Pulse Preamplifiers for CTA Camera Photodetectors PROYECTO FIN DE CARRERA Ignacio Diéguez EstremeraDepartamento 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 DoctoresD. José Miguel Miranda Pantoja y D. Pedro Antoranz Canales Departamento de Física Aplicada III (Electricidad y Electrónica) Facultad de Ciencias Físicas Universidad Complutense de Madrid Septiembre 2011
AgradecimientosAunque este trabajo está redactado en inglés, me voy a tomar la licencia deescribir estos párrafos en castellano. En primer lugar quiero dar las gracias a José Miguel y a Pedro porhaberme dado la oportunidad de hacer el proyecto con ellos durante doscursos. La experiencia adquirida con vosotros en el laboratorio no tieneprecio. Por supuesto, agradecer a José Manuel todos sus sabios consejos y lec-ciones con la instrumentación. Siempre has dejado tus quehaceres paraecharme 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 avosotros 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. Siempreme 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, siempreestais cerca. Finalmente, quiero dar las gracias a Gus, nuestro perro labrador, por sercomo es. v
AbstractThe Cherenkov light pulses coming from gamma ray induced atmosphericshowers are extremely weak and short, thus setting very demanding re-quirements in terms of sensibility and bandwidth to the photodetectorsand 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 areanalysed and preampliﬁer prototypes meeting most of the CTA speciﬁcationsare 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
List of Tables 2.1 Set of speciﬁcations for the preampliﬁer. . . . . . . . . . . . . 24 2.2 Estimated minimum and maximum current and voltage peaks. The voltage peak is calculated assuming a 50 Ω load. . . . . . 25 4.1 Basic feedback conﬁgurations. . . . . . . . . . . . . . . . . . . 45 4.2 Estimated total noise current integrated in the band 100 Khz - 750 MHz and SNR for diﬀerent photodetector capacitances. 56 4.3 Small signal parameters obtained with ngspice. . . . . . . . . 67 4.4 Prototype 1 total current and voltage noise integrated in the band 100 Khz - 750 MHz simulated with ngspice for diﬀerent photodetector capacitance. . . . . . . . . . . . . . . . . . . . . 67 4.5 Prototype 2 small signal parameters obtained with ngspice. . 73 4.6 Prototype 2 total current and voltage noise integrated in the band 100 Khz - 550 MHz simulated with ngspice for diﬀerent photodetector capacitance. . . . . . . . . . . . . . . . . . . . . 73 5.1 Parameters of the FR4 substrate. r is the dielectric constant, τ is the metal thickness and h is the dielectric thickness. . . . 77 6.1 Measure settings for the network analysers. The rest of pa- rameters are left to its default value. . . . . . . . . . . . . . . 86 6.2 Measure settings for the noise ﬁgure analyser. The rest of parameters are left to its default value. . . . . . . . . . . . . . 86 7.1 Pulse shape time measurements. . . . . . . . . . . . . . . . . 99 xv
Chapter 1Introduction Some idea of the vastness of the Universe may be gained by considering a model in which everything has been scaled down by a factor of a billion. In this model the Earth would have the dimensions of a grape. The Moon would resemble a grapeseed 40cm away while the Sun would a 1.4-meter diameter sphere at a distance of 150 meters. Neptune would be more than 4 km away. On this one-billionth scale, the nearest star would be at a distance of 40,000 km - more than the actual diameter of the Earth. One would have to travel ﬁve thousand times farther yet to reach the center of the Milky Way Galaxy, another 80 times farther to reach the next nearest spiral galaxy, and another several thousand times farther still to reach the limits of the known Universe. Gareth Wynn-Williams Summary: This chapter introduces the reader to gamma ray astron- omy, presents the most remarkable gamma ray telescopes and discusses 1
1.1. Thesis objetive and structure 2 the photodetectors used in IACT (Imaging Atmospheric Cherenkov Technique) experiments.1.1 Thesis objetive and structureThe primary objective of this thesis is the design, implementation and test ofbroadband, low noise and high dynamic range signal conditioning electron-ics for the CTA (Cherenkov Telescope Array). The prototypes developedare going to be tested with state of the art GAPD (Geiger mode AvalanchePhoto 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 ofthese two approaches will be analysed. This thesis also aims to provide a proof of concept of the viability ofthe engineering of electronic circuits using open source tools. The beneﬁtsand drawbacks of this approach against licensed commercial software will bediscussed. The work has been divided in eight chapters. Chapter 1 introduces thereader to gamma ray astronomy, presents the most remarkable gamma raytelescopes and discusses the photodetectors used in IACT (Imaging Atmo-spheric Cherenkov Technique) experiments. Chapter 2 introduces the front-end electronics and makes an analysis ofthe approaches used to amplify the signals generated by the photodetectors.It also reviews the speciﬁcations of the front-end that have been agreed bythe CTA collaboration and describes the state of the art of the front-endsfor CTA. In Chapter 3, the design of two prototypes based on the BGA614 MMICis described. This chapter also includes all the simulations performed withQUCS 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 theneed 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. Thetechnology used for the PCB (Printed Circuit Board ) will be introduced andthe created boards will be shown. Chapter 6 describes the setups used to test and measure the implementedprototypes. A review of the instrumentation available in the laboratory isdone. 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 astronomyThe outer space has fascinated the human kind since the ancient times. Formany years, the observation of the cosmos has been limited to the opticalwindow, mainly because our eyes are the only “antenna” we naturally haveto detect the electromagnetic energy radiated by celestial bodies. Opticaltelescopes have aided us in the exploration of outer space, but with thelimitation of exploring a very narrow band of the entire electromagneticspectrum. In 1865, the great scottish physicist James Clerk Maxwell published thefamous equations that carry his name, unifying the laws of electricity andmagnetism into a set of four succinct equations1 . More than two decades af-ter, in 1888, Heinrich Hertz proved the existence of electromagnetic waves bycreating them artiﬁcially, and in the beginning of the 20th century, GuglielmoMarconi layed the foundations of radio communications. But it was not until1931 when Karl G. Jansky, a radio engineer working for the Bell TelephoneLaboratories in Holmdel, New Jersey, in a attempt to study the interferencecaused by thunderstorms in the transoceanic radio link, accidentally discov-ered a strange RF (Radio Frequency) source, which he later proved to beextraterrestial by correlating the received power to the the earth’s rotation 1 A special mention to Oliver Heaviside must be made for his work done in simplifyingthe original set of 13 equations into a set of 4 equations in diﬀerential form as we knowthem 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 electromagneticenergy along speciﬁc bands of the spectrum (including visible light). Afterthe Second World War, radio astronomy developed quickly and ﬁrmly. Thiseye-opening to the space has provided a lot of information which wasn’tavailable in the optical window for many centuries, and has led to a signiﬁcantadvance in our understanding of the Universe.1.3 Gamma ray astronomyGamma ray astronomy is the study of gamma radiation emitted by extrater-restrial bodies. Gamma radiation is located at the top of the radiationspectrum, with wavelengths in the order of 10−12 m and energies of 106 eVand higher (see ﬁgure 1.2). High energy gamma rays, with energies ranging from GeV to TeV cannotbe generated by thermal emission from hot celestial bodies. The energy ofthermal radiation reﬂects the temperature of the emitting body. Apart fromthe Big Bang, there hasn’t been such a hot body in the known Universe.
1.3. Gamma ray astronomy 5 Figure 1.2: Electromagnetic spectrum, image courtesy of Wikipedia.Thus, gamma ray astronomy is the window within the electromagnetic spec-trum to probe the non thermal Universe. Gamma rays can be generatedwhen highly relativistic particles, accelerated for example in the giganticshock waves of stellar explosions, collide with ambient gas, or interact withphotons and magnetic ﬁelds. The ﬂux and energy of the gamma rays reﬂectsthe ﬂux and spectrum of the high-energy particles. They can therefore beused to trace these cosmic rays and electrons in distant regions of our ownGalaxy or even in the other galaxies. Gamma rays can also be producedby decays of heavy particles such as hypothetical dark matter particles orcosmic strings, both of which might be relics of the Big Bang. Gamma raystherefore provide a window on the discovery of the nature and constituentsof dark matter [1, chap.2]. Fortunately for us and all the living creatures in our planet, the Earth’satmosphere blocks most of the gamma radiation coming from outer space.Unfortunately for astrophysicists, gamma rays cannot be directly detectedfrom 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 ExplorerXI, which in 1961 discovered the ﬁrst gamma rays outside the atmosphere.The satellites of the Vella Network, initially designed to detect illegal nucleartests, detected in 1967 the ﬁrst gamma ray burst in history. Modern space
1.3. Gamma ray astronomy 6gamma ray telescopes include EGRET (Energetic Gamma Ray ExperimentTelescope), an instrument aboard the American satellite Compton GammaRay Observatory, and the Fermi Gamma-ray Space Telescope, launched inJune 2008. The other major technique used to detect gamma rays are the groundbased telescopes, see ﬁgure 1.3. The ground based telescopes detect gammaradiation 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 atspeeds 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 250mon the ground [1, chap 2.1.3]. This light is captured by the ground basedtelescopes’ camera pixels and is used to image the shower. Reconstructingthe 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 spacetelescopes [1, chap. 3]. The latest generation of IACT gamma ray telescopesinclude H.E.S.S, MAGIC, VERITAS, Cangaroo II and MILAGRO. The CTA proyect is to become the cutting-edge gamma ray telescopearray. It combines the experience of virtually all groups world-wide workingwith atmospheric Cherenkov telescopes to provide a never seen energy rangefrom about 100GeV to several TeV, angular resolutions in the arc-minuterange, which is about 5 times better than the typical values for current in-struments, excellent temporal resolution and full sky coverage from multipleobservatory sites [1, chap. 3]. In ﬁgure 1.4, a computer generated graphicwith 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 availablethrough Virtual Observatory Tools in order to make the access and analysisto data much easier [1, chap. 3].
1.4. Photodetectors used in IACTs 7Figure 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 IACTsA photodetector is a transducer that converts light energy into an electricalcurrent. In this section, the photodetectors mostly used in IACT experimentswill be introduced and compared. Special attention will be put in the GAPDfor 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 anevacuated glass tube (see ﬁgure 1.5). Light which enters a photomultiplier
1.4. Photodetectors used in IACTs 8tube 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 of106 ∼ 107 , which makes them suitable for single photon counting.Figure 1.5: Schematic of a PMT coupled to a scintillator, image courtesy ofWikipedia. 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 thephotocathode 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 theCherenkov light [2, chap. 3].
1.4. Photodetectors used in IACTs 9 Being the PMT a mature and well known technology, it has been usedin most of the IACT experiments and it has become the favourite canditatephotodetector to be used in the CTA project. The HPD (Hybrid Photon Detector ) combines the advantages of PMTand 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 (AvalanchePhoto Diode). This way, two stages of ampliﬁcation are applied: the ﬁrstdue to acceleration and impact on the semiconductor, and the second dueto the avalanche in the diode. Combined multiplication factors of 5 · 104can be achieved. These devices have much better energy resolution, sensi-tivity and QE than PMTs. The detection area is much bigger than that ofsolid state devices. The main drawbacks are the ageing of the photocathode,high rates of afterpulses, dark counts, temperature dependence or handlingof 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 beenbiased above its avalanche breakdown voltage, see ﬁgure 1.6. This way, asingle 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 acurrent pulse that can be detected when properly ampliﬁed. An integratedquenching resistor collapses the breakdown by lowering the voltage at then terminal during the breakdown. These devices are commercialised in theform of a matrix consisting in N × M individual cells. Each cell detects asingle photon. When n photons arrive, n of the N · M cells are very likelyto 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 upperlimit of detected photons is N · M . The most critical ﬁgures of merit which should be optimised in a GAPDin order to make it suitable for the application pursued in this work are listedbelow , • Gain: GAPDs produce a current pulse when any of the cells goes to breakdown. The amplitude Ai is proportional to the capacitance of
1.4. Photodetectors used in IACTs 10 Figure 1.6: GAPD cross section, image courtesy of Wikipedia. the cells times the overvoltage, Ai ≈ C(V − Vb ), being V the operating bias voltage and Vb the breakdown voltage. When many cells are ﬁred at the same time, the output is the sum of the individual pulses. • Dark counts: A breakdown can be triggered by an incoming photon or by any generation of free carriers. The latter produces dark counts with a rate of 100 KHz to several MHz per mm2 at 25o C. Carriers in the conduction band may be generated by the electric ﬁeld or by thermal agitation. Thermally generated carriers can be reduced by cooling the device. Another possibility is to operate the GAPD at a lower bias voltage resulting in a smaller electric ﬁeld and thereby lower gain. The dark counts can be reduced in the production process by minimizing the number of recombination centres, the impurities and the crystal defects. • Optical crosstalk : In an avalanche breakdown there are in average 3 photons emitted per 105 carriers with a photon energy higher than 1.14 eV, the bandgap of silicon. When these photons travel to a neighbour- ing cell, they can trigger a breakdown there. The optical crosstalk is an stochastic process and introduces an excess noise factor like in a normal APD or PMT. • Afterpulsing: Carrier trapping and delayed release causes afterpulses during a period of several µ-seconds after the breakdown.
1.5. Open Source CAD 11 • Photon detection eﬃciency: The PDE (Photon Detection Eﬃciency) is the product of the QE of the active area, a geometric factor which is the ratio of sensitive to total area and the probability that an incoming photon triggers a breakdown Ptrigger , so P DE = QE · · Ptrigger . • Recovery time: The time needed to recharge a cell after a breakdown has been quenched depends mostly on the cell size due to its capaci- tance and the individual resistor (RC). • Timing: The active layers of silicon are very thin (2-4 µm), so the avalanche breakdown process is fast and the signal amplitude is big. Therefore, very good timing properties even for single photons can be expected. There are more features that make GAPDs promising : • GAPDs work at low bias voltages (50 V ∼ 70 V). • have low power consumption (< 50 µW/mm2 ). • are insensitive to magnetic ﬁelds up to 15 T. • are compact and rugged. • tolerate accidental illumination. The main drawbacks that are limiting their use in IACT experiments arethe small detection area available and the high dark count rate.1.5 Open Source CADNowadays, the use of CAD software is a must in every engineering discipline,and Electronic Engineering is not an exception. Simulation of the designsis a mandatory phase of a project, as it provides invaluable insight on theperformance of the design before its implementation. Simulation CAD toolsin Electronic Engineering involve one or more of the following types [15,chap. 11]:
1.5. Open Source CAD 12 • SPICE, originally developed at the Electronics Research Laboratory of the Berkeley University, is a general purpose analog circuit simu- lator. It takes a text based netlist, which describes the circuit to be simulated and solves the system of non-linear diﬀerential equations for currents and voltages. SPICE also provides models for semiconductor devices which have become a standard both in industry and academic environments. The following analyses are typically supported by any SPICE implementation: – AC analysis: which performs an ac sweep in a selected frequency band and simulates the frequency response of the circuit. The non-linear devices, such as diodes or transistors, are linearised on its bias operating point and a small signal model is used. – DC analysis: calculates the DC quiescent point of non-linear de- vices. – Transient analysis: calculates the current and voltage in every node and branch of the circuit as a function of time by obtaining the time domain large signal solution of non-linear diﬀerential equations that arise from the circuit schematic. – Noise analysis: calculates the noise sources of each noisy element in the circuit. It also adds all the uncorrelated noise sources to obtain the equivalent input and output noise sources. – Distortion analysis: using Volterra series. The most common licensed SPICE implementation used today is Or- cad PSpice from Cadence. In this thesis, an alternative open source implementation called ngspice has been used. This tool is part of gEDA (Gnu EDA), an open source EDA (Electronic Design Automa- tion) suite which includes schematic capture, SPICE simulation and advanced PCB layout. • Linear simulators. These simulators are the dominant program types used in the RF and microwave world today. Linear simulators work by exploting S-parameter models for both active and passive devices.
1.5. Open Source CAD 13 These simulators are therefore more suitable for accurately simulating in high frequencies than SPICE based simulators. Some licensed software in this category include APLAC, which is an excellent simulator for high frequency circuits, or the superb and com- plete Agilent ADS and AWR Microwave Oﬃce. These packages oﬀer support for the entire design ﬂow, including schematic capture, simu- lation (linear, harmonic balance and 2D electromagnetic simulation), PCB layout integrated with the schematic, and many other function- ality. In this thesis, the excellent simulator QUCS has been used. Its inter- face is similar to Agilent ADS, and although it is not comparable to ADS, it can very well compare to APLAC. QUCS is capable of the following: – AC, DC, S-Parameter, harmonic balance, noise, digital and para- metric simulations. – Support for VHDL, Verilog-AMS and SPICE netlists. – Attenuator design tool, Smith chart tool for noise and power matching, ﬁlter synthesis tool, optimizer and transmission line calculator. In the future, the following capabilities will be implemented: – Layout editor for PCB and chip. – Monte Carlo simulation (device mismatch and process mismatch) based on real technology data. – Automated data aquisition from measumerent equipment. – Electromagnetic ﬁeld simulator, which is very useful for simulat- ing arbitrary planar structures (microstrip antennas, distributed ﬁlters, couplers, etc.) and obtain their scattering parameters. – Transient simulation using convolution for devices deﬁned in the frequency domain.
1.5. Open Source CAD 14 • Electromagnetic simulators: most of the planar electromagnetic anal- ysis software employs the Method of Moments to linearly simulate mi- crostrip, stripline or arbitrary 2D metallic and dielectric structure at RF and microwave frequencies. This category of simulators is able to accurately display the gain and return loss of distributed ﬁlters, microstrip antennas, transmission lines and more, in addition to pre- senting the actual current ﬂow and current density running through these mettalic structures. Two examples of electromagnetic simulators are the licensed commer- cial software Sonnet Suite and Moment, which is included in Agilent ADS. The open source software QUCS will include its own electromag- netic simulator in the future. CAD software is also an invaluable tool to implement the routing of the circuit, either in an integrated circuit or a PCB. In the ﬁeld of PCB design licensed software, there is Cadence Allegro, Eagle, Protel and many others. In this thesis, we will use the software PCB, which is part of the gEDA suite. PCB is a powerful tool that supports autorouting, DRC checks and up to 16 layers in a single board. There is a great community behind, both for support and footprint libraries. To perform some numerical computation and to generate some of the plots, the package Octave has been used. Octave is an open source nu- merical computation tool which is very similar to Matlab. Its syntax is almost identical and has many toolboxes available. Its main drawback is that it lacks of a functional Simulink equivalent, but this is not an issue for the purpose of this work.
Chapter 2Front-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 overviewPhotodetectors such as PMTs and GAPDs convert light signals into electricalsignals in the form of current. Detection of Cherenkov light showers results inextremely weak current pulses from the photodetectors. This current must beampliﬁed, conditioned and digitised for storing and further processing of thepulses. The complete chain, including preampliﬁcation, pulse conditioningand 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 shapingstage comprises any signal proccesing, such as ﬁltering, pulse shortening,buﬀering or converting to diﬀerential output that may be needed to drivethe digitiser. The digitiser includes the sampler and the ADC (Analog to 15
2.2. Preampliﬁcation approaches 16 photo detector Digitizer preamplifier signal conditioning Figure 2.1: Stages of the front-end.Digital Converter ). In most modern Cherenkov telescopes, the sampler isimplemented with a switched capacitor array. The complete chain must minimise signal distortion and must be able toresolve 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, lowpower, high linearity and very high dynamic range.2.2 Preampliﬁcation approachesThe current pulse from the photodetectors must be converted into a voltagepulse at some point of the ampliﬁcation stages. This is usually done at thepreampliﬁcation 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)
2.2. Preampliﬁcation approaches 17 • Charge ampliﬁcation: the output voltage is proportional to the time integral of the input current, which is the charge transferred by the photodetector to the ampliﬁer. The integrating element is a feedback capacitor, which makes this type of preampliﬁers not fast enough to meet the CTA speciﬁcations. Figure 2.2 shows the circuit topology of the two preampliﬁcation ap-proaches for a GAPD. The biasing circuit of the GAPD is also shown. Vcc Vcc Rbias Rbias Rf Rload 50 ohm Rload (a) Voltage preampliﬁer topology. (b) Transimpedance preampliﬁer topology.Figure 2.2: Circuit topologies for voltage and transimpedance approachesusing a GAPD. When using a voltage ampliﬁer, ﬁgure 2.2a, the GAPD is connected tothe ampliﬁer through a 50 Ω resistor. This resistor is only used for impedancematching, and it lowers the eﬀective impedance of the voltage ampliﬁer toRin || 50 Ω. Thus, if the ampliﬁer is close enough to the GAPD, the resistorcan be removed. The GAPD is connected directly to the input of the transimpedanceampliﬁer, 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 impedancemismatch, the preampliﬁer should be as close as possible to the GAPD.
2.2. Preampliﬁcation approaches 18 Let us consider a model of a solid state photodetector as an ideal currentsource with a shunt capacitance. The capacitance models the junction ca-pacitance of the reverse biased pn junction and any capacitive impedance atthe input of the preampliﬁer. This model is extremely simple and neglectsthe series and shunt resistance, but it ﬁts our purposes for the moment. When the photodetector is connected to a load, the load resistance formsa shunt RC circuit with the capacitance of the photodetector. This is shownin ﬁgure 2.3. In the following analysis, we will show that this shunt RCcircuit introduces a pole into the photodetector-ampliﬁer system that canlimit its frequency response. In ﬁgure 2.3a, the photodetector is connected to a voltage ampliﬁer withinput resistance Rin and voltage gain G(jω). It can be shown that the ﬁrstorder transfer function relating the output voltage to the input current isgiven by: vout G(jω) · Rin = (2.3) iin 1 + jωRin Cj 1 The transfer function 2.3 introduces a pole at ω0 = Rin Cj . This poleshows 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 pushthe 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 toa transimpedance ampliﬁer, with an open-loop gain G(jω) and a tran-simpedance gain ﬁxed by the feedback resistance, Ω(jω) ≈ −Rf , sinceG(jω) >> 1. All the current iin ﬂows through the feedback resistance andthe shunt capacitor, so the following equations apply: − iin = irf + icap (2.4) 1 − G(jω) vin − vout = irf Rf =⇒ vout = irf Rf (2.5) G(jω) jωCj vout icap = (2.6) G(jω) For frequencies lower than the cut-oﬀ frequency, we can approximate1−G G ≈ −1.
2.2. Preampliﬁcation approaches 19 Combining the equations we end up with the following tranfer function: vout Rf = − jωR Cj (2.7) iin f G(jω) − 1 G The transfer function 2.7 introduces a pole at ω0 = Rf Cj . This shows thatthe transimpedance feedback ampliﬁer shifts the pole to higher frequenciesby a factor of G, so the bandwidth of the system is considerably improved. G(jw) + iin Cj Rin vout - (a) Photodetector model connected to voltage ampliﬁer with input resistance Rin . Rf G(jw) + iin Cj vout - (b) Photodetector model connected to transimpedance ampliﬁer.Figure 2.3: Simpliﬁed photodetector model connected to voltage and tran-simpedance ampliﬁers. In ﬁgure 2.4, the output of the pulse response with the simpliﬁed pho-todiode model of the two prototypes developed in this thesis is shown. Thesimulation has been done with QUCS. The photodiode model used in thesimulation includes a pulse current source with an amplitude of 100 uA, risetime of 500 ps and pulse width of 4 ns; shunt junction capacitance Cj = 35pFand a shunt resistance Rshunt = 10KΩ. This capacitance is a typical valuefor 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
2.2. Preampliﬁcation approaches 20 BGA614 output 0.02 Transimpedance output 0.015 Output voltage (V) 0.01 0.005 0 0 2e-09 4e-09 6e-09 8e-09 1e-08 time (s)Figure 2.4: Simulated response of the BGA614 MMIC ampliﬁer (in blue)and the transimpedance ampliﬁer (in red) to a square current pulse withamplitude 100 µA, rise time 500 ps, pulse width 4 ns from a photodetectormodel with Cj = 35 pF and Rshunt = 10 KΩ.same bandwidth, the response of the MMIC preampliﬁer1 is much slowerthan that of the transimpedance preampliﬁer the gain is not the same forboth prototypes, but this fact is not relevant for the moment. The advantage of using a transimpedance preampliﬁer is clearly seenin the following noise analysis. The study of noise is important becauseit represents the lower limit of the size of the signal that can be detectedby a circuit. Noise is a random phenomena, so the language and tools ofstatistics are used to describe it. A noisy signal is modelled as a randomvariable of which the interesting parameter is its variance. If we measurea constant current ﬂowing through a conductor using an ideal amperimeterwe will notice that the current is not perfectly constant but it has slightﬂuctuations. These ﬂuctuations are generally speciﬁed in terms of its meansquare variation about the average value [4, chap. 11]: 1 Formally, the MMIC ampliﬁes power, not voltage, but at frequencies below 1 GHz wecan consider it as a voltage ampliﬁer with an input impedance of 50Ω.
2.2. Preampliﬁcation approaches 21 1 T i2 = (I − Iavg )2 = lim (I − Iavg )2 dt (2.8) T →∞ T 0 For the purpose of analysis, we will only take into account thermal noise.Other sources of noise in photodetectors, such as ﬂicker noise or shot noisewill be ignored, as they aﬀect both preampliﬁer conﬁgurations and will onlyadd mathematical complexity to the analysis. Thermal or Johnson noise isgenerated by any resistive material due to the thermal random motion of itscarriers. A resistor R generates thermal noise with a mean square variationgiven by: v 2 = 4kT R f (2.9) 1 i2 = 4kT f (2.10) R where k is the Boltzmann’s constant, T is the temperature in Kelvin and f is a narrow frequency band in Hz. The current spectral noise density is i2therefore given by f and has units of A2 /Hz. Every two port network generates noise. Even when there is no signalpresent at the input, there is a noise signal at the output. Noise generatedby a two port network is speciﬁed in terms of an equivalent noise voltageand an equivalent noise current, which is usually referred to the input, sothey are named EINV (Equivalent Input Noise Voltage) and EINC. Figure2.5 shows a noisy two port network modelled as a noiseless network with theequivalent noise generators at the input. These ﬁcticious noise generatorsare the generators that should be present at the input of the ideal noisylesstwo 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 (Signalto Noise Ratio) to the output SNR: SN Rin NF = (2.11) SN Rout In decibels:
2.2. Preampliﬁcation approaches 22 einv i2 + − Noisyless einc v2 two portFigure 2.5: Noisy two port network modelled as a noiseless network withinput referred noise generators. SN Rin N FdB = 10 · log (2.12) SN Rout Now that the basic noise concepts have been introduced, we proceed toanalyse the noise performance of voltage ampliﬁcation versus transimpedanceampliﬁcation 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 currentgenerators is ignored because they are uncorrelated, so the phase informationis not relevant. The total noise current at the input of the transimpedanceampliﬁer is given by: 1 1 i2 = i2 n 2 2 2 amp + ithermal + inf = iamp + 4kT f + 4kT f (2.13) Rs Rf From equation 2.13, it is clear that the sensitivity of the transimpedanceampliﬁer can only be improved by incrementing the feedback resistance Rf ,thus minimizing the current noise contribution of the feedback resistor. Thisalso increments the transimpedance gain. It can be seen in equation 2.7that, ideally, the bandwith of the system is not compromised because theincrement of Rf is compensated by the the open-loop gain G(jω). On the other hand, using voltage ampliﬁcation, the sensitivity can beimproved by incrementing the conversion resistance (ﬁgure 2.2a), but unfor-tunately, the bandwidth and noise of the system will be compromised. Usingthis ampliﬁcation approach, sensitivity is traded for bandwidth and noise. Finally, the high dynamic range required for the CTA front-end resultsin a huge voltage drop in the input impedance of the voltage ampliﬁer.
2.3. Speciﬁcations of the front-end 23The transimpedance ampliﬁer’s low input impedance is able to support suchdynamic ranges. inf Rf ithermal iampFigure 2.6: Transimpedance ampliﬁer and solid state photodetector with cur-rent noise generators. ithermal is the thermal noise generated in the resistivesemiconductor material of the photodetector; iamp is the EINC generator ofthe ampliﬁer; inf is thermal noise generated by the feedback resistor Rf .2.3 Speciﬁcations of the front-endCTA will be a cutting-edge Cherenkov telescope providing an extremely wideenergy range and sensitivity. The speciﬁcations have been extracted fromvarious documents in www.cta-observatory.org and have been summarisedin table 2.1. The response of the photodetector to 1 phe must be known for a completeunderstanding of the speciﬁcations. In general, we can estimate the currentpeak response of a photodetector operating at a gain Gp by obtaining thecharge Q delivered due to 1 phe in the time period τ using a triangularapproximation of the pulse: ipeak ipeak · τ Q= t · dt = (2.14) τ τ 2
2.3. Speciﬁcations of the front-end 24 Table 2.1: Set of speciﬁcations for the preampliﬁer. Broad band- ∼ 400 MHz The electronics must provide a bandwidth width matched to the length of the Cherenkov pulses of a few nanoseconds. The signal charge is obtained by integration over a time window of minimum duration to decrease the eﬀect of the NSB (Night Sky Background ). To use the shortest possible time window, the ana- log pulse duration must be kept as short as possible. This means that the analog band- width must be large enough not to widen the photodetector pulses. High dynamic ∼ 3000 phe (Photoelec- The high energy range above 10 TeV produce range trons) strong light showers, so the photodetector and the electronics must have a very high dynamic range to be able to detect the light pulse with- out clipping. √ Low noise ∼ 10 pA/ Hz Operating the photodetectors at a lower gain (∝ 104 ) lengthens the life time (for PMTs) and decreases the dark counts (for GAPDs). The electronics must be able to detect single photoelectrons, so the noise level must be be- low the signal delivered by the photodetector for a single photon response. The required signal to noise ratio is SN R ≈ 5 ∼ 10. Linearity <3% The response must be proportional to the number of incident photons, so highly lin- ear photodetectors and electronics are needed. Nonlinearities can be tolerated if they can be accurately corrected for in the calibration pro- cedure. Low power < 150 mW/channel The CTA consortium is planning to use up to ∼ 105 sensor channels. The front-end elec- tronics must be integrated in the camera clus- ter. Low cost
2.4. State of the art 25 Q = Gp · e (2.15) Where e = 1.602 · 10−19 C is the electron charge in coulombs. Solving for ipeak , we obtain: 2Gp · e ipeak = (2.16) τ In table 2.3, the minimum and maximum ratings are shown. This datagives us an estimation of the magnitude of the signals the front-end will haveto cope with.Table 2.2: Estimated minimum and maximum current and voltage peaks.The voltage peak is calculated assuming a 50 Ω load. Gain Pulse width Min ipeak Min vpeak Max ipeak Max vpeak 4· 104 3 ns 4.6 µA 0.23 mV 13.8 mA 0.69 V 7.5 · 105 40 ns 7 µA 0.35 mV 21 mA 1.05 V2.4 State of the artThere 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 themost 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.
2.4. State of the art 26 • ICC-UB, Universitat de Barcelona, Barcelona, Spain. • LPSC, Universite Joseph Fourier, INPG & IN2P3/CNRS, Grenoble, France. This collaboration includes the development of the PACTA preampliﬁer,the ACTA3 ampliﬁer and the NECTAr0 sampling ASIC (Application SpeciﬁcIntegrated Circuit). The NECTAr0 is a switched capacitor array analogmemory plus ADC in a chip. It is capable of sampling the pulses comingfrom the signal conditioning electronics at a sampling rate between 0.5 - 3GS/s, with an analog bandwith of ∼ 400MHz. The ADC has a resolution of12 bits. The ASIC has been implemented in 0.35 µm CMOS (ComplementaryMetal Oxide Semiconductor ) technology. The ACTA3 is the evolution of the ACTA ampliﬁer . It is a fullydiﬀerential voltage ASIC ampliﬁer implemented in 0.35 µm CMOS. Thebandwidth is below 300MHz, which doesn’t comply with the CTA front-endspeciﬁcations. The most interesting development of the NECTAr collaboration fromthis thesis point of view is the PACTA preampliﬁer. This state of the artpreampliﬁer for the CTA photodetectors is currently being developed by theICC-UB group from the University of Barcelona. The preampliﬁer has beendesigned with the following requirements in mind: low noise, high dynamicrange, high bandwidth, low input impedance, low power and high reliabilityand compactness . The design includes three basic blocks: super commonbase input, cascode current mirror with CB feedback and a fully diﬀerentialtransimpedance stage. In order to boost up the dynamic range, the designershave developed a novel technique to provide the ampliﬁer with two gains,thus achieving a photoelectron dynamic range above 6000 phe. The hightransimpedance gain of 1 KΩ ampliﬁes the low current generated by thephotodetectors under very weak light conditions. The low transimpedanceof 50 Ω comes into scene when the high gain saturates. The ﬁrst prototypehas been implemented in 0.35 µm SiGe BiCMOS technology and has thefollowing technical speciﬁcations: • Bandwith ∼ 500MHz.
2.4. State of the art 27 • Input impedance Zi < 10Ω. √ • Low noise in = 10pA/ Hz. • High dynamic range > 6000 phe. Finally, the NECTAr collaboration has developed a prototype board forthe 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. 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 MMICLEE-39+ by Mini-Circuits. There is an additional ampliﬁcation stage, themain ampliﬁer mezzanine, with three ampliﬁers. The high gain and low gainampliﬁer 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 theCTA front-end possible. The other ampliﬁer, based on the LMH6551 fromNational Semiconductor, is used for the trigger subsystem. The DRS4 isan 8 channel switched capacitor array sampling chip developed at the Paul
2.4. State of the art 28 (a) Photograph of the prototype including (b) Block diagram of the prototype. the PMTs. Figure 2.8: The DRAGON-Japan prototype, image courtesy of .Scherrer Institute, Switzerland. It is capable of sampling up to 5GS/s andhas an analog bandwidth of 950 MHz. The DRAGON-Italy prototype is being developed by the INFN Pisaand the University of Siena. This group is collaborating closely with theDRAGON-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 3MMIC 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 MMICThe miniaturization of communication equipment experienced in the lastdecade 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 evenASICs. From the CTA perspective, the main beneﬁts of this technology arethe 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 . This low noiseampliﬁer is very similar to the BGA616 used in  for the MAGIC front-endand, except for the dynamic range, it seems to meet the CTA speciﬁcationsand ﬁts the purposes of this thesis.3.2 Design of the prototypesThe BGA614 is a matched general purpose broadband MMIC ampliﬁer ina Darlington conﬁguration (see ﬁgure 3.1) . The device -3 dB bandwidthcovers DC up to 2.7 GHz with a typical gain of 18.5 dB at 1 GHz and sourceand load impedance of 50 Ω. At a device current of 40 mA, it has an output1 dB compression point of +12 dBm. At this same operating point, the noiseﬁgure is 2.3 dB at 2 GHz. The ampliﬁer is matched to 50 Ω and its unconditionally stable, so theonly 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. TheBGA614 is biased by applying a DC voltage to the the collectors of thetransistors. A resistor and a RFC (Radio Frequency Choke) inductor areadded in series, and coupling capacitors are added at the input and theoutput. The resistor is added to ﬁx and stabilise the desired collector current.Given a quiescent point (Ic , Vc ), the resistor value is given by: Vcc − Vc R= (3.1) Ic The BGA614 is designed to work with a collector current of 40 mA.For Vcc = 5V , the manufacturer recomends a series resistor R = 68 Ω. A
3.2. Design of the prototypes 31 Figure 3.1: Simpliﬁed circuit of the BGA614, image courtesy of Inﬁneon.precision resistor, with a tolerance of 0.1% will be used. The coupling capacitors block the DC current. This capacitors set thelower 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 thisfrequency. A value of C = 100nF is adecuate. For this value, the impedanceat 100 KHz is ∼ −j16 Ω. The inductor is used as a RFC to block the RF signal. It must present asigniﬁcant impedance to the lowest operation frequency, which is 100 KHz. Up to this point, we have considered the inductors and capacitors as idealelements, 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 forlumped components are shown. The parasitics form shunt or series LC cir-cuits, so real inductors and capacitors resonate at a frequency called theSRF (Self Resonant Frequency). This parameter is usually given by themanufacturer of the device, or can be found by measuring the frequency de-pendent impedance and ﬁtting into the high frequency model. The obtainedparameters can be plugged into the simulations for more accurate results. The parasitics characterisation of some commercially available inductors,
3.2. Design of the prototypes 32 2 − DC 5V Vcc + Cb1 1 1uF Rbias 68 Lrfc2 10uH Lrfc1 1uH Ccin X1 Ccout vin 100nF 1 3 vout In Out 100nF GND 1 2 + Vs dc 0 ac 1 Rload − 2 50 TITLE BGA614 mmic amplifier prototype 1 FILE: REVISION: PAGE OF DRAWN BY: Ignacio Dieguez Estremera Figure 3.2: Schematic of prototype 1 without parasitics.such as Murata, Epcos and Tdk has been done in . We shall use thesevalues of the parasitics in our simulations. For the selection of the capacitors, we have to make sure that the SRFmust 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 fromthe power supply unit. SMT inductors in the order of 1 ∼ 10 µH typically resonate at a frequencyof some tens of MHz. After the resonant frequency, the inductor no longerexhibits inductance and its reactance decays, thus we must make sure thatthe impedance shown to the RF signal is high enough at high frequencies. For this thesis, two prototypes of the BGA614 ampliﬁer have been de-
3.2. Design of the prototypes 33Figure 3.3: A component’s real life behaviour at high frequencies, imagecourtesy of .signed.3.2.1 Prototype 1The ﬁrst prototype designed includes two RFC inductors in series (see ﬁgure3.2). This design is based on the design for the BGA616 in . The useof two inductors increases the impedance for the RF signal. The value ofthese inductors is 1 µH and 10 µH. Figure contains the schematic of theprototype, captured with QUCS. As advanced by  and conﬁrmed by thesimulations done with QUCS and detailed in section 3.3, the self-resonanceof the inductors introduces a resonance peak at 108 MHz.  proposes theaddition of a 560 Ω resistor in parallel with the 10 µH inductor to lower itsquality factor Q.3.2.2 Prototype 2The 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 drawbackof losing gain at lower frequencies. To address this problem, additionalimpedance is introduced by narrowing the coplanar copper line connectingthe inductor.
3.3. Simulations 34 2 − DC 5V Vcc + Cb1 1 1uF Rbias 68 Lrfc1 10uH Ccin X1 Ccout vin 100nF 1 3 vout In Out 100nF GND 1 + 2 Vs dc 0 ac 1 Rload − 2 50 TITLE BGA614 mmic amplifier prototype 2 FILE: REVISION: PAGE OF DRAWN BY: Ignacio Dieguez Estremera Figure 3.4: Schematic of prototype 2 without parasitics.3.3 SimulationsIn this section, we present the simulations done with QUCS and discuss theobtained 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 withQUCS. Although Inﬁneon provides s2p ﬁles with the scattering parameters
3.3. Simulations 35of the device, these are a linearised small signal model of the device, whichmeans that they are bias point dependent. We have preferred to use theSPICE model as it is bias point independent and also takes into account thenon-linear eﬀects. The bias point of the transistors is obtained by the DCsimulation. Refer to 8.4 for the spice model of the BGA6184.108.40.206 Prototype 1Figure 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 . Vcc U=5 V Rbias1 Cb1 R=68 C=1 uF Pr1 Rrfc1 R=2.1 Ohm Crfc1 Equation C=2.342 pF dc simulation Lrfc1 Eqn1 DC1 dBGain=dB(S[2,1]) L=10 uH Kfactor=Rollet(S) S parameter dBS11=dB(S[1,1]) dBS22=dB(S[2,2]) simulation Mufactor=Mu(S) Rrfc2 Mufactorprime=Mu2(S) R=0.34 Ohm Crfc2 SP1 stabL=StabCircleL(S) C=0.106 pF Type=log Lrfc2 stabS=StabCircleS(S) Start=100 kHz L=1 uH Stop=1.5 GHz Points=100 number Pr1.I 1 0.0365 Rccin1 X1 Rccout1 R=0.565 Ohm R=0.565 Ohm 10 9 Ccin1 Lccin1 spice Ccout1 Lccout1 L=58.4 pH C=100 nF 11 L=58.4 pH C=100 nF P1 Ref P2 Num=1 Num=2 Z=50 Ohm Z=50 OhmFigure 3.5: QUCS schematic for frequency domain simulations of prototype1 with parasitics. Figure 3.6 shows the simulated S11 and S22 scattering parameters. In thisﬁgure, we can see that the prototype has a resonance peak at frequency 109
3.3. Simulations 36MHz, which makes it useless for our purpose. Figure 3.7 shows the simulatedpower gain of the ampliﬁer. Inﬁneon claims a power gain |S21 |2 ≈ 19 dBand these simulations predict a gain of ∼19 dB in the frequency band. Thepredicted -3 dB frequency band ranges from 147 KHz to approximately 2GHz. We can also appreciate the resonance peak at 109 MHz. frequency: 1.2e+08 dBS11: -15.1 -10 -12 -14dBS22dBS11 S[2,2] S[1,1] -16 -18 -20 -22 1e5 1e6 1e7 1e8 1e9 3e9 frequency frequency frequency frequencyFigure 3.6: Simulated S11 and S22 of prototype 1. Modulus in dB (left) andSmith chart (right). The stability simulations predict unconditional stability for f < 1 GHz(see ﬁgure 3.8). For f > 1 GHz, the simulations predict potential unstabilityfor source and load inductive loads. We have observed that the responsiblefor 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 thereference plane of the measured S parameters at the output pin of the inte-grated circuit, thus obtaining a diﬀerent set of parameters. We can concludethat the bias circuit with RFC inductors must be carefully designed. All ofthese issues have been addressed in prototype 2. Finally, the simulated noise ﬁgure of the prototype in ﬁgure 3.9 showsthe low noise performance of the prototype.
3.3. Simulations 37 19 18.5 18 17.5 dBS21 17 16.5 16 15.5 1e5 1e6 1e7 1e8 1e9 3e9 frequency Figure 3.7: Simulated S21 (modulus in dB) of prototype 1. Stability circles for source (blue) and load (red) impedance 1.4 1.3Mufactorprime Mufactor 1.2 1.1 1 0.9 1.5 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) frequency Figure 3.8: Simulated stability parameters µ and µ (left) and stability circles (right). 3.3.2 Prototype 2 The previous section showed that the two series inductors introduces a res- onance peak at 109 MHz that renders the prototype useless for pulse ampli- fying.  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 1.94 1.93 1.92 Noise figure (dB) 1.91 1.9 1.89 1.88 0 2e8 4e8 6e8 8e8 1e9 1.2e9 1.4e9 frequency (Hz) Figure 3.9: Simulated noise ﬁgure of prototype 1.LC circuit, thus removing the resonance peak. In this thesis, we have taken a diﬀerent approach. This prototype includesonly one RFC inductor of 10 µH in the bias circuit. This way we reduce thebias circuit to one resistor and one inductor, instead of two resistors and twoinductors. This implies less points of failure and therefore more reliability.The bandwidth is reduced to 1 GHz, which is much higher than the requiredfor the CTA front-end. Figure 3.10 shows the schematic of prototype 2 for frequency domainsimulations captured with QUCS. The schematic includes the parasitics forinductors 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. Inthis ﬁgure we can see the good matching obtained at the input an outputports. Figure 3.12 shows the simulated power gain of the ampliﬁer. Inﬁneonclaims 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 rangesfrom 147 KHz to approximately 1 GHz. The stability simulations (see ﬁgure
3.3. Simulations 393.13) 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 inthe transimpedance bandwidth. Figure 3.15 shows that the noise ﬁgure is below 2 dB. The simulationpredicts 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. Vcc1 Rcb2 U=5 V R=0.328 Ohm Rcb1 Cb2 Lcb2 R=0.328 Ohm C=10 nFL=25 pH Cb1 Lcb1 Rbias R=68 C=1 uF L=25 pH Equation dc simulation Prbias1 Eqn1 S21dB=dB(S[2,1]) S21phase=phase(S[2,1]) DC1 S11dB=dB(S[1,1]) S parameter S22dB=dB(S[2,2]) mufactor=Mu(S) CL11 simulation mufactorprime=Mu2(S) Subst=Subst1 stabL=StabCircleL(S) W=0.82 mm stabS=StabCircleS(S) S=3 mm L=2.2 mm SP1 Type=log Rrfc2 Start=100 kHz R=2.1 Ohm Stop=1.5 GHz Crfc1 C=2.342 pF Points=100 Noise=yes Lrfc2 L=10uH Subst1 er=4.6 h=1.57 mm number Prbias1.I t=0.37 mm 1 0.0366 tand=2e-4 CL9 rho=1.68e-8 Subst=Subst1 D=0.15e-6 W=0.82 mm S=3 mm L=3 mm CL5 CL6 CL7 CL8 Subst=Subst1 Subst=Subst1 Subst=Subst1 Subst=Subst1 W=3 mm W=1.5 mm W=1.5 mm W=3 mm S=3 mm S=3 mm X1 S=3 mm S=3 mm L=6 mm Rccin1 L=2.76 mm L=1.4 mm Rccout1 L=6 mm R=0.05 Ohm R=565 mOhm 10 9 Ccin1 Lccin1 spice Ccout1 Lccout1 L=58.4 pH C=100 nF L=58.4 pH C=100 nF 11 Ref P1 Num=1 P2 Z=50 Ohm Num=2 Z=50 OhmFigure 3.10: QUCS schematic for frequency domain simulations of prototype2 with parasitics and coplanar transmission line sections.
3.3. Simulations 40 -8 -10 -12S22dBS11dB S[2,2] S[1,1] -14 -16 -18 -20 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) frequencyFigure 3.11: Simulated S11 and S22 of prototype 2. Modulus in dB (left)and Smith chart (right). 19.5 19 18.5 18 17.5 frequency: 1.02e+09 S21dB 17 S21dB: 15.9 16.5 16 frequency: 1.47e+05 15.5 S21dB: 16 15 14.5 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) Figure 3.12: Simulated S21 (modulus in dB) of prototype 2.
3.3. Simulations 41 1.45 Stability circles for source (blue) and load (red) impedance 1.4 1.35 1.3mufactorprime mufactor 1.25 1.2 1.15 1.1 1e5 1e6 1e7 1e8 1e9 3e9 1.5 frequency (Hz) frequencyFigure 3.13: Simulated stability parameters µ and µ (left) and stabilitycircles (right). 50 acfrequency: 1.29e+09 Cs: 1e-15 45 voutdB: 43.4 40 35 Transimpedance gain (dB) 30 acfrequency: 7.38e+07 Cs: 3.5e-11 25 voutdB: 46.1 20 15 10 acfrequency: 3.14e+07 Cs: 3.2e-10 5 voutdB: 40.8 0 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz)Figure 3.14: Simulated transimpedance gain of prototype 2 for diﬀerentphotodetector capacitances.
Chapter 4Transimpedance AmpliﬁerDesign 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 conceptsThe most fundamental concept behind the design of a transimpedance am-pliﬁer is negative feedback. In ﬁgure 4.1, the negative feedback conﬁgurationfrom 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 , whichoutputs the feedback signal Sf b . The diﬀerence between the input signal Siand Sf b is the error signal Se , which is fed to the basic ampliﬁer. We canderive the following equations: So = a · Se (4.1) Sf b = f · So (4.2) 43
4.1. Basic feedback concepts 44 Se = Si − Sf b (4.3) Combining these equations we obtain the closed-loop gain: So a = (4.4) Si 1 + af If the loop gain af >> 1, the closed-loop gain can be approximated by So 1 ≈ (4.5) Si f which only depends on the feedback network. Basic amplifier Se Si a So + - Sfb ƒ Feedback network Figure 4.1: Ideal feedback conﬁguration. When dealing with real electronic networks, the previously deﬁned signalsare currents and voltages. This gives rise to four basic feedback conﬁgura-tions. These are speciﬁed according to whether the output signal So whichis sampled is a current or a voltage and whether the feedback signal Sf b isa current or voltage. The interested reader may refer to  for a rigoroustreatment of feedback. Table 4.1 summarises the feedback conﬁgurations. Traditionally, transimpedance ampliﬁers have been implemented usinga basic ampliﬁer in a shunt-shunt feedback conﬁguration (ﬁgure 4.2). Theoutput voltage vo is sensed and the feedback network generates a feedbackcurrent if b , so the transfer function f of the feedback network has units ofconductance, Ω−1 . The error current signal is ie = ii − if b . From equation
4.1. Basic feedback concepts 45 Table 4.1: Basic feedback conﬁgurations. Conﬁguration Sf b 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 ie + ii zi avi + vo − - ifb fvo vo Feedback network Figure 4.2: Shunt-shunt feedback conﬁguration.4.5, we can see that the closed-loop gain has units of resistance, Ω, hencethe 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 tosupply voltage variation, temperature changes, or device aging. A secondbeneﬁt is that negative feedback allows the designer to modify the input andoutput impedances of the circuit in any desired fashion and ﬁnally, it reducesthe signal distortion and increases the bandwidth . All these beneﬁts havea cost in gain and stability. When designing a circuit with feedback, thestability must be veriﬁed.
4.2. Rationale 464.2 RationaleIn this section we will provide a rationale justifying the need of designinga transimpedance ampliﬁer using discrete BJT transistors instead of usingcommercially 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 andenough transimpedance gain, the basic ampliﬁer, which can be an operationalampliﬁer, must have a huge GBP (Gain Bandwidth Product). Operationalampliﬁers are not designed for very high frequencies so, at the time of writ-ing this thesis, we have not found any commercially available operationalampliﬁer that suits our needs. We have also searched for COTS (Commer-cial Oﬀ-The-Shelf ) integrated transimpedance ampliﬁers. For example, theAN1435 family of transimpedance ampliﬁers from Philips Semiconductorshave a maximum bandwidth of 280 MHz, the SA5212A and closely relatedparts also from Philips Semiconductors has a bandwidth of 140 MHz. Thetransimpedance 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 theCTA requirements and the ampliﬁer is commercialised in die form, withoutpackage. Analog Devices have the AD8015 transimpedance ampliﬁer, but itonly 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. Inthis thesis, we have designed, implemented and tested a transimpedanceampliﬁer prototype with discrete transistors.4.3 Selection of the transistorThe most critical step in the design of an ampliﬁer is the selection of theactive device, the transistor. The ﬁrst design decision is to choose betweenFET (Field Eﬀect Transistor ) or BJT. Each family of transistors has itsadvantages and drawbacks.
4.4. Small signal models and distortion 47 The silicon junction transistor is one of the oldest and most popular activeRF device because of its low cost and good operating performance in terms offrequency range, power capacity and noise characteristics. Silicon junctiontransistors are useful for ampliﬁers up to the range of 2-10 GHz. Thesetransistors 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 developmentswith junction transistors using SiGe have demonstrated much higher cutoﬀfrequencies, making these devices useful in low cost circuits operating atfrequencies of 20 GHz or higher. Heterojunction bipolar transistors may useGaAs 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 OxideSemiconductor FET ), and the MISFET (Metal Insulator SemiconductorFET ). Unlike junction transistors, which are current controlled, FETs arevoltage 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 designof the prototype, since it is a low cost device which oﬀers high gain and lownoise. The chosen transistor is the BFP420 from Inﬁneon . This transistorhas a transition frequency fT = 25 GHz and a noise ﬁgure of 1.1 dB at 1.8GHz.4.4 Small signal models and distortionTransistors are essentially non-linear devices. The large signal behaviouris described mathematically by the Ebers-Moll model or the Gummel-Poonmodel, which considers more physics of the transistor [11, chap. 10] and it’sthe 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 twopn-junctions with the positive side connected to the base, each of them in
4.4. Small signal models and distortion 48parallel with a voltage-controlled current source pointing towards the base.Put mathematically: IE + IC + IB = 0 (4.6) qVBE qVBC IC = αF IES (e kT − 1) − ICS (e kT − 1) (4.7) qVBC qVBE IE = αR ICS (e kT − 1) − IES (e kT − 1) (4.8) αF IES = αR ICS (4.9) αF βF = (4.10) 1 − αF The currents IES and ICS are the reverse-bias B-E and B-C junctioncurrents, 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 thetransistor working in forward active mode, which is more adequate for analogdesign, we must linearise the Ebers-Moll equations and add the diﬀusion andjunction capacitance of the B-E and B-C junctions. The linearisation is doneby keeping only the ﬁrst-order terms of the Taylor series expansion of theequations around the bias point Q: f (Q) f (Q) f (3) (Q) f (x) = f (Q)+ (x−Q)+ (x−Q)2 + (x−Q)3 +· · · (4.11) 1! 2! 3! From the two-variable Taylor series expansion of the Ebers-Moll currentequations, and taking into account the diﬀusion and junction capacitances,the following parameters are derived: ∂IC qIC • Transconductance: gm = ∂VBE = kT • B-E diﬀusion capacitance: Cπ = τF gm where τF is the forward base transit time.
4.5. Design of the prototypes 49 Cµ B C rπ Cπ gmvbe ro E Figure 4.3: Simpliﬁed Hybrid-Pi small signal model of the BJT. β0 ic • B-E diﬀusion resistance: rπ = gm where β0 = ib is the small signal current gain of the transistor. ∂VCE VA • Output resistance due to Early eﬀect: r0 = ∂IC = IC where VA is the Early voltage. • Reverse biased junction capacitance: Cµ The simpliﬁed small signal circuital model for the BJT is shown in ﬁgure4.3. The high order terms of the Taylor expansion are distortion terms thatmust be minimised. We will deal with these terms when designing for lowdistortion.4.5 Design of the prototypes4.5.1 Systematic design procedureThe design strategy used for the prototypes is the structured electronic designmethodology proposed in . This methodology attacks the design problemorthogonally, which means that each ﬁgure of merit (noise, signal power andbandwidth) of the circuit is optimised independently. Obviously, no designparameter is trully orthogonal in real life, but the appropriate assumptionswill be made so that an orthogonal design can be made without deviatingtoo much from the optimum. For the three design aspects, the followingassumptions on orthogonality hold: • When noise is evaluated, signal power aspects, like distortion, are not considered. Therefore, the linear small signal models of the components
4.5. Design of the prototypes 50 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. Thesesimpliﬁcations yield a superior performance than the actual performance, sowe will obtain an upper bound of the performance. The designed prototypeswill be simulated to verify more accurately the real behaviour of the circuitbefore 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. Design of the prototypes 514.5.2 Checking device parametersIt is useful to perform some basic simulations using the SPICE model ofthe BFP420 transistor to gain insight on the large signal behaviour. Thefollowing 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 networkThe design of the feedback network involves the substitution of the activecircuit by a theoretical circuit element called nullor. A nullor is deﬁned asa two-port network (ﬁgure 4.5) with the following ABCD parameters [17,chap. 2.2.2]: vi 0 0 vo = (4.12) ii 0 0 io Being an ideal element, the nullor has inﬁnite current gain, voltage gain,transconductance and transimpedance. As an example, an ideal operationalampliﬁer is modelled as a nullor. The nullor has a nullator at its input and a norator at its output. Anorator is a theoretical current or voltage source that can generate arbitrarycurrent or voltage. A nullator is another theoretical element with no currentﬂow nor voltage drop. The transimpedance ampliﬁer works in a shunt-shunt feedback conﬁgu-ration. This means that the feedback network senses a voltage and outputsa current which is compared to the reference current coming from the inputcurrent source. The nullor actively imposes the condition to the error currentie = ii − if b = 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∞ =
4.5. Design of the prototypes 52 BFP420 Infineon NPN BJT common emitter output characteristics 0.025 Ib = 0 uA Ib = 40 uA Ib = 80 uA Ib = 120 uA Ib = 160 uA Ib = 200 uA 0.02 0.015 Ic (A) 0.01 0.005 0 0 1 2 3 4 5 VCE (V) (a) Common emmiter output characteristics. BFP420 Infineon NPN BJT Forward Beta vs Ic for VCE=1V 100 80 60 Forward Beta 40 20 0 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 10 10 10 10 10 10 10 10 10 10 Ic (A) (b) Beta vs IC for VCE = 1V BFP420 Infineon NPN BJT IC,IB vs VBE for VCE=1V 100 Ic Ib -2 10 -4 10 10-6 (A) -8 10 -10 10 -12 10 -14 10 0 0.2 0.4 0.6 0.8 1 VBE (V) (c) IC and IB vs VBE in logarithmic vertical scale. Figure 4.4: Large signal plots of the BFP420 BJT transistor.
4.5. Design of the prototypes 53 ii io + + vi Nullor vo - - Figure 4.5: The nullor.−Rf . The real closed-loop gain will be somehow smaller depending in howclose the active circuit resembles a nullor. The prototypes designed have transimpedance gains Rf = 300 Ω and1.5 KΩ.4.5.4 Design of the ﬁrst nullor stage: noiseA multistage active circuit must be implemented to orthogonally optimisethe noise, bandwidth and distortion performance of the ampliﬁer. According to the Friis formula (equation 4.13), the noise characteristicsof the ampliﬁer can be improved taking only into account the ﬁrst stage ofthe nullor implementation, F2 − 1 F3 − 1 F4 − 1 Ftotal = F1 + + + + ··· (4.13) G1 G 1 G2 G1 G 2 G3 The reduction of the noise ﬁgure of the following stage is conditioned bythe gain of the ﬁrst stage. Additionally, for an optimal implementation of thenullor, the loop gain must be maximised. These facts makes common-emitterthe most suitable conﬁguration for the ﬁrst stage of the nullor, since it pro-vides more gain than the other transistor conﬁgurations. The common-baseconﬁguration was also considered, since its low input impedance implementsthe nullator as a current probe and thus, rejects the inﬂuence of the sourcecapacitance in the ampliﬁer’s performance. Figure 4.6 shows the noise analysis of the feedback network and the ﬁrststage of the nullor implementation. In step 1 (4.6a), the noise generators areidentiﬁed. The thermal noise generator of the load RL can be neglected due
4.5. Design of the prototypes 54 vnf Rf + − + − ven + − + - + + + − + − vnl ien Zs RL - + - - (a) Step1: The v-shift transform enables us to split ven in the two branches. (ven + vnf)/Rf Rf + - + + ien RL Zs ven/Zs - + - - (b) Step2: ven and vnf are uncorrelated noise generators and can be added into a single noise generator ven + vnf . The i-shift transform ven +vnf enables us to split the current noise generator Rf in 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 theﬁrst stage of the nullor implementation.to the inﬁnite gain of the nullor. Using the v-shift transform , the voltagenoise generator ven is moved into the two connected branches. In step 2, thevoltage noise generators are transformed into their equivalent current noise ven +vnfgenerators and, using the i-shift transform, the generator Rf is movedto the input and the output branches (ﬁgure 4.6b). Adding the current noise generator at the input node we obtain the totalinput referred noise current: ven ven + vnf in = ien + + ZS Rf 1 1 vnf in = ien + ven + + (4.14) ZS Rf Rf
4.5. Design of the prototypes 55 The noise generators ven and ien are the input referred equivalent noisegenerators of the common emitter BJT that implements the ﬁrst stage ofthe nullor. The mean square spectral noise density is given by 2 ven 1 rb = 4kT rb + 2qIC 2 + 2 f gm βF 1 thermal noise shot noise 2qIC ≈ 4kT rb + 2 (4.15) gm i2 en 2qIC = 2qIb + 2 f βF 1 shot noise shot noise ≈ 2qIb (4.16) Plugging equations 4.15 and 4.16 into equation 4.14, we obtain 2 i2 n 2qIC 1 4kT Rf = 2qIb + 4kT rb + 2 · 2πf CS + + 2 f gm Rf Rf 2 IC 2qIC 1 4kT = 2q + 4kT rb + 2 · 2πf CS + + (4.17) βF 1 gm Rf Rf 1 Note that ZS = 2πf CS in equation 4.17, where CS is the capacitance ofthe 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].
4.5. Design of the prototypes 56 We will minimise the noise by choosing a collector current that yieldsa current noise low enough to meet the speciﬁcations. In ﬁgure 4.7a, the i2integrated noise current in = B n f df over the frequency band 100KHz - 750 MHz is plotted as a function of IC with Rf = 300. The plothas been generated for diﬀerent values of the photodetector’s capacitanceCS . The transistor parameter βF 1 is obtained with a SPICE simulation andthe base bulk resistance rb is speciﬁed in the SPICE model of the BFP420transistor. 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 fordiﬀerent values of CS and IC = 2 mA. This ﬁgure shows the strong inﬂuenceof 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 = 7 µA (see chapter2.3).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 0.232 µA 30 35 pF 1.35 µA 5 320 pF 11.9 µA 0.64.5.5 Design of the last stage: distortionWe distinguish two types of distortion, weak distortion and clipping distor-tion. Weak distortion arises from the linear approximation of the non-linearbehaviour of the transistors in the ampliﬁer. Clipping distortion results fromthe limited range in which the transistors operate in the linear region of thecharacteristics and enters the saturation and cutoﬀ regions. To be able to prevent clipping distortion, we must know the maximumexpected output signal for the device and use a bias point that is far from
4.5. Design of the prototypes 57 0 10 1 pF 35 pF 320 pF 10-2 10-4 Input noise current (A ) 2 -6 10 -8 10 10-10 -12 10 -14 10 10-12 10-10 10-8 10-6 10-4 10-2 100 Ic (A) (a) Current noise vs IC for various values of CS and Rf = 300 Ω 10-18 1 pF 35 pF 320 pF -19 10 / Hz) 2 Input noise current density (A 10-20 10-21 -22 10 -23 10 5 6 7 8 9 10 10 10 10 10 f (Hz) i2 n (b) Current noise density f 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
4.5. Design of the prototypes 58with low power consumption. It is clear that a non-linear dynamic rangecompression or the bi-gain scheme with diﬀerential inputs and outpus usedin 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, sowe will relax this requirement for our prototype. We must not forget thatthe objective of this thesis is to analyse the beneﬁts of using transimpedancepreampliﬁcation instead of an MMIC or voltage preampliﬁcation. The relaxed dynamic range is 1 to 200 phe. This implies a maximumvoltage at the output of the ampliﬁer of about 0.42 V. Considering a 50 Ωload, the peak output current will be 8.4 mA. As a matter of fact, the highgain stage of the PACTA ampliﬁer has a dynamic range ∼ 200 phe . Thedesign 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 currentsand voltages it will handle. We will employ a common collector stage. Itdoesn’t invert the signal, so only the common emitter stage is inverting. Itprovides voltage gain, needed for the loop gain. The loop phase is 180o ,which is needed for negative feedback. The low output impedance of thecommon collector conﬁguration makes it suitable for the implementation ofthe 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 stabilityThe transfer function of any linear electronic system can be expressed as aratio of complex polynomials: N (s) a0 + a1 s + a2 s2 · · · am sm a(s) = = (4.18) D(s) b0 + b1 s + b2 s2 · · · bn sn where the order m of the numerator is the number of zeros in the systemand the order n of the denominator is the number of poles in the system. We can factorise polynomials in the numerator and denominator of thetransfer function 4.18 to make the poles and zeros explicit:
4.5. Design of the prototypes 59 s s s 1− z1 1− z2 ··· 1 − zm a(s) = a0 (4.19) s s s 1− p1 1− p2 ··· 1 − pn 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 islargely limited by the dominant pole, i.e. the lowest frequency pole, if itexists. For the dominant pole |p1 | << |p2 |, |p3 |, · · ·, so we can approximatethe gain magnitude in the frequency domain as a0 |a(jω)| ≈ (4.20) ω 1+ p1 This is the dominant pole approximation and is accurate as long as theﬁrst order pole is really dominant and there are no zeros near the dominantpole 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 functionin equation 4.4, a0 1+ ps a0 1 A(s) = a0 = s 1+ s f (1 + ao f ) + p1 p1 ao 1+ao f = (4.21) 1 + (1+as f )p1 o Equation 4.21 shows that the eﬀect of feedback is a shift of the pole tohigher frequencies by a factor 1+ao f and a gain reduction of the same factor. Up to this point, our nullor implementation has a common-emitter inputstage and a common-collector output stage. It is interesting to estimate thebandwidth performance of the ampliﬁer. To do this, the dominant pole andthe loop gain must be calculated. A direct calculation using the small signalmodel of the ampliﬁer is tedious and prone to errors, so only the loop gainwill be computed. The RR (Return Ratio) is a good approximation of the loop gain . Thetotal gain around the feedback loop is obtained by breaking the loop at some
4.5. Design of the prototypes 60convenient point and inserting a test signal. Figure 4.8 shows the circuit usedto calculate the return ratio of the ampliﬁer. The dependent current sourcegm1 v1 is replaced by the test signal ix . To gain insight on the factors thatdetermine the bandwidth its enough to obtain the low frequency loop gain,so the capacitances have been removed from the models. The return ratio is gm1 v1 L(0) = ix βF 1 βF 2 RL RC1 = − (4.22) βF 2 RL (rπ1 + Rf ) + (rπ1 + Rf + RL )(RC1 + rπ2 ) Rf C2 B1 C1 B2 + + v1 rπ1 ix RC1 v2 rπ2 gm2v2 - - E2 E1 RLFigure 4.8: Small signal model with test signal ix used to calculate the lowfrequency return-ratio of the ampliﬁer. The load resistance RC1 at the collector of Q1 is needed to bias thecollector current IC1 , but it degrades the loop gain, so it must be maximised.For narrowband ampliﬁers, a small RFC inductance is used to present inﬁniteimpedance and remove any inﬂuence of the bias circuit in the small signalparameters. For very broadband ampliﬁers, these RFC need to be quitebig and their parasitics introduce unpredictable eﬀects which are diﬃcult toaddress. We have decided not to use an inductor and try to use a big valuefor RC1 . If RC1 → ∞, the return ratio is given by βF 1 βF 2 RL L(0) = − (4.23) rπ1 + Rf + RL
4.5. Design of the prototypes 61 The feedback resistance Rf is in the denominator of equation 4.23. Thismeans 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 decreaseof the bandwidth but also the nullor implementation moves away from theideal so the ampliﬁer’s performance is lower. On the other hand, a decreaseof Rf (more feedback) will increase the loop gain and the ampliﬁer mayoscillate. The loop gain is a measure of the maximum bandwidth capacity of theampliﬁer. 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. gm ωT 2. At high frequencies βF (jω) ≈ jω(Cπ +Cµ ) = jω , 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 to10 mA without compromising its noise behaviour. The stability of the ampliﬁer will depend on Rf , the feedback factor andthe impedance of the photodetector. For small values of Rf , the loop gainincreases and the ampliﬁer has signiﬁcant ringing. To reduce this ringing forlow 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
4.5. Design of the prototypes 62 Rf Q1 Q2 RL stage1 stage2 Figure 4.9: Final conﬁguration of the ampliﬁer in two CE-CC stages. 1 1+Rf Cf s f = Rf . 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 = − Rf1Cf , 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 stagesof the ampliﬁer.4.5.7 Bias circuit and output matchingThere is a wide catalogue of biasing circuits, ranging from simple resistornetworks to sophisticated active bias circuits which provide very stable biascurrents. Current mirrors are widely used for bias and active loading in integratedampliﬁers. For the prototype designed here, a much more simpler resistorscheme 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 thetransistors. 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 thefrequencies of operation. The input, output and feedback capacitors are only
4.5. Design of the prototypes 63used 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 assumedthat RL = 50 Ω. The matching resistor halves the eﬀective transimpedancegain, due to voltage division. The design of a more eﬃcient output matchingscheme is left for future work. An improvement of the bias circuit results in prototype 2 (ﬁgure 4.11). VCC RC1 RB1 RC2 Q1 Q2 Rmatch RE2 RL RfFigure 4.10: Prototype 1 with bias network, coupling capacitors, and outputmatching resistor.4.5.8 Prototype 1The ﬁrst designed prototype is going to be used with transimpedance gainsRf = 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 sourceimpedances. The simulations of the scattering parameters have predictedthat the ampliﬁer is not unconditionally stable for f > 1 GHz. Since thesource impedance ZS of the photodetector is quite complex, it is convenientto make the prototype unconditionally stable. This has been accomplishedby introducing a 30 Ω resistor between the output and ground. The bias network design is straightforward. For IC1 = 10 mA, IC1 = 20
4.5. Design of the prototypes 64 VCC RC1 RB1 Q1 Q2 Rmatch RE2 RL RfFigure 4.11: Prototype 2 with bias network, coupling capacitors and outputmatching resistor.mA and VCE2 = 2 V, the calculation of the bias resistors follows: VCC − VCE2 Rc2 + RE2 = = 150 Ω (4.24) IC2 We choose RC2 = 100 Ω and RE2 = 50 Ω. VB2 = VC1 = VCE1 = VE2 + VBE2 ≈ 1 V + 0.8 V = 1.8 V (4.25) VCC − VC1 RC1 = = 320 Ω (4.26) IC1 The simulations and experimental measurements have conﬁrmed thatthe dynamic range of this prototype is very limited and does not meet theCTA requirements. Additionally, the input impedance is too high. For thisreasons, a new prototype with improved biasing has been designed.4.5.9 Prototype 2The second prototype addresses the ﬂaws of the ﬁrst prototype. The weakpoint of prototype 1 is the limited dynamic range, of about 47 dB for a
4.6. Simulations 65transimpedance of 300. For Rf = 1500 Ω, the dynamic range gets evenworse, as expected. The weak point for dynamic range was identiﬁed as the bias resistor atthe collector of Q2, RC2 . This resistor limits severely the voltage swing atthe output of the ampliﬁer. For this reason, it has been removed from thebias network. Another weak point of the ﬁrst design is the input impedance. The smallsignal parameters and the series 7 Ω resistor for ringing reduction causesthe input impedance not to be low enough. Thus, the input series resistor isreduced to 3 Ω and the loop gain is increased by reducing the bias currentIC1 to 5 mA and IC2 to 10 mA, without increasing the noise. This resultsin a bias resistor RC1 = 600 Ω, which reduces the gain loss and the powerconsumption. 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-emittervoltage is forced to VCE1 = VE2 + VBEon ≈ 1.85 V, and we are neglecting thebase current of Q2. The resistor for setting the base current of Q1, takingthe typical βF = 90 from the datasheet , is RB1 = 21.6K Ω.4.6 SimulationsIn 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 66valid up to 6 GHz. Refer to 8.4 for the SPICE model.4.6.1 Prototype 1Figure 4.12 shows the schematic used for the SPICE simulations, which arethe DC and small signal simulations, and the noise simulation. It includesthe parasitics of the capacitors implemented as subcircuits for the sake ofclarity. A5 SPICE model Model name: 0805_PARASITICS_CAP File: /home/nacho/ingenieria_electronica/proyecto/characterizations/passive_elements/capacitors/parasitic_spice_models/0805_capacitor.cir A1 SPICE model Model name: M_BFP420 File: /home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/transistors/BFP420_spar10GHz_noisepar6GHz_spice10GHz/BFP420_SPICE.cir 0805_PARASITICS_CAP_100nF A2 SPICE directive 0805_PARASITICS_CAP_1uF * ?.AC DEC 100 100kHz 1.5Giga 1 + A3 SPICE directive Vcc DC 5V - XCb2 XCb3 * ?.TRAN 10.00p 10.00n 0.00n RC1 RC2 2 A4 SPICE directive 316 100 * ?.OP A6 SPICE directive .NOISE V(out) Is DEC 100 100kHz 750Meg ? RB1 3 BFP420 2 XQ2 10k SPICE-NPN XCd2 1 50 XCd1 3 BFP420 Rcomp 2 XQ1 0805_PARASITICS_CAP_100nF Rmatch RE2 SPICE-NPN 0805_PARASITICS_CAP_100nF 7 Rstab 1 50 RL 30 50 Is Rsh Rf noisy=0 Cs AC 1A 35pF 10k noisy=0 300 XCd3 0805_PARASITICS_CAP_100nF TITLE Prototype 1: Two stage CE-CC transimpedance amplifier with parasitics FILE: REVISION: PAGE OF DRAWN BY: Ignacio Diéguez Estremera Figure 4.12: Prototype 1 with parasitics for SPICE simulations. With the .OP SPICE directive, the small signal parameters have beenobtained with ngspice and are shown in table 4.3. With the .NOISE SPICE directive, the noise currents and voltages havebeen obtained and are shown in table 4.4. The noise currents obtained herewith the simulation are very close to those calculated in the noise analysisof 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 thiscapacitance 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−13Table 4.4: Prototype 1 total current and voltage noise integrated in theband 100 Khz - 750 MHz simulated with ngspice for diﬀerent photodetectorcapacitance. CS in vn 1 pF 0.324 µA 25.2 µV 35 pF 1.36 µA 80.6 µV 320 pF 12.26 µA 87.6 µVampliﬁer and the photodetector capacitance, which is dominant. The lowinput impedance of the transimpedance ampliﬁer limits this eﬀect to a greatextend. 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 ac simulation dc simulation Parameter sweep V1 AC1 DC1 U=5 V Type=log Start=10 kHz SW2 Cb2 Cb3 Stop=3 GHz transient Sim=AC1 C=1 uF C=100 nF Points=1000 simulation Type=list Param=Cf Values=[0.1 pF; 0.2 pF; 0.3 pF; 0.4 pF; 0.5pF] RC1 RC2 Parameter TR1 R=316 Ohm R=100 Ohm sweep Type=lin Equation Start=0 Stop=20 ns Eqn2 SW1 transZ=dB(vout.v) Sim=AC1 RB1 Type=list R=10k Ohm Param=Cs Values=[1 fF; 35 pF; 320 pF] XQ1 XQ2 Inputcurrent 2 1 2 1 Lcd1 Rmatch Cd1 Rcd1 Rcomp1 spice spice R=50 Ohm C=100 nFL=58.4 pH R=0.565 Ohm R=7 Ohm 3 3 vout I1 Cs Rsh I1=0 C=Cs I2 R=100 kOhm I=1 A Rcd3 RE2 Lcd2 I2=1 uA Ref Ref Cd2 Rcd2 R=0.565 Ohm R=50 Ohm L=58.4 pH R3 T1=6 ns C=100 nF R=0.565 Ohm RL R=30 Ohm T2=11 ns R=50 Ohm Lcd3 L=58.4 pH Cd3 C=100 nF Rf R=300Figure 4.13: Protototype 1 schematic with parasitics for AC and transtientsimulations 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 thehigher 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 thestability circles for source and load impedances. The simulations predictunconditional stability in the simulated frequency band. Finally, the simulated power consumption is 150 mW, which is accept-able.4.6.2 Prototype 2Figure 4.19 shows the schematic used for the SPICE simulations. The smallsignal parameters of the transistors are shown in table 4.5. As before, the noise currents and voltages have been obtained and areshown 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 scatteringparameters. 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 50 40 30 Cs=320pF:transimpedance Cs=35pF:transimpedance Cs=5pF:transimpedance Cs=0:transimpedance 20 10 0 -10 -20 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) (a) Rf = 300 Ω. 60 55 50 45 40 35 Cs=320pF:transimpedance Cs=35pF:transimpedance Cs=5pF:transimpedance Cs=0pF:transimpedance 30 25 20 15 10 5 0 -5 -10 -15 -20 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) (b) Rf = 1.5 KΩFigure 4.14: Inﬂuence of photodetector capacitance on the transimpedancebandwidth of prototype 1. CS = 0 pF, 35 pF and 320 pF. Transimpedancegain is plotted in dB.parameter is shown in ﬁgure 4.22. The transimpedance gain for diﬀerent photodetector capacitance is shownin 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 CL18 Subst=Subst1 W=0.75 mm S=1.121 mm L=5.7 mm V1 U=5 V Equation Cb2 Cb1 C=1 uF C=100 nF Pr1 dc simulation CL12 CL14 Eqn1 Subst=Subst1 Subst=Subst1 S21dB=dB(S[2,1]) W=0.75 mm W=0.75 mm S11dB=dB(S[1,1]) Subst1 DC1 S=1.121 mm RC1 S=1.121 mm S22dB=dB(S[2,2]) er=4.6 R=316 Ohm L=6 mm L=3.9 mm mufactor=Mu(S) h=1.57 mm mufactorprime=Mu2(S) t=0.37 mm S parameter stabL=StabCircleL(S) tand=2e-4 RC2 simulation stabS=StabCircleS(S) rho=1.68e-8 R=100 Ohm D=0.15e-6 RB1 R=10k Ohm SP1 Type=log CL8 Start=10 kHz CL9 Subst=Subst1 Stop=2 GHz Subst=Subst1 W=0.75 mm CL13 number Pr1.I W=0.75 mm S=1.121 mm Points=100 Subst=Subst1 1 0.0292 S=1.121 mm L=2.11 mm W=0.75 mm L=2.4 mm S=1.121 mm XQ1 XQ2 L=2.11 mm CL7 CL3 CL4 CL6 Subst=Subst1 Subst=Subst1 Subst=Subst1 Subst=Subst1 2 1 2 1 W=1.12 mm W=2.55 mm W=2.55 mm W=2.55 mm S=1.121 mm S=1.121 mm S=1.121 mm S=1.121 mm Lcd3 L=2.92 mm L=3.6 mm L=3.4 mm Rmatch1 L=4.26 mm Cd3 Rcd3 Rcomp1 spice spice R=50 Ohm CL5 C=100 nF L=58.4 pH R=0.565 Ohm CL1 R=7 Ohm CL11 3 CL19 3 P2 Subst=Subst1 Subst=Subst1 Subst=Subst1 Subst=Subst1 Num=1 W=2.55 mm W=2.55 mm W=1.12 mm W=1.12 mm Ref Ref Cd1 Lcd2 Rcd2 Z=50 Ohm S=1.121 mm S=1.121 mm S=1.121 mm S=1.121 mm CL17 L=58.4 pH R=0.565 Ohm C=100 nF L=3.56 mm L=2.4 mm L=3.56 mm L=5 mm Subst=Subst1 P1 W=1.12 mm Rstab Num=2 CL15 R=30 Ohm Subst=Subst1 S=1.121 mm Z=50 Ohm W=1.12 mm L=3.9 mm RE1 S=1.121 mm R=50 Ohm L=2.55 mm CL2 Rcd1 Subst=Subst1 R=0.565 Ohm W=1.12 mm S=1.121 mm Lcd1 L=2.55 mm L=58.4 pH Cd4 C=100 nF Rf1 CL16 R=300 Ohm Subst=Subst1 W=1.12 mm S=1.121 mm L=3.15 mmFigure 4.15: Protototype 1 schematic with parasitics and coplanar lines forS-parameter simulations with QUCS. 5 0 -5 -10 -15Rf=1500:S22dBRf=1500:S11dBRf=300:S22dBRf=300:S11dB Rf=1500:S[2,2] Rf=1500:S[1,1] Rf=300:S[2,2] Rf=300:S[1,1] -20 -25 -30 -35 -40 -45 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz)Figure 4.16: Simulated S11 and S22 of prototype 1. Modulus in dB (left)and Smith chart (right).dict unconditional stability in the simulated frequency band. The predictedpower consumption is lowered to 78 mW.
4.6. Simulations 72 A5 SPICE model Model name: 0805_PARASITICS_CAP File: /home/nacho/ingenieria_electronica/proyecto/characterizations/passive_elements/capacitors/parasitic_spice_models/0805_capacitor.cir A1 SPICE model Model name: M_BFP420 File: /home/nacho/ingenieria_electronica/proyecto/amplifier_2011/transimpedance/transistors/BFP420_spar10GHz_noisepar6GHz_spice10GHz/BFP420_SPICE.cir 0805_PARASITICS_CAP_100nF A2 SPICE directive 0805_PARASITICS_CAP_1uF * ?.AC DEC 100 100kHz 1.5Giga 1 + A3 SPICE directive Vcc DC 5V - XCb2 XCb3 * ?.TRAN 10.00p 10.00n 0.00n RC1 2 A4 SPICE directive 600 * ?.OP A6 SPICE directive .NOISE V(out) Is DEC 100 100kHz 550Meg ? RB1 3 BFP420 2 XQ2 21.6k SPICE-NPN XCd2 1 50 XCd1 3 BFP420 out Rcomp 2 XQ1 Rmatch RE2 SPICE-NPN 0805_PARASITICS_CAP_100nF 0805_PARASITICS_CAP_100nF 3 1 100 RL 50 Is Rsh Rf noisy=0 Cs AC 1A 35pF 10k noisy=0 1000 XCd3 0805_PARASITICS_CAP_100nF TITLE Prototype 2: Improved dynamic range FILE: REVISION: PAGE OF DRAWN BY: Ignacio Diéguez Estremera Figure 4.19: Prototype 2 with parasitics for SPICE simulations. CL20 V1 Subst=Subst1 U=5 V W=0.75 mm Equation S=1.121 mm CL14 L=7 mm Subst=Subst1 Pr1dc simulation CL12 Eqn1 W=0.75 mm Subst=Subst1 S21dB=dB(S[2,1]) S=1.121 mm W=0.75 mm S11dB=dB(S[1,1]) Subst1 RC1 L=34 mm S=1.121 mmDC1 S22dB=dB(S[2,2]) er=4.6 R=600 Ohm L=6 mm mufactor=Mu(S) h=1.57 mm Cb2 mufactorprime=Mu2(S) t=0.37 mmS parameter stabL=StabCircleL(S) C=1 uF tand=2e-4simulation stabS=StabCircleS(S) rho=1.68e-8 D=0.15e-6 RB1 R=21.6k Ohm Cb1 C=100 nFSP1Type=log CL9 CL8Start=10 kHz Subst=Subst1 Subst=Subst1 CL13 number Pr1.I W=0.75 mm W=0.75 mmStop=2 GHz Subst=Subst1Points=200 1 0.0156 S=1.121 mm S=1.121 mm W=0.75 mm L=2.4 mm L=2.11 mm S=1.121 mm XQ1 XQ2 L=2.33 mm CL7 CL3 CL6 Subst=Subst1 Subst=Subst1 Subst=Subst1 2 1 2 1 W=1.12 mm W=2.55 mm W=2.55 mm CL19 S=1.121 mm S=1.121 mm S=1.121 mm Lcd3 Rcd3 Rcomp1 L=2.92 mm L=3.2 mm Rmatch1 L=5 mm Cd3 spice Subst=Subst1 spice R=50 Ohm CL5 C=100 nF L=58.4 pH R=0.565 Ohm CL1 R=3 Ohm CL11 3 W=1.12 mm 3 P2 Subst=Subst1 Subst=Subst1 Subst=Subst1 S=1.121 mm Num=1 W=2.55 mm W=2.55 mm W=1.12 mm L=5 mm Ref Ref Cd1 Lcd2 Rcd2 Z=50 Ohm S=1.121 mm S=1.121 mm S=1.121 mm CL17 L=58.4 pH R=0.565 Ohm C=100 nF L=3.56 mm L=2.4 mm L=3.56 mm Subst=Subst1 W=0.75 mm P1 CL15 Num=2 Subst=Subst1 S=1.121 mm L=3.25 mm Z=50 Ohm W=1.12 mm RE1 S=1.121 mm R=100 L=2.55 mm CL2 Rcd1 Subst=Subst1 R=0.565 Ohm W=1.12 mm S=1.121 mm Lcd1 L=2.55 mm L=58.4 pH Cd4 C=100 nF Rf1 CL16 R=1000 Ohm Subst=Subst1 W=1.12 mm S=1.121 mm L=3.15 mmFigure 4.20: Protototype 2 schematic with parasitics and coplanar lines forS-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−13Table 4.6: Prototype 2 total current and voltage noise integrated in theband 100 Khz - 550 MHz simulated with ngspice for diﬀerent photodetectorcapacitance. CS in vn 1 pF 0.149 µA 63.5 µV 35 pF 0.767 µA 219 µV 320 pF 6.86 µA 280 µV
4.6. Simulations 74 0 frequency: 7.53e+06 S11dB: -5.31 -5 -10 -15S22dBS11dB S[2,2] S[1,1] -20 -25 -30 -35 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) frequency (Hz)Figure 4.21: Simulated S11 and S22 of prototype 2. Modulus in dB (left)and Smith chart (right). 24 22 20 18 S21dB 16 frequency: 5.52e+08 frequency: 3.21e+04 S21dB: 20.1 S21dB: 19.9 14 12 10 8 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) Figure 4.22: Simulated S21 of prototype 2.
4.6. Simulations 75 60 55 50 45 acfrequency: 3.48e+07 Cs=320pF:transZ: 50.2 40 35 Transimpedance gain (dB) 30 acfrequency: 3.34e+08 Cs=35pF:transZ: 50.2 25 20 acfrequency: 6.85e+08 15 Cs=0pF:transZ: 50.2 10 5 acfrequency: 1.16e+09 0 Cs=5pF:transZ: 50.2 -5 -10 1e4 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz)Figure 4.23: Inﬂuence of photodetector capacitance on the transimpedancebandwidth of prototype 2. CS = 0 pF, 5 pF, 35 pF and 320 pF. Tran-simpedance gain is plotted in dB. 20 15mufactorprime mufactor stabS stabL 10 5 0 1.5 1e4 1e5 1e6 1e7 1e8 1e93e9 frequency (Hz) Figure 4.24: Simulated noise parameters of prototype 2.
Chapter 5Implementation of thePrototypes 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 overviewThe prototypes have been implemented in two layer PCB technology. Theﬁberglass 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. r is the dielectric constant, τis the metal thickness and h is the dielectric thickness. r 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 77impedance of 50 Ω have been used for the input and output traces. Thebias traces have been kept narrow to increase its impedance. Coplanar lineshave some advantages over traditional microstrip lines, such as: increasedelectromagnetic ﬁeld conﬁnement, thus lowering radiation losses and it makesthe connection to ground easier since the ground and the signal traces areon the same board plane. The top and bottom ground planes are connectedusing vias. There should be enough grounded vias along the path of thesignal traces. This way, the ﬁeld conﬁnement is improved and resonanceeﬀects are reduced [2, chap. 3.1]. All the traces should be kept as short aspossible in order to prevent distributed eﬀects. The dimensions of the traces for 50 Ω operation have been calculatedwith the transmission line calculator included with QUCS. The dimensionsin 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 butare easier to manipulate and hand solder than the smaller packages such as0402. All the boards have been designed using PCB, the printed circuit boardeditor of gEDA.
5.2. MMIC prototypes 785.2 MMIC prototypesAs we saw in section 3, the simulations of the S parameters of prototype 1showed an unwanted resonance peak. This issue was solved with the designof prototype 2. In this section, only the implementation of prototype 2 willbe 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 the50 Ω coplanar lines. The biasing trace has been made very narrow comparedto the input and output traces to increase its impedance and improve thegain of the prototype. The package of the MMIC is SOT-343 and all the SMT componentsused are 0805, except the inductor, which is packaged in 1206. The RFconnectors used are male SMA (SubMiniature version A) coaxial connectorswith 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 prototypesFor the implementation of the transimpedance ampliﬁer prototypes, specialcare 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 longitudein 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 coaxialconnectors with an impedance of 50 Ω. The power connector is a verticalmale SMA. The size of the board is 42mm × 40 mm.5.4 GAPD biasing circuitsThe GAPD is operated in Geiger mode. To achieve this mode of operation, areverse bias higher than the breakdown voltage must be applied. The biasingcircuits 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 30mm × 40 mm.output bias circuit (ﬁgures 5.5a and 5.5b), in which the current is convertedinto a voltage using a resistor. This topology is suggested in the datasheet. When the resistor value is 50 Ω, it is also used for impedance matchingwhen the GAPD is connected to a 50 Ω MMIC, so we will connect this circuitto the input of the BGA614 prototype.
5.4. GAPD biasing circuits 80 (a) PCB layer mode (b) PCB photo mode. (c) Final board.Figure 5.3: The transimpedance prototype 1 layout. The size of the boardis 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 thetransimpedance ampliﬁer. We will also connect this circuit to the input ofthe MMIC. The current will be converted into a voltage at the input 50 Ωimpedance.
5.4. GAPD biasing circuits 81 (a) PCB layer mode (b) PCB photo mode.Figure 5.4: The transimpedance prototype 2 layout. The size of the boardis 42mm × 40 mm. VCC VCC RBIAS = 10K 1uF RBIAS = 10K iout vout 50 (a) Voltage output mode. (b) Voltage output board. (c) Current output mode. (d) Current output board. Figure 5.5: GAPD bias circuits.
Chapter 6Measurements 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 InstrumentationThe Laboratorio de Microondas of the Departamento de Fisica Aplicada III:Electricidad y Electronica in the Universidad Complutense de Madrid, wherethis thesis has been developed, is dedicated to the research in high frequencyelectronics. It has modern measure instruments needed for microwave andhigh frequency electronics characterisation. Among the most relevant, thereare two network analysers, a very high frequency oscilloscope, a calibratednoise source, a spectrum analyser, signal generators and very stable pro-grammable power supplies. The network analysers available are the HP8720C (ﬁgure 6.1) and theAgilent Fieldfox RF analyser N9912A. These instruments measure the scat-tering parameters of two-port active or passive devices. The HP8720C iscompletely 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 aportable network analyser for ﬁeld applications. It only provides phase in- 82
6.1. Instrumentation 83formation 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 (ShortOpen Load Thru) calibration kit.Figure 6.1: HP87020C network analyser with HP85020D 3.5 mm calibrationkit. The Agilent Inﬁnium DSO81204B (ﬁgure 6.2) is a state-of-the-art 4 50Ω channel digital sampling oscilloscope capable of sampling an analog sig-nal at a maximum sampling frequency of 40 GSa/s. The maximum analogbandwidth 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 84quency 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 200MHz. It has two 50 Ω independent channels that can output pulses of 5 nswith an amplitude of 50 mV. The power supplies used are the Keithley 6487 and the Hameg HMP2030.6.2 Test setupsOne 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 byone 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 sothat these are repeatable and reproducible.6.2.1 Measuring S-parametersThe measurement of the scattering parameters is performed with the twoavailable network analysers. The HP8720C is used to characterise the BGA614prototype, 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 containsthe settings that have been used for the measurements. Before measuring, the network analyser must be calibrated to removethe 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 SOLTcalibration kit. For the N9912A, the user must select this calibration kitexplicitly in the calibration menu. The resulting measurements are saved in Touchstone ﬁle format (*.s1por *.s2p).
6.2. Test setups 85Table 6.1: Measure settings for the network analysers. The rest of parametersare 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 = 10016.2.2 Measuring the noise ﬁgureWe use the E4402B noise ﬁgure analyser and the noise source Agilent 346Ato measure the noise ﬁgure of the prototypes with the y-factor technique.Table 6.2 contains the settings that have been used for the measurementswith 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 Vdcsource at the back of the analyser. The second step is to calibrate the noisesource. Finally, to perform the measurement, we connect the noise sourceto the input of the DUT (Device Under Test) and the output of the DUT isconnected to the input of the noise analyser. The setup is shown in ﬁgure6.3. The analyser measures both the gain and the noise ﬁgure. The resultingmeasurements 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 GAPDThe GAPD used is the Hamamatsu S10362-33-050C . The key parametersof this device are an eﬀective area of 3 × 3 mm, a terminal capacitance of320 pF and a gain of 7.5 · 105 . The GAPD is biased with the circuits described in 5.4. The bias voltage isset with the Keithley 6487 power supply. An ultraviolet LED (Light EmittingDiode) (Optosource 260019) excites the GAPD through a ﬁber optic. TheLED is connected to one channel of the Tektronix AFG3252 signal generator,which is programmed to output a train of square pulses with a FWHM (FullWidth at Half Maximum) of 5 to 10 ns to resemble the Cherenkov pulses. Theother channel of the signal generator is used to generate an identical pulsetrain that will be used as the trigger signal for the DSO81204B oscilloscope. The connection of the GAPD bias circuit to the ampliﬁers is done withan SMA male to male connector, to keep the distance between the GAPDand the ampliﬁers as short as possible. Figure 6.4 shows this connectiongraphically. The ampliﬁers are powered with the Hameg HMP2030 power supply. Thevoltage supply is 5 V for all the prototypes. The connection of the output ofthe 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 isisolated inside a shielded black box  (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 88the 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 photonsarrive to the GAPD. The output pulses from the GAPD will correspond tosingle or very few photons. With the help of the oscilloscope, we will generatean histogram of the amplitudes detected in a narrow strip of the time scalewhere the pulse peaks are. As the GAPD pulse peak is proportional to thenumber of detected photons, the histogram will ideally consist in a set ofequally separated peaks, each of them corresponding to the amplitude of1, 2, 3, · · · , n, n + 1 detected photons.6.2.4 Measuring the dynamic rangeTo measure the dynamic range and linearity of the DUT, we connect theinput of the DUT to the Tektronix AFG3252 signal generator, which isprogrammed to generate a train of square pulses of amplitude Vlow = 0Vand variable Vhigh and FWHM 5 ns. The lowest value of Vhigh is 50 mV. Using the DSO81204B oscilloscope, the measurement procedure consistsin recording pairs (Vhigh , Voutpeakprototype ) where Voutpeakprototype is the peakof the output pulse of the prototype. From the obtained points (Vhigh , Voutpeakprototype ) we calculated the linearﬁt and the 1-dB compression point. The residuals of the linear ﬁt are ameasure of the DUT non-linearity. It should be noted that working in pulsed mode, the linearity is betterthan with continuous mode.
Chapter 7Experimental results anddiscussion Summary: In this chapter, the experimental measurements and tests on the implemented prototypes are presented and discussed.7.1 S-parametersThe measurement of the scattering parameters has been done with the setupdescribed in 6.2.1. Figure 7.1 shows the measured s-parameters. The plotscontain both the simulated and measured parameters and show that thesimulations model quite accurately the prototypes.7.2 Noise ﬁgureThe measurement of the noise ﬁgure has been done with the setup describedin 6.2.2. The measured noise ﬁgure is shown in ﬁgure 7.2. This ﬁgureshows the excellent noise performance of the BGA614 prototype and thetransimpedance prototype 1 with Rf = 1500 Ω. In particular, the noiseﬁgure of prototype 1 with Rf = 1500 Ω is between 1.39 dB and 2.23 dB forfrequencies below 1 GHz. The improvement of the noise ﬁgure compared toRf = 300 Ω is because of the reduction of the equivalent input noise current. 89
7.2. Noise ﬁgure 90 20 -8 19 -10 18 -12simulation:S22dBsimulation:S11dB simulation:S21dB 17 S22dB S11dB S21dB -14 16 -16 15 -18 14 -20 13 1e5 1e6 1e7 1e8 1e9 3e9 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) frequency (Hz) (a) BGA614 prototype 2. 0 14 -10 12simulation:S22dBsimulation:S11dB simulation:S21dB -20 10 S22dB S11dB S21dB 8 -30 6 -40 4 -50 2 1e5 1e6 1e7 1e8 1e9 3e9 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) frequency (Hz) (b) Transimpedance ampliﬁer prototype 1 with Rf = 300 Ω. 25 0 20 -10simulation:S22dBsimulation:S11dB simulation:S21dB 15 S22dB S11dB S21dB -20 10 -30 5 -40 0 1e5 1e6 1e7 1e8 1e9 3e9 1e5 1e6 1e7 1e8 1e9 3e9 frequency (Hz) frequency (Hz) (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 voltagesby the following equation 2 vn i2 n F =1+ + 1 (7.1) 4kT RS f 4kT RS f Unfortunately, since we have two unknowns vn , i2 and only one equa- 2 n
7.2. Noise ﬁgure 91 10 bga614 prototype 2 TIA prototype 1 Rf=300 TIA prototype 1 Rf=1500 8 Noise figure (dB) 6 4 2 0 2e+08 4e+08 6e+08 8e+08 1e+09 1.2e+09 1.4e+09 freq (Hz)Figure 7.2: Measured noise ﬁgure. The peaking at 900 MHz is due to mobilenetworks interference.tion, it is not easy to translate the noise ﬁgure speciﬁcation to the equivalentnoise currents and voltages. Nevertheless, we can obtain an upper bound of 2the noise current of the transimpedance prototypes if we consider vn = 0,which gives i 1 √n < (F − 1) · 4kT (7.2) f RS It is important to remark that equation 7.2 is only valid for a sourceimpedance RS = 50 Ω. The noise performance with the photodetectorimpedance will be diﬀerent. The transimpedance prototype 1 with Rf = 300 Ω has a noise ﬁgureN F ∼ 3 dB for frequencies < 1 GHz. From equation 7.2, we obtain an i √upper bound of the noise current with RS = 50 Ω of √ n < 18.12 pA/ Hz. f in √Prototype 1 with Rf = 1500 Ω performs √ < 13.92 pA/ Hz, the same fas the BGA614 prototype.
7.3. Dynamic range 927.3 Dynamic rangeWe had problems trying to measure the dynamic range of the transimpedanceprototypes. The signal generator Tektronix AFG3252 is only able to outputa minimum pulse peak Vhigh = 50 mV. Since the output impedance of thegenerator is 50 Ω, it is easy to obtain the minimum current delivered to thetransimpedance ampliﬁer vhigh i= ≈ 714 µA. (7.3) 50 Ω + 20 Ω To address this problem, we have used the attenuators available in thelaboratory. We have added an attenuation of -12 dB to the input of theTIA (TransImpedance Ampliﬁer ) prototypes. Figures 7.3 and 7.4 show themeasured 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. Forprototype 1 with Rf = 1500 Ω, the dynamic range lowers to 39 dB. As weanticipated, the dynamic range is too low. The dynamic range issue in the TIA prototypes has been addressed withthe 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 ifwe lowered the transimpedance gain of this prototype to 300 Ω, we would begetting a dynamic range of 61 dB, but a lower gain of course. In terms ofbits, the dynamic range of this prototype is 8.48 bits. The BGA614 prototype was succesfully characterised. Figure 7.6 showsthe measured dynamic range of the BGA614 prototype 2 along with therelative error of the linear ﬁt. The 1-dB compression point is found to beat an input voltage of 300 mV. Taking into account the voltage peak ofthe pulses corresponding to 1 phe, which are speciﬁed in section 2.3, themeasured dynamic range is roughly 59 dB. In bits, the dynamic range is 9.7bits. It should be noted that the simulations predict with great accuracy the
7.4. Pulse shape 93dynamic range of the prototypes. This is because we are using accurateSPICE models of the devices. 250 200 Output voltage (mV) 150 100 50 50 100 150 200 250 300 Signal generator voltage (mV) 2 1 Relative error (%) 0 -1 -2 -3 50 100 150 200 250 300 Signal generator voltage (mV)Figure 7.3: Measured dynamic range of the transimpedance prototype 1 withRf = 300 Ω.7.4 Pulse shapeThe 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 presentedin ﬁgure 7.7. In this ﬁgure, the BGA614 prototype is connected to theGAPD voltage output board (ﬁgure 5.5b) and to the current output board(ﬁgure 5.5d). With the voltage output board, the eﬀective input resistanceis 50 Ω || 50 Ω = 25 Ω, which is very close to the input resistance of thetransimpedance ampliﬁer with Rf = 300 Ω. The relevant time measurements are recorded in table 7.1. From this
7.5. Photon counting 94 360 340 320 Output voltage (mV) 300 280 260 240 220 200 50 60 70 80 90 100 110 Signal generator voltage (mV) 1 0.5 Relative error (%) 0 -0.5 -1 50 60 70 80 90 100 Signal generator voltage (mV)Figure 7.4: Measured dynamic range of the transimpedance prototype 1 withRf = 1500 Ω.measurements, it is clear that an increase in the impedance seen by theGAPD results in a wider pulse response. We expected the transimpedance to outperform the BGA614 in termsof pulse width and specially pulse rise time, but it has not. The reason forthis, after carefully reviewing the Hamamatsu MPPC technical note , isthe integrated polysilicon quenching resistor at the anode of each pixel. Thisresistor of ∼ 200 KΩ at ambient temperature, which was initially overlooked,along with the capacitance of each pixel, dominate the frequency responseof the device.7.5 Photon countingThe 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
7.5. Photon counting 95 1200 Output voltage (mV) 1000 800 600 400 200 500 1000 1500 2000 2500 3000 3500 4000 Input current (uA) 0.5 Relative error (%) 0 -0.5 -1 -1.5 0 200 400 600 800 1000 1200 1400 Input current (uA)Figure 7.5: Simulated dynamic range of the transimpedance prototype 2with Rf = 1000 Ω.color grade function and the histogram of the DSO81204B oscilloscope. The testing conﬁguration of the Tektronix AFG3252 signal generator isfrepetition = 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 themanufacturer. The DSO81204B oscilloscope is conﬁgured with a reduced bandwidth of1 GHz to reduce the noise integration band. Figure 7.8 shows the measurements. The pulse amplitude histogramconsists in a set of amplitude peaks corresponding to 1, 2, 3, · · · , n, n + 1detected photons. Note that the envelope of the peaks forms a Poissoniandistribution, which describes the statistics of photon arrival. In addition,the peaks are superimposed to undesired noisy detections. This can be seenin the form of a Gaussian shaped distribution. The three prototypes are able to obtain single photon counting patterns
7.5. Photon counting 96 1600 simulated 1400 measured Output voltage (mV) 1200 1000 800 600 400 200 0 0 50 100 150 200 250 300 Input voltage (mV) 4 Relative error (%) 2 0 -2 -4 -6 50 100 150 200 250 Input voltage (mV) Figure 7.6: Dynamic range of the BGA614 prototype 2.with the GAPD, although it is clear that the transimpedance prototypesoutperform the BGA614. The peaks are better deﬁned and the noise is muchlower, probably because of a lower input current noise. The single photonspectrum obtained with the transimpedance prototype 1 (Rf = 1500 Ω) isexcellent (ﬁgure 7.8c).
7.5. Photon counting 97 0.12 bga614 prototype 2 25 Ohm bga614 prototype 2 50 Ohm TIA prototype 1 Rf=300 0.1 0.08 0.06 Vout (V) 0.04 0.02 0 -0.02 0 2e-08 4e-08 6e-08 8e-08 time (s) 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- 2.22 82.33 26.56 type 2 GAPD + 50 Ω + BGA614 1.902 36.54 16.10 Prototype 2 GAPD + TIA Prototype 1 2.04 33.30 12.64 Rf = 300 Ω GAPD + TIA Prototype 1 2.30 42.39 16.78 Rf = 1500 Ω
Chapter 8Conclusions and Future Work Summary: In this chapter, the obtained results are analysed and compared. The future work is also described.8.1 Prototype speciﬁcationTables 8.1 and 8.2 show the performance of the prototypes developed in thismaster thesis. In general, all the prototypes implemented in this work deliver excellentperformance 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 simulatedspeciﬁcation is shown.8.2 AccomplishmentsIn this master thesis, ﬁve preampliﬁer prototypes have been designed andthree have been implemented and tested. The implemented prototypes haveshown 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 havebeen reached. On the other hand, the dynamic range of the prototypes isreasonable, 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 = Prototype 1 Rf = Prototype 2 300 Ω 1500 Ω √ √ 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 canbe succesfully used in any application where accurate single photon countingis needed. Only open source tools have been used to develop the work of this masterthesis, and although there is still a long way to reach high-end commercialCAD packages, these tools, for sure, outperform the average commercialsoftware of their kind.
8.3. MMIC vs Transimpedance 1018.3 MMIC vs TransimpedanceFrom the results obtained in this thesis, it is clear that the transimpedanceprototypes 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 noiseof the TIA is reduced. The pulse shape is narrower when using a TIA, due to its lower inputresistance, although the eﬀective resistance of the MMIC can be lowered to25 Ω with a matching 50 Ω resistor attached to the GAPD. The advantage of MMICs is probably its reduced cost, its reliability andits compactness.8.4 Future workThe transimpedance prototypes have been designed with discrete compo-nents. It would be interesting to translate these designs to an ASIC. Ofcourse, the design should be carefully revised. The TIA prototype 2 hasn’t been tested, due to time constraints. A fulltest of this design is left for future work. Even the prototype with improved dynamic range doesn’t meet the 3000phe requirement, so an alternative ultra high dynamic range design shouldbe considered in the future. Finally, the developed prototypes should be tested with PMTs, as theyare, for the moment, the candidate photodetectors for the CTA camera.
Bibliography  Design concepts for the cherenkov telescope array cta. Technical report, The CTA Consortium, May 2010.  P. Antoranz. Contributions to the high frequency electronics of MAGIC II Gamma Ray Telescope. Phd, Universidad Complutense de Madrid, 2009.  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.  P. R. Gray and R. G. Meyer. Analysis and Design of Integrated Circuits. John Wiley & Sons, Inc., New York, NY, USA, 3rd edition, 1992.  Hamamatsu. Multi pixel photon counter. Technical report.  Hamamatsu. Photomultiplier Handbook.  Inﬁneon. BFP420 Datasheet, February 2006.  Inﬁneon. BGA614 Datasheet, March 2008.  H. Kubo. Dragon-japan status. In WP ELEC/FPI Madrid, April 2011. D. F. Miller. Basics of Radio Astronomy for the Goldstone-Apple Val- ley Radio Telescope. Jet Propulsion Laboratory, California Institute of Technology, 1998. D. Neamen. Semiconductor physics and devices: basic principles. McGraw-Hill, 2003. 102
Bibliography 103 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. D. Pozar. Microwave engineering. J. Wiley, 2005. D. Renker. Geiger-mode avalanche photodiodes, history, properties and problems. Nuclear Instruments & Methods in Physics Research., 2006. C. W. Sayre. Complete Wireless Design. McGraw-Hill Professional, 2001. F. Toussenel. Status of the nectar project. In WP ELEC/FPI Madrid, April 2011. C. Verhoeven. Structured electronic design: negative-feedback ampliﬁers. Kluwer Academic Publishers, 2003.
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. Thisincludes the unitary price for each part. The total cost of the material is42.026 eur. 107
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 thefront layer, back layer and the assembly. 109
**************************************************************** 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 Infineons* 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 3CBEPAR 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