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 BGA622.214.171.124 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