.
• LPSC, Universite Joseph Fourier, INPG & IN2P3/CNRS, Grenoble,
France.
This collaboration includes the development of the PACTA preamplifier,
the ACTA3 amplifier and the NECTAr0 sampling ASIC (Application Specific
Integrated Circuit). The NECTAr0 is a switched capacitor array analog
memory plus ADC in a chip. It is capable of sampling the pulses coming
from the signal conditioning electronics at a sampling rate between 0.5 - 3
GS/s, with an analog bandwith of ∼ 400MHz. The ADC has a resolution of
12 bits. The ASIC has been implemented in 0.35 µm CMOS (Complementary
Metal Oxide Semiconductor ) technology.
The ACTA3 is the evolution of the ACTA amplifier [3]. It is a fully
differential voltage ASIC amplifier implemented in 0.35 µm CMOS. The
bandwidth is below 300MHz, which doesn’t comply with the CTA front-end
specifications.
The most interesting development of the NECTAr collaboration from
this thesis point of view is the PACTA preamplifier. This state of the art
preamplifier for the CTA photodetectors is currently being developed by the
ICC-UB group from the University of Barcelona. The preamplifier has been
designed with the following requirements in mind: low noise, high dynamic
range, high bandwidth, low input impedance, low power and high reliability
and compactness [12]. The design includes three basic blocks: super common
base input, cascode current mirror with CB feedback and a fully differential
transimpedance stage. In order to boost up the dynamic range, the designers
have developed a novel technique to provide the amplifier with two gains,
thus achieving a photoelectron dynamic range above 6000 phe. The high
transimpedance gain of 1 KΩ amplifies the low current generated by the
photodetectors under very weak light conditions. The low transimpedance
of 50 Ω comes into scene when the high gain saturates. The first prototype
has been implemented in 0.35 µm SiGe BiCMOS technology and has the
following technical specifications:
• Bandwith ∼ 500MHz.

43. 2.4. State of the art 27
• Input impedance Zi < 10Ω.
√
• Low noise in = 10pA/ Hz.
• High dynamic range > 6000 phe.
Finally, the NECTAr collaboration has developed a prototype board for
the camera which includes the NECTAr0 chip and the readout electronics.
A photograph of this prototype is shown in figure 2.7.
Figure 2.7: Photograph of the NECTAr prototype board, image courtesy of
[16].
The CTA-Japan collaboration has developed the DRAGON-Japan pro-
totype based on the DRS4 (Domino Sampler Ring version 4 ) sampling chip.
The prototype is shown in figure 2.8.
The preamplifier, located at the base of the PMT, is based on the MMIC
LEE-39+ by Mini-Circuits. There is an additional amplification stage, the
main amplifier mezzanine, with three amplifiers. The high gain and low gain
amplifier are based on the ADA4927 and ADA4950 from Analog Devices.
These amplifiers are designed to drive ADCs and provide differential output.
The use of a bi-gain scheme makes the high dynamic range required for the
CTA front-end possible. The other amplifier, based on the LMH6551 from
National Semiconductor, is used for the trigger subsystem. The DRS4 is
an 8 channel switched capacitor array sampling chip developed at the Paul

44. 2.4. State of the art 28
(a) Photograph of the prototype including (b) Block diagram of the prototype.
the PMTs.
Figure 2.8: The DRAGON-Japan prototype, image courtesy of [9].
Scherrer Institute, Switzerland. It is capable of sampling up to 5GS/s and
has an analog bandwidth of 950 MHz.
The DRAGON-Italy prototype is being developed by the INFN Pisa
and the University of Siena. This group is collaborating closely with the
DRAGON-Japan group. They propose the following solutions for the front-
end amplifiers:
• Discrete solution based on the ADA4927 amplifier.
• Discrete solution based on the japanese design.
• Discrete solution based on the new ADA components. They claim that
this will lower the power consumption.
• ASIC solution based on the PACTA chip.

45. Chapter 3
MMIC Amplifier Design
Summary: In this chapter, the design of two prototypes based on
the BGA614 MMIC is described. This chapter also includes all the
simulations performed with QUCS to validate the designs before im-
plementation.
3.1 Selection of the MMIC
The miniaturization of communication equipment experienced in the last
decade needs the RF and microwave circuitry to be integrated in a chip.
Nowadays, commercial general purpose MMIC technology offers, in average,
superior performance than discrete circuits for specific applications or even
ASICs. From the CTA perspective, the main benefits of this technology are
the following:
• Easy design. Many design parameters such as noise matching, stability,
bandwidth and gain are already engineered. The designer needs only
to choose the MMIC that fits his needs and design the bias circuit.
• Fast time to market and shorter design cycles, because the design with
MMICs is straightforward. This translates into lower design costs.
• More reliability, as the developers of the commercial MMICs include
quality assurance into their processes. These commercial integrated
29

46. 3.2. Design of the prototypes 30
circuits are used in defense and aerospace applications, in which safety
and reliability are critical.
• Better reproducibility because the variations in the fabrication process
are minimized. ASICs also have this property.
• Better integration, as they occupy much less space than discrete de-
signs. ASICs also have this property.
The selected MMIC is the BGA614 from Infineon [8]. This low noise
amplifier is very similar to the BGA616 used in [2] for the MAGIC front-end
and, except for the dynamic range, it seems to meet the CTA specifications
and fits the purposes of this thesis.
3.2 Design of the prototypes
The BGA614 is a matched general purpose broadband MMIC amplifier in
a Darlington configuration (see figure 3.1) . The device -3 dB bandwidth
covers DC up to 2.7 GHz with a typical gain of 18.5 dB at 1 GHz and source
and load impedance of 50 Ω. At a device current of 40 mA, it has an output
1 dB compression point of +12 dBm. At this same operating point, the noise
figure is 2.3 dB at 2 GHz.
The amplifier is matched to 50 Ω and its unconditionally stable, so the
only design issues are the DC bias circuit and the AC coupling capacitors.
In figure 3.2, a schematic diagram of the bias circuit is shown. The
BGA614 is biased by applying a DC voltage to the the collectors of the
transistors. A resistor and a RFC (Radio Frequency Choke) inductor are
added in series, and coupling capacitors are added at the input and the
output.
The resistor is added to fix and stabilise the desired collector current.
Given a quiescent point (Ic , Vc ), the resistor value is given by:
Vcc − Vc
R= (3.1)
Ic
The BGA614 is designed to work with a collector current of 40 mA.
For Vcc = 5V , the manufacturer recomends a series resistor R = 68 Ω. A

47. 3.2. Design of the prototypes 31
Figure 3.1: Simplified circuit of the BGA614, image courtesy of Infineon.
precision resistor, with a tolerance of 0.1% will be used.
The coupling capacitors block the DC current. This capacitors set the
lower frequency of operation of the amplifier. Our design goal for this pa-
rameter is 100 KHz, so the capacitors must present a low impedance at this
frequency. A value of C = 100nF is adecuate. For this value, the impedance
at 100 KHz is ∼ −j16 Ω.
The inductor is used as a RFC to block the RF signal. It must present a
significant impedance to the lowest operation frequency, which is 100 KHz.
Up to this point, we have considered the inductors and capacitors as ideal
elements, but unfortunately, real life devices have parasitics due to packag-
ing and bonding wires which have a significant impact in their behaviour,
specially at high frequencies. In figure 3.3, the high frequency models for
lumped components are shown. The parasitics form shunt or series LC cir-
cuits, so real inductors and capacitors resonate at a frequency called the
SRF (Self Resonant Frequency). This parameter is usually given by the
manufacturer of the device, or can be found by measuring the frequency de-
pendent impedance and fitting into the high frequency model. The obtained
parameters can be plugged into the simulations for more accurate results.
The parasitics characterisation of some commercially available inductors,

48. 3.2. Design of the prototypes 32
2
−
DC 5V
Vcc +
Cb1
1
1uF
Rbias
68
Lrfc2
10uH
Lrfc1
1uH
Ccin X1 Ccout
vin 100nF 1 3 vout
In Out 100nF
GND
1 2
+
Vs
dc 0 ac 1
Rload
−
2
50
TITLE BGA614 mmic amplifier prototype 1
FILE: REVISION:
PAGE OF DRAWN BY: Ignacio Dieguez Estremera
Figure 3.2: Schematic of prototype 1 without parasitics.
such as Murata, Epcos and Tdk has been done in [2]. We shall use these
values of the parasitics in our simulations.
For the selection of the capacitors, we have to make sure that the SRF
must be beyond the highest frequency of operation. We shall select a capac-
itor with SRF > 1 GHz. The size of the SMT (Surface Mount Technology)
package will be 0805, which has better frequency response than bigger pack-
ages and can be manipulated and soldered more easily than smaller packages.
Additionally, we connect bypass capacitors to filter the ripple coming from
the power supply unit.
SMT inductors in the order of 1 ∼ 10 µH typically resonate at a frequency
of some tens of MHz. After the resonant frequency, the inductor no longer
exhibits inductance and its reactance decays, thus we must make sure that
the impedance shown to the RF signal is high enough at high frequencies.
For this thesis, two prototypes of the BGA614 amplifier have been de-

49. 3.2. Design of the prototypes 33
Figure 3.3: A component’s real life behaviour at high frequencies, image
courtesy of [15].
signed.
3.2.1 Prototype 1
The first prototype designed includes two RFC inductors in series (see figure
3.2). This design is based on the design for the BGA616 in [2]. The use
of two inductors increases the impedance for the RF signal. The value of
these inductors is 1 µH and 10 µH. Figure contains the schematic of the
prototype, captured with QUCS. As advanced by [2] and confirmed by the
simulations done with QUCS and detailed in section 3.3, the self-resonance
of the inductors introduces a resonance peak at 108 MHz. [2] proposes the
addition of a 560 Ω resistor in parallel with the 10 µH inductor to lower its
quality factor Q.
3.2.2 Prototype 2
The second prototype includes only one RFC of 10 µH (see figure 3.4).
The use of one inductor removes the resonance peak, but has the drawback
of losing gain at lower frequencies. To address this problem, additional
impedance is introduced by narrowing the coplanar copper line connecting
the inductor.

50. 3.3. Simulations 34
2
−
DC 5V
Vcc +
Cb1
1
1uF
Rbias
68
Lrfc1
10uH
Ccin X1 Ccout
vin 100nF 1 3 vout
In Out 100nF
GND
1
+ 2
Vs
dc 0 ac 1
Rload
−
2
50
TITLE BGA614 mmic amplifier prototype 2
FILE: REVISION:
PAGE OF DRAWN BY: Ignacio Dieguez Estremera
Figure 3.4: Schematic of prototype 2 without parasitics.
3.3 Simulations
In this section, we present the simulations done with QUCS and discuss the
obtained results. The following simulations have been done:
• DC simulation.
• Scattering parameter simulation.
• AC simulation.
• Stability circles and µ-factor simulations.
• Noise simulation.
The SPICE model of the MMIC has been used for the simulations with
QUCS. Although Infineon provides s2p files with the scattering parameters

51. 3.3. Simulations 35
of the device, these are a linearised small signal model of the device, which
means that they are bias point dependent. We have preferred to use the
SPICE model as it is bias point independent and also takes into account the
non-linear effects. The bias point of the transistors is obtained by the DC
simulation. Refer to 8.4 for the spice model of the BGA614.
3.3.1 Prototype 1
Figure 3.5 shows the schematic of prototype 1 for frequency domain simula-
tions captured with QUCS. The schematic includes the parasitics for induc-
tors and capacitors. The values have been taken from [2].
Vcc
U=5 V
Rbias1 Cb1
R=68 C=1 uF
Pr1
Rrfc1
R=2.1 Ohm Crfc1 Equation
C=2.342 pF
dc simulation
Lrfc1 Eqn1
DC1 dBGain=dB(S[2,1])
L=10 uH
Kfactor=Rollet(S)
S parameter dBS11=dB(S[1,1])
dBS22=dB(S[2,2])
simulation Mufactor=Mu(S)
Rrfc2
Mufactorprime=Mu2(S)
R=0.34 Ohm Crfc2 SP1
stabL=StabCircleL(S)
C=0.106 pF Type=log
Lrfc2 stabS=StabCircleS(S)
Start=100 kHz
L=1 uH Stop=1.5 GHz
Points=100 number Pr1.I
1 0.0365
Rccin1 X1 Rccout1
R=0.565 Ohm R=0.565 Ohm
10 9
Ccin1 Lccin1 spice Ccout1 Lccout1
L=58.4 pH
C=100 nF 11 L=58.4 pH
C=100 nF
P1 Ref
P2
Num=1
Num=2
Z=50 Ohm
Z=50 Ohm
Figure 3.5: QUCS schematic for frequency domain simulations of prototype
1 with parasitics.
Figure 3.6 shows the simulated S11 and S22 scattering parameters. In this
figure, we can see that the prototype has a resonance peak at frequency 109

52. 3.3. Simulations 36
MHz, which makes it useless for our purpose. Figure 3.7 shows the simulated
power gain of the amplifier. Infineon claims a power gain |S21 |2 ≈ 19 dB
and these simulations predict a gain of ∼19 dB in the frequency band. The
predicted -3 dB frequency band ranges from 147 KHz to approximately 2
GHz. We can also appreciate the resonance peak at 109 MHz.
frequency: 1.2e+08
dBS11: -15.1
-10
-12
-14
dBS22
dBS11
S[2,2]
S[1,1]
-16
-18
-20
-22
1e5 1e6 1e7 1e8 1e9 3e9
frequency
frequency
frequency
frequency
Figure 3.6: Simulated S11 and S22 of prototype 1. Modulus in dB (left) and
Smith chart (right).
The stability simulations predict unconditional stability for f < 1 GHz
(see figure 3.8). For f > 1 GHz, the simulations predict potential unstability
for source and load inductive loads. We have observed that the responsible
for the non conditional stability are the RFC inductors used. The manu-
facturer has used a bias tee for the biasing of the device and has set the
reference plane of the measured S parameters at the output pin of the inte-
grated circuit, thus obtaining a different set of parameters. We can conclude
that the bias circuit with RFC inductors must be carefully designed. All of
these issues have been addressed in prototype 2.
Finally, the simulated noise figure of the prototype in figure 3.9 shows
the low noise performance of the prototype.

53. 3.3. Simulations 37
19
18.5
18
17.5
dBS21
17
16.5
16
15.5
1e5 1e6 1e7 1e8 1e9 3e9
frequency
Figure 3.7: Simulated S21 (modulus in dB) of prototype 1.
Stability circles for source (blue) and load (red) impedance
1.4
1.3
Mufactorprime
Mufactor
1.2
1.1
1
0.9 1.5
1e5 1e6 1e7 1e8 1e9 3e9
frequency (Hz) frequency
Figure 3.8: Simulated stability parameters µ and µ (left) and stability circles
(right).
3.3.2 Prototype 2
The previous section showed that the two series inductors introduces a res-
onance peak at 109 MHz that renders the prototype useless for pulse ampli-
fying. [2] solves the problem by introducing a 560 Ω shunt resistor to the
10 µH inductor. This shunt resistor lowers the quality factor of the parasitic

54. 3.3. Simulations 38
1.94
1.93
1.92
Noise figure (dB)
1.91
1.9
1.89
1.88
0 2e8 4e8 6e8 8e8 1e9 1.2e9 1.4e9
frequency (Hz)
Figure 3.9: Simulated noise figure of prototype 1.
LC circuit, thus removing the resonance peak.
In this thesis, we have taken a different approach. This prototype includes
only one RFC inductor of 10 µH in the bias circuit. This way we reduce the
bias circuit to one resistor and one inductor, instead of two resistors and two
inductors. This implies less points of failure and therefore more reliability.
The bandwidth is reduced to 1 GHz, which is much higher than the required
for the CTA front-end.
Figure 3.10 shows the schematic of prototype 2 for frequency domain
simulations captured with QUCS. The schematic includes the parasitics for
inductors and capacitors and it also includes the sections of coplanar trans-
mission lines used in the implemented board. Refer to section 5.1 for a com-
plete description of the substrate and the coplanar trasmission lines used.
Figure 3.11 shows the simulated S11 and S22 scattering parameters. In
this figure we can see the good matching obtained at the input an output
ports. Figure 3.12 shows the simulated power gain of the amplifier. Infineon
claims a power gain |S21 |2 ≈ 19 dB and these simulations predict a gain of
∼19 dB in the frequency band. The predicted -3 dB frequency band ranges
from 147 KHz to approximately 1 GHz. The stability simulations (see figure