pulse preamplifiers for cta camera photodetectors

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

Pulse Preamplifiers for

CTA Camera

Photodetectors

Proyecto de Ingeniería Electrónica

Dirigido por los Doctores

D. José Miguel Miranda Pantoja y D. Pedro AntoranzCanales

Departamento de Física Aplicada III (Electricidad yElectrónica)

Facultad de Ciencias Físicas

Universidad Complutense de Madrid

Septiembre 2011

A Ana, a mis padres y a mis hermanos.

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

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

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

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

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

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 =

10KΩ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.5 Noisy two port network modelled as a noiseless network with

input referred noise generators. . . . . . . . . . . . . . . . . . 22

x

http://magic.mppmu.mpg.de


www.cta-observatory.org


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



3.12 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

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



4.17 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

List of Figures xiii



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

http://wcalc.sourceforge.net/coplanar.html


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

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. εr 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

List of Tables xvi

8.1 BGA614 prototype specification. . . . . . . . . . . . . . . . . 102

8.2 TIA prototype specification. . . . . . . . . . . . . . . . . . . . 102

Chapter 1

Introduction

Some idea of the vastness of theUniverse may be gained by considering a

model in which everything has beenscaled down by a factor of a billion. In

this model the Earth would have thedimensions of a grape. The Moon wouldresemble a grapeseed 40cm away whilethe Sun would a 1.4-meter diametersphere 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 theEarth. One would have to travel five

thousand times farther yet to reach thecenter of the Milky Way Galaxy, another80 times farther to reach the next nearest

spiral galaxy, and another severalthousand 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

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.

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 rotation1A 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.

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 10−12m and energies of 106eV

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.


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


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].

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





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].


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


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 25oC. 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.

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 ε which is

the ratio of sensitive to total area and the probability that an incoming

photon triggers a breakdown Ptrigger, so PDE = QE · ε · 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 (< 50µW/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]:


• 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.


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.


• 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.

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

2.2. Preamplification approaches 16

photodetector

preamplifier signal conditioning

Digitizer

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)


• 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.

Rload50 ohm

Rbias

Vcc

(a) Voltage preamplifier topology.

Rf

Rload

Vcc

Rbias

(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.


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:voutiin

=G(jω) ·Rin1 + jωRinCj

(2.3)

The transfer function 2.3 introduces a pole at ω0 = 1RinCj

. 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)

vin − vout = irfRf =⇒ vout

(1−G(jω)

G(jω)

)= irfRf (2.5)

icap =jωCjvoutG(jω)

(2.6)

For frequencies lower than the cut-off frequency, we can approximate1−GG ≈ −1.


Combining the equations we end up with the following tranfer function:

voutiin

= − RfjωRfCjG(jω) − 1

(2.7)

The transfer function 2.7 introduces a pole at ω0 = GRfCj

. 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.

+

-

voutRinCjiin

G(jw)

(a) Photodetector model connected to voltage amplifier with input

resistance Rin.

+

-

voutCjiin

G(jw)

Rf

(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


0

0.005

0.01

0.015

0.02

0 2e-09 4e-09 6e-09 8e-09 1e-08

Output voltage (V)

time (s)

BGA614 output

Transimpedance output

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 = 10KΩ.

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]:1Formally, 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.


〈i2〉 = 〈(I − Iavg)2〉 = limT→∞

1

T

∫ T

0(I − Iavg)2dt (2.8)

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:

〈v2〉 = 4kTR4f (2.9)

〈i2〉 = 4kT1

R4f (2.10)

where k is the Boltzmann’s constant, T is the temperature in Kelvin and

4f is a narrow frequency band in Hz. The current spectral noise density is

therefore given by 〈i2〉4f 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:

NF =SNRinSNRout

(2.11)

In decibels:


+−

Noisyless

two port

einc

einv i2

v2

Figure 2.5: Noisy two port network modelled as a noiseless network with

input referred noise generators.

NFdB = 10 · log(SNRinSNRout

)(2.12)

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:

〈i2n〉 = 〈i2amp〉+ 〈i2thermal〉+ 〈i2nf 〉 = 〈i2amp〉+ 4kT1

Rs4f + 4kT

1

Rf4f (2.13)

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.

2.3. Specifications of the front-end 23

The transimpedance amplifier’s low input impedance is able to support such

dynamic ranges.

Rf

inf

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:

Q =

∫τ

ipeakτ

t · dt =ipeak · τ

2(2.14)


2.3. Specifications of the front-end 24

Table 2.1: Set of specifications for the preamplifier.

Broad band-

width

∼ 400 MHz The electronics must provide a bandwidth

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

range

∼ 3000 phe (Photoelec-

trons)

The high energy range above 10 TeV produce

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 SNR ≈ 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

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:

ipeak =2Gp · eτ

(2.16)

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 vpeak4 · 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.


• 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.


• 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


(a) Photograph of the prototype including

the PMTs.

(b) Block diagram of the prototype.

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.

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

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:

R =Vcc − Vc

Ic(3.1)

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


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,


FILE: REVISION:

DRAWN BY: PAGE OF

TITLE

In1

Out3

GN

D2

X1Ccin

100nF

Ccout

100nF

BGA614 mmic amplifier prototype 1

Ignacio Dieguez Estremera

1

+

2−

VccDC 5V

Lrfc

1 1uH

Rbi

as

68

Rlo

ad

50

vout

1

+

2

−

Vsdc 0 ac 1

vin

Cb1

1uF

Lrfc

2 10uH

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-


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 560Ω 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.

3.3. Simulations 34

FILE: REVISION:

DRAWN BY: PAGE OF

TITLE

In1

Out3

GN

D2

X1Ccin

100nF

Ccout

100nFvout

BGA614 mmic amplifier prototype 2

Ignacio Dieguez Estremera

1

+

2−

VccDC 5V

Rbi

as

68

Rlo

ad

50

1

+

2

−

Vsdc 0 ac 1

vin

Cb1

1uF

Lrfc

1 10uH

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

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].

Ccin1C=100 nF

Lccin1L=58.4 pH

Lccout1L=58.4 pH

Ccout1C=100 nF

Rccout1R=0.565 Ohm

Rccin1R=0.565 Ohm

P2Num=2Z=50 Ohm

P1Num=1Z=50 Ohm

spice

10 9

11

Ref

X1

Crfc2C=0.106 pF

Crfc1C=2.342 pF

Rrfc1R=2.1 Ohm

Lrfc1L=10 uH

Rrfc2R=0.34 Ohm

Lrfc2L=1 uH

Cb1C=1 uF

VccU=5 V

Rbias1R=68

Pr1

dc simulation

DC1

S parametersimulation

SP1Type=logStart=100 kHzStop=1.5 GHzPoints=100

Equation

Eqn1dBGain=dB(S[2,1])Kfactor=Rollet(S)dBS11=dB(S[1,1])dBS22=dB(S[2,2])Mufactor=Mu(S)Mufactorprime=Mu2(S)stabL=StabCircleL(S)stabS=StabCircleS(S)

number1

Pr1.I0.0365

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

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.

frequencyfrequency

S[1

,1]

S[2

,2]

1e5 1e6 1e7 1e8 1e9 3e9-22

-20

-18

-16

-14

-12

-10

frequencyfrequency

dBS

11dB

S22

frequency: 1.2e+08dBS11: -15.1frequency: 1.2e+08dBS11: -15.1

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.

3.3. Simulations 37

1e5 1e6 1e7 1e8 1e9 3e915.5

16

16.5

17

17.5

18

18.5

19

frequency

dBS

21

Figure 3.7: Simulated S21 (modulus in dB) of prototype 1.

1e5 1e6 1e7 1e8 1e9 3e90.9

1

1.1

1.2

1.3

1.4

frequency (Hz)

Mufactor

Mufactorprim

e

1.5

frequency

Stability circles for source (blue) and load (red) impedance

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

3.3. Simulations 38

0 2e8 4e8 6e8 8e8 1e9 1.2e9 1.4e9

1.88

1.89

1.9

1.91

1.92

1.93

1.94

frequency (Hz)

Noi

se fi

gure

(dB

)

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

3.3. Simulations 39

3.13) predict unconditional stability.

The transimpedance gain has been simulated for different values of pho-

todetector capacitance. Figure 3.14 shows the effect of this capacitance in

the transimpedance bandwidth.

Figure 3.15 shows that the noise figure is below 2 dB. The simulation

predicts very good noise performance.

The simulated response of this prototype makes it suitable for implemen-

tation in a PCB. Chapter 5 contains all the implementation details.

spice

10 9

11

Ref

X1

P1Num=1Z=50 Ohm

Lccin1L=58.4 pH

Rccin1R=0.05 Ohm

CL6Subst=Subst1W=1.5 mmS=3 mmL=2.76 mm

CL5Subst=Subst1W=3 mmS=3 mmL=6 mm

Ccin1C=100 nF

P2Num=2Z=50 Ohm

dc simulation

DC1

Subst1er=4.6h=1.57 mmt=0.37 mmtand=2e-4rho=1.68e-8D=0.15e-6

CL8Subst=Subst1W=3 mmS=3 mmL=6 mm

Ccout1C=100 nF

Rccout1R=565 mOhm


Equation

Eqn1S21dB=dB(S[2,1])S21phase=phase(S[2,1])S11dB=dB(S[1,1])S22dB=dB(S[2,2])mufactor=Mu(S)mufactorprime=Mu2(S)stabL=StabCircleL(S)stabS=StabCircleS(S)

Lccout1L=58.4 pH


SP1Type=logStart=100 kHzStop=1.5 GHzPoints=100Noise=yes

Lcb1L=25 pH

Cb1C=1 uF

Rcb1R=0.328 Ohm

Vcc1U=5 V

Lcb2L=25 pH

Rcb2R=0.328 Ohm

Cb2C=10 nF

Prbias1

RbiasR=68

Lrfc2L=10uH

Crfc1C=2.342 pF

Rrfc2R=2.1 Ohm

CL9Subst=Subst1W=0.82 mmS=3 mmL=3 mm


number

1

Prbias1.I

0.0366

Figure 3.10: QUCS schematic for frequency domain simulations of prototype

2 with parasitics and coplanar transmission line sections.

3.3. Simulations 40

1e5 1e6 1e7 1e8 1e9 3e9

-20

-18

-16

-14

-12

-10

-8

frequency (Hz)

S1

1d

B

S2

2d

B

frequency

S[1

,1]

S[2

,2]

Figure 3.11: Simulated S11 and S22 of prototype 2. Modulus in dB (left)

and Smith chart (right).

1e5 1e6 1e7 1e8 1e9 3e9

14.5

15

15.5

16

16.5

17

17.5

18

18.5

19

19.5

frequency (Hz)

S21dB

frequency: 1.47e+05S21dB: 16frequency: 1.47e+05S21dB: 16

frequency: 1.02e+09S21dB: 15.9frequency: 1.02e+09S21dB: 15.9

Figure 3.12: Simulated S21 (modulus in dB) of prototype 2.

3.3. Simulations 41

1e5 1e6 1e7 1e8 1e9 3e9

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

frequency (Hz)

mu

fact

or

mu

fact

orp

rime

1.5

frequency

Sta

bili

ty c

ircle

s fo

r so

urc

e (

blu

e)

an

d lo

ad

(re

d)

imp

ed

an

ce

Figure 3.13: Simulated stability parameters µ and µ′ (left) and stability

circles (right).

1e4 1e5 1e6 1e7 1e8 1e9 3e9

0

5

10

15

20

25

30

35

40

45

50

frequency (Hz)

Transimpedance gain (dB)

acfrequency: 7.38e+07Cs: 3.5e-11voutdB: 46.1


acfrequency: 1.29e+09Cs: 1e-15voutdB: 43.4

acfrequency: 1.29e+09Cs: 1e-15voutdB: 43.4



Figure 3.14: Simulated transimpedance gain of prototype 2 for different

photodetector capacitances.

3.3. Simulations 42

0 2e8 4e8 6e8 8e8 1e9 1.2e9 1.4e9

1.86

1.88

1.9

1.92

frequency (Hz)

Nois

e fig

ure

(dB

)

Figure 3.15: Simulated noise figure of prototype 2.

Chapter 4

Transimpedance Amplifier

Design

Summary: This chapter deals with the design of transimpedance

preamplifier prototypes. Firstly, negative feedback is introduced. Then,

the rationale of the need of the design and the selection of the appro-

priate transistor is discussed. Finally, the design is developed and the

simulations are presented.

4.1 Basic feedback concepts

The most fundamental concept behind the design of a transimpedance am-

plifier is negative feedback. In figure 4.1, the negative feedback configuration

from a system point of view is shown. The output signal of the basic ampli-

fier So is fed back to the feedback network with transfer function f , which

outputs the feedback signal Sfb. The difference between the input signal Siand Sfb is the error signal Se, which is fed to the basic amplifier. We can

derive the following equations:

So = a · Se (4.1)

Sfb = f · So (4.2)

43

4.1. Basic feedback concepts 44

Se = Si − Sfb (4.3)

Combining these equations we obtain the closed-loop gain:

SoSi

=a

1 + af(4.4)

If the loop gain af >> 1, the closed-loop gain can be approximated by

SoSi≈ 1

f(4.5)

which only depends on the feedback network.

ƒ

Feedback network

Basic amplifier

aSe

Si

Sfb

So+

-

Figure 4.1: Ideal feedback configuration.

When dealing with real electronic networks, the previously defined signals

are currents and voltages. This gives rise to four basic feedback configura-

tions. These are specified according to whether the output signal So which

is sampled is a current or a voltage and whether the feedback signal Sfb is

a current or voltage. The interested reader may refer to [4] for a rigorous

treatment of feedback. Table 4.1 summarises the feedback configurations.

Traditionally, transimpedance amplifiers have been implemented using

a basic amplifier in a shunt-shunt feedback configuration (figure 4.2). The

output voltage vo is sensed and the feedback network generates a feedback

current ifb, so the transfer function f of the feedback network has units of

conductance, Ω−1. The error current signal is ie = ii − ifb. From equation

4.1. Basic feedback concepts 45

Table 4.1: Basic feedback configurations.

Configuration Sfb So f

Series-shunt Voltage Voltage Dimensionless

Shunt-shunt Current Voltage Conductance (Ω−1)

Shunt-series Current Current Dimensionless

Series-series Voltage Current Resistance (Ω)

+

−

Basic amplifier

Feedback network

+

-

vo

vofvo

zi avi

ie

ifb

ii

Figure 4.2: Shunt-shunt feedback configuration.

4.5, we can see that the closed-loop gain has units of resistance, Ω, hence

the name of transresistance or transimpedance.

The use of feedback produces several benefits. Negative feedback sta-

bilises the gain of the amplifier against changes in the active devices due to

supply voltage variation, temperature changes, or device aging. A second

benefit is that negative feedback allows the designer to modify the input and

output impedances of the circuit in any desired fashion and finally, it reduces

the signal distortion and increases the bandwidth [4]. All these benefits have

a cost in gain and stability. When designing a circuit with feedback, the

stability must be verified.

4.2. Rationale 46

4.2 Rationale

In this section we will provide a rationale justifying the need of designing

a transimpedance amplifier using discrete BJT transistors instead of using

commercially available transimpedance amplifiers.

One of the key requirements for the prototypes developed in this the-

sis is the broad bandwidth > 400 MHz. To obtain such a bandwidth and

enough transimpedance gain, the basic amplifier, which can be an operational

amplifier, must have a huge GBP (Gain Bandwidth Product). Operational

amplifiers are not designed for very high frequencies so, at the time of writ-

ing this thesis, we have not found any commercially available operational

amplifier that suits our needs. We have also searched for COTS (Commer-

cial Off-The-Shelf ) integrated transimpedance amplifiers. For example, the

AN1435 family of transimpedance amplifiers from Philips Semiconductors

have a maximum bandwidth of 280 MHz, the SA5212A and closely related

parts also from Philips Semiconductors has a bandwidth of 140 MHz. The

transimpedance amplifiers TZA3013A and TZA3013B (Philips Semiconduc-

tors) offer good performance, with a low equivalent input noise current of 8

pA/√Hz and a bandwidth from DC to 1.7 GHz with a photodetector capac-

itance of 0.5 pF. However, the dynamic range of 49 dB is not enough for the

CTA requirements and the amplifier is commercialised in die form, without

package. Analog Devices have the AD8015 transimpedance amplifier, but it

only performs well up to 240 MHz and has a limited dynamic range.

It is clear that the cutting-edge performance of CTA requires the engi-

neering of a custom amplifier that meets the demanding specifications. In

this thesis, we have designed, implemented and tested a transimpedance

amplifier prototype with discrete transistors.

4.3 Selection of the transistor

The most critical step in the design of an amplifier is the selection of the

active device, the transistor. The first design decision is to choose between

FET (Field Effect Transistor) or BJT. Each family of transistors has its

advantages and drawbacks.

4.4. Small signal models and distortion 47

The silicon junction transistor is one of the oldest and most popular active

RF device because of its low cost and good operating performance in terms of

frequency range, power capacity and noise characteristics. Silicon junction

transistors are useful for amplifiers up to the range of 2-10 GHz. These

transistors show very low 1/f noise but are subject to shot and thermal noise,

so their noise figures are not as good as that of FETs. Recent developments

with junction transistors using SiGe have demonstrated much higher cutoff

frequencies, making these devices useful in low cost circuits operating at

frequencies of 20 GHz or higher. Heterojunction bipolar transistors may use

GaAs or InP, and can operate at frequencies exceeding 100 GHz [13, chap.

10.4].

Field effect transistors can take many forms, including the MESFET

(Metal Semiconductor FET ), the HEMT (High Electron Mobility Transis-

tor), the PHEMT (Pseudomorphic HEMT ), the MOSFET (Metal Oxide

Semiconductor FET ), and the MISFET (Metal Insulator Semiconductor

FET ). Unlike junction transistors, which are current controlled, FETs are

voltage controlled devices, and can be made with either a p-channel or n-

channel. GaAS MESFETs can perform well up to 40 GHz [13, chap. 10.4].

We have chosen a npn BJT transistor with Si technology for the design

of the prototype, since it is a low cost device which offers high gain and low

noise. The chosen transistor is the BFP420 from Infineon [7]. This transistor

has a transition frequency fT = 25 GHz and a noise figure of 1.1 dB at 1.8

GHz.

4.4 Small signal models and distortion

Transistors are essentially non-linear devices. The large signal behaviour

is described mathematically by the Ebers-Moll model or the Gummel-Poon

model, which considers more physics of the transistor [11, chap. 10] and it’s

the base of the SPICE model.

The Ebers-Moll model of a npn BJT defines the transistor currents posi-

tive if they flow into the device. It models the B-E and B-C junctions as two

pn-junctions with the positive side connected to the base, each of them in

4.4. Small signal models and distortion 48

parallel with a voltage-controlled current source pointing towards the base.

Put mathematically:

IE + IC + IB = 0 (4.6)

IC = αF IES(eqVBEkT − 1)− ICS(e

qVBCkT − 1) (4.7)

IE = αRICS(eqVBCkT − 1)− IES(e

qVBEkT − 1) (4.8)

αF IES = αRICS (4.9)

βF =αF

1− αF(4.10)

The currents IES and ICS are the reverse-bias B-E and B-C junction

currents, the parameters αF and αF are the forward and reverse common-

base current gain and βF is the forward common-emitter current gain.

The large signal models are not suitable for hand calculation, and thus,

are used mainly for computer simulation. To obtain a linear model of the

transistor working in forward active mode, which is more adequate for analog

design, we must linearise the Ebers-Moll equations and add the diffusion and

junction capacitance of the B-E and B-C junctions. The linearisation is done

by keeping only the first-order terms of the Taylor series expansion of the

equations around the bias point Q:

f(x) = f(Q)+f ′(Q)

1!(x−Q)+

f ′′(Q)

2!(x−Q)2+

f (3)(Q)

3!(x−Q)3+· · · (4.11)

From the two-variable Taylor series expansion of the Ebers-Moll current

equations, and taking into account the diffusion and junction capacitances,

the following parameters are derived:

• Transconductance: gm = ∂IC∂VBE

= qICkT

• B-E diffusion capacitance: Cπ = τF gm where τF is the forward base

transit time.


B C

E

rπ Cπ

Cµ

gmvbe ro

Figure 4.3: Simplified Hybrid-Pi small signal model of the BJT.

• B-E diffusion resistance: rπ = β0gm

where β0 = icib

is the small signal

current gain of the transistor.

• Output resistance due to Early effect: r0 = ∂VCE∂IC

= VAIC

where VA is

the Early voltage.

• Reverse biased junction capacitance: Cµ

The simplified small signal circuital model for the BJT is shown in figure

4.3.

The high order terms of the Taylor expansion are distortion terms that

must be minimised. We will deal with these terms when designing for low

distortion.

4.5 Design of the prototypes

4.5.1 Systematic design procedure

The design strategy used for the prototypes is the structured electronic design

methodology proposed in [17]. This methodology attacks the design problem

orthogonally, which means that each figure of merit (noise, signal power and

bandwidth) of the circuit is optimised independently. Obviously, no design

parameter is trully orthogonal in real life, but the appropriate assumptions

will be made so that an orthogonal design can be made without deviating

too much from the optimum. For the three design aspects, the following

assumptions on orthogonality hold:

• When noise is evaluated, signal power aspects, like distortion, are not

considered. Therefore, the linear small signal models of the components


can be used. Frequency behaviour is taken into account when the noise

performance is evaluated, but the bandwidth demands on the complete

circuit are not considered.

• When signal power is evaluated, neither noise nor frequency behaviour

are considered. Static large signal models will be used. Noise is as-

sumed to be small enough to obtain negligible correlation with the

non-linear behaviour of a circuit.

• When bandwidth is evaluated, signal power (distortion) and noise are

not considered, so again small signal models are used.

We will use simple models of the transistors for the initial design. These

simplifications yield a superior performance than the actual performance, so

we will obtain an upper bound of the performance. The designed prototypes

will be simulated to verify more accurately the real behaviour of the circuit

before implementation.

The design procedure has two basic steps:

1. The design of the feedback network, while modelling the active circuit

a nullor, which is the ideal active circuit. This step includes:

(a) Detailed source, load and transfer specification.

(b) Determination of the amplifier topology and dimensioning of the

feedback network.

2. The design of the active circuit whose properties approach that of the

nullor as good as required for the application. This step includes the

orthogonal design for:

(a) Noise

(b) Distortion

(c) Bandwidth


4.5.2 Checking device parameters

It is useful to perform some basic simulations using the SPICE model of

the BFP420 transistor to gain insight on the large signal behaviour. The

following plots have been made using ngspice:

• A plot of the common-emitter output characteristics (figure 4.4a).

• A plot of the current gain factor βF as a function of IC (figure 4.4b).

• A plot of the collector current IC and the base current IB as a function

of VBE (figure 4.4c).

4.5.3 Design of the feedback network

The design of the feedback network involves the substitution of the active

circuit by a theoretical circuit element called nullor. A nullor is defined as

a two-port network (figure 4.5) with the following ABCD parameters [17,

chap. 2.2.2]:

vi

ii

=

0 0

0 0

vo

io

(4.12)

Being an ideal element, the nullor has infinite current gain, voltage gain,

transconductance and transimpedance. As an example, an ideal operational

amplifier is modelled as a nullor.

The nullor has a nullator at its input and a norator at its output. A

norator is a theoretical current or voltage source that can generate arbitrary

current or voltage. A nullator is another theoretical element with no current

flow nor voltage drop.

The transimpedance amplifier works in a shunt-shunt feedback configu-

ration. This means that the feedback network senses a voltage and outputs

a current which is compared to the reference current coming from the input

current source. The nullor actively imposes the condition to the error current

ie = ii − ifb = 0.

The feedback network is a resistor Rf connecting the output to the input,

thus the asymptotical closed-loop gain (under nullor condition) is A∞ =


0

0.005

0.01

0.015

0.02

0.025

0 1 2 3 4 5

Ic (

A)

VCE (V)

BFP420 Infineon NPN BJT common emitter output characteristics

Ib = 0 uAIb = 40 uAIb = 80 uA

Ib = 120 uAIb = 160 uAIb = 200 uA

(a) Common emmiter output characteristics.

0

20

40

60

80

100

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Forw

ard

Beta

Ic (A)

BFP420 Infineon NPN BJT Forward Beta vs Ic for VCE=1V

(b) Beta vs IC for VCE = 1V

10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

0 0.2 0.4 0.6 0.8 1

(A)

VBE (V)

BFP420 Infineon NPN BJT IC,IB vs VBE for VCE=1V

IcIb

(c) IC and IB vs VBE in logarithmic vertical scale.

Figure 4.4: Large signal plots of the BFP420 BJT transistor.


vi

ii io

vo

+

-

+

-

Nullor

Figure 4.5: The nullor.

−Rf . The real closed-loop gain will be somehow smaller depending in how

close the active circuit resembles a nullor.

The prototypes designed have transimpedance gains Rf = 300 Ω and

1.5KΩ.

4.5.4 Design of the first nullor stage: noise

A multistage active circuit must be implemented to orthogonally optimise

the noise, bandwidth and distortion performance of the amplifier.

According to the Friis formula (equation 4.13), the noise characteristics

of the amplifier can be improved taking only into account the first stage of

the nullor implementation,

Ftotal = F1 +F2 − 1

G1+F3 − 1

G1G2+

F4 − 1

G1G2G3+ · · · (4.13)

The reduction of the noise figure of the following stage is conditioned by

the gain of the first stage. Additionally, for an optimal implementation of the

nullor, the loop gain must be maximised. These facts makes common-emitter

the most suitable configuration for the first stage of the nullor, since it pro-

vides more gain than the other transistor configurations. The common-base

configuration was also considered, since its low input impedance implements

the nullator as a current probe and thus, rejects the influence of the source

capacitance in the amplifier’s performance.

Figure 4.6 shows the noise analysis of the feedback network and the first

stage of the nullor implementation. In step 1 (4.6a), the noise generators are

identified. The thermal noise generator of the load RL can be neglected due


-

+

+

-

+

-

+

-

+−

+

−

Rf

Zs

ven

ien

RL

vnl

+−

vnf

+−

+−

(a) Step1: The v-shift transform enables us to split ven in the two

branches.

-

+

+

-

+

-

+

-

Rf

Zs ven/Zsien RL

(ven + vnf)/Rf

(b) Step2: ven and vnf are uncorrelated noise generators and can be

added into a single noise generator ven + vnf . The i-shift transform

enables us to split the current noise generator ven+vnf

Rfin the two

branches, and the voltage noise generators are transformed into their

equivalent current noise generators.

Figure 4.6: Transforms on the noise generators that affect the noise perfor-

mance. ven and ien are the equivalent input referred noise generators of the

first stage of the nullor implementation.

to the infinite gain of the nullor. Using the v-shift transform [17], the voltage

noise generator ven is moved into the two connected branches. In step 2, the

voltage noise generators are transformed into their equivalent current noise

generators and, using the i-shift transform, the generator ven+vnfRf

is moved

to the input and the output branches (figure 4.6b).

Adding the current noise generator at the input node we obtain the total

input referred noise current:

in = ien +venZS

+ven + vnf

Rf

in = ien + ven

(1

ZS+

1

Rf

)+vnfRf

(4.14)


The noise generators ven and ien are the input referred equivalent noise

generators of the common emitter BJT that implements the first stage of

the nullor. The mean square spectral noise density is given by

〈v2en〉4f

= 4kTrb︸︷︷︸thermal noise

+ 2qIC︸︷︷︸shot noise

(1

g2m+

rbβ2F1

)

≈ 4kTrb +2qICg2m

(4.15)

〈i2en〉4f

= 2qIb︸︷︷︸shot noise

+2qICβ2F1︸︷︷︸

shot noise

≈ 2qIb (4.16)

Plugging equations 4.15 and 4.16 into equation 4.14, we obtain

〈i2n〉4f

= 2qIb +

(4kTrb +

2qICg2m

)·(

2πfCS +1

Rf

)2

+4kTRfR2f

= 2qICβF1

+

(4kTrb +

2qICg2m

)·(

2πfCS +1

Rf

)2

+4kT

Rf(4.17)

Note that ZS = 12πfCS

in equation 4.17, where CS is the capacitance of

the GAPD.

Three types of noise optimizations can be applied:

• Noise matching: the noise figure of a two-port amplifier can be opti-

mized by modifying the source impedance (admittance) presented to

the transistor [13, chap. 11]. This technique is used in the design of

microwave transistor amplifiers.

• Optimization of the bias current of the first stage: equation 4.17 shows

that the only parameter under control is the collector current IC . We

can bias the first stage with the IC that minimises in.

• Connecting several input stages in series/parallel: when n identical

stages are placed in series, the voltage noise increases by factor√n,

while the current noise decreases by a factor√n [17, chap. 4.7.3].


We will minimise the noise by choosing a collector current that yields

a current noise low enough to meet the specifications. In figure 4.7a, the

integrated noise current in =

√(∫B〈i2n〉4f df

)over the frequency band 100

KHz - 750 MHz is plotted as a function of IC with Rf = 300. The plot

has been generated for different values of the photodetector’s capacitance

CS . The transistor parameter βF1 is obtained with a SPICE simulation and

the base bulk resistance rb is specified in the SPICE model of the BFP420

transistor. From this plot, we choose a bias collector current IC = 2 mA.

Figure 4.7b shows the noise current density as a function of frequency for

different values of CS and IC = 2 mA. This figure shows the strong influence

of the photodetector’s capacitance in the noise performance of the amplifier.

Table 4.2 shows the total integrated noise current and the SNR consid-

ering the current peak corresponding to 1 phe ipeak = 7µA (see chapter

2.3).

Table 4.2: Estimated total noise current integrated in the band 100 Khz -

750 MHz and SNR for different photodetector capacitances.

CS in SNR

1 pF 0.232µA 30

35 pF 1.35µA 5

320 pF 11.9µA 0.6

4.5.5 Design of the last stage: distortion

We distinguish two types of distortion, weak distortion and clipping distor-

tion.

Weak distortion arises from the linear approximation of the non-linear

behaviour of the transistors in the amplifier. Clipping distortion results from

the limited range in which the transistors operate in the linear region of the

characteristics and enters the saturation and cutoff regions.

To be able to prevent clipping distortion, we must know the maximum

expected output signal for the device and use a bias point that is far from


10-14

10-12

10-10

10-8

10-6

10-4

10-2

100

10-12

10-10

10-8

10-6

10-4

10-2

100

Input noise current (A2)

Ic (A)

1 pF35 pF

320 pF

(a) Current noise vs IC for various values of CS and Rf = 300 Ω

10-23

10-22

10-21

10-20

10-19

10-18

105

106

107

108

109

Input noise current density (A2 / Hz)

f (Hz)

1 pF35 pF

320 pF

(b) Current noise density 〈i2n〉4f vs frequency for various values of CS

and Rf = 300 Ω, IC = 2 mA.

Figure 4.7: Influence of photodetector’s capacitance on noise current.

saturation and cutoff. These values have been calculated in chapter 2.3.

When designing for clipping distortion, a trade between power consump-

tion and dynamic range must be made. For sure, the most demanding re-

quirement for the preamplifier is the huge dynamic range of 3000 phe along


with low power consumption. It is clear that a non-linear dynamic range

compression or the bi-gain scheme with differential inputs and outpus used

in the design of PACTA (see section 2.4) are necessary to achieve the re-

quired dynamic range. Unfortunately, this is out the scope of this thesis, so

we will relax this requirement for our prototype. We must not forget that

the objective of this thesis is to analyse the benefits of using transimpedance

preamplification instead of an MMIC or voltage preamplification.

The relaxed dynamic range is 1 to 200 phe. This implies a maximum

voltage at the output of the amplifier of about 0.42 V. Considering a 50 Ω

load, the peak output current will be 8.4 mA. As a matter of fact, the high

gain stage of the PACTA amplifier has a dynamic range ∼ 200 phe [12]. The

design of a better output stage is left for future work.

The last stage of the amplifier is the most prone to clipping distortion.

The bias point must be considerably larger than the maximum currents

and voltages it will handle. We will employ a common collector stage. It

doesn’t invert the signal, so only the common emitter stage is inverting. It

provides voltage gain, needed for the loop gain. The loop phase is 180o,

which is needed for negative feedback. The low output impedance of the

common collector configuration makes it suitable for the implementation of

the norator as a voltage source, the recommended for shunt-shunt feedback.

The chosen bias point for the last stage is VCE = 3 V and Ic = 20 mA.

4.5.6 Bandwidth and stability

The transfer function of any linear electronic system can be expressed as a

ratio of complex polynomials:

a(s) =N(s)

D(s)=a0 + a1s+ a2s

2 · · · amsm

b0 + b1s+ b2s2 · · · bnsn(4.18)

where the order m of the numerator is the number of zeros in the system

and the order n of the denominator is the number of poles in the system.

We can factorise polynomials in the numerator and denominator of the

transfer function 4.18 to make the poles and zeros explicit:


a(s) = a0

(1− s

z1

) (1− s

z2

)· · ·(1− s

zm

)(1− s

p1

) (1− s

p2

)· · ·(1− s

pn

) (4.19)

where ao is the gain at s = 0 (low frequency), zi is the i-th zero and piis the i-th pole.

It can be shown that the -3 dB frequency response of the amplifier is

largely limited by the dominant pole, i.e. the lowest frequency pole, if it

exists. For the dominant pole |p1| << |p2|, |p3|, · · ·, so we can approximate

the gain magnitude in the frequency domain as

|a(jω)| ≈ a0√1 +

(ωp1

) (4.20)

This is the dominant pole approximation and is accurate as long as the

first order pole is really dominant and there are no zeros near the dominant

pole so their influence can be neglected.

From control theory we know that feedback enhances the frequency re-

sponse of the open loop system. Recalling the closed-loop transfer function

in equation 4.4,

A(s) =

a01+ s

p1

1 + a0sp1

f=

a0(1 + aof) + s

p1

=

ao1+aof

1 + s(1+aof)p1

(4.21)

Equation 4.21 shows that the effect of feedback is a shift of the pole to

higher frequencies by a factor 1+aof and a gain reduction of the same factor.

Up to this point, our nullor implementation has a common-emitter input

stage and a common-collector output stage. It is interesting to estimate the

bandwidth performance of the amplifier. To do this, the dominant pole and

the loop gain must be calculated. A direct calculation using the small signal

model of the amplifier is tedious and prone to errors, so only the loop gain

will be computed.

The RR (Return Ratio) is a good approximation of the loop gain [4]. The

total gain around the feedback loop is obtained by breaking the loop at some


convenient point and inserting a test signal. Figure 4.8 shows the circuit used

to calculate the return ratio of the amplifier. The dependent current source

gm1v1 is replaced by the test signal ix. To gain insight on the factors that

determine the bandwidth its enough to obtain the low frequency loop gain,

so the capacitances have been removed from the models. The return ratio is

L(0) =gm1v1ix

= − βF1βF2RLRC1

βF2RL(rπ1 +Rf ) + (rπ1 +Rf +RL)(RC1 + rπ2)(4.22)

B1 C1

E1

rπ1 RC1 rπ2 gm2v2

+

-

v1

+v2

-

Rf

RL

B2

E2

C2

ix

Figure 4.8: Small signal model with test signal ix used to calculate the low

frequency return-ratio of the amplifier.

The load resistance RC1 at the collector of Q1 is needed to bias the

collector current IC1, but it degrades the loop gain, so it must be maximised.

For narrowband amplifiers, a small RFC inductance is used to present infinite

impedance and remove any influence of the bias circuit in the small signal

parameters. For very broadband amplifiers, these RFC need to be quite

big and their parasitics introduce unpredictable effects which are difficult to

address. We have decided not to use an inductor and try to use a big value

for RC1.

If RC1 →∞, the return ratio is given by

L(0) = − βF1βF2RLrπ1 +Rf +RL

(4.23)


The feedback resistance Rf is in the denominator of equation 4.23. This

means that we trade transimpedance gain for loop gain. If Rf is increased

(less feedback), there is a decrease of the loop gain which implies a decrease

of the bandwidth but also the nullor implementation moves away from the

ideal so the amplifier’s performance is lower. On the other hand, a decrease

of Rf (more feedback) will increase the loop gain and the amplifier may

oscillate.

The loop gain is a measure of the maximum bandwidth capacity of the

amplifier. The exact bandwidth will depend on the position of the poles.

There are two ways of improving the loop gain:

1. Adding more stages. Each additional stage adds a βF factor to the

numerator of 4.23, thus improving the loop gain. These stages are

placed in the middle of the chain. Remember that the first and last

stages are used for noise and distortion optimization. Care must be

taken to ensure that the stages provide a 180o phase shift to guarantee

negative feedback.

2. At high frequencies βF (jω) ≈ gmjω(Cπ+Cµ)

= ωTjω , where ωT is the transi-

tion angular frequency. ωT depends on IC , so we can tune the bias of

the stages we have already added, taking care not to compromise the

noise or distortion.

Option 2 is going to be used to improve the bandwidth of the amplifier.

From figure 4.7a, the collector current of the first stage can be increased to

10 mA without compromising its noise behaviour.

The stability of the amplifier will depend on Rf , the feedback factor and

the impedance of the photodetector. For small values of Rf , the loop gain

increases and the amplifier has significant ringing. To reduce this ringing for

low Rf < 400 Ω, the following solutions can be adopted:

1. Add a small series resistor at the input of the amplifier. This resistor

reduces the ringing but the increase of input impedance has a negative

impact on the bandwidth.

2. Add a small capacitor in parallel with Rf to the feedback network. This

compensation capacitance introduces a zero in the feedback network


RLQ1 Q2

stage1 stage2

Rf

Figure 4.9: Final configuration of the amplifier in two CE-CC stages.

1f =

1+RfCf sRf

. This technique is called phantom-zero compensation

[17, chap. 7.4.1]. The zero is only visible in the feedback transfer, not

in the closed-loop transfer function. The closed-loop transfer function

will see a new pole at s = − 1RfCf

, so it is important to keep Cf small.

The effect of the zero in the feedback network is to reduce the amount

of feedback at high frequencies.

The bandwidth and stability of the amplifier will be checked with a com-

puter simulation. Figure 4.9 shows the final arrangement of the two stages

of the amplifier.

4.5.7 Bias circuit and output matching

There is a wide catalogue of biasing circuits, ranging from simple resistor

networks to sophisticated active bias circuits which provide very stable bias

currents.

Current mirrors are widely used for bias and active loading in integrated

amplifiers. For the prototype designed here, a much more simpler resistor

scheme will be used.

The transistor stages will be DC coupled. This avoids the use of an inter-

stage coupling capacitor, but makes the biasing a little bit more complicated.

A resistor network is used to set the correct bias currents and voltages of the

transistors. Figure 4.10 shows the biasing circuit of prototype 1. All capaci-

tors have a capacitance of 100 nF. They provide a low impedance path in the

frequencies of operation. The input, output and feedback capacitors are only


used for AC coupling. To match the output impedance to 50 Ω, a match-

ing resistor Rmatch = 50 Ω has been included at the output. It is assumed

that RL = 50 Ω. The matching resistor halves the effective transimpedance

gain, due to voltage division. The design of a more efficient output matching

scheme is left for future work.

An improvement of the bias circuit results in prototype 2 (figure 4.11).

RL

Q1 Q2

Rf

RB1

VCC

RC1

RE2

Rmatch

RC1RC1

RC2

Figure 4.10: Prototype 1 with bias network, coupling capacitors, and output

matching resistor.

4.5.8 Prototype 1

The first designed prototype is going to be used with transimpedance gains

Rf = 300 Ω and Rf = 1500 Ω. This prototype includes a small 7 Ω series re-

sistor at the input to reduce the ringing, specially for small capacitive source

impedances. The simulations of the scattering parameters have predicted

that the amplifier is not unconditionally stable for f > 1 GHz. Since the

source impedance ZS of the photodetector is quite complex, it is convenient

to make the prototype unconditionally stable. This has been accomplished

by introducing a 30 Ω resistor between the output and ground.

The bias network design is straightforward. For IC1 = 10 mA, IC1 = 20


RL

Q1 Q2

Rf

RB1

VCC

RC1

RE2

Rmatch

Figure 4.11: Prototype 2 with bias network, coupling capacitors and output

matching resistor.

mA and VCE2 = 2 V, the calculation of the bias resistors follows:

Rc2 +RE2 =VCC − VCE2

IC2= 150 Ω (4.24)

We choose RC2 = 100 Ω and RE2 = 50 Ω.

VB2 = VC1 = VCE1 = VE2 + VBE2 ≈ 1V + 0.8V = 1.8V (4.25)

RC1 =VCC − VC1

IC1= 320 Ω (4.26)

The simulations and experimental measurements have confirmed that

the dynamic range of this prototype is very limited and does not meet the

CTA requirements. Additionally, the input impedance is too high. For this

reasons, a new prototype with improved biasing has been designed.

4.5.9 Prototype 2

The second prototype addresses the flaws of the first prototype. The weak

point of prototype 1 is the limited dynamic range, of about 47 dB for a

4.6. Simulations 65

transimpedance of 300. For Rf = 1500 Ω, the dynamic range gets even

worse, as expected.

The weak point for dynamic range was identified as the bias resistor at

the collector of Q2, RC2. This resistor limits severely the voltage swing at

the output of the amplifier. For this reason, it has been removed from the

bias network.

Another weak point of the first design is the input impedance. The small

signal parameters and the series 7 Ω resistor for ringing reduction causes

the input impedance not to be low enough. Thus, the input series resistor is

reduced to 3 Ω and the loop gain is increased by reducing the bias current

IC1 to 5 mA and IC2 to 10 mA, without increasing the noise. This results

in a bias resistor RC1 = 600 Ω, which reduces the gain loss and the power

consumption.

The bias network is calculated as before. For IC2 = 10 mA, VCE2 = 4 V,

the bias resistor at the emitter of Q2 must be RE2 = 100 Ω. For IC2 = 5 mA,

the bias resistor at the collector of Q1 is RC1 = 600 Ω. The collector-emitter

voltage is forced to VCE1 = VE2+VBEon ≈ 1.85 V, and we are neglecting the

base current of Q2. The resistor for setting the base current of Q1, taking

the typical βF = 90 from the datasheet [7], is RB1 = 21.6K Ω.

4.6 Simulations

In this section, we present the simulations done with ngspice and QUCS,

and discuss the obtained results. The following simulations have been done:

• DC simulation and small signal parameter calculation.

• AC simulation.

• Scattering parameter simulation.

• Stability circles and µ-factor simulations.

• Noise simulation.

The SPICE model of the BFP420 transistor by Infineon has been used.

This model includes all the SOT-343 package parasitics and it claims to be

4.6. Simulations 66

valid up to 6 GHz. Refer to 8.4 for the SPICE model.

4.6.1 Prototype 1

Figure 4.12 shows the schematic used for the SPICE simulations, which are

the DC and small signal simulations, and the noise simulation. It includes

the parasitics of the capacitors implemented as subcircuits for the sake of

clarity.

FILE: REVISION:

DRAWN BY: PAGE OF

TITLE

SPICE directiveA2

?*.AC DEC 100 100kHz 1.5Giga

SPICE directiveA3

?*.TRAN 10.00p 10.00n 0.00n

SPICE directiveA4

?*.OP

Is

AC 1A

Cs

35pF

Rsh

10knoisy=0

1

+

2

-

VccDC 5V

RC

1

316

XCd1

0805_PARASITICS_CAP_100nF

RB

1

10k

RC

2100

RL

50

noisy=0

RE

2

50

SPICE model

Model name:File:

A1

M_BFP420/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/transistors/BFP420_spar10GHz_noisepar6GHz_spice10GHz/BFP420_SPICE.cir

Prototype 1: Two stage CE-CC transimpedance amplifier with parasitics


Rf

300

SPICE model

Model name:File:

A5

0805_PARASITICS_CAP/home/nacho/ingenieria_electronica/proyecto/characterizations/passive_elements/capacitors/parasitic_spice_models/0805_capacitor.cir

XCd2


XCd3


XC

b2

0805_P

AR

AS

ITIC

S_C

AP

_100nF

XC

b3

0805_P

AR

AS

ITIC

S_C

AP

_1uF

3

1

2

SPICE-NPNXQ1

BFP420

3

1

2

SPICE-NPNXQ2

BFP420

Rmatch

50

SPICE directiveA6

?.NOISE V(out) Is DEC 100 100kHz 750Meg

Rcomp

7

Rsta

b

30

Figure 4.12: Prototype 1 with parasitics for SPICE simulations.

With the .OP SPICE directive, the small signal parameters have been

obtained with ngspice and are shown in table 4.3.

With the .NOISE SPICE directive, the noise currents and voltages have

been obtained and are shown in table 4.4. The noise currents obtained here

with the simulation are very close to those calculated in the noise analysis

of section 4.5.4.

The transimpedance gain has been simulated with QUCS (figure 4.13)

for different photodetector capacitance. It is interesting to show how this

capacitance limits the frequency response of the preamplifier in figure 4.14.

This effect is the result of the pole introduced by the input impedance of the

4.6. Simulations 67

Table 4.3: Small signal parameters obtained with ngspice.

Parameter Q1 Q2

ic 0.00962582 0.0192799

ib 9.94762e−05 0.000204747

ie −0.00972529 −0.0194847

vbe 0.865451 0.883853

vbc −0.92826 −1.07667

gm 0.36289 0.714074

gpi 0.0039011 0.00803366

gmu 1e−12 1e−12

gx 0.183105 0.186919

go 0.000364441 0.000737624

cpi 2.39952e−12 4.03333e−12

cmu 1.19316e−13 1.14508e−13

cbx 3.97995e−14 3.82009e−14

csub 1.95316e−13 1.59148e−13

Table 4.4: Prototype 1 total current and voltage noise integrated in the

band 100 Khz - 750 MHz simulated with ngspice for different photodetector

capacitance.

CS in vn

1 pF 0.324µA 25.2µV

35 pF 1.36µA 80.6µV

320 pF 12.26µA 87.6µV

amplifier and the photodetector capacitance, which is dominant. The low

input impedance of the transimpedance amplifier limits this effect to a great

extend.

The scattering parameters of prototype 1 have been simulated with QUCS.

Figure 4.15 shows the schematic used for the simulations. In figure 4.16, the

4.6. Simulations 68

Cd2C=100 nF

Lcd2L=58.4 pH

Rcd2R=0.565 Ohm

RmatchR=50 Ohm

Rcomp1R=7 Ohm

RB1R=10k Ohm

RE2R=50 Ohm

Rcd3R=0.565 Ohm

Lcd3L=58.4 pH

Cd3C=100 nF

RfR=300

RLR=50 Ohm

R3R=30 Ohm

RC1R=316 Ohm

RC2R=100 Ohm

Cb3C=100 nF

Cb2C=1 uF

V1U=5 V

spice

12

3

Ref

XQ1

spice

12

3

Ref

XQ2

Inputcurrent

Rcd1R=0.565 Ohm

Lcd1L=58.4 pH

Cd1C=100 nF

I1I1=0I2=1 uAT1=6 nsT2=11 ns

I2I=1 A

CsC=Cs

RshR=100 kOhm

dc simulation

DC1

transientsimulation

TR1Type=linStart=0Stop=20 ns

Parametersweep

SW1Sim=AC1Type=listParam=CsValues=[1 fF; 35 pF; 320 pF]

ac simulation

AC1Type=logStart=10 kHzStop=3 GHzPoints=1000

Parametersweep

SW2Sim=AC1Type=listParam=CfValues=[0.1 pF; 0.2 pF; 0.3 pF; 0.4 pF; 0.5pF]

Equation

Eqn2transZ=dB(vout.v)

vout

Figure 4.13: Protototype 1 schematic with parasitics for AC and transtient

simulations with QUCS.

simulated parameters S11 and S22 are plotted. These plots show the low in-

put impedance and matched output impedance of the prototype. With the

higher feedback resistor Rf , the amplifier presents a higher input impedance.

Figure 4.17 show the simulated S21.

Figure 4.18 shows the noise parameters (µ and µ′ noise factors) and the

stability circles for source and load impedances. The simulations predict

unconditional stability in the simulated frequency band.

Finally, the simulated power consumption is 150 mW, which is accept-

able.

4.6.2 Prototype 2

Figure 4.19 shows the schematic used for the SPICE simulations. The small

signal parameters of the transistors are shown in table 4.5.

As before, the noise currents and voltages have been obtained and are

shown in table 4.6. There is a improvement in in with respect to prototype1,

but vn gets worse.

Figure 4.20 shows the schematic used for the simulations of the scattering

parameters. In figure 4.21, the simulated parameters S11 and S22 are plotted.

The input impedance of this prototype is lower than prototype 1. The S21

4.6. Simulations 69

1e4 1e5 1e6 1e7 1e8 1e9 3e9-20

-10

0

10

20

30

40

50

frequency (Hz)

Cs=0:transimpedance

Cs=5pF:transimpedance



(a) Rf = 300 Ω.

1e4 1e5 1e6 1e7 1e8 1e9 3e9-20

-15

-10

-5

0

5

10

15

20

25

30

35

40

45

50

55

60

frequency (Hz)





(b) Rf = 1.5KΩ

Figure 4.14: Influence of photodetector capacitance on the transimpedance

bandwidth of prototype 1. CS = 0 pF, 35 pF and 320 pF. Transimpedance

gain is plotted in dB.

parameter is shown in figure 4.22.

The transimpedance gain for different photodetector capacitance is shown

in figure 4.23

Finally, figure 4.24 shows the noise parameters (µ and µ′ noise factors)

and the stability circles for source and load impedances. The simulations pre-

4.6. Simulations 70

Lcd3L=58.4 pH

Rcd3R=0.565 Ohm

Cd3C=100 nF CL1

Subst=Subst1W=2.55 mmS=1.121 mmL=2.4 mm

CL5Subst=Subst1W=2.55 mmS=1.121 mmL=3.56 mm




CL12Subst=Subst1W=0.75 mmS=1.121 mmL=6 mm






Rcd1R=0.565 Ohm

Lcd1L=58.4 pH

Cd4C=100 nF



P1Num=2Z=50 Ohm

Rmatch1R=50 Ohm






Rcd2R=0.565 Ohm

Cd1C=100 nF

Lcd2L=58.4 pH

RC2R=100 Ohm

RB1R=10k Ohm

RC1R=316 Ohm

RE1R=50 Ohm

Cb2C=1 uF

Cb1C=100 nF

V1U=5 V

Pr1

P2Num=1Z=50 Ohm

Rcomp1R=7 Ohm

spice

12

3

Ref

XQ1

spice

12

3

Ref

XQ2

Rf1R=300 Ohm

RstabR=30 Ohm


Equation

Eqn1S21dB=dB(S[2,1])S11dB=dB(S[1,1])S22dB=dB(S[2,2])mufactor=Mu(S)mufactorprime=Mu2(S)stabL=StabCircleL(S)stabS=StabCircleS(S)

dc simulation

DC1


SP1Type=logStart=10 kHzStop=2 GHzPoints=100

number

1

Pr1.I

0.0292

Figure 4.15: Protototype 1 schematic with parasitics and coplanar lines for

S-parameter simulations with QUCS.

1e4 1e5 1e6 1e7 1e8 1e9 3e9-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

frequency (Hz)

Rf=

1500:S

11dB

Rf=

1500:S

22dB

Rf=

300:S

11dB

Rf=

300:S

22dB

Rf=

1500:S

[1,1

]R

f=1500:S

[2,2

]R

f=300:S

[1,1

]R

f=300:S

[2,2

]



dict unconditional stability in the simulated frequency band. The predicted

power consumption is lowered to 78 mW.

4.6. Simulations 71

1e4 1e5 1e6 1e7 1e8 1e9 3e9-15

-10

-5

0

5

10

15

20

25

frequency (Hz)

Rf=1500:S21dB

Rf=300:S21dB

frequency: 3.35e+08Rf=1500:S21dB: 20.9frequency: 3.35e+08Rf=1500:S21dB: 20.9

frequency: 1.86e+09Rf=300:S21dB: 10.2frequency: 1.86e+09Rf=300:S21dB: 10.2

Figure 4.17: Simulated S21 of prototype 1.

1e4 1e5 1e6 1e7 1e8 1e9 3e9

0

10

20

30

frequency (Hz)

mufactor

mufactorprime

1.5

stabS

Figure 4.18: Simulated noise parameters of prototype 1.

4.6. Simulations 72

FILE: REVISION:

DRAWN BY: PAGE OF

TITLE

SPICE directiveA2

?*.AC DEC 100 100kHz 1.5Giga

SPICE directiveA3

?*.TRAN 10.00p 10.00n 0.00n

SPICE directiveA4

?*.OP

Is

AC 1A

Cs

35pF

Rsh

10knoisy=0

1

+

2

-

VccDC 5V

RC

1

600

XCd1


RB

1

21.6k

RL

50

noisy=0

RE

2

100

SPICE model

Model name:File:

A1

M_BFP420/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/transistors/BFP420_spar10GHz_noisepar6GHz_spice10GHz/BFP420_SPICE.cir

Prototype 2: Improved dynamic range


Rf

1000

SPICE model

Model name:File:

A5

0805_PARASITICS_CAP/home/nacho/ingenieria_electronica/proyecto/characterizations/passive_elements/capacitors/parasitic_spice_models/0805_capacitor.cir

XCd2


XCd3


XC

b2

0805_P

AR

AS

ITIC

S_C

AP

_100nF

XC

b3

0805_P

AR

AS

ITIC

S_C

AP

_1uF

3

1

2

SPICE-NPNXQ1

BFP420

3

1

2

SPICE-NPNXQ2

BFP420

Rmatch

50

SPICE directiveA6

?.NOISE V(out) Is DEC 100 100kHz 550Meg

Rcomp

3

out

Figure 4.19: Prototype 2 with parasitics for SPICE simulations.





Rcd1R=0.565 Ohm

Lcd1L=58.4 pH

Cd4C=100 nF




Rcd2R=0.565 Ohm

Cd1C=100 nF

Lcd2L=58.4 pH

V1U=5 V

Pr1


Equation

Eqn1S21dB=dB(S[2,1])S11dB=dB(S[1,1])S22dB=dB(S[2,2])mufactor=Mu(S)mufactorprime=Mu2(S)stabL=StabCircleL(S)stabS=StabCircleS(S)

dc simulation

DC1


Cb2C=1 uF

Cb1C=100 nF

Lcd3L=58.4 pH

Rcd3R=0.565 Ohm

Cd3C=100 nFCL5

Subst=Subst1W=2.55 mmS=1.121 mmL=3.56 mm

P2Num=1Z=50 Ohm


RB1R=21.6k Ohm

RC1R=600 Ohm


Rcomp1R=3 Ohm

RE1R=100





spice

12

3

Ref

XQ2

spice

12

3

Ref

XQ1


SP1Type=logStart=10 kHzStop=2 GHzPoints=200

Rf1R=1000 Ohm

CL3Subst=Subst1W=2.55 mmS=1.121 mmL=3.2 mm Rmatch1

R=50 Ohm


P1Num=2Z=50 Ohm

number

1

Pr1.I

0.0156

Figure 4.20: Protototype 2 schematic with parasitics and coplanar lines for

S-parameter simulations with QUCS.

4.6. Simulations 73

Table 4.5: Prototype 2 small signal parameters obtained with ngspice.

Parameter Q1 Q2

ic 0.00496827 0.0105059

ib 4.9988e−05 0.000100725

ie −0.00501826 −0.0106067

vbe 0.847898 0.865769

vbc −1.04541 −2.99878

gm 0.189038 0.396676

gpi 0.00195901 0.0039501

gmu 1e−12 1e−12

gx 0.179356 0.173283

go 0.000184466 0.000368943

cpi 1.60993e−12 2.55075e−12

cmu 1.1547e−13 8.10914e−14

cbx 3.85136e−14 2.70469e−14

csub 1.91295e−13 1.24743e−13

Table 4.6: Prototype 2 total current and voltage noise integrated in the

band 100 Khz - 550 MHz simulated with ngspice for different photodetector

capacitance.

CS in vn

1 pF 0.149µA 63.5µV

35 pF 0.767µA 219µV

320 pF 6.86µA 280µV

4.6. Simulations 74

1e4 1e5 1e6 1e7 1e8 1e9 3e9

-35

-30

-25

-20

-15

-10

-5

0

frequency (Hz)

S11dB

S22dB

frequency: 7.53e+06S11dB: -5.31frequency: 7.53e+06S11dB: -5.31

frequency (Hz)

S[1

,1]

S[2

,2]



1e4 1e5 1e6 1e7 1e8 1e9 3e98

10

12

14

16

18

20

22

24

frequency (Hz)

S21dB



Figure 4.22: Simulated S21 of prototype 2.

4.6. Simulations 75

1e4 1e5 1e6 1e7 1e8 1e9 3e9

-10

-5

0

5

10

15

20

25

30

35

40

45

50

55

60

frequency (Hz)

Transimpedance gain (dB)

acfrequency: 6.85e+08Cs=0pF:transZ: 50.2acfrequency: 6.85e+08Cs=0pF:transZ: 50.2




Figure 4.23: Influence of photodetector capacitance on the transimpedance

bandwidth of prototype 2. CS = 0 pF, 5 pF, 35 pF and 320 pF. Tran-

simpedance gain is plotted in dB.

1e4 1e5 1e6 1e7 1e8 1e93e90

5

10

15

20

frequency (Hz)

mufactor

mufactorprime

1.5

stabS

stabL

Figure 4.24: Simulated noise parameters of prototype 2.

Chapter 5

Implementation of the

Prototypes

Summary: This chapter deals with the implementation details of

the prototypes designed in chapter 3 and chapter 4. The technology

used for the PCBs will be introduced and the created boards will be

shown.

5.1 Printed circuit board technology overview

The prototypes have been implemented in two layer PCB technology. The

fiberglass substrate is compliant with the FR4 standard. The relevant sub-

strate parameters are summarised in table 5.1.

Table 5.1: Parameters of the FR4 substrate. εr is the dielectric constant, τ

is the metal thickness and h is the dielectric thickness.

εr 4.6

τ 37µm

h 1.57mm

Grounded coplanar transmission lines (figure 5.1) with a characteristic

76

5.1. Printed circuit board technology overview 77

impedance of 50 Ω have been used for the input and output traces. The

bias traces have been kept narrow to increase its impedance. Coplanar lines

have some advantages over traditional microstrip lines, such as: increased

electromagnetic field confinement, thus lowering radiation losses and it makes

the connection to ground easier since the ground and the signal traces are

on the same board plane. The top and bottom ground planes are connected

using vias. There should be enough grounded vias along the path of the

signal traces. This way, the field confinement is improved and resonance

effects are reduced [2, chap. 3.1]. All the traces should be kept as short as

possible in order to prevent distributed effects.

The dimensions of the traces for 50 Ω operation have been calculated

with the transmission line calculator included with QUCS. The dimensions

in millimetres are W = 1.5 mm, S = 0.3 mm (see figure 5.1).

Figure 5.1: Coplanar transmission line, image courtesy of http://wcalc.

sourceforge.net/coplanar.html.

Only SMT components have been used, because they offer better per-

formance than through-hole components at frequencies above 100 MHz [15,

chap. 13.2]. The size of the SMT package is 0805 for resistors and capaci-

tors, which has lower parasitics than the bigger packages such as 1206 but

are easier to manipulate and hand solder than the smaller packages such as

0402.

All the boards have been designed using PCB, the printed circuit board

editor of gEDA.



5.2. MMIC prototypes 78

5.2 MMIC prototypes

As we saw in section 3, the simulations of the S parameters of prototype 1

showed an unwanted resonance peak. This issue was solved with the design

of prototype 2. In this section, only the implementation of prototype 2 will

be addressed.

Figure 5.2 shows the layout of prototype 2. In this figure, we can appreci-

ate the vias connecting the top and bottom ground planes running along the

50 Ω coplanar lines. The biasing trace has been made very narrow compared

to the input and output traces to increase its impedance and improve the

gain of the prototype.

The package of the MMIC is SOT-343 and all the SMT components

used are 0805, except the inductor, which is packaged in 1206. The RF

connectors used are male SMA (SubMiniature version A) coaxial connectors

with an impedance of 50 Ω. The power connector is a vertical male SMA.

The size of the board is 30 mm × 40 mm.

5.3 Transimpedance prototypes

For the implementation of the transimpedance amplifier prototypes, special

care has been taken to keep the traces as short as possible. To avoid unex-

pected effects, the longitude of the traces in the pcb agrees with the longitude

in the simulations (figures 5.3 and 5.4).

The package of the BFP420 transistor is SOT-343 and all the SMT com-

ponents used are 0805. The RF connectors used are male SMA coaxial

connectors with an impedance of 50 Ω. The power connector is a vertical

male SMA. The size of the board is 42mm × 40 mm.

5.4 GAPD biasing circuits

The GAPD is operated in Geiger mode. To achieve this mode of operation, a

reverse bias higher than the breakdown voltage must be applied. The biasing

circuits consist of a voltage source and a current limiting resistor.

In this thesis, we have implemented two biasing circuits. The voltage

5.4. GAPD biasing circuits 79

(a) PCB layer mode (b) PCB photo mode.

(c) Final board.

Figure 5.2: The BGA614 prototype 2 layout. The size of the board is 30

mm × 40 mm.

output bias circuit (figures 5.5a and 5.5b), in which the current is converted

into a voltage using a resistor. This topology is suggested in the datasheet

[5]. When the resistor value is 50 Ω, it is also used for impedance matching

when the GAPD is connected to a 50 Ω MMIC, so we will connect this circuit

to the input of the BGA614 prototype.



(c) Final board.

Figure 5.3: The transimpedance prototype 1 layout. The size of the board

is 45mm × 40 mm.

The current mode output bias circuit, shown in figures 5.5c and 5.5d,

is designed to be connected to the transimpedance prototype. The out-

put current from the GAPD flows through the low input impedance of the

transimpedance amplifier. We will also connect this circuit to the input of

the MMIC. The current will be converted into a voltage at the input 50 Ω

impedance.



Figure 5.4: The transimpedance prototype 2 layout. The size of the board

is 42mm × 40 mm.

RBIAS

= 10K

VCC

50

vout

1uF

(a) Voltage output mode. (b) Voltage output board.

RBIAS

= 10K

VCC

iout

(c) Current

output mode.

(d) Current output board.

Figure 5.5: GAPD bias circuits.

Chapter 6

Measurements and Tests

Summary: This chapter describes the setups used to test and mea-

sure the implemented prototypes. A review of the instrumentation

available in the laboratory is done.

6.1 Instrumentation

The Laboratorio de Microondas of the Departamento de Fisica Aplicada III:

Electricidad y Electronica in the Universidad Complutense de Madrid, where

this thesis has been developed, is dedicated to the research in high frequency

electronics. It has modern measure instruments needed for microwave and

high frequency electronics characterisation. Among the most relevant, there

are two network analysers, a very high frequency oscilloscope, a calibrated

noise source, a spectrum analyser, signal generators and very stable pro-

grammable power supplies.

The network analysers available are the HP8720C (figure 6.1) and the

Agilent Fieldfox RF analyser N9912A. These instruments measure the scat-

tering parameters of two-port active or passive devices. The HP8720C is

completely vectorial, so it measures scattering parameters in complex form,

with both magnitude and phase information. It has a measurement band-

width between 50 MHz and 20 GHz. The Agilent Fieldfox N9912A is a

portable network analyser for field applications. It only provides phase in-

82

6.1. Instrumentation 83

formation for S11 and S22. It can measure from 2 MHz to 6 GHz. The cali-

bration of both analysers is done with the HP85020D 3.5 mm SOLT (Short

Open Load Thru) calibration kit.

Figure 6.1: HP87020C network analyser with HP85020D 3.5 mm calibration

kit.

The Agilent Infinium DSO81204B (figure 6.2) is a state-of-the-art 4 50

Ω channel digital sampling oscilloscope capable of sampling an analog sig-

nal at a maximum sampling frequency of 40 GSa/s. The maximum analog

bandwidth is 12 GHz. We will use this instrument for time domain measure-

ments.

Figure 6.2: Agilent Infinium DSO81204B oscilloscope.

The Agilent E4402B spectrum analyser is capable of measuring the fre-

6.2. Test setups 84

quency spectrum signal. It can also measure the noise figure with the cali-

brated noise source Agilent 346A.

The signal generator is the Tektronix AFG3252, with a bandwidth of 200

MHz. It has two 50 Ω independent channels that can output pulses of 5 ns

with an amplitude of 50 mV.

The power supplies used are the Keithley 6487 and the Hameg HMP2030.

6.2 Test setups

One important property of testing and measuring is repeatability and repro-

ducibility. If this properties cannot be enforced, the measure will be useless.

Repeatability refers to the variability of the measurements obtained by

one person while measuring the same item repeatedly. In contrast, repro-

ducibility refers to the variability of the measurement system caused by dif-

ferences in operator behaviour.

In this section the measurement setups and procedures are described so

that these are repeatable and reproducible.

6.2.1 Measuring S-parameters

The measurement of the scattering parameters is performed with the two

available network analysers. The HP8720C is used to characterise the BGA614

prototype, while the N9912A is used to characterise the transimpedance pro-

totypes. For an unknown reason, the HP8720C analyser measured unaccu-

rately the s-parameters of the transimpedance prototypes. Table 6.1 contains

the settings that have been used for the measurements.

Before measuring, the network analyser must be calibrated to remove

the influence of the transmission lines connected to the ports of the network.

The calibration of both analysers is done with the HP85020D 3.5 mm SOLT

calibration kit. For the N9912A, the user must select this calibration kit

explicitly in the calibration menu.

The resulting measurements are saved in Touchstone file format (*.s1p

or *.s2p).

6.2. Test setups 85

Table 6.1: Measure settings for the network analysers. The rest of parameters

are left to its default value.

HP8720C N9912A

BW = 50 MHz - 1.5 GHz BW = 2 MHz - 1.5 GHz

Output power = -10 dBm Output power low

Averaging = 16 Averaging = 16

IF BW 3000 Hz IF BW 30.00 KHz

No. of points = 801 No. of points = 1001

6.2.2 Measuring the noise figure

We use the E4402B noise figure analyser and the noise source Agilent 346A

to measure the noise figure of the prototypes with the y-factor technique.

Table 6.2 contains the settings that have been used for the measurements

with the E4402B.

Table 6.2: Measure settings for the noise figure analyser. The rest of param-

eters are left to its default value.

BW = 10 MHz - 3 GHz

Averaging = 32

No. of points = 30

The first step is to connect the noise source power input to the 28 Vdc

source at the back of the analyser. The second step is to calibrate the noise

source. Finally, to perform the measurement, we connect the noise source

to the input of the DUT (Device Under Test) and the output of the DUT is

connected to the input of the noise analyser. The setup is shown in figure

6.3.

The analyser measures both the gain and the noise figure. The resulting

measurements are saved in csv file format.

6.2. Test setups 86

Figure 6.3: Noise measurement setup, image courtesy of Agilent.

6.2.3 Measurements with the GAPD

The GAPD used is the Hamamatsu S10362-33-050C [5]. The key parameters

of this device are an effective area of 3 × 3 mm, a terminal capacitance of

320 pF and a gain of 7.5 · 105.

The GAPD is biased with the circuits described in 5.4. The bias voltage is

set with the Keithley 6487 power supply. An ultraviolet LED (Light Emitting

Diode) (Optosource 260019) excites the GAPD through a fiber optic. The

LED is connected to one channel of the Tektronix AFG3252 signal generator,

which is programmed to output a train of square pulses with a FWHM (Full

Width at Half Maximum) of 5 to 10 ns to resemble the Cherenkov pulses. The

other channel of the signal generator is used to generate an identical pulse

train that will be used as the trigger signal for the DSO81204B oscilloscope.

The connection of the GAPD bias circuit to the amplifiers is done with

an SMA male to male connector, to keep the distance between the GAPD

and the amplifiers as short as possible. Figure 6.4 shows this connection

graphically.

The amplifiers are powered with the Hameg HMP2030 power supply. The

voltage supply is 5 V for all the prototypes. The connection of the output of

the amplifier to the DSO81204B oscilloscope is done with an SMA pigtail.

The setup is shown in 6.6.

To minimise the background light and any electromagnetic interference

6.2. Test setups 87

Figure 6.4: Connection of the GAPD to the transimpedance amplifier.

that may couple into the circuits, the set GAPD bias circuit + amplifier is

isolated inside a shielded black box [2] (figure 6.5).

(a) Outside. (b) Inside.

Figure 6.5: Shielded black box.

Figure 6.6: Setup for pulse shape and single photon counting measurements.

For single photon counting, the amplitude of the generated pulse from

6.2. Test setups 88

the signal generator is lowered until the condition of single photon is reached.

Under this condition, the light from the LED is so faint that very few photons

arrive to the GAPD. The output pulses from the GAPD will correspond to

single or very few photons. With the help of the oscilloscope, we will generate

an histogram of the amplitudes detected in a narrow strip of the time scale

where the pulse peaks are. As the GAPD pulse peak is proportional to the

number of detected photons, the histogram will ideally consist in a set of

equally separated peaks, each of them corresponding to the amplitude of

1, 2, 3, · · · , n, n+ 1 detected photons.

6.2.4 Measuring the dynamic range

To measure the dynamic range and linearity of the DUT, we connect the

input of the DUT to the Tektronix AFG3252 signal generator, which is

programmed to generate a train of square pulses of amplitude Vlow = 0V

and variable Vhigh and FWHM 5 ns. The lowest value of Vhigh is 50 mV.

Using the DSO81204B oscilloscope, the measurement procedure consists

in recording pairs (Vhigh, Voutpeakprototype) where Voutpeakprototype is the peak

of the output pulse of the prototype.

From the obtained points (Vhigh, Voutpeakprototype) we calculated the linear

fit and the 1-dB compression point. The residuals of the linear fit are a

measure of the DUT non-linearity.

It should be noted that working in pulsed mode, the linearity is better

than with continuous mode.

Chapter 7

Experimental results and

discussion

Summary: In this chapter, the experimental measurements and tests

on the implemented prototypes are presented and discussed.

7.1 S-parameters

The measurement of the scattering parameters has been done with the setup

described in 6.2.1. Figure 7.1 shows the measured s-parameters. The plots

contain both the simulated and measured parameters and show that the

simulations model quite accurately the prototypes.

7.2 Noise figure

The measurement of the noise figure has been done with the setup described

in 6.2.2. The measured noise figure is shown in figure 7.2. This figure

shows the excellent noise performance of the BGA614 prototype and the

transimpedance prototype 1 with Rf = 1500 Ω. In particular, the noise

figure of prototype 1 with Rf = 1500 Ω is between 1.39 dB and 2.23 dB for

frequencies below 1 GHz. The improvement of the noise figure compared to

Rf = 300 Ω is because of the reduction of the equivalent input noise current.

89

7.2. Noise figure 90

1e5 1e6 1e7 1e8 1e9 3e9

-20

-18

-16

-14

-12

-10

-8

frequency (Hz)

S11dB

S22dB

simulation:S11dB

simulation:S22dB

1e5 1e6 1e7 1e8 1e9 3e913

14

15

16

17

18

19

20

frequency (Hz)

S21dB

simulation:S21dB

(a) BGA614 prototype 2.

1e5 1e6 1e7 1e8 1e9 3e9

-50

-40

-30

-20

-10

0

frequency (Hz)

S11dB

S22dB

simulation:S11dB

simulation:S22dB

1e5 1e6 1e7 1e8 1e9 3e9

2

4

6

8

10

12

14

frequency (Hz)

S21dB

simulation:S21dB

(b) Transimpedance amplifier prototype 1 with Rf = 300 Ω.

1e5 1e6 1e7 1e8 1e9 3e9

-40

-30

-20

-10

0

frequency (Hz)

S11dB

S22dB

simulation:S11dB

simulation:S22dB

1e5 1e6 1e7 1e8 1e9 3e9

0

5

10

15

20

25

frequency (Hz)

S21dB

simulation:S21dB

(c) Transimpedance amplifier prototype 1 with Rf = 1500 Ω.

Figure 7.1: Measured (circles) and simulated (solid line) scattering parame-

ters.

In general, the noise figure is related to the noise currents and voltages

by the following equation

F = 1 +〈v2n〉

4kTRS4f+

〈i2n〉4kT 1

RS4f

(7.1)

Unfortunately, since we have two unknowns 〈v2n〉, 〈i2n〉 and only one equa-

7.2. Noise figure 91

0

2

4

6

8

10

2e+08 4e+08 6e+08 8e+08 1e+09 1.2e+09 1.4e+09

Noise figure (dB)

freq (Hz)

bga614 prototype 2TIA prototype 1 Rf=300

TIA prototype 1 Rf=1500

Figure 7.2: Measured noise figure. The peaking at 900 MHz is due to mobile

networks interference.

tion, it is not easy to translate the noise figure specification to the equivalent

noise currents and voltages. Nevertheless, we can obtain an upper bound of

the noise current of the transimpedance prototypes if we consider 〈v2n〉 = 0,

which gives

〈in〉√4f

<

√(F − 1) ·

(4kT

1

RS

)(7.2)

It is important to remark that equation 7.2 is only valid for a source

impedance RS = 50 Ω. The noise performance with the photodetector

impedance will be different.

The transimpedance prototype 1 with Rf = 300 Ω has a noise figure

NF ∼ 3 dB for frequencies < 1 GHz. From equation 7.2, we obtain an

upper bound of the noise current with RS = 50 Ω of 〈in〉√4f

< 18.12 pA/√Hz.

Prototype 1 with Rf = 1500 Ω performs 〈in〉√4f

< 13.92 pA/√Hz, the same

as the BGA614 prototype.

7.3. Dynamic range 92

7.3 Dynamic range

We had problems trying to measure the dynamic range of the transimpedance

prototypes. The signal generator Tektronix AFG3252 is only able to output

a minimum pulse peak Vhigh = 50 mV. Since the output impedance of the

generator is 50 Ω, it is easy to obtain the minimum current delivered to the

transimpedance amplifier

i =vhigh

50 Ω + 20 Ω≈ 714µA. (7.3)

To address this problem, we have used the attenuators available in the

laboratory. We have added an attenuation of -12 dB to the input of the

TIA (TransImpedance Amplifier) prototypes. Figures 7.3 and 7.4 show the

measured dynamic ranges of prototype 1. Note that the horizontal axis con-

tains the output in millivolts of the signal generator. Due to the attenuators,

the current flowing into the TIA is not easy to obtain accurately.

The measured dynamic range is 49 dB. The dynamic range can be ex-

pressed in bits by taking the log2 instead of 20 · log10, to be 8.87 bits. For

prototype 1 with Rf = 1500 Ω, the dynamic range lowers to 39 dB. As we

anticipated, the dynamic range is too low.

The dynamic range issue in the TIA prototypes has been addressed with

the design of prototype 2. Figure 7.5 shows the dynamic range of this pro-

totype. The simulated dynamic range is approximately 51 dB. Note that if

we lowered the transimpedance gain of this prototype to 300 Ω, we would be

getting a dynamic range of 61 dB, but a lower gain of course. In terms of

bits, the dynamic range of this prototype is 8.48 bits.

The BGA614 prototype was succesfully characterised. Figure 7.6 shows

the measured dynamic range of the BGA614 prototype 2 along with the

relative error of the linear fit. The 1-dB compression point is found to be

at an input voltage of 300 mV. Taking into account the voltage peak of

the pulses corresponding to 1 phe, which are specified in section 2.3, the

measured dynamic range is roughly 59 dB. In bits, the dynamic range is 9.7

bits.

It should be noted that the simulations predict with great accuracy the

7.4. Pulse shape 93

dynamic range of the prototypes. This is because we are using accurate

SPICE models of the devices.

-3

-2

-1

0

1

2

50 100 150 200 250 300

Rela

tive e

rror

(%)

Signal generator voltage (mV)

50

100

150

200

250

50 100 150 200 250 300

Outp

ut voltage (

mV

)


Figure 7.3: Measured dynamic range of the transimpedance prototype 1 with

Rf = 300 Ω.

7.4 Pulse shape

The test setup described in 6.2.3 has been used for the pulse shape tests.

The response of the prototypes to a pulse train with frepetition = 200 KHz,

FWHM = 5 ns, VHIGH = 3.2 V from the signal generator, is presented

in figure 7.7. In this figure, the BGA614 prototype is connected to the

GAPD voltage output board (figure 5.5b) and to the current output board

(figure 5.5d). With the voltage output board, the effective input resistance

is 50 Ω || 50 Ω = 25 Ω, which is very close to the input resistance of the

transimpedance amplifier with Rf = 300 Ω.

The relevant time measurements are recorded in table 7.1. From this

7.5. Photon counting 94

-1

-0.5

0

0.5

1

50 60 70 80 90 100

Rela

tive e

rror

(%)


200

220

240

260

280

300

320

340

360

50 60 70 80 90 100 110

Outp

ut voltage (

mV

)


Figure 7.4: Measured dynamic range of the transimpedance prototype 1 with

Rf = 1500 Ω.

measurements, it is clear that an increase in the impedance seen by the

GAPD results in a wider pulse response.

We expected the transimpedance to outperform the BGA614 in terms

of pulse width and specially pulse rise time, but it has not. The reason for

this, after carefully reviewing the Hamamatsu MPPC technical note [5], is

the integrated polysilicon quenching resistor at the anode of each pixel. This

resistor of ∼ 200KΩ at ambient temperature, which was initially overlooked,

along with the capacitance of each pixel, dominate the frequency response

of the device.

7.5 Photon counting

The performance of the prototypes for single photon counting is shown here.

The test setup is described in 6.2.3. The plots have been obtained with the


200

400

600

800

1000

1200

500 1000 1500 2000 2500 3000 3500 4000

Output voltage (mV)

Input current (uA)

-1.5

-1

-0.5

0

0.5

0 200 400 600 800 1000 1200 1400

Relative error (%)

Input current (uA)

Figure 7.5: Simulated dynamic range of the transimpedance prototype 2

with Rf = 1000 Ω.

color grade function and the histogram of the DSO81204B oscilloscope.

The testing configuration of the Tektronix AFG3252 signal generator is

frepetition = 200 KHz, FWHM = 5 ns, VHIGH = 3.0 V. The GAPD S10362-

33-050C is biased with a voltage Vbias = 71.27 V, recommended by the

manufacturer.

The DSO81204B oscilloscope is configured with a reduced bandwidth of

1 GHz to reduce the noise integration band.

Figure 7.8 shows the measurements. The pulse amplitude histogram

consists in a set of amplitude peaks corresponding to 1, 2, 3, · · · , n, n + 1

detected photons. Note that the envelope of the peaks forms a Poissonian

distribution, which describes the statistics of photon arrival. In addition,

the peaks are superimposed to undesired noisy detections. This can be seen

in the form of a Gaussian shaped distribution.

The three prototypes are able to obtain single photon counting patterns


-6

-4

-2

0

2

4

50 100 150 200 250

Relative error (%)

Input voltage (mV)

0

200

400

600

800

1000

1200

1400

1600

0 50 100 150 200 250 300

Output voltage (mV)

Input voltage (mV)

simulatedmeasured

Figure 7.6: Dynamic range of the BGA614 prototype 2.

with the GAPD, although it is clear that the transimpedance prototypes

outperform the BGA614. The peaks are better defined and the noise is much

lower, probably because of a lower input current noise. The single photon

spectrum obtained with the transimpedance prototype 1 (Rf = 1500 Ω) is

excellent (figure 7.8c).


-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 2e-08 4e-08 6e-08 8e-08

Vout (V)

time (s)

bga614 prototype 2 25 Ohmbga614 prototype 2 50 Ohm

TIA prototype 1 Rf=300

Figure 7.7: Output pulse shape.

Table 7.1: Pulse shape time measurements.

Device Under Test Rise time (ns) Fall time (ns) FWHM (ns)

GAPD 1.446 46.30 27.13

GAPD + 7 dB attenuator 2.121 60.56 22.93

GAPD + BGA614 Proto-

type 2

2.22 82.33 26.56

GAPD + 50Ω + BGA614

Prototype 2

1.902 36.54 16.10

GAPD + TIA Prototype 1

Rf = 300 Ω

2.04 33.30 12.64

GAPD + TIA Prototype 1

Rf = 1500 Ω

2.30 42.39 16.78


(a) BGA614. Scale 10 ns / 2.00 mV

(b) TIA prototype 1 Rf = 300 Ω. Scale 10 ns / 2.00 mV

(c) TIA prototype 1 Rf = 1500 Ω. Scale 20 ns / 5.00 mV

Figure 7.8: Photon counting measurements.

Chapter 8

Conclusions and Future Work

Summary: In this chapter, the obtained results are analysed and

compared. The future work is also described.

8.1 Prototype specification

Tables 8.1 and 8.2 show the performance of the prototypes developed in this

master thesis.

In general, all the prototypes implemented in this work deliver excellent

performance except for the dynamic range. TIA prototype 2 has been de-

signed to fix this issue, but there was no time to test it, so only the simulated

specification is shown.

8.2 Accomplishments

In this master thesis, five preamplifier prototypes have been designed and

three have been implemented and tested. The implemented prototypes have

shown very good performance with the GAPD. For example, the single pho-

ton counting patterns obtained with the transimpedance amplifier are excel-

lent. The key requirements, low noise, high bandwidth, low power, all have

been reached. On the other hand, the dynamic range of the prototypes is

reasonable, given the power consumption and cost of the prototypes.

99

8.2. Accomplishments 100

Table 8.1: BGA614 prototype specification.

BGA614 prototype 2

Noise (50Ω) < 13.92 pA/√Hz

-3 dB BW (50Ω) 1 GHz

Gain (dBΩ) 46

Input resistance 50 Ω

Dynamic range (dB) 59

Power consumption 180 mW

Table 8.2: TIA prototype specification.

Prototype 1 Rf =

300 Ω

Prototype 1 Rf =

1500 Ω

Prototype 2

Noise (50Ω) < 18.12 pA/√Hz < 13.92 pA/

√Hz -

-3 dB BW (50Ω) 800 MHz 325 MHz 550 MHz

Gain (dBΩ) 43 55 53

Input resistance 19 Ω 44 Ω 27 Ω

Dynamic range (dB) 49 39 51

Power consumption 160 mW 160 mW 78 mW

Additionally, the transimpedance prototypes developed in this thesis can

be succesfully used in any application where accurate single photon counting

is needed.

Only open source tools have been used to develop the work of this master

thesis, and although there is still a long way to reach high-end commercial

CAD packages, these tools, for sure, outperform the average commercial

software of their kind.

8.3. MMIC vs Transimpedance 101

8.3 MMIC vs Transimpedance

From the results obtained in this thesis, it is clear that the transimpedance

prototypes are superior to the BGA614 MMIC prototype. The former pro-

vides much more transimpedance gain than the latter for the same tran-

simpedance bandwidth. Also, as transimpedance gain is increased, the noise

of the TIA is reduced.

The pulse shape is narrower when using a TIA, due to its lower input

resistance, although the effective resistance of the MMIC can be lowered to

25 Ω with a matching 50 Ω resistor attached to the GAPD.

The advantage of MMICs is probably its reduced cost, its reliability and

its compactness.

8.4 Future work

The transimpedance prototypes have been designed with discrete compo-

nents. It would be interesting to translate these designs to an ASIC. Of

course, the design should be carefully revised.

The TIA prototype 2 hasn’t been tested, due to time constraints. A full

test of this design is left for future work.

Even the prototype with improved dynamic range doesn’t meet the 3000

phe requirement, so an alternative ultra high dynamic range design should

be considered in the future.

Finally, the developed prototypes should be tested with PMTs, as they

are, for the moment, the candidate photodetectors for the CTA camera.

Bibliography

[1] Design concepts for the cherenkov telescope array cta. Technical report,

The CTA Consortium, May 2010.

[2] P. Antoranz. Contributions to the high frequency electronics of MAGIC

II Gamma Ray Telescope. Phd, Universidad Complutense de Madrid,

2009.

[3] E. Delagnes, A. Sanuy, and D. Gascon. Wideband pulse amplifiers

for the integrated camera of the cherenkov telescope array. In WP

ELEC/FPI Aachen, September 2010.

[4] P. R. Gray and R. G. Meyer. Analysis and Design of Integrated Circuits.

John Wiley & Sons, Inc., New York, NY, USA, 3rd edition, 1992.

[5] Hamamatsu. Multi pixel photon counter. Technical report.

[6] Hamamatsu. Photomultiplier Handbook.

[7] Infineon. BFP420 Datasheet, February 2006.

[8] Infineon. BGA614 Datasheet, March 2008.

[9] H. Kubo. Dragon-japan status. In WP ELEC/FPI Madrid, April 2011.

[10] D. F. Miller. Basics of Radio Astronomy for the Goldstone-Apple Val-

ley Radio Telescope. Jet Propulsion Laboratory, California Institute of

Technology, 1998.

[11] D. Neamen. Semiconductor physics and devices: basic principles.

McGraw-Hill, 2003.

102

Bibliography 103

[12] J. Paredes, L. Garrido, M. Ribo, X. Sieiro, A. Sanuy, and D. Gascon.

First prototype of a low noise high dynamic range preamplifier: results

and outlook. In WP ELEC/FPI Madrid, April 2011.

[13] D. Pozar. Microwave engineering. J. Wiley, 2005.

[14] D. Renker. Geiger-mode avalanche photodiodes, history, properties and

problems. Nuclear Instruments & Methods in Physics Research., 2006.

[15] C. W. Sayre. Complete Wireless Design. McGraw-Hill Professional,

2001.

[16] F. Toussenel. Status of the nectar project. In WP ELEC/FPI Madrid,

April 2011.

[17] C. Verhoeven. Structured electronic design: negative-feedback amplifiers.

Kluwer Academic Publishers, 2003.

List of Acronyms

ADC . . . . . . . . . . Analog to Digital Converter

APD . . . . . . . . . . Avalanche Photo Diode

ASIC. . . . . . . . . . Application Specific Integrated Circuit

BJT . . . . . . . . . . . Bipolar Junction Transistor

CAD . . . . . . . . . . Computer Aided Design

CMOS . . . . . . . . Complementary Metal Oxide Semiconductor

COTS . . . . . . . . . Commercial Off-The-Shelf

CTA . . . . . . . . . . Cherenkov Telescope Array

DRS4 . . . . . . . . . Domino Sampler Ring version 4

DUT . . . . . . . . . . Device Under Test

EDA . . . . . . . . . . Electronic Design Automation

EGRET . . . . . . . Energetic Gamma Ray Experiment Telescope

EINC . . . . . . . . . Equivalent Input Noise Current

EINV . . . . . . . . . Equivalent Input Noise Voltage

FET . . . . . . . . . . Field Effect Transistor

FWHM . . . . . . . Full Width at Half Maximum

GAPD . . . . . . . . Geiger mode Avalanche Photo Diode

104

Bibliography 105

GBP . . . . . . . . . . Gain Bandwidth Product

gEDA . . . . . . . . . Gnu EDA

HEMT . . . . . . . . High Electron Mobility Transistor

HPD . . . . . . . . . . Hybrid Photon Detector

IACT . . . . . . . . . Imaging Atmospheric Cherenkov Technique

LED . . . . . . . . . . Light Emitting Diode

MAGIC . . . . . . . Major Atmospheric Gamma-ray Imaging Cherenkov tele-

scope

MESFET . . . . . Metal Semiconductor FET

MISFET . . . . . . Metal Insulator Semiconductor FET

MMIC . . . . . . . . Monolithic Microwave Integrated Circuit

MOSFET . . . . . Metal Oxide Semiconductor FET

NECTAr . . . . . New Electronics for the Cherenkov Telescope Array

NF . . . . . . . . . . . . Noise Figure

NSB . . . . . . . . . . Night Sky Background

PCB . . . . . . . . . . Printed Circuit Board

PDE . . . . . . . . . . Photon Detection Efficiency

phe . . . . . . . . . . . Photoelectrons

PHEMT . . . . . . Pseudomorphic HEMT

PMT . . . . . . . . . . Photo Multiplier Tube

QE . . . . . . . . . . . . Quantum Efficiency

QUCS . . . . . . . . . Quite Universal Circuit Simulator

RF . . . . . . . . . . . . Radio Frequency

Bibliography 106

RFC . . . . . . . . . . Radio Frequency Choke

RR . . . . . . . . . . . . Return Ratio

SMA . . . . . . . . . . SubMiniature version A

SMT . . . . . . . . . . Surface Mount Technology

SNR . . . . . . . . . . Signal to Noise Ratio

SOLT . . . . . . . . . Short Open Load Thru

SPICE . . . . . . . . Simulation Program with Integrated Circuit Emphasis

SRF . . . . . . . . . . . Self Resonant Frequency

TIA . . . . . . . . . . . TransImpedance Amplifier

VHE . . . . . . . . . . Very High Energy

Bill of Materials

Summary: This annex contains the bill of materials along with the

unitary price.

The following table contains the Bill of Materials for the prototypes. This

includes the unitary price for each part. The total cost of the material is

42.026 eur.

107

TIA Prototype 1

Cd1 100nF "0805"Decouplingcapacitor 08055C104KAT2A AVX 464-6688 0,093 €



Cb1 100nF "0805"Bypassingcapacitor 08055C104KAT2A AVX 464-6688 0,093 €


Cb3 1uF "0805"Bypassingcapacitor 0805YG105ZAT2A AVX 391-292 0,093 €

RB1 10K Ohm 0,1% "0805" Biasing resistor 0,318 €RC1 316 Ohm 0,1% "0805" Biasing resistor ERA6AEB3160V 708-5972 0,318 €RC2 100 Ohm 0,1% "0805" Biasing resistor 0,318 €RE2 50 Ohm 0,1% "0805" Biasing resistor 0,318 €Rf 300 Ohm 0,1% "0805" Feedback resistor CRCW0805300RFKEAVishay 679-1257 0,02 €Rf 400 Ohm 0,1% "0805" Feedback resistor CRCW0805402RFKEAVishay 679-1392 0,02 €

RComp1 6.98 Ohm 1% "0805"Compensatingresistor for stability

RS-0805-6R98-1%-0.125W RS 717-1847 0,03 €

RComp2 30 Ohm 1% "0805"Compensatingresistor for stability

RS-0805-30R-5%-0.125W RS 697-9949 0,02 €

Q1 SOT-343 NPN RF BJT BFP420E6327InfineonTechnologies 195-0209 0,348 €

Q2 SOT-343 NPN RF BJT BFP420E6327InfineonTechnologies 195-0209 0,348 €

Input SMA ENDLAUNCH JK 1.07PCB RF Connector 526-5763 6,45 €Output SMA ENDLAUNCH JK 1.07PCB RF Connector 526-5763 6,45 €Power SMA ENDLAUNCH JK 1.07PCB RF Connector 526-5763 6,45 €

BGA614 Prototype2

BGA614 SOT-343 MMIC amplifier BGA 614 H6327InfineonTechnologies 1,73 €

CCin 100nF "0805"Decouplingcapacitor 08055C104KAT2A AVX 464-6688 0,093 €

CCout 100nF "0805"Decouplingcapacitor 08055C104KAT2A AVX 464-6688 0,093 €



LRFC1 10uH 10% "1210"Radio frequencychoke inductance LQH32CN100K33L Murata 109-598 0,01 €

LRFC2 100uH 10% "1210"Radio frequencychoke inductance LQH32CN101K53L Murata 106-561 0,01 €

Rbias 68 Ohm 0,1% "0805" Biasing resistor 0,318 €Input SMA ENDLAUNCH JK 1.07PCB RF Connector 526-5763 6,45 €Output SMA ENDLAUNCH JK 1.07PCB RF Connector 526-5763 6,45 €Power SMA ENDLAUNCH JK 1.07PCB RF Connector 526-5763 6,45 €

Refdes Value Tolerance Package Purpose Part number Manufacturer RS code Unit price

Layouts

Summary: In this annex, the PCB layouts of the implemented pro-

totypes are included.

The layouts have been attached in the following order: BGA614 proto-

type 2, TIA prototype 1 and TIA prototype 2. Each layout includes the

front layer, back layer and the assembly.

109

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/bga614/pcb/bga614_for_pcb_prototype2.pcbfront, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/bga614/pcb/bga614_for_pcb_prototype2.pcbback, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/bga614/pcb/bga614_for_pcb_prototype2.pcbfrontassembly, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/pcb/TIA_prototype1_layout2.pcbfront, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/pcb/TIA_prototype1_layout2.pcbback, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/pcb/TIA_prototype1_layout2.pcbfrontassembly, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/pcb/TIA_prototype2.pcbfront, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/pcb/TIA_prototype2.pcbback, scale = 1:1.000

/home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/pcb/TIA_prototype2.pcbfrontassembly, scale = 1:1.000

SPICE Models

Summary: This appendix contains the SPICE models of the BGA614

MMIC amplifier and the BFP420 npn BJT used in the simulations

done in this work.

119

BGA614

Preliminary SPICE Model 1 2003-09-05

Preliminary

SPICE Model BG614BG614-Chip

Transistor Chip Data T1 (Berkley-SPICE 2G.6 Syntax).MODEL T1 NPN(+ IS = 2.6e-015 BF = 105 NF = 1.021 VAF = 1000+ IKF = 2.262 ISE = 2.978E-12 NE = 3.355 BR = 100+ NR = 1 VAR = 1.2 IKR = 0.00631 ISC = 1.923E-14 + NC = 2.179 RB = 2.674 IRB = 1.8E-05 RBM = 2.506+ RE = 0.472 RC = 2.105 XTB = -0.9 EG = 1.114+ XTI = 3.43 CJE = 3.716E-13 VJE = 0.8986 MJE = 0.3152 + TF = 1.306E-12 XTF = 2.71 VTF = 0.492 ITF = 2.444+ PTF = 0 CJC = 2.256E-13 VJC = 0.7395 MJC = 0.3926+ XCJC = 1 TR = 3.884E-10 CJS = 6E-14 VJS = 0.5+ MJS = 0.5 FC = 0.8215)

Package Equivalent Circuit

3

1

2

R1

R2 R3 R4

Q1

Q2

Q1 T1

Q2 T1 (area factor: 0.5)

R1 600Ω

R2 2000Ω

R3 100Ω

R4 4Ω

Valid up to 3GHz

LBI 0.47 nHLB0 0.53 nHLEI 0.23 nHLEO 0.05 nHLCI 0.56 nHLCO 0.58 nHCBE 136 fFCCB 6.9 fFCCE 134 fF

BGA616Chip

LBO

CBE CCE

CB

E

LBI LCI LCO

LEI

LEO

1

2

3

CCB

**************************************************************** Infineon Technologies AG* GUMMEL-POON MODEL IN SPICE 2G6 SYNTAX* VALID UP TO 10 GHZ* >>> BFP420 <<<* (C) 2009 Infineon Technologies AG* Version 0.9 November 2009**************************************************************** - Please use the global SPICE parameter TEMP to set the junction* temperature of this device in your circuit to get correct DC * simulation results. * - TEMP is calculated by TEMP=TA+P*(RthJS+RthSA). The junction * temperature TEMP is the sum of the ambient temperature TA and * the increment of temperature caused by the dissipated power * P=VCE*IC (IC collector current, VCE collector-emitter voltage). * - RthJS is the thermal resistance between the junction and the * soldering point. RthJS for this device is 260 K/W. RthSA is the * thermal resistance of the PCB, from the soldering point to the * ambient. For determination of RthSA please refer to Infineon's * Application Note "Thermal Resistance Calculation" AN077.* - The model has been verified in the junction temperature range* -25ºC to +125ºC.* - TNOM=25 ºC is the nominal ambient temperature.* Please do not change this value.*****************************************************************.OPTION TNOM=25, GMIN= 1.00e-12*BFP420 C B E.SUBCKT BFP420 1 2 3

CBEPAR 22 33 5.02808E-014CBCPAR 22 11 6.50742E-014CCEPAR 11 33 2.78355E-014LB 22 20 9.32483E-011LE 33 30 1.03341E-015LC 11 10 2.55694E-010CBEPCK 20 30 3.83937E-014CBCPCK 20 10 1.2239E-014CCEPCK 10 30 0LBX 20 2 1.64141E-009LEX 30 3 1.99415E-010LCX 10 1 4.32831E-010Q1 11 22 33 4 M_BFP420*Q1 1 2 3 M_BFP420

.MODEL M_BFP420 NPN(+ IS = 2.87E-017+ BF = 170+ NF = 0.984+ VAF = 45.38+ IKF = 0.9166+ ISE = 2.314E-015+ NE = 1.756+ BR = 48.18+ NR = 0.9205+ VAR = 1.974+ IKR = 0.004954+ ISC = 6.172E-026

+ NC = 0.7018+ RB = 8.43882+ IRB = 0+ RBM = 1.48677+ RE = 0.156599+ RC = 6.96071+ XTB = -0.1945+ EG = 1.11+ XTI = 5.65+ CJE = 4.91174E-013+ VJE = 0.9719+ MJE = 0.3268+ TF = 4.4544E-012+ XTF = 245.951+ VTF = 32.6635+ ITF = 6.437+ PTF = 1+ CJC = 2.3726E-013+ VJC = 0.6899+ MJC = 0.4687+ XCJC = 0.7499+ TR = 1.247E-005+ CJS = 3.63308E-013+ MJS = 0.5918+ VJS = 0.9683 + FC = 0.5+ KF = 0+ AF = 1)***************************************************************

.ENDS BFP420

pulse preamplifiers for cta camera photodetectors

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