UDK 621.3:(53+54+621 +66)(05)(497.1 )=00 ISSN 0352-9045 Strokovno društvo za mikroelektroniko elektronske sestavne dele in materiale MIDEM 2008 Strokovna revija za mikroelektroniko, elektronske sestavne dele in materiale Journal of Microelectronics, Electronic Components and Materials INFORMACIJE MIDEM, LETNIK 38, ŠT. 3(127), LJUBLJANA, september 2008 LMFE Laboratorij za Mikroelektroniko 488? FAKULTETA ZA ELEKTROTEHNIKO UNIVERZA V LJUBLJANI ■ UDK 621.3:(53+54+621+66)(05)(497.1)=00 ISSN 0352-9045 INFORMACIJE MIDEM a o 2008 INFORMACIJE MIDEM LETNIK 38, ŠT. 3(127), LJUBLJANA, SEPTEMBER 2008 INFORMACIJE MIDEM VOLUME 38, NO. 3(127), LJUBLJANA, SEPTEMBER 2008 Revija izhaja trimesečno (marec, junij, september, december). Izdaja strokovno društvo za mikroelektroniko, elektronske sestavne dele in materiale - MIDEM. Published quarterly (march, june, september, december) by Society for Microelectronics, Electronic Components and Materials - MIDEM. Glavni in odgovorni urednik Editor in Chief Dr. Iztok Šorli, univ. dipl.inž.fiz., MIKROIKS, d.o.o., Ljubljana Tehnični urednik Executive Editor Dr. Iztok Šorli, univ. dipl.inž.fiz. MIKROIKS, d.o.o., Ljubljana Uredniški odbor Editorial Board Dr. Barbara Malič, univ. dipl.inž. kem., Institut "Jožef Stefan", Ljubljana Prof. dr. Slavko Amon, univ. dipl.inž. el., Fakulteta za elektrotehniko, Ljubljana Prof. dr. Marko Topič, univ. dipl.inž. el., Fakulteta za elektrotehniko, Ljubljana Prof. dr. Rudi Babič, univ. dipl.inž. el., Fakulteta za elektrotehniko, računalništvo in informatiko Maribor Dr. Marko Hrovat, univ. dipl.inž. kem., Institut "Jožef Stefan", Ljubljana Dr. Wolfgang Pribyl, Austria Mikro Systeme Intl. AG, Unterpremstaetten Časopisni svet Prof. dr. Janez Trontelj, univ. dipl.inž. el., Fakulteta za elektrotehniko, Ljubljana, International Advisory Board PREDSEDNIK - PRESIDENT Prof. dr. Cor Claeys, IMEC, Leuven Dr. Jean-Marie Haussonne, EIC-LUSAC, Octeville Darko Belavič, univ. dipl.inž. el., Institut "Jožef Stefan", Ljubljana Prof. dr. Zvonko Fazarinc, univ. dipl.inž., CIS, Stanford University, Stanford Prof. dr. Giorgio Pignatel, University of Padova Prof. dr. Stane Pejovnik, univ. dipl.inž., Fakulteta za kemijo in kemijsko tehnologijo, Ljubljana Dr. Giovanni Soncini, University of Trento, Trento Prof. dr. Anton Zalar, univ. dipl.inž.met., Institut Jožef Stefan, Ljubljana Dr. Peter Weissglas, Swedish Institute of Microelectronics, Stockholm Prof. dr. Leszek J. Golonka, Technical University Wroclaw Naslov uredništva Uredništvo Informacije MIDEM Headquarters MIDEM pri MIKROIKS Stegne 11, 1521 Ljubljana, Slovenija tel.: + 386 (0)1 51 33 768 faks: + 386 (0)1 51 33 771 e-pošta: Iztok.Sorli@guest.arnes.si http://www.midem-drustvo.si/ Letna naročnina je 100 EUR, cena posamezne številke pa 25 EUR. Člani in sponzorji MIDEM prejemajo Informacije MIDEM brezplačno. Annual subscription rate is EUR 100, separate issue is EUR 25. MIDEM members and Society sponsors receive Informacije MIDEM for free. Znanstveni svet za tehnične vede je podal pozitivno mnenje o reviji kot znanstveno-strokovni reviji za mikroelektroniko, elektronske sestavne dele in materiale. Izdajo revije sofinancirajo ARRS in sponzorji društva. Scientific Council for Technical Sciences of Slovene Research Agency has recognized Informacije MIDEM as scientific Journal for microelectronics, electronic components and materials. Publishing of the Journal is financed by Slovene Research Agency and by Society sponsors. Znanstveno-strokovne prispevke objavljene v Informacijah MIDEM zajemamo v podatkovne baze COBISS in INSPEC. Prispevke iz revije zajema ISI® v naslednje svoje produkte: Sci Search®, Research Alert® in Materials Science Citation Index™ Scientific and professional papers published in Informacije MIDEM are assessed into COBISS and INSPEC databases. The Journal is indexed by ISI® for Sci Search®, Research Alert® and Material Science Citation Index™ Po mnenju Ministrstva za informiranje št.23/300-92 šteje glasilo Informacije MIDEM med proizvode informativnega značaja. Grafična priprava in tisk BIRO M, Ljubljana Printed by Naklada 1000 izvodov Circulation 1000 issues Poštnina plačana pri pošti 1102 Ljubljana Slovenia Taxe Perçue UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana ZNANSTVENO STROKOVNI PRISPEVKI PROFESSIONAL SCIENTIFIC PAPERS J. Trontelj, J. Trontelj, |L. Trontelj: Varnostni rob na živčno-mišičnem stiku sesalcev, primer pomembnosti natančnega merjenja časa v nevrobiologiji 155 J. Trontelj, J. Trontelj, |L. Trontelj: Safety Margin at Mammalian Neuromuscular Junction - an Example of the Significance of Fine Time Measurements in Neurobiology Z. Fazarinc: Newton, Runge-Kutta in simulacije v znanosti 161 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations F. Ivanek: 4G: kam gremo? 170 F. Ivanek: 4G: Where Are We Going? M. Jagodič: Fiksno-mobilna konvergenca 175 M. Jagodič: Fixed-mobile Convergence J. Trontelj jr.: Priporočila za načrtovanje elektromagnetno robustnih mikroelektronskih sistemov po naročilu 180 J. Trontelj jr.: Design Guidelines for a Robust Electromagnetic Compatibility Operation of Aplication Specific Microelectronic Systems R. Osredkar, M. Maček: Mikro bolometer namenjen uporabi v daljnem IR območju, zgrajen na osnovi tanke, polikristaline silicijeve plasti dopirane z borom 186 R. Osredkar, M. Maček: A Micro-bolometer for Far Infrared (FIR) Applications Based on Boron Doped Polycrystalline Silicone Layers D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Temperaturne lastnosti kapacitivnega senzorja tlaka narejenega v LTCC tehnologiji 191 D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Temperature Behaviour of Capacitive Pressure Sensor Fabricated With LTCC Technology M. Možek, D. Vrtačnik, D. Resnik, S. Amon: Izboljšava izplena umerjanja in nadzor kakovosti pametnih senzorjev 197 M. Možek, D. Vrtačnik, D. Resnik, S. Amon: Calibration Yield Improvement and Quality Control of Smart Sensors R. Osredkar: Prof. dr. Lojze Trontelj (1934 - 2008) Pionir mikroelektronike 206 R. Osredkar: Prof. Dr. Lojze Trontelj (1934 - 2008) A pioneer of Slovenian Microelectronics F. Rode: Prof. dr. Lojze Trontelj, Vizionar in pionir slovenske mikroelektronike 212 F. Rode: Prof. dr. Lojze Trontelj, Visionary and Pioneer of Slovenian Microeelectronics MIDEM prijavnica 214 MIDEM Registration Form Slika na naslovnici: LMFE- laboratorij za mikroelektroniko Fakultete za elektrotehniko. Laboratorij je ustanovil Prof. Lojze Trontelj leta 1970 in s tem uvrstil Ljubljansko univerzo med redke evropske univerze s takim laboratorijem Front page: LMFE - Laboratory for Microelectronics on Faculty of electronic Engineering in Ljubljana The Laboratory was founded by Lojze Trontelj in1970 placing University of Ljubljana among rare Universities with such a modern microelectronics laboratory VSEBINA CONTENT Obnovitev članstva v strokovnem društvu MIDEM in iz tega izhajajoče ugodnosti in obveznosti Spoštovani, V svojem več desetletij dolgem obstoju in delovanju smo si prizadevali narediti društvo privlačno in koristno vsem članom.Z delovanjem društva ste se srečali tudi vi in se odločili, da se v društvo včlanite. Življenske poti, zaposlitev in strokovno zanimanje pa se z leti spreminjajo, najrazličnejši dogodki, izzivi in odločitve so vas morda usmerili v povsem druga področja in vaš interes za delovanje ali članstvo v društvu se je z leti močno spremenil, morda izginil. Morda pa vas aktivnosti društva kljub temu še vedno zanimajo, če ne drugače, kot spomin na prijetne čase, ki smo jih skupaj preživeli. Spremenili so se tudi naslovi in način komuniciranja. Ker je seznam članstva postal dolg, očitno pa je, da mnogi nekdanji člani nimajo več interesa za sodelovanje v društvu, se je Izvršilni odbor društva odločil, da stanje članstva uredi in vas zato prosi, da izpolnite in nam pošljete obrazec priložen na koncu revije. Naj vas ponovno spomnimo na ugodnosti, ki izhajajo iz vašega članstva. Kot član strokovnega društva prejemate revijo »Informacije MIDEM«, povabljeni ste na strokovne konference, kjer lahko predstavite svoje raziskovalne in razvojne dosežke ali srečate stare znance in nove, povabljene predavatelje s področja, ki vas zanima. O svojih dosežkih in problemih lahko poročate v strokovni reviji, ki ima ugleden IMPACT faktor.S svojimi predlogi lahko usmerjate delovanje društva. Vaša obveza je plačilo članarine 25 EUR na leto. 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Prijavnice pošljite na naslov: MIDEM pri MIKROIKS Stegne 11 1521 Ljubljana Ljubljana, september 2008 Izvršilni odbor društva UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)2, Ljubljana SAFETY MARGIN AT MAMMALIAN NEUROMUSCULAR JUNCTION - AN EXAMPLE OF THE SIGNIFICANCE OF FINE TIME MEASUREMENTS IN NEUROBIOLOGY Jože Trontelj*, Janez Trontelj** and tLojze Trontelj** *Institute of Clinical Neurophysiology, University Medical Centre of Ljubljana, Slovenia; **Laboratory for Microelectronics, Faculty of Electrical Engineering, University of Ljubljana, Slovenia Key words: neuromuscular transmission, neuromuscular junctions, single fibre electromyography, jitter, safety factor. Abstract: Single fibre electromyography with axonal microstimulation was used to study the margin of safety of neuromuscular transmission in human and in rat muscle. The latter has been claimed to have a significantly wider safety margin compared to man. There is an inverse relationship between the jitter of the neuromuscular junction (NMJ) and its safety factor. Jitter was measured at 498 NMJs of the extensor communis muscle of 16 healthy human volunteers and at 177 NMJs in the tibialis anterior of 6 Wistar rats. The mean jitter expressed as MCD was 17.1 |s (SD 8.2) and 17. 7 |s (SD 6.1) for the human and the rat muscle, respectively. Moreover, the scatter of the individual jitter values was remarkably similar. These closely similar findings (P < 0.5) demonstrate that no significant difference exists in the safety margin of neuromuscular transmission between the two muscles in man and in the rat. An essential condition for studies of this kind has been adequate resolution of time measurement, < 1 |s. This could have been achieved by using a home-designed system for finely adjustable microstimulation amplitude at pulse width < 0.01 ms and for jitter measurement at a resolution of 0.0001 ms, both of which is still unsurpassed by the commercially available equipment for single fibre electromyography. Varnostni rob na živčno-mišičnem stiku sesalcev, primer pomembnosti natančnega merjenja časa v nevrobiologiji Kjučne besede: živčno-mišični prenos, živčno-mišični stik, elektromiografija posamičnih vlaken, živčno-mišični drget, varnostni koeficient Izvleček: V raziskavi varnostnega roba živčno-mišičnega prenosa v človeški in podganji mišici je bila uporabljena elektromiografija posamičnih vlaken z mikrostimulacijo motoričnih aksonov. Ta je po splošnem prepričanju pri podgani mnogo širši kot pa pri človeku. Obstaja obratno sorazmerje med razponom drgeta živčno-mišičnega stika (NMJ) in varnostnim koeficientom. Razpon drgeta je bil merjen v mišici extensor digitorum communis na 498 motoričnih ploščicah 16 zdravih prostovoljcev in na 177 motoričnih ploščicah v mišici tibialis anterior 6 podgan rase Wistar. Povprečni drget, izražen kot MCD, je bil 17.7 |s (SD 8.2) pri človeški mišici in 17.8 |s (SD 6.1) pri podganji mišici. Tudi raztros posameznih vrednosti drgeta je bil zelo podoben. Ti zelo podobni rezultati (P<0.5) kažejo, da ni pomembne razlike med varnostnim koeficientom za pregledani mišici pri človeku in podgani. Ključni pogoj za take raziskave pa je ustrezna ločljivost in natančnost merjenja časa, ki mora biti boljša od ene mikrosekunde. To je bilo možno doseči z lastno zasnovo fino nastavljive amplitude mikrostimulacije pri širinah impulza < 0.01ms in merjenje latenc z ločljivostjo 0.0001 ms, kar je veliko boljše, kot je dosegljivo s komercialno dostopnimi napravami za elektromiografijo posamičnih mišičnih vlaken. 1. Introduction Single fibre EMG is a method which allows recording of action potentials of single muscle fibres in humans or animals, in vivo and in situ. The method, originally developed by Ekstedt and Stalberg (1964 and 1966) and later supplemented by axonal microstimulation (Trontelj and Stalberg 1992), has been introduced in clinical neurology as a highly sensitive and specific diagnostic technique, mainly for the diagnosis of disorders of neuromuscular transmission. In research, it has contributed many new observations regarding the microphysiology and structure of the motor unit (Stalberg, Trontelj 1994). The essence of the technique is in its high selectivity of recording, higher than with the conventional needle electrodes used in standard clinical electromyography. The physical dimensions and the input impedance of the active electrode, 25 mm platinum surface exposed in a side port of a cannula, provide a happy compromise resulting in relatively high amplitudes of the recorded single muscle fibre action potentials (most often 1-7 mV, and up to 15 mV). On the other hand, the size of the recording area is comparatively small (a hemisphere of about 300 |im) and is well suited to record from only a limited number of closely adjacent muscle fibres (1-3, rarely up to 10). Later it became apparent that this number does not change much in muscle atrophy in spite of the smaller fibre size, since atrophic fibres are weaker electric generators, and the recording area also becomes smaller. Thus a restricted, more or less standard fraction of the motor unit territory can be investigated. With some experience, the intramuscular position of the electrode can be manually adjusted and maintained for periods of up to more than an hour, thus allowing prolonged recordings from individual muscle fibres. With constant position, the amplitude, shape, and duration of single fibre action potentials clear-cut biphasic spikes remain remarkably constant on consecutive discharges. This makes it possible to accurately identify the moment of depolarization of muscle fibre membrane at the 155 J. Trontelj, J. Trontelj and |L. Trontelj: Safety Margin at Mammalian Informacije MIDEM 38(2008)3, str. 155-160 Neuromuscular Junction - An Example of the Significance of Fine Time ... Fig. 1. Jitter study with axonal stimulation technique. The jitter is measured between the stimulus and the action potentials from one muscle fibre. Different degrees of jitter at the same myasthenic NMJ are produced in this case by changing stimulation rate. With 50 % block in the 3rd pane the safety margin of neuromuscular transmission is zero. (From Trontelj et al. 2001, with permission). electrode surface. Time measurements, e.g. between stimulus and response or between two action potentials from neighbouring fibres with a resolution as high as 100 nanoseconds are not only possible but may, in certain cases, have a physiological significance (Trontelj et al, 1990). When a motor axon is stimulated repetitively above its threshold and responses are recorded from a single muscle fibre there is latency variability of the order of tens of microseconds. This phenomenon is called the jitter. The term jitter was introduced to denote variation of neuromuscular transmission time at a single or a pair of neuromuscular junctions (NMJs). It is usually expressed as mean of consecutive differences of delay, the MCD (Stalberg, Trontelj 1994). The main source of the jitter in normal muscle is at the NMJ. The jitter is discussed in detail elsewhere (e. g., Stalberg and Trontelj 1994). At the normal NMJ, it is mainly due to small fluctuations in the firing threshold of the subs-ynaptic sarcolemma, which result in variable neuromuscular transmission time. Moreover, minor variations in amplitude and therefore slope of the end-plate potential, which are due to the variable number of released ACh quanta, contribute to the variability of this synaptic delay in normal muscle (Fig. 2a). 40 n 30- o o 20- 10- I 15 30 MCD (ms) ~n— 45 20- 10- o b 10- 20- Human Extensor Dig. Comm. Mean MCD = 17.1 ±8,2|is n = 498 Trps,W,TT, , I , , £ SO |IS -m p = 0.20 Rat Tibialis anterior K/laan MCD = 17.7 ±6.1 fis n = 177 Fig. 2. A. Jitter values of the 177 rat tibialis anterior NMJs. B. Jitter of 498 NMJs in the human extensor digitorum muscle of 16 subjects plotted against jitter values at 177 tibialis anterior NMJs of 6 rats. The means and distributions are closely similar. Normal jitter varies among different NMJs in the same muscle, and the normal range of mean jitter values varies among muscles. In a study of the effects of regional curarization (Schiller, Stalberg and Schwartz 1975) it was shown that the magnitude of the jitter is related to the safety margin of neuromuscular transmission. In other words, the jitter depends on the height of the tip of the endplate potential above a b 156 J. Trontelj, J. Trontelj and |L. Trontelj: Safety Margin at Mammalian Neuromuscular Junction - An Example of the Significance of Fine Time ... Informacije MIDEM 38(2008)3, str. 155-160 Muscle Number of NMJs Minimum [)»] 95% centUe IN Mean [[is] SD [|is] Extensor dig. comm. (man) 498 5 35.5 17.1 8.2 Tibialis ant. (rat) 177 6 30.5 17.7 6.1 the muscle fibre firing threshold, i.e., on the excess of the acetylcholine receptors activated per nerve impulse. This means that in a normal muscle, the NMJs have a rather different safety margin. When a disease process, such as myasthenia gravis, affects the structure and function of the NMJs, the jitter becomes increased and at a certain point, most often with jitter values between 60 and 120 |is, intermittent blocking of transmission sets in. At this point, the safety margin is close to zero. With increasing jitter values, for example during continued activity, the blocking becomes more frequent and may finally persist. This safety margin can be semi-quantitatively estimated in vivo in experiments with axonal stimulation during ischae-mia or treatment with neuromuscular blocking agents (Dahlbäck et al. 1970; Ekstedt, Stälberg 1969; Schiller et al. 1975; Trinkaus et al. 2007). Jitter measurement was originally described during voluntary muscle contraction, where the phenomenon is displayed as changing intervals between action potentials of two muscle fibres of the same motor unit during repetitive discharges. The technique was later made simpler and independent of patient's cooperation by replacing voluntary contraction with axonal microstimulation. In this way it became possible to use it also in animals (Trontelj et al. 1986). Moreover, the perfect control of firing patterns and rates over a wide range exceeding that of physiological discharge rates combined with high resolution time measurement made possible new types of in vivo research into physiology and pathology of neuromuscular transmission in intact man or animal. The purpose of this study was to compare the jitter, and thus the safety margin of neuromuscular transmission, in a human and the rat limb muscle. 2. Materials and Methods 2.1. Human subjects Sixteen normal subjects participated in the study, their ages ranging between 25 and 45 years. All were in good health and without evidence or past history of neurological problems. The jitter measurement was performed at 10 Hz stimulation at 498 NMJs in the extensor communis muscle. The details of the technique are described elsewhere (Trontelj, Stälberg 1992, Stälberg, Trontelj 1994). Part of the data has been published (Trontelj et al. 2002). 2.2. Animals Adult male rats (Wistar strain, 200-300 g) were used. The animals were maintained on a standard diet with food and water ad libitum and all efforts were made to assure their comfort. Uretan (Fluka, EU) in 25 % normal saline solution was applied i.p. in a dose of 1.75 g per kg of animal weight for anaesthesia. Tibialis anterior muscle was used; the jitter was measured at 177 NMJs of 6 animals. The same standard stimulation SFEMG technique was used on the human subjects as well as in the animals (Trontelj, Stalberg 1992). A pair of Teflon coated monofilar needle electrodes were inserted into the belly of the muscle just proximally to its middle, so that the uninsulated tips were 36 mm apart. Stimuli were 0.04 |s rectangular pulses of 0.1 - 5.0 mA, adjusted to be suprathreshold for the studied motor axon. They were presented at 10 Hz, although rates of 0.5, 1, 15 and 20 Hz were tried on some NMJs to examine the presence of intratetanic potentiation or exhaustion. Recording was made with a standard SFEMG electrode inserted proximally or distally into the twitching portion of the muscle, between 5 and 12 mm away from the tips of the stimulating needle electrodes (Fig. 1). The stimulation, recording and jitter measurement were performed on a Keypoint EMG system by Medtronic. The jitter programme in this equipment uses a peak-detection algorithm, so the jitter is measured between the stimulus and the negative peak of the single muscle fibre action potential. The jitter is expressed in the standard way as the mean of absolute latency differences between consecutive responses (MCD) to a series of 100 stimuli. The accuracy of measurement was tested by measuring the jitter on simulated single fibre action potentials delivered by a pulse generator with zero jitter, and the measurement error for the conditions used was < 3 |is (MCD). This degree of time resolution was considered less than an optimum, but still adequate for recognising so called low jitter, which indicates direct stimulation of muscle fibres (i.e., not via the nerve and the NMJ). Responses with jitter < 5 |is (MCD) were excluded (Trontelj et al. 1990), but they were infrequent with the position of the stimulating and recording electrodes used. In accordance with the national guidelines, the study was approved by the National Medical Ethics Committee of Slovenia and the Veterinary Administration of the Slovene Ministry for Agriculture, Forestry and Food, for the human and animal part, respectively. 3. Results The results obtained are shown in Fig. 2 and in Table. The mean of all MCD values for the 498 NMJs of the human EDC muscle was 17.1 |is (SD 8.2), and for the 177 NMJs of the rat tibialis anterior muscle it was 17.7 |is (SD 6.1). The difference between the two sets of values is nonsignificant (P = 0.20). Even the distribution of the individual values within the two muscles closely resembled each other (Fig. 2). It is obvious that the jitter in the rat tibialis anterior muscle is nearly identical with that in the human extensor digitorum communis muscle. The scatter of the results among the individual animals was small (Fig. 3), again similar to the findings in the human subjects. 157 J. Trontelj, J. Trontelj and |L. Trontelj: Safety Margin at Mammalian Informacije MIDEM 38(2008)3, str. 155-160 Neuromuscular Junction - An Example of the Significance of Fine Time ... Fig. 3. The variation of the mean jitter values and the SD between the individual animals is relatively small. With the position of the stimulating and recording electrodes used, there were few responses that could be suspected to be due to direct stimulation of the muscle fibres. As indicated above, the equipment used was barely satisfactory to measure the jitter with the precision required, so some doubt remained with the responses with the jitter in the neighbourhood of 5 |is. Experience gained with the original equipment that served during the development of the technique and the criterion to exclude any slightly 'noisy' action potentials with jitter just above 5 |is were helpful in eliminating direct responses, and were not considered to have introduced a bias towards higher jitter values. 4. Discussion The jitter of normal neuromuscular transmission at NMJs of human muscles is between 5 and 55 ms. It has been shown that the size of the jitter at a NMJ reflects the amplitude of the end-plate potentials and is inversely related to the safety margin of impulse transmission at that NMJ. A MCD value of less than 5 ms measured between two different single fibre action potentials or between a stimulus and the response is termed low jitter; the impulse in this case has not crossed a NMJ, as neuromuscular jitter always exceeds this value (Trontelj et al. 1986). An example of this is the jitter between action potentials of branches of a split muscle fibre. The jitter of a directly stimulated muscle fibre is low, provided that the stimulus is above the threshold. This could be reliably confirmed by using specially designed equipment and measuring technique (Mihelin et al. 1975) allowing an accuracy of 100 ns (Trontelj et al. 1990). With stimulation pulse width of 10 ms (Trontelj et al. 1967) and good recording conditions this system makes it possible to accurately identify cases of direct muscle fibre stimulation. Commercially available EMG equipment does not provide this degree of temporal resolution. Yet, the test of the equipment indicated an acceptable error of measurement, provided that the noise was kept at a low level. On the other hand, the jitter of a directly stimulated muscle fibre activated at threshold may be large, between a few tens and a few hundreds of ms, when the discharge rhythm is disturbed by intermittent drop out of the responses and the discharge rate is higher than 1 Hz. This variation in latency is due to changes in muscle fibre conduction velocity (Stalberg 1966, Trontelj et al. 1990). A similar situation arises when stimulation is via the motor axon and threshold stimulus intensity is used, so that some of the responses fail (false blocking due to insufficient stimulus). Such situations were carefully avoided by adjusting the stimulus strength well above the threshold. The jitter of neuromuscular transmission results from variability of the time needed for the end-plate potential (EPP) to reach the depolarization threshold of the juxta-junction-al sarcolemma (Fig. 4). A part of this variability is due to oscillation of the depolarization threshold of the muscle fibre (the JUXTA-junctional component of the jitter). This is not known to be associated with any pathology and is assumed to represent a significant share of the normal jitter. Moreover, the EPP slope varies from discharge to discharge in a random fashion. The EPP slope in the region of threshold depends on the (extrapolated) EPP amplitude. The mean EPP amplitude and the variation of the EPP slope determine the junctional component of the jitter. This component depends on the amount of ACh released per nerve impulse and on the sensitivity of the postsynaptic membrane. The junctional part of the jitter thus reflects the safety margin of neuromuscular transmission, and is proportional to the (excess) amplitude of the extrapolated EPP potential above the level of muscle fibre discharge threshold. The effect of fluctuation of the discharge threshold (the juxta-junctional component of jitter) is inversely proportional to the EPP slope. The combination of these factors actually determines the safety margin of neuromuscular transmission (Stalberg, Trontelj 1994). The postjunctional part of the jitter, mainly due to changes in muscle fibre conduction velocity resulting from different degrees of "supernormality" following previous activity, is largely avoided by the uniform discharge rates during electrical stimulation. (The contribution of this factor may be large when intermittent blocking occurs, resulting in disrupted rhythm.) There is a possibility for a pre-junctional contribution to the jitter, seen as latency variation of the end-plate potential. The end-plate potential jitter is usually negligible (<1-2 |is); it may however become large after intoxication with some organophosphates (De Blaquiere et al. 1998). A large EPP jitter may also be seen in botulism or experimental intoxication with botulinum toxin B (Maselli et al. 1992; Gansel et al. 1987). Neither pre- nor postjunctional factors could have influenced the measured jitter in this study. The measured values can therefore be safely considered to reflect the true variation of time taken for transmission at the NMJ itself, and thus its safety margin. 158 J. Trontelj, J. Trontelj and |L. Trontelj: Safety Margin at Mammalian Neuromuscular Junction - An Example of the Significance of Fine Time ... Informacije MIDEM 38(2008)3, str. 155-160 Fig. 4. Schematic explanation of the relationship between the jitter and the safety margin. At the normal NMJ, the variation in neuromuscular transmission time (the jitter) is generated mainly by oscillations of the firing threshold at which muscle fibre action potential (AP) is triggered. High amplitude EPPs have a steeper slope and a shorter course through the firing threshold range, and the jitter generated is smaller. Another source of the jitter is the variation in endplate potential (EPP) amplitude and therefore slope. The amplitude of the extrapolated EPPs exceeding the firing threshold represents the safety margin. In cases of postsynaptic dysfunction (such as myasthenia gravis), the variation of neuromuscular transmission time is increased due to lower EPPs, which take a longer path through the firing threshold range; some EPPs do not reach the threshold and the transmission is blocked. In cases of presynaptic dysfunction (such as the Lambert Eaton syndrome, LEMS), the EPP amplitude is not only low but is also excessively variable. The safety margin at the individual NMJs has been semiquantitative^ estimated in vivo in experiments with axonal stimulation during ischaemia or treatment with neuromuscular blocking agents (Schiller et al. 1975; Stalberg et al. 1975). However, the exact relationship between the magnitude of the jitter and the safety factor is difficult to establish. A computer simulation study suggested an exponential-like relationship, which was supported by the actual data from myasthenic NMJs (Lin, Cheng 1998b, Trontelj et al. 2002). It suggested a safety factor of 8-10 for human NMJs. In contrast, it was estimated at up to 20 or more in some animals (Waud, Waud 1975; Lin, Cheng 1998b). In this study, the rat tibialis anterior muscle has been found to have practically identical jitter as the human extensor digitorum muscle and therefore equally wide safety margin. On the other hand, the NMJs in the rat tibialis anterior muscle have a narrower safety margin than those of the human orbicularis oculi or mentalis muscle. One might argue that comparison should be made between identical muscles of man and the rat. However, the human tibialis anterior muscle has rather large jitter values. This has been suggested to be due to subclinical microtrauma-tisation of the peroneal nerve at the head of the fibula, for example while sitting with crossed legs. As a result, some denervation and reinnervation is going on in the peroneal supplied muscle. New NMJs are known to have larger jitter (Stalberg, Trontelj 1994). This mechanism is unlikely to operate in the rat. Our results are actually similar to those of Lin and Cheng (1998a), who studied the rat gastrocnemius muscle. Yet they found some NMJs with small jitter (about 5 |is) which they took as evidence of extremely high safety factor of neuromuscular transmission in the rat. However, such values can be recorded in human muscles and are seen in a similar (small) proportion of the NMJs in a muscle. Indeed, the jitter and thus the safety margin of neuromuscular transmission may vary in one and the same muscle of a single individual quite considerably. In the human extensor digitorum communis muscle, about 20 % of the NMJs are found to have relatively larger jitter (Trontelj et al 2002). Slightly smaller jitter was reported for 81 gluteus medius NMJs of 8 Lewis rats (Verschuuren et al. 1990). The mean MCD at 10 Hz stimulation in this study was 11.5 |is (SD 4.0). Considerably smaller jitter was found in the mouse gastrocnemius muscle: MCD 5-15 |is; mean 7.9, 11.3 and 6.1; SD 3, 4 and 2, respectively, for mice of three different strains (Gooch, Mosier 2001). Such low values would be compatible with a significantly wider safety margin. However, one has to exclude technical reasons. The gas-trocnemius muscle in the mouse is small and the position of both stimulating and recording electrodes is more critical. One possibility for obtaining small jitter values is unrecognized direct stimulation of muscle fibres (rather than through their axons), which would result in 'low' jitter. With less than optimal recording conditions, and in particular with unsatisfactory resolution of time measurement, the values may exceed the 5 |is criterion and be erroneously considered as normal NMJ jitter. As a result, false-low readings will shift the calculated mean towards lower figures. Another possible explanation for relatively small mean jitter values found in some studies could be superimposition of action potentials from several fibres. The resulting spike, when well synchronised, may in fact resemble a single fibre action potential. However, the jitter of the composite potential may be smaller than that of the individual muscle fibre components, as has been demonstrated by a computer simulation (Stalberg et al. 1992). In our experience, such recordings are common in the rat tibialis anterior muscle, and their inadvertent inclusion could result in a significantly underestimated mean jitter. Good recording 159 J. Trontelj, J. Trontelj and |L. Trontelj: Safety Margin at Mammalian Informacije MIDEM 38(2008)3, str. 155-160 Neuromuscular Junction - An Example of the Significance of Fine Time ... conditions, including absence of noise are an essential prerequisite for a reliable distinction between an axonal and a direct muscle fibre stimulation. Single fibre action potentials used for measurement of jitter should have a peak-to-peak amplitude of at least 1.0 mV. Criteria for single fibre action potentials must be strictly observed, in order to avoid measurements on composite spikes. The effective resolution of latency measurement should be at least 1 |is. Jitter measurement based on peak detection algorithm used in some equipment for diagnostic SFEMG, is reliable and convenient for clinical use, where the aim is to detect and measure large jitter, but may, near the low jitter values, become unreliable. In conclusion, this study failed to confirm the assumption of a wider safety margin of neuromuscular transmission in the limb muscle of the rat compared to a similar muscle in man. On the contrary, there does not seem to be any difference between the mean safety factors of human and rat NMJs. Acknowledgements This study is part of a research project on the protection and treatment of intoxication with neurochemical warfare agents (M3-0142). The contributions of Dr. Janez Sketelj, Dr. Miha Trinkaus, Dr. Špela Glišovič, Dr. Marjan Mihelin, Mrs. Tatjana Trontelj, Mr. Ignac Zidar and Tone Žakelj to the experimental work, data collection and analysis are gratefully acknowledged. References /1/ De Blaquiere GE, Williams FM, Blain PG, Kelly SS (1998). A comparison of the electrophysiological effects of two organo-phosphates, mipafox and ecothiopate, on mouse limb muscles. Toxicol Appl Pharmacol 150(2): 350-360. /2/ Dahlbäck L-O, Ekstedt J, Stälberg E (1970). Ischemic effect on impulse transmission to muscle fibres in man. Electroencepha-logr Clin Neurophysiol 29: 579-591. /3/ Ekstedt J (1964). Human single muscle fibre action potentials. Acta Physiol Scand, Suppl 226, 61: 1-96. /4/ Ekstedt J, Stälberg E (1969). The effect of non-paralytic doses of d-tubocurarine on individual motor endplates in man, studied with a new neurophysiological method. Electroencephalogr Clin Neurophysiol 27: 557-562. /5/ Gansel M, Penner R, Dreyer F (1987). Distinct sites of clostridial neurotoxins revealed by double-poisoning of mouse motor nerve terminals. Pflügers Arch 409: 533-539. /6/ Gooch CL, Mosier DR (2001). Stimulated single fibre electromyography in the mouse: technique and normative data. Muscle Nerve 24: 941-945. /7/ Lin TS, Cheng KS (1998b). Characterization of the relationship between motor end-plate jitter and the safety factor. Muscle Nerve 21: 628-636. /8/ Lin TS, Cheng TJ (1998a). Stimulated single fibre electromyography in the rat. Muscle Nerve 21: 482-489. /9/ Maselli RA, Burnet MA, Tongaard JH (1992). In vitro microelec-trode study of neuromuscular transmission in a case of botulism. Muscle Nerve 15: 273-276. /10/ Mihelin M, Trontelj JV, Trontelj JK (1975). Automatic measurement of random interpotential intervals in single fibre electromyography. Int J Biomed Comput 6: 181-191. /11/ Schiller HH, Stälberg E, Schwartz MS (1975). Regional curare for the reduction of the safety factor in human motor endplates studied with single fibre electromyography. J Neurol Neurosurg Psychiatry 38: 805-809. /12/ Stalberg E (1966) Propagation velocity in single human muscle fibres in situ. Acta Physiol Scand, Suppl 287, 1-112. /13/ Stalberg E, Schiller HH, Schwartz MS (1975). Safety factor of single human motor end plates studied in vivo with single fibre electromyography. J Neurol Neurosurg Psychiatry 38: 799-804. /14/ Stalberg E, Trontelj JV (1994) Single Fibre Electromyography. Studies in Healthy and Diseased Muscle, 2nd edition. New York: Raven Press, pp. 291. /15/ Stalberg E, Trontelj JV, Mihelin M (1992). Electrical microstimulation with single-fibre electromyography: a useful method to study the physiology of the motor unit. J Clin Neurophysiol 9: 105-119. /16/ Trinkaus M, Sketelj J, Mihelin M, Trontelj J. Jitter in organophos-phate intoxicated rats. Proceedings, XVIth International SFEMG and QEMG Course and IXth Quantitative EMG Conference with the 23rd Dr. Janez Faganel Memorial Lecture, Ljubljana, Slovenia, June 2-6, 2007: 181 (FC-16). /17/ Trontelj JV, Khuraibet A, Mihelin M (1988). The jitter in stimulated orbicularis oculi muscle: technique and normal values. J Neurol Neurosurg Psychiatry 51: 814-819. /18/ Trontelj JV, Mihelin M, Fernandez JM, Stalberg E (1986). Axonal stimulation for end-plate jitter studies. J Neurol Neurosurg Psychiatry 49: 677-685. /19/ Trontelj J.V., Mihelin M., Khuraibet A (2002). Safety margin at single neuromuscular junctions. Muscle Nerve, Suppl 11: S21-27. /20/ Trontelj JV, Stalberg E (1992). Jitter measurements by axonal stimulation. Guidelines and technical notes. Electroencephalogr Clin Neurophysiol, EMG and Motor Control 85: 30-37. /21/ Trontelj JV, Stalberg E (2002). Single fibre and macro electromyography. In: Bertorini TE (Ed.), Clinical Evaluation and Diagnostic Tests for Neuromuscular Disorders. Butterworth-Heineman / Elsevier Science, Woburn, MA, USA, pp. 417-447. /22/ Trontelj JV, Stalberg E, Mihelin M (1990). Jitter in the muscle fibre. J Neurol Neurosurg Psychiatry 53: 49-54. /23/ Trontelj JK, Trontelj L, Trontelj JV (1967). A voltage-controlled multi- channel electrical stimulator for programmed afferent functional stimulation. Digest of the 7th Internat Conf on Medical and Biological Engineering. Stockholm: 356. /24/ Verschuuren JJ, Spans F, De Baets MH (1990). Single fiber elec-tromyography in experimental autoimmune myasthenia gravis. Muscle Nerve 1990;13:485-492. /25/ Waud DR, Waud BE (1975). In vitro measurement of margin of safety of neuromuscular transmission. Am J Physiol 229: 1632-1634. akademik dr. Jože Trontelj, dr. med., profesor, višji svetnik Inštitut za klinično nevrofiziologijo, Nevrološka klinika, Univerzitetni klinični center v Ljubljani Zaloška 7, SI-1525 Ljubljana, Slovenija. Tel. (01) 522 1525, 041 576 218. Faks (01) 522 1533 elektronski naslov: joze.trontelj@kclj.si dr. Janez Trontelj, univ. dipl. ing., profesor, Laboratorij za mikroelektroniko Fakulteta za elektrotehniko Tzržaška 25, 1000 Ljubljana tdr. Lojze Trontelj, univ. dipl. ing., profesor emeritus, Laboratorij za mikroelektroniko Fakulteta za elektrotehniko Tzržaška 25, 1000 Ljubljana Prispelo (Arrived): 01.09.2008 Sprejeto (Accepted): 15.09.2008 160 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)2, Ljubljana NEWTON, RUNGE-KUTTA AND SCIENTIFIC SIMULATIONS Zvonko Fazarinc Palo Alto, California, USA Key words: Scientific simulations, accelerated motion, numeric integration of Newton's equations, fourth order Runge-Kutta, Heun algorithm Abstract: Scientific simulations of natural phenomena are powerful predictors of likely experimental outcomes. Improvement of their reliability and accuracy translates directly into time savings. Simulations are also powerful supporters of education. Created as teaching tools, simulations provide unique insights into mechanisms of addressed phenomena and can serve as experimental breadboards to the student. Visual display of simulated behaviour is usually the last step in writing a simulation code. The relevant algorithms that convert forces into motion to be displayed are seldom given the attention of the expert scientist. His focus is understandably elsewhere and the simulation of motion has to draw on previous work or on libraries of integration algorithms. This paper addresses the motion algorithm from the viewpoint of Newton's Laws and deals with the haphazard usage of pre-computer integration formulas such as the high order Runge-Kutta schemes. As these are offered as the" high accuracy" and conveniently packaged answer to all integration needs, these formulas have gained high acceptance without a demonstrated justification. The goal of this paper is to highlight the mismatch with the computer age of the fourth order Runge-Kutta (FORK) integration formula and to analyze its performance in light of simpler formulas with more transparency and less expenditure of computer cycles. I wish to dedicate this paper to the memory of my late friend and colleague professor dr.Lojze Trontelj with whom I had the pleasure to discuss the potential value of scientific simulations in the early days of computer evolution. Newton, Runge-Kutta in simulacije v znanosti Kjučne besede: simulacije v znanosti, pospešeno gibanje, numerična integracija Newtonovih enačb, metoda Runge-Kutta četrtega reda, Heunov algoritem Izvleček: Znanstvene simulacije naravnih pojavov so pomembni napovedovalci verjetnih eksperimentalnih izidov. Povečanje njihove zanesljivosti in natančnosti ima za neposredno posledico velike prihranke časa. Simulacije so tudi močna podpora pri izobraževanju. Ustvarjene kot orodja za učenje, simulacije omogočajo edinstven vpogled v mehanizme obravnavanih fenomenov in študentom lahko služijo kot eksperimentalni poligon. Vizualni prikaz simuliranega pojava je navadno zadnji korak pri pisanju simulacijskega računalniškega programa. Relevantnim algoritmom, ki sile prevedejo v prikazano gibanje, izkušeni strokovnjak le redko posveča posebno pozornost. Razumljivo je, da je osredotočen drugam, in simulacija gibanja se mora zato naslanjati na prejšnje raziskovalne rezultate ali na knjižnice integracijskih algoritmov. Članek obravnava algoritem gibanja s stališča Newtonovih zakonov in nestrogo uporabo integracijskih formul, ki izvirajo iz predračunalniških časov, kot na primer postopke Runge-Kutta višjih redov. Ker jih ponujajo kot "natančne" in priročno prirejene odgovore na vse potrebe po integraciji, so te formule splošno sprejete brez dokazne upravičenosti. Namen tega članka je osvetliti neskladje med računalniško dobo in Runge-Kutta (FORK) integracijsko formulo četrtega reda ter analiza njene uspešnosti v primerjavi s preprostejšimi, preglednejšimi formulami, ki zahtevajo manj računalniških ciklov. Ta članek posvečam spominu na svojega preminulega prijatelja in kolego, profesorja dr. Lojzeta Trontlja, s katerim sem še v zgodnjih časih evolucije računalnikov razpravljal o potencialni vrednosti simulacij v znanosti 1 Introduction Scientific simulations of natural phenomena can predict the outcomes of practical experiments if done correctly. For dangerous experiments their value is unprecedented, for expensive ones it is fiscally advantageous. Scientific simulation can also provide unique insights into the underlying mechanisms of phenomena studied. In this mode their educational potential is without precedent. The task of a simulation designer is to assign relevant natural forces to objects that mimic their natural counterparts. The running simulation allows the objects to mutually interact and their resulting collective behaviour is studied. One of the common tools for tracking the evolution of a simula- tion is a dynamic visual display. This must contain some algorithm that converts the forces on objects into their velocity and position. This task is the focus of this paper. The conversion of forces acting on objects into their positional changes would seem quite trivial to Isaac Newton and it may appear trivial to a practitioner of scientific simulations as well. A double integration of the forces acting on the mass in question is all that is necessary to obtain the object's instantaneous position. According to Newton's First Law of Motion /1/, an object's momentum M is preserved. It is defined for an object of mass m moving at velocity vas M = mv. The change of momentum dM/dt can be caused only by some force F acting on the object. Their relationship is given by Newton's Second Law of Motion as 161 Informacije MIDEM 38(2008)3, str. 161-169 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations dM/dt=F. Because we will ignore the change of mass in the continuation of this paper we will assign all changes of momentum to the velocity v. Consequently dv(t) = F(t)dt/m (1) Furthermore, the temporal change of an object's position ds/dt is equal to its velocity v, thus ds(t)=v(t)dt (2) The motion algorithm we employ in a simulation context must conform to equations (1) and (2) in the discrete domain of finite differences i+Ar Av(0 = v(t + At)~ v{t) = F At / m (3) and As(i) =s(( + M)-s(f) = vAt (4) where At is the smallest discrete time resolution of the simulation. Yet, the algorithms that are used to perform the two respective integrations do not necessarily produce the correct answers. In most cases they are chosen from a library of numerical integration routines with poorly defined behaviour, without relevance to the particular problem, sometimes producing inaccurate object positions and always consuming unnecessarily excessive computer resources. The positional accuracy of an object, which is subject to accelerating forces, can be critically important when the force is a function of object's position. Such is the case with gravitational and electromagnetic simulations as well as with all simulations of interacting objects. In this paper we will use Newton's Laws of Motion /1/ as the reference for a critical analysis of the most frequently recommended integration algorithm known as the Fourth Order Runge-Kutta method /2/ in light of other integration algorithms. 2 Approach The numerical double integration of forces may be addressed from a mathematician's viewpoint without regard to the physics of the problem. This approach had led to the majority of the numeric integration formulas in existence today and was driven by the quest for reduction of manual computation effort without compromising the accuracy of the approximation. We will elaborate on this in later sections. The same integration question may also be addressed from the physicist's viewpoint and be driven by the demand for a match between Newton's Laws of Motion and the results produced by its discrete mimicry. This will be our approach in the search for the ideal algorithm. Let us first put on the mathematician's hat. 2.1 Discrete Integration Method from Mathematicians Viewpoint All numeric integration formulas are based on the definition of the derivative's integral over a finite interval At J y'(t)dt = y(t + At)-y(t) Various approximations of this integral lead to different families of numeric integration formulas. Newton's Interpolation formula, for example, leads to the Adams family while Taylor's expansion gives rise to the Runge-Kutta family. We will focus on the latter, which is based on y(t+At)-y(t) = Aty\t) + t) + At3 A t* + -'»(,) +-y««(t)+...... 3! 41 (5) The mathematician's task is now to decide where to truncate the infinite expansion, providing an acceptable error. A good guess is that the truncation error /3/ may be in the order of power of At of the first neglected term. Retaining then as many terms as reasonable and using as small a time step At as practical seems appropriate. Now the former would complicate the formula while the latter would require more repetitive evaluations to cover a desired time span. Neither of these seems to be an overriding consideration for today's computer performance. But we must consider the fact that a vast majority of existing numeric integration formulas were developed before and at the turn of the 20th century, which this author likes to call the BC (before computers) era. The problems that needed to be addressed by numerical means were usually low order, nonlinear differential equations for which their changes, i.e. the first derivatives were known, arising usually from observations or measurements. When the humans were faced with a choice between numerous repetitive manual evaluations of a simpler formula versus fewer executions of a more complex formula, they would understandably choose the latter. And this is how the more complex integration formulas gained their BC fame. 2.1.1 Newton We will first choose a driving force function F(t) = ,4cos (pi), which is representative of all force functions that can be decomposed into Fourier series. This excludes the Dirac function. First we integrate (1) and (2) to obtain our reference data A A v(t) =-sin(co t) s(t) ---j cos(cd t) rrm mat v(0) = 0 m=- (6) m(ù 2.1.2 Fourth-Order Runge-Kutta (FORK) Had we followed the mindset of the BC era we would have included at least the first three or four terms of the expansion (5) thus placing the anticipated truncation error into the fourth or fifth order of At, respectively. This would then allow us the choice of a larger time increment as is desir- 162 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations Informacije MIDEM 38(2008)3, str. 161-169 able for manual integration. In turn, this would lead to a fairly complex, yet very popular Fourth-Order Runge-Kutta (FORK) formula /2/. Its systematic derivation involves much algebra and the interested reader is directed to this reference. The FORK formula is k0 = Aty'[t,y(t)] kt = Aty' \t+At/2 ,y(t)+Atk0/ 2 ] k2 = Aty'\t+ At/2 ,y(t)+Ai^/2] £3 = Aty^ + At^ift + Atk^ Jcq H~ "I- 2k2 k^ (7) y(t) = yQ-At)+- In (7) the slope is allowed to be the function of time and of the dependent variable y(t) should such be the case. We will use this formula to evaluate the motion quantities (3) and (4) and will then compute the deviation from Newton's answers in (6). To evaluate (3) and (4) we must plug the respective values of F and v into (7). Because these are only functions of time the FORK parameters ko through k3 adopt very simple forms. The result is shown below AAtr n v(t) = v(t - At) +-[cos 0)(i - At) + 4 cosoa(i - 0.5Ai) + cos CM J 6m s(t) = s(t-At)+—[v(t-At)+ 4 v(t-0.5 At) + v(/)] 6 (8) In Fig.1 we have superimposed the positions s(t) as calculated from (6) and from (8) as functions of the number of time increments At. Fig. 1: Newton and FORK position for cosinusoidal driving force. While deviations are not discernible in Fig.1 we have depicted in Fig.2 the percentage deviation between the FORK evaluated s(t) and that predicted by Newton. These are actual errors associated with our particular example and have nothing to do with the elaborate but often meaningless truncation errors /3/ Fig. 2: Fractional error between Newton and FORK positions for cosinusoidal driving force 2.1.3 Second Order Runge-Kutta Let us now choose to include only the first two terms of the Taylor expansion (5) With this choice we are committing, in the mathematician's mind, to a mere third order accuracy yet we do retain the control over At. The second term of expansion (5) calls for y"(t), which we do not know but can approximate by the central difference [y\t + At/2)-y\t -Ai/2)]/Ai, by the forward difference \y'(f+At)-y'(t)~\lAt or by the backward difference [/(0 -/(f-Af)] We will return to this later but choose for now the forward difference and obtain instantly the following second order formula y(f+Ao+/(<) y(t + At) =y(f) + Af- (9) Expression (9) is known as the trapezoidal but also as the Heun or Second Order Runge-Kutta formula /4/ in which we have replaced the fractional times with their linear approximations. Belonging to the second order brand this formula was discouraged by the BC mathematicians and remained in disrepute ever since. So let us now take a quantitative look at the error issue in light of what we have just learned about the FORK formula behaviour. To this end we adopt the same force function F(t) = A cos((oi) with its initial conditions spelled out in (6) to obtain from (3) and (4) the following equations v(t + At) =v(i) + :^[cosG)(i + Ai)+cosa)i] 2m s(t + At) = v(t)+^- [v(i+ Ai) + v(0] (10) Fig. 3: Superposition of Newton and Heun position for cosinusoidal driving force. 163 Informacije MIDEM 38(2008)3, str. 161-169 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations Fig.3 displays the position s(t) as function of index t/At and Fig.4 the percentage deviation of s(t) from the true position given by (6). This time we have experimentally adjusted the time increment At in such a way that the errors in Fig.4 and in Fig.2 are about the same. As discernible from two sets of plots we had to compute almost twice as many points in (10) as we did in (8) to obtain the match of errors. Thus, the FORK formula gives us the same accuracy with fewer passes. No real surprise here but to compare the net computational effort we must establish some measurable criteria. Ignoring the memory accesses and all other overhead and not allowing any duplicate computations, we can count the number of floating point operations (FLOPs) needed for each time step. Fig. 4: Fractional error between Newton and Heun positions for cosinusoidal driving force Formula (10) requires 30 FLOPs while (8) requires 49 provided that we have precomputed the repeating quantities such as AAtHm, AAt/6m, Ai/2, etc. and allotted 10 FLOPs for each trigonometric function evaluation. One could then say that the two formulas are identical in terms of net computational effort for the same accuracy. But formula (10) gives us 70% more individual computed points. We will reexamine this issue after we have completed a more severe comparative test of the two formulas from a physicist's viewpoint. 2.2 Discrete Integration from Physicist's Viewpoint While the truncation error /3/ might be the sole criterion to a mathematician when judging various integration formulas, to a physicist it is the trustworthiness of the simulated phenomenon that matters. We will therefore subject formulas (7) and (9) to a more realistic scrutiny because in simulations we seldom encounter a simple, clean textbook case of a well defined external force. The force is commonly self induced by the motion and is then fed back to the object involved. We will therefore make the force a function of the object's position and elect the following relationship. F Av(t) 2 — - —- -o) s(t) m At (11) opposing functional dependence of force on position is commonly encountered in gravitational, electromagnetic, Van DerWall and other simulations of natural phenomena / 5/, /6/. 2.2.1 Newton First we solve Newton's equations (1) and (2) for the case of force function (11) dv(t) 2 ,. —— - -ti) s(t) dt d2s (Q dt2 ds(t) dt =- m2s(t) = v(0 or Solving for s(t) this second order differential equation yields the harmonic solution s (t) = s( 0) cos co t+sin co t co v(i) =v(0)coscoi-s(0)cosincoi (12) where m2 is a proportionality constant for the moment. Such Position s(t) from equation (12) with v(0) = 0 is plotted in Fig.5 as the black solid line. 2.2.2 FORK formula We introduce the force function (11) into equation (3) and then use the FORK formula (7) in both (3) and (4) to end up with an expression for position s(t). Because the FORK formula integrates only one first order equation at a time, we would need a separate application of (7) to (3) and another to (4). Two sets of distinguishable factors "k" would have to be employed in general. But because (3) and (4) are coupled the following simplification is available from /7/ mo = AC % y{i), / (i)] ml = Aty'\t + At/2,y(t) + y'(t)At/2,y'(t) + m0 /2] m2 = Atyx\t + At/2,y(t) + y'{t)At / 2 + m0At / 4,y'(t)+ m1 /2] m} = Aty'\t + At,y{t) + Aty\t) + mxAt I 2, y'^ + m^ y '(t + At) = y \t) + (nig + 2ml + 2m2 + m3) / 6 y(t + At) = y(t) + Aty '(t) + Ai(m0 + rr^ + rr^) / 6 Because for our case the slope y'(t) = v'(t) = -co2s(t) is only a function of time t the above equations simplify to m0 =-A to? s(t) ml-m2--At(02s(t + At/2) (13) mi =-At(02s(f)\-At s(t+At) = s(t)+Atv(t)+At(m0 +ml+m2)/6 v(t+At) = v(t)+(m0 + 2ml + 2m2 +m3)/6 At this time we must point out that scientific simulations are commonly run with constant time increments At for a variety of practical reasons. One is the preservation of relative temporal occurrences of events under observation while simplicity of coding does not lag far behind. The half increment appearing in m1 and m2 must therefore be ap- 164 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations Informacije MIDEM 38(2008)3, str. 161-169 proximated by a linear interpolation s(t)+s(t+At) ml—m2 — — Aid) Fig. 5: Newton and FORK position when the driving force depends on position. With this substitution the Runge-Kutta equation (13) produces the position s(t), shown in Fig. 5, superimposed on Newton's prediction from (12). The plot was computed for aAt=1, which is just over six points per period of the resulting harmonic motion s(t). The rugged waveform is the consequence of that. It was chosen intentionally for later comparisons with other options. 13 1 JO 03 0J0 -03 -1 JO -13 -N F Fig. 6: Long term behaviour of Newton and FORK with positional feedback. In order to gain an insight into the long term stability of the FORK solution we have plotted in Fig.6 the Newton prediction for 8500 time increments and superimposed on it the FORK answer from (13) for 8000 time increments. It is not doubtable that the FORK solution (13) would continue to provide stable answers beyond 8000 points but we will later prove this to be the case. 2.2.3 Second Order Formula Let us continue to retain the physicist's viewpoint and argue with the mathematician who would want to convince us that only an infinite number of terms in the Taylor expansion would guarantee a perfect match of a numeric algorithm with Newton's formulas. On the other hand there are no doubts that Newton's equations (1) and (2) describe a second order system. Why should a second order numer- ic formula not suffice to adequately describe the accelerated motion? So, instead of choosing an existing integration algorithm we will force a second order integration formula to conform to Newton's laws of motion. We start again from formulas (3) and (4). In them we have intentionally avoided the specification of respective temporal arguments of Fand v. The discrete domain, characterized by finite time increments, often confronts us with the question of what happens before something else. We could, for example, compute the new velocity from Equation (3) by using the present force F(i+Ai), the previous force F(t), their average as seen before or some other more general combination of the two. Similarly, we could compute the position s(t) from Equation (4) using some arbitrary combination of the previously evaluated and contemporaneous velocities. Without knowing the outcomes produced by a given choice, we have no reason to prefer one over the other. Therefore we will elect as yet undefined fractions of the force a F(t +A i) and (1-a) F(t) as the contributions to velocity changes as indicated below v(t + At) = v(i) +-[aF(t + At) + (l-a)F(t)] (14) m Furthermore we will choose as yet unknown fractions of two primary velocity choices to determine their relative contributions to the change of position s(t + At) = s(t) + [bv(t + At)+(l-b)v (t)]At (15) Parameters a and b have values between zero and unity and we will try to extract them by a parameter optimization procedure designed to force a match between the simulated results produced by the above equations and the true accelerated motion expressed by Newton's Laws. We will do this for our specific choice of force defined by (11), which yields the following version of (14) v(t + At) = v(t)-(i>2At[as(t+ At) + (1 - a)s(i)] (16) Expressions (15) and (16) represent the numeric integration algorithm that we are trying to force in compliance with (1) and (2).To this end we must find a closed form solution of the coupled equations (15) and (16). We have done this in the Appendix AP1 with the result s(nAt)=s(0)B"n cos/iQAi+ + sWnteQ»-*)/4 +v(0)/a> N/l-co2Ai2(a-&)2/4 B_l+(l-Z>)(l-fl)(02Ai2 1+aba2At1 (17) r»A . _i . J1 -(0 At (a - b) 4 QAi = tan 'coAi—-\ / „— 1 - (a+A - 2ab)a? At /2 A comparison of position s(t) in (17) with that in (12) suggests that the quantity B"n must be unity, calling for l + (l-i)(l-a)fi)2Ai2 = 1+ aba2 At2, which further entails a + b = 1. The numerator of the second term of the s(nAt) expression in (17) demands b - a = 0 to conform to (12). 165 Informacije MIDEM 38(2008)3, str. 161-169 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations These two requirements imply the following overall conclusion of our analysis a = b = 0.5 (18) Our final form of the set (15) and (16) is now highly remi-niscnet of the Heun formula (19) v(t + At) = v (t) - CD2 A t [s (t + At)+s (0 ] / 2 s(t + At) = s(t) +At[v(t+At)+v (£)]/2 For a = b = 0.5 expression (17) takes on the form.which except for the angular frequency Q matches Newton's prediction (12) in all other details. s(nAt) = 5(0) cos nQAt+sinnQAi QAt = tan 1 COAi (20) Vl-0)2Ai2/4 Fig. 7: Newton and Heun position when driving force depends on position It should therefore not come as a surprise that an evaluation of (20) produces Figs.7 and 8 for which we have chosen the parameter coAi=0.38. Figs.5 and 6, on the other hand, were obtained with (oAt = 1 as stated earlier. The ratio of 1 to 0.38 happens to match the ratio 21 to 8 of floating point operations needed to execute (13), versus (19). This, in turn, assures equal computation time for both formulas with (19) providing 2.6 times as many time increments. Fig. 8: Long term behaviour of Newton and Heun with positional feedback. A debate over the relative accuracy of one or the other formula is irrelevant since both appear to match the Newton waveform except for the angular frequencies as seen from the graphs. For the Heun case defined in (20), the fractional deviation of Q from m is established as (tan"1 [a>Ai/ Vl-co2A;2 /4]-l)/coAi and is plotted in Fig.9 versus coAi. In the Appendix AP2 we have also found an analytic expression for the angular frequency Q of the Runge-Kutta case and its relevant deviation from the nominal m as (tan"1 [rnWl-co2Ai2/12/ (1 -co2Ai2 /3)] - 1^/toAi .This is also plotted in Fig.9 as R.. 10 0.1 0 01 0 001 1 1 1 1 1 0-0L (u \ ' ^ L0 -H ---R Fig. 9: Fractional error of FORK and Heun simulated frequency. There is a slight difference in favor of Heun in terms of angular frequencies but more significant is the fact that for same expenditure of computer cycles Heun delivers more computed points with shorter time increments. Both of these are desirable for dynamic simulations, which demand displays of velocities and positions of objects. 3. Conclusion In summary the Heun algorithm has been found to numerically integrate Newton's laws of motion with the same accuracy as the FORK formula in tests from the highest frequencies down to the Nyquist limit. The superiority of Heun formula over the FORK algorithm is its ability to deliver 260% more computed points at proportionately reduced time increment for same expenditure of computer cycles. Both of these are criteria important to simulation practitioners. Furthermore, its simplicity of implementation leaves the designer in control of the last stage of his dynamic simulation code. i.e. of computing the new velocities v(i+Ai) and the new positions i(i+Ai) of his objects from forces F(t+At) currently acting on them. When we consider our starting force (11) we can present the preferred result of our analysis for general force functions as At v(t+At) = v(t) +-[F(t + At) + F(t)] 2m , . » ✓ 4 v(t + At) + v(t) s(t+At) = s(t) + ---——At (21) 166 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations Informacije MIDEM 38(2008)3, str. 161-169 A simulation program in which (21) was implemented has been tested with 100 spherical particles with randomly assigned initial velocities. They were allowed to interact through mutual gravitation, through three-dimensional collisions and individually by bouncing off the box walls. The gravitational masses of particles were adjusted so that their naturally formed clusters were able to disperse as their rotational velocity increased. This assured a continuous activity of all 100 particles. While there is no method available to evaluate the accuracy of observed simulated behaviour of this many objects, the physics comes to the rescue. Unless a loss mechanism or a source of energy is coded into the system the total energy must remain constant. Therefore we have monitored the overall energy through one million passes, during which each of the 100 particles received an update of position and velocity from the Heun algorithm from formula (21). During the whole observation time of one hour and 23 minutes that was needed for the experiment, the total energy of particles remained unchanged. Appendix API Closed form solution of equations (15) and (16) They are respectively s(t + A/) = s(t) + [bv(t + At) +(1 - b)v(t)]At (APP1) v(t+At) = v(i) -to2 [as(t+At) + (1 -aM*)]Af (APP2) Take the first forward difference of (APP1) s (t + 2At)-s(t + At) = s(t + At)~ s(t) + bAt[v(t + 2 A t)~ -v(t + Ai)] + (1 - b)At[v(t + AO - v(0] . Note that the first bracketed term arises directly from (APP2) as -(»2Ai2[a.y(i+2Ai) + (l-aMi+Ai)] and the second one as —di2At2[as(t + At) + (1- a) s (i)] Substitute these into the above equation and collect contemporaneous terms to obtain s(t + 2Ai)(l+ aba1 At2)-2s(t + Ai)[l- (a+b -2ab)w2At2 /2]+ +s(t)[l+(1 - a)(l -6)co2A/2] = 0 This equation is equivalent to s(t + 2At)-2As(t+At)+ Bs($) = Q with A = B = \-(a + b-lab)(ù2At2 /2 \ + ab(û2At2 1 + (1 — a)(l —b)(ü2At2 l + ab(ü2At2 (APP3) (APP3) has two closed form solutions dependent on the relative magnitude of A and B. The case B>A is of interest to us. Application of the Z-transform /8/ results in the following Z-domain equation for s(i) in which the transformed variable is defined as SÇ) =Z[s(i)] S(z)z2 — j(0)z2 - s(At)z — 2AS(z)z + 2As(0)z + BS(z) = 0 From this follows immediately SV- s(0)z2 + s (Ai) z - 2As(0)z _ s(0)z2 + s(At)z-2As(0)z z2-2Az+B (z-z,)(z-z2) where ± 7 tan i -Jb-a2 (APP4) z12 = A± jslB-A2 =|z|e±Jfl> =-JHe The inversion is done by the sum of residui since we are dealing with an analytic function /9/. We have discretized time as t =nAt in the following expressions s{nAt) = S(z )(z - Z[ )zn~1\z^2i+S(z )(z - z2 )z"_1 _s(0)zl+s(At)-2s(0)A„n , s(0)z2 + s{At)-2s{d)A Because z, - z2 = 2j^B-A2 we get s(nAt) s(0)(v4+ jjB-A2^ s(p)(A-jjB-A2) 2 j^lB-A2 1 Ij^B-A2 2 s(At)-2s(0)A ,n i - vz1 z2> 2 jylB-A2 or s(nAt)= + ^ + 2j\IB-A2 2 S(At)-2S(0)A „ + Ij^B-A2 (Zl "Z2> From (APP4) it follows jn tan —» —n / r> n ■ Zj —z2= ■siB e = 2j-Jß" sinn tan . -ivb-a2 -yf¥t -jn tan -1 -jb-a2 a — Jb-a2 z?+zn2=4F = 2-Jb" cos n tan -jb-a* . ■■ib-a' 1 a , ~jntsa S +e , 4B-A2 Then s(nAt) = s(0)4b" cosnClAt + sin n QAt -JB-A2 (APP5) where £2Ai = tan ., VB-A2 The denominator of the second right hand term of (APP5) can be found with straightforward but time consuming algebraic manipulations as \B—A =a>AtJ—--v /- l + ab(0 At (APP6) 167 Informacije MIDEM 38(2008)3, str. 161-169 Z. Fazarinc: Newton, Runge-Kutta and Scientific Simulations s(Ai) is extracted directly from (APP1) as s(At) = i(0) + bAtv(At) + (1 -b)Atv(O) while v(Ai) = v(0)-tt>2Aia.s(A/)-fi)2Ai(l-a).s(0) is obtained from (APP2). From expressions (APP5) and (APP6) and from the definition of A in (APP3) we obtain via tedious but elementary algebraic manipulation s(A/)-5(0)^ (sAt(a-b)/2 -1 — = ty((J) —¡= + JB-A2 -2At2(a-b)2 /4 -;-=C0A t-- l+ab(o2At2 \+aba>2At2 = coA/ •Jl-(a2At2(a-b)2 /4 l-(a + b-2ab)o)2At2/2 l-(a+b-2ab)a2At2 /2 With these values our solution for s(t) becomes | s(0)(i>Al(b — a)/2 +v(0)/co^/2dnp_f ^l-(02At2(a-b)2/4 2A .2 5 = _ 1+(1-a )(!-&) eaAf I + aba)2 At2 (APP7) _i 4 J l-(ö2At2(a-b)2 / 4 iiAt - tan 1oaAi- y v 7 1 - (a + b -2ab)(»2At2 /2 AP2. Closed Form solution of FORK equation (13) We reproduce the relevant expressions m0 — At(o2s(t) m1=m2 = -At(D2s(t + At)/2 (APP8) m3 = -At(ü2s(t)+At and s(t+At) = s(t)+Atv(t) + At(m0+ml+m2)/6 (APP9) v(t+At) = v(t) + (m0 + 2mi + 2m2+m.i)/6 (APP10) When we substitute the m-factors from (APP8) into (APP9) we obtain s{t+At) = s(t) + v(t)At-mAt [s(0 + 2s(t+At/2)] 6 In scientific simulations the stepping time increment At is commonly maintained at a fixed value and consequently the s(t+At/2) quantity is simply not available. In the time period when the FORK algorithm was developed, the rele- vant slopes were extracted from measurements or observations so there was no problem to satisfy the above formulas. But in simulations we are forced to either run at halved increments and use only every second result, do some fancy iteration to extract the fractional time values or approximate the half time quantity. Only a linear interpolation is available in the second order systems so we will make the following substitution: s(t+AtH) = [i(i) + i(i+A/)]/2 This leads to + Ai) = i(i) + v(f)Ai-(o2Ai2 [2s(f)+.s(/ + Ai)]/6 A simple collection of terms yields s{t + At) = s (0(1 -a2 At2/ 3) / (1+oo2Ai2 / 6)+ + v(t)At / (l+co2Ai2 / 6) Take the first difference, which yields s(t+2At)- s(t + At) = [s(t + At) -s(f)] 1 - cö2At2 / 3 [v(t+At)- v(t)]At (APP11) (APP12) l+Q)2Ai2 / 6 l+G)2Ai2 /6 We need the velocity term in (APP12). To this end we insert the m-factors from (APP8) into velocity equation (APP10) to get v(t + At) = v(t)~ [s(t) + 4s(t+At/2)+s(t+ Ai)] , 6 After making the same approximation to the half increment term we obtain v(i + A0-v(0 = -^^[3s(0+3.)--——+v(0) 1+co Ar/6 sinusoidal term is found as 1+co2AÍ2 / 6 . Multiplier of the s(At)-s(0)A _ JB-A2 ~ s( 0) l-co2Ai2/3 1-ÍO2AÍ2/3 v(0)Af l+co2Át2/6 + l+(o2Át2/6 S( 'i + aW/ó (0AiVl-ö)2Ai2/12 1+co2 Ai2/6 v(0) coVl-ffl2Ai2/12 The closed form solution of the FORK equation (13) is now v(0) oWl-oo2Ai2/12 Vl-(02Ai2 /12 s(«Ai) = 5(0) cos OA/ + —. v 7 sin i2Ai QAi = tan"1 coAi , , 1-coAi /3 The fractional angular frequency deviation is i2At-(pAt _ tan"'(oWl-co2A^ /12 /(1-cq2A^2 /3) coAi coAi References /1/ J.S Newton "Philosophiae Naturalis Principia Mathematica", Translation by Andrew Motte, UC CAL Press, Berkeley, CA, 1946 p. 13 /2/ F.B.Hildebrand "Introduction to Numerical Analysis", Second Edition, Dover Publications, New York 1974, p.285-292 /3/ Ibid pp.5-10 /4/ Ibid p.290 /5/ Z.Fazarinc, "Getting Physics into the Bounce", IEEE Potentials Vol.14 No.1, Feb./March 1995, pp.21-25 /6/ Z. Fazarinc, "Potential Theory, Maxwell's Equations, Relativity, Radiation and Computers", CAEE, Vol.7, No.2, John Wiley&Sons, Inc 1999 pp.51-86 /7/ F.B.Hildebrand "Introduction to Numerical Analysis", Second Edition, Dover Publications, New York 1974, pp.291-292 /8/ John A. Aseltine, "Transform Method in Linear Systems Analysis", McGraw-Hill Book Co., Inc. 1958, p.260 /9/ Ibid, p.276. Dr. Zvonko Fazarinc Formerly director of R&D laboratory at Hewlett Packard Co in Palo Alto and Consulting professor of EE at Stanford University, California 620 Sand Hill Road, 417D, Palo Alto, California 94304 Tel.: (001) (650) 330 0310; Fax: (001) (650) 330 1967 E-mail: z.fazarinc@comcast.net Prispelo (Arrived): 26.06.2008 Sprejeto (Accepted): 15.09.2008 169 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana 4G: WHERE ARE WE GOING? Ferdo Ivanek Palo Alto, California, USA Key words: Mobile communication, broadband communication, communication standards, radio spectrum management, communication system planning. Abstract: While deployment of 3G broadband cellular mobile systems still leaves ample room for growth and upgrades, recently developed international standards and new spectrum allocation changes, as well as new systems development, stimulate early 4G deployment. The possible impact of these new developments is exemplified and quantified in terms of 4G aggregate throughput to be shared between individual users. The available data indicate that the user experience with the exemplified candidate 4G systems can be expected to be within the range of current wireline ADSL and cable modem broadband services. 2G/3G deployment indicators are presented that apparently have a bearing on the prevailing evolutionary 3G/4G trends among the leading incumbent mobile service providers aiming at 4G deployment to start in 2010, and attention is drawn to announced plans by other mobile service providers planning to start commercial 4G services in 2008 and 2009, respectively. Three possible scenarios for future 4G convergence and competition are submitted and discussed. 4G: Kam gremo? Kjučne besede: mobilne komunikacije, širokopasovne komunikacije, komunikacijski standardi, upravljanje z radijskim spektrom, načrtovanje komunikacijskih sistemov Izvleček: Čeprav uporaba širokopasovnih 3G celičnih mobilnih sistemov še vedno omogoča rast in izboljšave, pred kratkim sprejeti mednarodni standardi in spremembe v dodelitvi frekvenc, kot tudi razvoj novih sistemov, vzpodbujajo zgodnjo uvedbo sistemov 4G. Možen vpliv tega napredka ponazarja in kvantificira skupna prepustnost sistemov 4G, ki si jo med seboj naj delijo posamezni uporabniki. Dostopni podatki kažejo, da bi izkušnje uporabnikov s predlaganimi sistemi 4G, ki so navedeni kot primer, lahko bile primerljive s storitvami obstoječih žičnih ADSL in širokopasovnih kabelskih modemskih sistemov. Predstavljene izkušnje z uvajanjem sistemov 2G/3G imajo očitno zelo močan vpliv na razvojne usmeritve sistemov 3G/4G vodilnih obstoječih ponudnikov mobilnih storitev, ki nameravajo začeti z uvajanjem sistemov 4G v letu 2010. Obravnavani so tudi napovedani načrti drugih ponudnikov mobilnih storitev, ki načrtujejo komercialno uvedbo storitev 4G v letu 2008 ali v letu 2009. Opisani in obravnavani so trije možni scenariji bodoče 4G konvergence in konkurence. Preface My selection of the subject of this article is based on wishful thinking about still being able to chat with Lojze over the telephone or visiting him in his home. I imagine he could have said: "I read the August 2008 Focused Issue of the IEEE Microwave Magazine that you edited. Timely subject; would also be of interest to the readers of our Journal "Informacije MIDEM". Could you condense the information into a single article and include your comments?" This is what I decided to do. 1. Introduction A straightforward single answer to the question in the title is elusive due to the complex interplay of a number of technological, regulatory and business issues. To develop an understanding of where we are really going, it is indispensable to direct attention to the activities of the International Telecommunication Union (ITU), the world's supreme standardization and regulatory body for telecommunications, in which the leading regional and national standardization development organizations (SDOs) and regulatory agencies systematically cooperate. ITU's Radiocommunication Sector (ITU-R) is therefore the most authoritative source of relevant information needed to evaluate the progress of cellular mobile communications. Presenting key relevant information on this subject in a convenient format for use by the membership of the IEEE Microwave Theory and Techniques Society (MTT-S) was the intent of the August 2008 Focused Issue of the IEEE Microwave Magazine, one of the periodicals published by MTT-S. The focus was on convergence and competition on the way toward the 4th generation of cellular mobile communication systems (4G), which are necessarily of great interest to a large segment of MTT-S membership, primarily those involved in or affected by the development of mobile communications. The author of this article served as guest editor /1/, and was fortunate to benefit from the participation of a prominent international group of authors engaged at the forefront of cellular mobile systems development and standardization /2-5/. The following sections highlight the fundamental issues of convergence and competition on the way toward 4G, based primarily on the referenced articles /1-5/ that provide extensive reference lists for use by readers interested in more detail. Section 2 highlights the framework for 3G and 4G standards evolution, Section 3 summarizes frequency spectrum availability, Section 4 focuses on the effective spectral efficiency and throughput as key performance metrics, Section 5 highlights the 2G/3G deployment indicators and 4G trends, and Section 6 offers conclusions and comments. 170 F. Ivanek: 4G: Where are We Going? Informacije MIDEM 38(2008)3, str. 170-174 2. Standards development ITU-R standards development for cellular mobile systems started in 1985 and underwent a number of organizational changes /4/. The current framework consists of "International Mobile Telecommunications-2000" (IMT-2000) and "IMT-Advanced"; the term "IMT" was adopted for both collectively /6/. Two standards deserve particular attention: Recommendation ITU-R M.1457 on specifications of the IMT-2000 radio interfaces /7/, and Recommendation ITU-R M.1645 on objectives of the future development of IMT-2000 and systems beyond IMT-2000 /8/. Both refer to IMT-2000 as "third generation mobile systems". Recommendation ITU-R M.1457, originally adopted in 2000 and updated annually, introduced a family of five different 3G radio interfaces, including the two code division multiple access (CDMA) varieties currently deployed worldwide: wideband CDMA (WCDMA) and CDMA 2000. When Recommendation ITU-R M.1645, adopted in 2003, introduced a new category of mobile systems for more demanding future applications, tentatively named "Systems beyond IMT-2000", it was commonly considered to represent 4G, although this Recommendation does not refer to it as such. Figures 1 and 2 illustrate the concept of systems beyond IMT-2000 as described in Recommendation ITU-R M.1645. Fig. 1: Illustration of capabilities of IMT-2000 and systems beyond IMT-2000/8/ (By authorization, ITU Legal Affairs.) Generational identification was also avoided when "Systems beyond IMT-2000" was renamed "IMT-Advanced", and when Revision 7 of Recommendation ITU-R M.1457 was adopted, both in 2007. Notably, Revision 7 introduced orthogonal frequency division multiple access (OFDMA) radio interfaces. One of them is a new IMT-2000 member based on IEEE Std 802.16, supported by the WiMAX Fo- Fig. 2: Future network of systems beyond IMT-2000 including a variety of potential interworking access systems/8/ (By authorization, ITU Legal Affairs.) rum, and the three additional ones represent 3G evolution, e.g. the long term evolution (LTE) and the ultra mobile broadband (UMB) versions that are broadband evolutions from WCDMA and CDMA2000, respectively /2-4/. Since an OFDMA radio interface is commonly considered as a key characteristic of 4G systems, Revision 7 of Recommendation ITU-R M.1457, which was initiated as a vehicle for 3G standardization, actually became a framework for transition to 4G. This unanticipated development seems to justify past avoidance of 4G identification in Recommendation ITU-R M.1645, and it makes it plausible at the current stage of Recommendation ITU-R M.1457 updating. Outside ITU-R, however, the generational terms are in widespread use, and WiMAX, LTE and UMB are commonly considered to represent 4G. The ITU-R framework for IMT-Advanced standardization was defined in 2007 /9/. The schedule calls for submitting proposals for candidate radio interface technologies (RITs) by October 2009, and for developing the necessary Recommendations and Reports by 2011. Foremost among the key features of IMT-Advanced are "target peak data rates of up to approximately 100 Mbit/s for high mobility such as mobile access and up to approximately 1 Gbit/s for low mobility such as nomadic/local wireless access" /8/. The relationship between peak data rates and throughput, which is indicative of expected user experience, is addressed in Section 5. 3. Frequency spectrum availability Adequate frequency spectrum availability is a prerequisite for satisfactory mobile service provisioning. Growing market demand drives the expanding spectrum needs that are accommodated through appropriate revisions of the Table of Frequency Allocations in the ITU Radio Regulations. This is done at World Radio Conferences (WRCs) that take place every three to four years. In ITU-R terminology, frequency spectrum for IMT is "identified" within bands allocated to the mobile service. After the additions approved at WRC- 171 Informacije MIDEM 38(2008)3, str. 170-174 F. Ivanek: 4G: Where are We Going? 07, the frequency spectrum availability for IMT is as follows /1, 5/: 450-470 MHz 698-960 MHz 1 710-2 025 MHz 2 110-2 200 MHz 2 300-2 400 MHz 2 500-2 690 MHz 3 400-3 600 MHz The current total of 1 077 MHz appears insufficient in view of the consensus estimates of IMT spectrum needs for the year 2010, which range from 1 280 MHz for low demand to 1 720 MHz for high demand, respectively /5/. The bands 806-960 MHz, 1710-2025 MHz and 21102200 MHz are in current use for 2G and 3G services. The bands 450-470 MHz, 698-862 MHz, 2 300-2 400 MHz, and 3 400-3 600 MHz were additionally identified for IMT at WRC-07. There was also a proposal for adding the bands 3600-4200 MHz and 4400-4900 MHz for estimated additional future IMT needs, but it was not adopted due to objections from current users of these bands, foremost the fixed satellite service. No WRC follow up is scheduled at this time; the matter is neither on the WRC-11 agenda, nor on the WRC-15 preliminary agenda. Importantly, a number of regulatory restrictions on spectrum usage apply to specific bands in different regions and countries. The necessary follow-up regulatory proceedings for the newly identified bands for IMT, such as spectrum auctions and radio-frequency channel arrangements, are in progress at various stages in the different regions and countries. Since frequency spectrum is a limited natural resource, spectral efficiency is of particular significance. Of special interest is the spectrum "refarming" undertaken in Japan to make the bands 3 600-4 200 MHz and 4 4004 900 MHz available for IMT applications starting in 2012 /5/. This national initiative may stimulate international identification of one or both of these bands for IMT at a future Spectral efficiency erosion _Loss through guard band protection ^^^_^HLosifrequency selective fading management H Loss through practical mcdulaion Seeding _■ Signalling overhead Loss through rriperfffit RF mplemertaion Effective spectral efficiency Fig. 3: Illustration of representative spectral efficiency erosion on an approximate dB scale. (Courtesy of Vodafone R&D.) WRC. The beneficial result would be to align spectrum availability closer with the estimated spectrum needs quoted above. 4. Effective spectral efficiency and throughput The nominal spectral efficiency, which is the ratio of the peak system data rate to the channel bandwidth, is most commonly quoted. However, the more useful metric for system evaluation is the effective spectral efficiency, which accounts for system implementation losses /2/. Figure 3 illustrates the "erosion" from the nominal to the effective spectral efficiency. The quantitative erosion of spectral efficiency determines the aggregate per carrier-sector throughput, which is available for sharing by simultaneous cell users. The most informative comparison of representative 3G and 4G systems presented in Table 1 of /3/ reveals the important fact that the effective spectral efficiencies for 4G systems are about double in comparison with 3G systems. Table 1 below, which is an excerpt from the referenced table /3/, compares the current candidate 4G systems, both frequency-division duplex (FDD) and time-division duplex (TDD). Table 1: 4G comparison (excerpt from Table 1 in /3/). Based on 64 QAM in the downlink (DL), 16 QAM in the uplink (UL), spectrum reuse 1, and signalling overheads included /3/. OFDMA + 2x2 MIMO (4G) Wil MAX UMB LTE TDD (2:1)/FDD TDD (10 MHz) FDD (5+5 MHz) FDD (5+5 MHz) TDD (10 MHz) FDD (5+5 MHz) Peak data rate (Mbit/s) DL 37.44 28.63 37.25 47.48 37.5 UL 5.04 7.56 19.5 9.33 12.5 Aggregate throughput per carrier-sector (Mbit/s) DL 7.88 5.25 8.1 11.93 7.95 UL 2.55 3.83 4.0 2.5 3.75 Spectral efficiency (bits/s/Hz/carrier-sector) DL 1.28 1.62 1.59 UL 0.72 0.8 0.79 172 F. Ivanek: 4G: Where are We Going? Informacije MIDEM 38(2008)3, str. 170-174 The aggregate throughput figures in Table 1 suggest that the user experience with the exemplified candidate 4G systems can be expected to be within the range of current wireline ADSL and cable modem broadband services. The achievable throughput for any individual mobile user depends on a number of parameters, such as specific system characteristics, propagation and interference conditions, traffic patterns, and the number of simultaneous cell users /8/. 5. 2G/3G deployment indicators and 4G trends The most significant single statistical indicator is that global mobile penetration in terms of subscriptions recently surpassed 50%, which is an impressive achievement in spite of multiple subscriptions that are not accounted for /10/. About 99% of the world's mobile subscribers are served by two 2G/3G system families: GSM/WCDMA and cdmaOne/CDMA2000, respectively /1-3/. Their relative market shares are thus important statistical indicators. The last period for which directly comparable worldwide statistics for both 2G/3G families are available in the public domain as of this writing is the end of the first quarter of 2008 /11-12/. Their combined total number of subscribers amounted to about 3.5 billion. By comparison, the current number of fixed telephone lines totals about 1.3 billion. It is informative to differentiate the total mobile subscriptions in two ways, by system families, and by system generation. The approximate results are: - market shares by system families were 87% for GSM/ WCDMA vs. 13% for cdmaOne/CDMA2000; - market shares by system generation were 81% for 2G vs. 19% for 3G. Of particular interest are the market shares of the currently deployed advanced broadband versions of the two system families, high speed packet access (HSPA) and evolutiondata optimized (1xEV-DO): 3.7% combined for end Q1 2008; 0.9% for HSPA and 2.8% for 1xEV-DO. Their modest broadband capabilities, e.g. aggregate per sector downlink throughputs of 0.95 Mbit/s in a 1.25 MHz band, and 2.6 Mbit/s in a 5 MHz band, respectively (Table 1 in /3/), indicate that 3G broadband deployment is still in its beginnings. HSPA and 1xEV-DO upgrades in progress are intended to substantially enhance 3G capabilities and improve cost effectiveness. The above 2G/3G statistical indicators have apparently a bearing on prevailing 4G trends among the leading incumbent mobile service providers. The predominant ones that currently use the GSM/WCDMA system family naturally decided in favor of their own candidate, LTE, and are cooperatively supporting its standardization and development, aiming at commercial LTE launch in 2010 /13/. This includes even Verizon that currently uses the cdmaOne/ CDMA 2000 system family /14/. However, another major incumbent service provider currently using the cdmaOne/ CDMA 2000 system family, Sprint, is already deploying the commercially available WiMAX, and plans to start offering service in late 2008 /15/. And there are new competitive service entrants that decided to exploit the current time to market advantage of WiMAX, e.g. QU Communications in Japan, with plans to start commercial service in 2009 /16/. What next for 4G? One possible scenario is a replay of 2G/3G history when cdmaOne was the trailblazer, evolved into CDMA 2000, and was the catalyst for WCDMA, but captured only a minor 2G/3G market share. In the replay, WiMAX is the trailblazer, and apparently the catalyst for LTE, but may likewise end up with a minor 4G market share as a consequence of the existing GSM/WCDMA dominance of the 2G/3G markets. Nevertheless, even a minor 4G market share is attractive. Another possible scenario is WiMAX-LTE convergence that is within reach due to their commonalities. This possibility was already publicly recognized both among service providers and system suppliers, e.g. /17, 18/. The IMT-Advanced framework /9/ offers an opportunity for implementing convergence but, at least as of this writing (September 2008), the IEEE 802.16m and LTE Advanced proposals for IMT-Advanced radio interfaces seem to progress in competition with each other and without apparent attempts toward convergence /4, 19/. Still another possible scenario is the use of a new OFDM radio interface variant, such as the one applying variable spreading factor (VSF) control to OFDM (VSF-Spread OFDM), which experimentally demonstrated 1 Gbit/s peak downlink data rate in a 100 MHz channel using 4x4 MIMO at speeds of up to about 30 km/hr /5/. 6. Conclusions and comments Synergy between technological progress and service development stimulates convergence through standards development, on the one hand, and competition among both systems suppliers and service providers, on the other. While 3G deployment progressed slower than anticipated and still leaves ample opportunity for broadband upgrading, OFDMA technology push enables leapfrogging to all-IP 4G that offers substantially improved broadband capabilities, spectral efficiencies and cost effectiveness. This increases the service providers' options in satisfying the growing market pull for mobile broadband access with capabilities comparable to those of fixed networks. The IMT-Advanced peak data rate objective of 100 Mbit/s for mobile applications is within reach of emerging 4G systems. However, their aggregate per carrier-sector throughputs available for sharing between simultaneous users are substantially lower due to system implementation losses. This means that 4G mobile broadband user experience can be expected to be comparable to current ADSL and cable modem broadband services. The IMT-Advanced objective of 1 Gbit/s peak data rate for nomadic applications promises aggregate throughputs that would assure user experience comparable to current fiber optic access, 173 Informacije MIDEM 38(2008)3, str. 170-174 F. Ivanek: 4G: Where are We Going? but pursuit of this objective seems less compelling because usage at such high data rates is more likely to occur in fixed locations. Nevertheless, mobile services are under unabated pressure to offer performance as close as possible to fixed networks, and this pressure is increasing with the growth of the mobile web /20/. Acknowledgement The author is grateful to the authors of key references /2-5/, who kindly reviewed the manuscript and provided constructive suggestions: Dr. Stanley Chia, Senior Director, Vodafone Group R&D; Dr. José M. Costa, Senior Manager, Wireless Access Standards, Nortel, and Vice Chairman, ITU-R Study Group 5 - Terrestrial Services; Dr. Roger B. Marks, Senior Vice President - Industry Relations, Next-Wave Wireless, and Chairman, IEEE 802.16 Working Group on Wireless Access; Dr. Akira Hashimoto, Managing Director, Wireless Standardization Department, NTT DoCoMo, and Chairman, ITU-R Study Group 5 - Terrestrial Services. References /1/ F. Ivanek, "Convergence and Competition on the Way Toward 4G", IEEE Microwave Magazine, vol. 9, no. 4, pp. 6-14, August 2008. /2/ S. Chia et al., "3G Evolution", IEEE Microwave Magazine, vol. 9, no. 4, pp. 52-63, August 2008. /3/ W. Tong et al., "The Broadband Multimedia Experience", IEEE Microwave Magazine, vol. 9, no. 4, pp. 64-71, August 2008. /4/ R. B. Marks et al., "The Evolution of WirelessMAN", IEEE Microwave Magazine, vol. 9, no. 4, pp. 72-79, August 2008. /5/ A. Hashimoto et al., "Roadmap of IMT-Advanced Development", IEEE Microwave Magazine, vol. 9, no. 4, pp. 80-88, August 2008. /6/ "Naming for International Mobile Telecommunications", Resolution ITU-R 56, 2007 /Online/. Available: http://www.itu.int/ publ/R-RES-R.56-2007/en /7/ "Detailed specifications of the radio interfaces of International Mobile Telecommunications-2000 (IMT-2000) ", Recommendation ITU-R M.1457, 2007. /8/ "Framework and overall objectives of the future development of IMT-2000 and systems beyond IMT-2000", Recommendation ITU-R M.1645, 2003. /9/ "ITU global standard for international mobile telecommunications 'IMT-Advanced'", ITU Radiocommunication Sector (ITU-R) /Online/. Available: http://www.itu.int/ITU-R/ index.asp?category=information&rlink=imt-advanced&lang=en /10/ "Mobile phones for half the world's population", ITU News, no. 1, Jan.-Feb. 2008 /Online/. Available: http://www.itu.int/ itunews/manager/main.asp?lang=en&ciYear= 2008&ciNum-ber=01 /11/ "Subscriber connections Q1 2008", GSM World /Online/. Available: http://www.gsmworld.com/news/statistics/pdf/ gsma_stats_q1_08.pdf /12/ "1Q 2008 Subscriber Statistics", CDMA Development Group (CDG), /Online/. Available: http://www.cdg.org/worldwide/ cdma_world_subscriber.asp /13/ "Towards Global Mobile Broadband", White Paper, UMTS Forum, February 2008 /Online/. Available: http://www.3gpp.org/ news/2008_04_LTE_A.htm„ /14/ "Verizon Selects LTE as 4G Wireless Broadband Direction", Verizon Investor News, /Online/. Available: http:// investor.verizon.com/news/view.aspx?NewsID=872 /15/ "Sprint and Samsung Declare Mobile WiMAX Technology is Now Ready for Commercial Service", Sprint News Release, May 15, 2008 /Online/. Available: http://newsreleases.sprint.com/ phoenix.zhtml?c=127149&p=irol- newsArticle_newsroom&ID= 1146239&highlight= /16/ M. Nohara, "Mobile WiMAX to Become Real in Japan", IEEE Microwave Magazine, vol. 9, no. 4, pp. 36-42, August 2008. /17/ "Sarin calls for simplification", GSMA Mobile World Congress Daily, Wednesday 13th February 2008, pp. 1-3 /Online/. Available: http://www.wdisdigital.com/index.php?db=GSMA&jnl= DAILIES&vcab=624 /18/ Brad Smith, "Intel Seeking WiMAX-LTE Marriage?", Wireless-Week, June 05, 2008 /Online/. Available: http:// www.wirelessweek.com/article.aspx?id=160528 /19/ "Beyond 3G: 'LTE-Advanced' Workshop, Shenzen, China", 3GPP News Release, 11th April 2008 /Online/. Available: http:// www.3gpp.org/news/2008_04_LTE_A.htm /20/ "Making Web access from a mobile device as simple as Web access from a desktop device", W3C Mobile Web Initiative, August 2008 /Online/. Available: http://www.w3.org/Mobile/ Ferdo Ivanek Palo Alto, California, USA Prispelo (Arrived): 01.09.2008 Sprejeto (Accepted): 15.09.2008 174 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana FIXED-MOBILE CONVERGENCE Marko Jagodic RASKOM d.o.o., Ljubljana Key words: fixed communications, mobile communications, device convergence, service convergence, network convergence, trends, long term perspectives Abstract: Fixed-mobile convergence (FMC) is a phenomenon which is dominating at present the development of fixed as well as mobile communications around the world. The article tries to clarify the background for different understanding of FMC and the main reasons which started it and influenced its evolution. The article also addresses some of the more important FMC supporting technologies like Unlicensed Mobile Access (UMA), IP Multimedia Subsystem (IMS) and Femtocells, describes and discusses the most important development phases of FMC as well as the rationale for investing in it. Fiksno-mobilna konvergenca Kjučne besede: fiksne komunikacije, mobilne komunikacije, konvergenca naprav, konvergenca storitev, konvergenca omrežij, razvojne smeri, dolgoročna perspektiva Izvleček: Fiksno-mobilna konvergenca (FMC) je pojav, ki trenutno obvladuje razvoj tako fiksnih kot tudi mobilnih komunikacij po svetu. Članek poizkuša najprej pojasniti ozadja za različno razumevanje FMC in glavne razloge, ki so sprožili njen začetek in vplivali na njen razvoj. Članek tudi predstavi nekatere za razvoj FMC najbolj pomembne tehnologije, kot so Unlicensed Mobile Access (UMA), IP Multimedia Subsystem (IMS) and femtocelice, predstavi in komentira najbolj pomembne razvojne faze FMC in razloge za njeno uvajanje. 1. Introduction Fixed-Mobile Convergence (FMC) is a process which started when mobile communications, based primarily on voice services, reached a worldwide maturity and mobile customers began to look for new more complex services involving voice, data, and video. One of the most important technologies behind, which persistently expands the availability of these new services to fast growing number of mobile users, is microelectronics, the domain in which Prof. Lojze Trontelj excelled producing innovative products of worldwide importance. The article will try first to explain the different perceptions of FMC by different players in the area of electronic communications. The description of current evolution towards FMC will follow complemented by some important technological aspects as well as development phases of FMC. The rationale for introducing FMC will be addressed at the end of the article. 2. What is Fixed - Mobile Convergence? Mr. Ilkkka Nakaniemi from Nokia Siemens Networks made an excellent summary of FMC at OECD Forum in October 2006 /1/saying that FMC is rather complex process which does not involve only service and application convergence. Device and network convergence are equally if not more important and all of them are leading to industry convergence as shown in Fig. 1 Different people understand FMC quite differently. For an operator such as Iceland Telecom, a hosted PBX Centrex service focused on SMEs understands FMC as a combi- Fig. 1 Fixed - Mobile Convergence elements nation of PSTN, ISDN and GSM to provide an identical set of services for mobile and fixed workers. An operator like BT views FMC as a new and over-reaching integrated wireline/wireless business opportunity, with variations to serve both consumer and corporate customers. Ryan Jarvis, BT chief of convergence products, describes the FMC phenomenon as three dimensional: "One stratum is network convergence which enables devices to move between networks. Then you have service convergence where you 175 Informacije MIDEM 38(2008)3, str. 175-179 M. Jagodic: Fixed-mobile Convergence have one bill and one customer contact centre that supports that device across multiple networks. And then you have commercial convergence which is usually called bundling - it's effectively one product". FMC enables really rich set of services using the same device - mobile phone. Users expect and want to have access to all available services on device they have with them at the time (mobile phone, laptop or others) regardless of the operator the device is connected to, fixed or mobile, the one they are subscribed to or another, native or foreign. 3. The evolution towards FMC The Organisation for Economic Co-operation and Development (OECD) has come up with the following findings related to the evolution of FMC /2/: - Dual-mode cellular/Wi-Fi handsets exist using Wi-Fi modems in the home environment to access VoIP through ADSL connections - There are less evolved forms of FMC using cellular/ Wi-Fi dual-mode handsets that do not have a handover function or have a handover function but do not utilize a fixed voice or broadband network in the home. - Services also exist linking both fixed and mobile networks which are not technologically converged, such as those offering a single voice mailbox over both fixed and mobile networks. - Voice and data services for cellular networks are being bundled, although data services are sometimes provided through wireless cards for laptops. In this case, there is no interface between cellular and Wi-Fi networks and those services tend to remain separate. - Mobile based dual-mode services using home-zones are being provided by offering a virtual fixed line within a designated home-zone area. Prices in the home-zone tend to be in line with prices charged by fixed network operators and lower than cellular rates charged outside the home-zone. Obviously there are many ways being used to provide FMC services some of which are more technologically integrat- ed than others. FMC services are definitely representing a significant challenge to all telecommunication operators. Bundling of disparate services over separate networks is considered as a marketing step necessary to support customers. From the viewpoint of services, the fixed network operators are endangered by the penetration of mobile services into their market, while the mobile operators are faced with the saturation of mobile markets based on the second generation equipment and the need to persuade customers to shift to third generation equipment. At the same time, at least in some countries, more and more fixed network operators which traditionally did not provide mobile services are entering into mobile markets through MVNO-s (Mobile Virtual Network Operators). Nevertheless both mobile and fixed telecommunications operators have to compete with IP based services using fixed or Wi-Fi networks and therefore they are forced to invest either into the development of Next Generation Networks (NGN) or into support systems like the IP Multimedia Subsystem (IMS). Cable operators are also beginning to offer FMC services and are keen to provide multiple play services such as triple play or quadruple play and are becoming direct competitors to PSTN operators. It is expected that this direct competition will increase in the future. The FMC service called home-zone service is known for more then 10 years already. Here, mobile operators offer through their mobile network a virtual fixed line area called the home-zone (for example: UnoFon service by Sonofon in Denmark from 1997 on). Strictly speaking, this type of service is better described as fixed-to-mobile substitution leading to an increase in the amount of mobile call volumes with respect to all voice volumes. For better understanding of evolution towards FMC it is very illustrative to take a look at the role Wi-Fi hotspots are playing in promoting FMC. The availability of such hotspots is quite impressive as it can be seen from Table 1. Wi-Fi hot spots are promoting FMC through VoIP-enabled wireless telephony (VoWi-Fi) by utilizing devices that use Table 1 Number of Wi-Fi hotspots (as of 11.09.2006) Top 10 Countries Top 10 Cities Top 10 Location Types US 41 007 Seoul 2 056 Hotel i Resort 31 887 UK 14 933 London 1 943 Restaurant 25 480 Germany 12 509 Tokyo 1 843 Cafe 15 802 South Korea 9 415 Taipei 1 786 Store 1 Shopping Mall 14 834 Japan 6 258 Paris 1 204 Other 7 350 France 5 334 Berlin 823 Pub 5 348 Taiwan 2 899 San Francisco 805 Office Building 2 386 Italy 2 549 Daegu 787 Gas Station 1 735 Netherlands 2 517 Singapore 671 Airport 1 580 Australia 2 180 New York 66S Libra ry 1 400 Source: J ¡Wire f http jjwww. i i wi re. com/sea rch-h ots pot-loc at io n 5. htm 1. 176 M. Jagodic: Fixed-mobile Convergence Informacije MIDEM 38(2008)3, str. 175-179 Wi-Fi to connect to a VoIP service such as Skype rather than roam between cellular and wireless LAN systems. Most of the VoWi-Fi operators are at present providing Wi-Fi based only services, but some are starting to offer FMC services by combining cellular services with VoWi-Fi. Mobile telecommunications operators are also challenged by Wi-Fi hotspot operators allied with Skype. Therefore some mobile operators seriously consider connecting their cellular networks with Wi-Fi hotspots. Namely the availability of Wi-Fi hotspots is also continuously growing. For example, in the United Kingdom, the number of Wi-Fi hotspots almost doubled between June 2005 and June 2006. On top of Wi-Fi new wireless technologies are coming such as mobile WiMAX which will definitely influence the delivery of FMC services. The high penetration of mobile phones in OECD countries has resulted in significant substitution of fixed network traffic with mobile network traffic. For example, in France, the volume of voice calls through fixed networks has decreased while voice calls through mobile networks have increased as indicated in Fig. 2 Fig. 2 Volume of voice calls in France In the United Kingdom the substitution was not as extensive as in France. One study indicates that the majority of those examined in the United Kingdom (65%) were not so much in favor to abandon their fixed line services as in other European countries surveyed. Fig. 3 Volume of voice calls in United Kingdom To get the right indication of the future trends of FMC services it is necessary to watch the changes in these trends in individual countries. One important variable influencing future trend could be the number of mobile-only households. At present the percentage of households that only use mobile phones within the EU25 countries is 18 %. Another important variable is the ratio of mobile call volumes to all voice volumes. This ratio is close to 70% in Finland, over 50% in Austria, more than 40% in France and around 30% in the United Kingdom. In Germany this it is only 12% which means an opportunity for German mobile operators to take a market share from fixed network operators, especially through the provision of home-zone type services. It should be also noted that in the process of transition to NGN or IMS, FMC does not relates to voice calls only but covers a much broader range of services including television and other multimedia services. Some incumbent fixed operators, that also provide cellular services, are integrating their fixed and mobile operations in order to offer converged services and take advantage of the economies of scope and scale provided by next generation switching systems. Telekom Slovenia has decided to follow this course. 4. Technological aspects UMA (Unlicensed Mobile Access) This technology enables access to GSM and GPRS mobile services over unlicensed spectrum using Bluetooth and WLAN 802.11. Subscribers are able to roam and handover between cellular networks and public and private unlicensed wireless networks using dual-mode mobile handsets. The advantage of UMA is its ability to provide FMC capabilities based on existing wireless networks. How UMA works? IMS IMS, proposed by 3GPP (3rd Generation Partnership Project), was originally intended to provide IP-based communications over mobile network /3/. Later on it developed into the leading standard for the NGN because it can also be used with fixed IP-based networks. It is based on using SIP protocol. Some operators are still hesitant to decide for IMS mainly because of the still high initial investment cost. However, advanced standards, improved capabilities, and decreasing cost of introducing IMS will convince more and more operators to accept IMS. Namely IMS provides a better method for charging multimedia sessions, because the identity management (IM) is an integral part of the core IMS technology structure and IMS can be used by all kind of operators, fixed, mobile, and integrated operators. It helps to ensure a level playing field among operators and service providers at the technological level. The main reasons to invest in IMS are: - for mobile operators: deployment of novel services to increase usage 177 Informacije MIDEM 38(2008)3, str. 175-179 M. Jagodic: Fixed-mobile Convergence - for fixed operators: reduction of CAPEX and OPEX and capability to offer competitive services - for integrated operators: achieving service continuity across different domains Femtocells A femtocell is a small cellular base station designed to be located inside a home and using a DSL/Cable connection to the backhaul traffic. UMA-enabled cellular/Wi-Fi dualmode handsets require Wi-Fi access points. This kind of access could be very expensive especially with picocells. Femtocells do not require subscribers to change their mobile handsets into dual-mode handsets, and UMA enabled femtocells, which are at present applicable for 3G or even for 2.5G, can have air interface with existing handsets. Using a single handset improves customer loyalty and reduces churn. In addition, the backhaul traffic from femtocell stations to a mobile core network will run through fixed broadband, thus giving fixed operators a motivation to be involved in this kind of access especially with FTTH as dominating fixed network access technology. Development phases of FMC - Service bundling - FMC using broadband /Wi-Fi connections (cellular/ Wi-Fi dual-mode service) - Mobile based 'dual-mode' services - Network convergence Service bundling At the very beginning of FMC operators were offering bundling of fixed and mobile services without any technological interface between the two types of networks /2/. While bundling provides subscribers with price discount the use of new technologies brings very little added value for them. Cellular voice and data services can be bundled too, although for data services the use of laptops is generally preferred. Usually without an interface between cellular and Wi-Fi networks those services are not packaged in the way FMC services are offered, since data is regarded as an optional service or may be classified as only for business use. There are also services which link both fixed and mobile networks but are not technically converged like services offering a single voice mailbox over both fixed and mobile networks. Many offers on the market are based on discounts for calls made between fixed and mobile networks to specific subscribers, but are not based on converged fixed-mobile services. FMC using broadband /Wi-Fi connections (cellular/ Wi-Fi dual-mode service) There are several variants of this kind of FMC services /2/: - Dual-mode services using a mobile handset and Wi-Fi modems in the home environment to access VoIP through ADSL connections (for example "Unik" in France). These are examples of incumbents "cannibalizing" their PSTN traffic. New entrants use the same technology but rely on local loop unbundling (LLU) like "Home Free" in Denmark. - Services through cellular/Wi-Fi dual-mode handsets that do not have a handover function from one mode to another, offering each mode separately (for example "surf & talk" in Switzerland). - Cellular/Wi-Fi dual mode voice service which has a handover function from one mode to another, but it does not utilize a fixed voice or broadband network in the home (for example "Hotspot@Home" in USA) When subscribers are within the Wi-Fi zone, the calling fee is very low or free, and when they are calling within the cellular network, the tariff for cellular calls is applied. With this type of service, the switch between the Wi-Fi and GSM networks is handled automatically. Mobile based 'dual-mode' services Mobile-based services using home-zones are a variant of FMC. In this case mobile operators offer their customers a virtual fixed line within a designated home-zone area. Tariffs in the home zone tend to be in line with rates charged by fixed network operators and lower than cellular rates charged outside the home zone. The main incentive for mobile operators to offer this type of services is that they must compete with the fixed line operators encroaching through FMC into the market which was traditionally reserved for mobile operators. Another important incentive for mobile operators to offer dual-mode services is to free up valuable licensed spectrum when the customer is within the home zone area. Many of the fixed operators are doing so through Mobile Virtual Network Operators. Network Convergence For the really consequential and sustainable long term network convergence, which is the enabling basis for the fixed-mobile convergence of services and devices, it is not enough to focus only on adopting the principle of all IP networks. This is good enough for the immediate and short term actions in the direction of FMC. For a successful long term FMC much more is needed. With the global acceptance of FMC as the most appropriate mode of electronic communications in the future the existing networks themselves have to be reassessed from the point of view of suitability of their structures to confront with: the exponential growth of traffic, the required geographical coverage, and the need to set up a simple system to support inter-working of the fixed and mobile domains as well as operators. Photonic technology in the access area has been gaining momentum all the time, driven by the continuous growth of bandwidth, essential for the successful introduction of new services and applications. The most fundamental challenge at this point of evolution of optical networking is to achieve convergence at multiple levels, among them optical - wire- 178 M. Jagodic: Fixed-mobile Convergence Informacije MIDEM 38(2008)3, str. 175-179 less being very important to be able to build an integrated optical platform for an efficient end-to-end service delivery with guaranteed performance. It is expected that the total amount of end users and end devices needing broadband connections in the near future will rise to the order of trillions. Therefore a considerable enhancements in the access part of the network are needed including the convergence of optical and wireless technology leading to a hybrid optical - wireless access infrastructure that will facilitate user mobility and support the vast number of connected devices and sensors, while the simultaneous introduction of WDM will help to increase bandwidth and to enhance ability to upgrade networks /6/. 5. The rationale for FMC The rationale to invest into FMC depends very much on the type of operator /4/, /5/. The fixed network operators see in FMC the opportunity to generate new revenue through quick response to fixed and mobile customers by developing themselves into one-stop-shops for their needs. At the same time FMC is also the best tool to defend them efficiently against mobile substitution. The mobile network operators have different rationale to invest in FMC. They are faced with market saturation in second generation mobile markets and declining average revenue per user in their existing markets. They are also faced with competition from voice calls made over the Internet and over Wi-Fi or Mobile WiMAX networks. FMC helps them by facilitating the number portability and by reducing the price of mobile calling and access to data using mobile terminals through the provision of cellular/Wi-Fi dual-mode services. On the other side shifting to an all IP-based network architecture FMC works well simultaneously for both fixed and mobile network operators by reduction of longer-term maintenance costs and allowing the provision of higher value-added services through service bundling. It is expected that the next generation network technology will bring substantial cost reductions which will certainly increase the profitability of most operators. 6. References /1/ Ilkka Lakaniemi, Views on FMC, OECD Convergence Forum, Oct. 2006 /2/ Report DSTI/ICCP/CISP(2006)4/FINAL, OECD 2006 /3/ Stephen Hayes, Fixed Mobile Convergence - Evolution of IMS, ITU-T Workshop on Multimedia in NGN, Sept. 2007 /4/ Telephony and NXTcomm08, Independent insights: IOC investment and service strategies, June 2008 /5/ Frost&Sullivan and Tekelec, Network Evolution: Migration Strategies for Success, 2007 /6/ Ioannis Tomkos, Kostis Kanonakis, COST DC-ICT Action Proposal: Converged optical network infrastructure in support of future internet and grid services, Sept 2008 Prof. Dr. Marko Jagodič, univ.dipl.ing. RASKOM d.o.o. Omersova 62, SI-1000 Ljubljana, Slovenia E-mail: jagodic.marko@guest.arnes.si Prispelo (Arrived): 08.05.2008 Sprejeto (Accepted): 15.09.2008 179 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana DESIGN GUIDELINES FOR A ROBUST ELECTROMAGNETIC COMPATIBILITY OPERATION OF APLICATION SPECIFIC MICROELECTRONIC SYSTEMS Janez Trontelj jr. Faculty of Electrical Engineering, Ljubljana, Slovenia Key words: Electromagnetic compatibility, EMC, EMI, ASIC, GTEM, Abstract: Proper operation of microelectronic systems is often influenced by electromagnetic interference. While the geometry and power supply voltage of the microelectronic structures are decreasing, the demand for emission robust integrated circuits is increasing. Designing the integrated circuit for electromagnetic compatibility is therefore necessary, to achieve the desired functional performance, as well as to meet legal requirements. Example here can be automotive market, where several strict regulations must be fulfilled. It is a good practice, to incorporate known guidelines and use simulation tools for electromagnetic compatibility from the beginning of the project. Later redesign of the microelectronic system, to fulfill the electromagnetic compatibility test, is very expensive and can cause serious product delays and consecutive market loss. Conversely, incorporating all the best electromagnetic immunity practice at the beginning, can lead to the product being over engineered and expensive to produce. In this article several electromagnetic compatibility design guidelines and practical solutions for microelectronic systems are presented. Priporočila za načrtovanje elektromagnetno robustnih mikroelektronskih sistemov po naročilu Kjučne besede: Elektromagnetna združljivost, EMC, EMI, ASIC, GTEM, Izvleček: Na pravilno delovanje mikroelektronskih sistemov pogosto vplivajo elektromagnetne motnje. Z zmanjševanjem velikosti mikroelektronskih struktur in njihovih napajalnih napetosti, so se povečale zahteve za elektromagnetno robustnost integriranih vezij. Upoštevanje elektromagnetne združljivosti, je torej potrebno tako zaradi pravilnega delovanja vezja, kot tudi zaradi upoštevanja predpisanih zakonov elektromagnetne združljivosti. Dober primer je tržišče avtomobilske elektronike, kjer je potrebno striktno upoštevati strogo zakonodajo. Priporočila in rezultate simulacijskih orodij za elektromagnetno združljivost je smiselno upoštevati že od samega začetka projekta. Popravljanje končanih, elektromagnetno nezdružljivih mikroelektronskih sistemov je drago opravilo. Običajno povzroči tudi veliko zamudo izdelka in posledično izgubo tržišča. Po drugi strani pa lahko preveč striktno upoštevanje vseh faktorjev glede elektromagnetne združljivosti po nepotrebnem podraži izdelek. V članku smo navedli priporočila in praktične rešitve za elektromagnetno združljivost mikroelektronskih sistemov. 1 Introduction The technique of electromagnetic compatibility (EMC) is very important engineering process, to ensure that various electrical devices may operate simultaneously without interfering with each other. EMC is mostly influenced by internal or external electromagnetic emissions that are usually caused by pulsing electrical current. The transition time of such pulse is very important. It determines the spectral image of possible electromagnetic interference (EMI), which may disturb the normal operation of another device or microelectronic system. Fast transition time generates wider spectral image that can more easily cause electromagnetic interference at certain frequencies. This phenomenon may degrade the quality of analog signals or corrupt digital signals. Some claim, that only fifteen percents of devices that have not been designed for EMC, are likely to pass EMC testing for the first time. We can say, that device is electromagnetically compatible, when it is capable to satisfy all the operating specifications in electromagnetic environment and meet all legal requirements about electromagnetic emissions. More precisely, microelectronic system is electromagnetically com- patible with its environment, when it satisfies the following criteria: - It does not cause EMI to other systems. - It is not sensitive to EMI from other systems - It does not cause EMI to itself. Various EMC standards for different applications specify levels and test methods to minimize these problems. EMI occurs, if the received amount of energy is strong enough, to cause the receptor to behave in erratic way. Electromagnetic energy can be transferred via different coupling modes: - Radiated coupling (electromagnetic field) - Inductive coupling (magnetic field) - Capacitive coupling (electric field) - Conductive coupling (electric current) Figure 1 presents such system with emitter, coupling path and receiver. The sensitivity to electromagnetic interference of the receiver is also quite important. Therefore the first step to reduce the amount of transferred electromagnetic energy would be to suppress the emis- 180 J. Trontelj jr.:Design Guidelines for a Robust Electromagnetic Compatibility Operation of Aplication Specific Microelectronic Systems Informacije MIDEM 38(2008)3, str. 180-185 Fig. 1: EMC radiated coupling path with emitter and receiver sion at its source. Further improvement of the problem, is to make the coupling path as inefficient as possible and the next step is, to make the receptor less susceptible to EMC. Minimizing the cost factor of the selected solution is also quite important. For example, to shield low cost systems with simple and effective conductive enclosure is usually too expensive. EMC Directive in general is that electrical devices shall be so designed and manufactured, having regard to the state of the art and as to ensure that the electromagnetic disturbance generated does not exceed the level above which radio and telecommunications equipment or any other equipment cannot operate as intended and it has a level of immunity to the electromagnetic disturbance to be expected in its intended use which allows it to operate without unacceptable degradation of its intended use. The European Union's harmonized EMC Standards provide guidelines and limits for testing and include descriptions of test layout and methods, as well as defined maximum permissible limits of electro-magnetic emission and immunity levels. 2 Methods for better EMC compatibility of the integrated circuits When designing an application specific integrated circuit (ASIC), we must consider several aspects of EMC. The most common trouble spots are EMI influence on power supply lines and input connections. Here we treat digital and analog input pins differently. Output emissions can be most efficiently suppressed by pulse shaping. 2.1 EMC and power supply lines Power supply usually delivers to an integrated circuit some kind of AC signal, superimposed on the DC power line. Such AC signals can reach up to 100Vpp. Influence on power supply is presented on Figure 2. It is needless to say, how the difference in power supply for 1 or 2 volts affects modern low power and low voltage microelectronic systems. The solution here is to properly increase the decoupling on the Vdd. High frequencies and transient currents can flow through a capacitor, in this case in preference to the Fig. 2: EMC and power supply lines harder path through the decoupled circuit, but DC cannot go through the capacitor, so continues on to the decoupled circuit. Some additional LC filters on power supply lines are also helpful. The best way to avoid this problem is to design the ASIC in a way that minimizes the influence of alterations in power supply voltage. In other words, we must guarantee by design as high as possible power supply rejection ratio (PSRR) at high frequencies. 2.2 EMI influence on digital input pins and solution Figure 3 presents similar situation on digital input pin. Electromagnetic interference can easily generate additional ones and zeroes. Beside digital communication protocol automatic error correction, the solution of the problem is presented on figure 4. Each digital input pin should have some protective structures that will rectify at much higher voltages. For example, this solution is typical for automotive IC market. Fig. 3: EMI influence on digital input pin and solution Fig. 4: Solution of EMI influence on digital input pin 2.3 EMI influence on analog input pins and solution The biggest problems for EMC are analog input pins. If possible, the problem should be solved by an external LC 181 J. Trontelj jr.:Design Guidelines for a Robust Electromagnetic Informacije MIDEM 38(2008)3, str. 180-185 Compatibility Operation of Aplication Specific Microelectronic Systems filter. Figure 5 presents the solution for analog input pins. The protective structure is quite similar to that for the digital input pins. The difference is that here the integrated filter consist from LC and RC part. Fig. 5: EMI influence on analog input pins and solution 2.4 Methods to decrease electromagnetic emissions The straight edge of the digital pulse (if perfectly vertical = zero rise time) represents a sinewave of almost infinitely high frequency. The faster the digital signal gets, wider is the slot of the frequency spectrum it occupies. Unfortunately such digital signals will radiate and cause interference in pretty much the same way, as may some intentional analog wave transmitters. The solution is presented on figure 6. By increasing the rise and fall time, such emissions can be drastically improved. It is also a good idea to keep the clock frequency as low as possible and rather to use some parallelism for speeding up the circuit. CVdd tr=tf=—T--(1) Fig. 6: Decreasing EMI with signal shaping Another method to decrease the influence of the electromagnetic emission is in proper partitioning and positioning of the integrated circuit components. The topology of the ASIC and of the corresponding printed circuit environment should consider some of the following rules: - Reduce the serial inductance to avoid resonance (package) - Place Vdd and Vss supply as close as possible (use Vdd and Vss pad pairs) - Use a grid of power supply network on chip - Decoupling capacitance should be used for each active part of the circuit - Identify and isolate noisy blocks - use separate supplies Fig. 7: GTEM cell with typical RF emissions test setup - High frequency interconnections should be as short as possible - Very sensitive analog or digital lines should be short -■ Sensitive interconnections should be shielded - with ground wires or other layers if possible - It is better to use two capacitors than one with the same nominal value - High frequency interconnections should be away from the input and output structures 2.5 Measuring methods Almost all EMC measuring methods require some generation of low and high frequency, high density electromagnetic field. Some tests require immunity of up to 300V/m. Testing should be done in an environment that allows measurements without disruption from external environment. For both, electromagnetic emission and immunity debugging purpose it is quite important to have a reflection and radio frequency free area for proper accommodating our device under test (DUT). For small components there are several EMC compliance test cells with field strength sensor available on the market. They are basically divided in TEM (Transverse Electro Magnetic) and GTEM (Gigahertz Transverse Electro Magnetic) cells. TEM cell is a small enclosure, to be used in normal laboratory environment for emission and immunity analysis. They are relatively inexpensive and do not require a high power amplifier; the drawback is that they can not operate at very low frequencies. By increasing its size, the lower frequency limit can be extended. GTEM cell is larger. The tapered point and anechoic absorbers at the larger side of the pyramid shape, allow GTEM cell to operate well into the gigahertz range. Figure 7 presents GTEM cell with typical RF emissions test setup and figure 8 presents GTEM cell with typical RF immunity 182 J. Trontelj jr.:Design Guidelines for a Robust Electromagnetic Compatibility Operation of Aplication Specific Microelectronic Systems Informacije MIDEM 38(2008)3, str. 180-185 Fig. 8: GTEM cell with typical RF immunity test setup test setup. A small, from 30W to 100W power amplifier with bandwidth from approximately 100 MHz to 1GHz will do the basic job. It boosts the spot frequency signals to achieve the required field strength. Tested device is exposed to each field for a fixed amount of time. Operation within specifications is checked and procedure is repeated for another, different DUT orientation within the test cell. For emission compliance, the equivalence between testing in GTEM cell and testing in open area test site (OATS) has been formerly endorsed. On the other hand, the RF immunity testing in GTEM cell can be more or less used only as a pre-compliance verification. Final RF immunity verification should be done in an anechoic chamber. Better is the pre-compliance verification, shorter is the time in expensive anechoic chamber. Alternatively, the radiated immunity can also be tested in somehow cheaper reverberation chambers. Entire truck or bus can be proofed for EMC in such chambers. They usually have a rotating tuner on the ceiling. Technically they are like a big microwave oven. RF energy is injected into a corner of the chamber and allowed to reflect off the walls, ceiling, floor and rotating tuner. At each reflection the wave loses a little of its magnitude. Consequently the reflected waves arrive at our measuring point inside the chamber with different magnitudes. The revolving tuner also changes the path lengths and the number of reflections of the waves. From few Hz to several GHz can be generated. The larger are the dimensions of the reverberation chamber the lower is the chamber's minimum operating frequency. The maximum useable frequency seems to be related only to the maximum power available to drive the chamber. Figure 9 presents such chamber. However, measuring a field in a reverberation chamber looks more like measuring a noise and it doesn't give the Fig. 9: Reverberation chamber with tuner on the ceiling operator any information about the direction and polarization. In the reverberation chamber we can measure only the total radiated power and not the electric field at a specified distance, as required by most test standards. The full compliance EMC testing can be usually done in anechoic chambers. The materials used on the walls and ceiling of an anechoic chamber are such that there is a little, or no reflection of electromagnetic waves. This is accomplished by the geometry and the absorptive nature of these materials. They usually have a rotating platform for DUT. Such anechoic chambers are quite expensive and EMC measurements may take a considerable amount of time. So it is a good idea, to do some pre-compliance EMC measurements with ordinary laboratory equipment, when it is possible. 3 3.1 Examples of EMC measurements and solutions Example of pre-compliance testing for EMC of automotive airbag sensor Sensor for automotive airbag was developed in Laboratory of Microelectronics at University of Ljubljana. As guideline for measurements we used EMC standard MIL-STD-461 E (5.18.4 RS 101 alt. test procedure AC Helmholtz coil). Sensor was measured in magnetic field that was generated by two opposite coils. Sensor was rotated in six different positions. Two such positions with the coils for the magnetic field generation are presented on figure 10. Frequency was varied from 50Hz to 10 kHz. Sensor passed the later EMC measurements successfully. 3.2 EMC solution for automotive steering wheel sensor Automotive steering wheel sensor was also developed in Laboratory of Microelectronics at University of Ljubljana. The principle of sensor operation is to determine the automotive steering wheel position on the maximum interfer- 183 J. Trontelj jr.:Design Guidelines for a Robust Electromagnetic Informacije MIDEM 38(2008)3, str. 180-185 Compatibility Operation of Aplication Specific Microelectronic Systems a b Fig. 10: Example of different sensor positions while doing pre-compliance measurements of automotive airbag sensor for EMC ence basis. The EMC problem here was that sensor was very susceptible to electromagnetic interference. Employment of shielding for the entire sensor did not satisfy the EMC, as well as extensive blocking of input and output pins. The problem was solved by modifying the sensor in a way, that sensor actually detects, when the electromagnetic interference happens on its momentarily operating frequency. Then it automatically switches to another frequency and continues an undisturbed operation. Figure 11 presents such disassembled, steering wheel sensor. 4 Conclusions The situation about EMC is getting worse, since we are using more and more wireless electrical equipment. That equipment operates at higher and higher frequencies and data rates. For example, the basic clock frequency of the common personal computer nowadays is higher than the transmission frequency used by cellular phones. Scaling down the integrated circuits and decreasing operating voltages to reduce power consumption makes modern elec- Fig. 11: Automotive steering wheel sensor with capability of switching operating frequencies to avoid EMI tronic much more vulnerable to interference. Lower is the supply voltage, less tolerance we have for transients. And not at least, more and more digital transmission signals are cleverly packaged to fit as many separate channels as possible in the available spectrum. Such signals are usually hopelessly complicated mesh of the fundamental frequency, a load of harmonics, switching transients, sidebands and music from the local radio transmitter. Beside that, also heavy equipment is drawing large currents and strong electrical motors in particular, may cause transients that can propagate very far over the power supply network. Fortunately all kind of modern data communications protocols include at least some type of error checking and correction. Few lost bits in home DVD player may not cause a serious problem, yet few lost bits in medical or military equipment may be catastrophic. The problem is also with standards compliance. It is often left up to the manufacturer to choose the most appropriate standard and the selected one may not be the most stringent one available, to match the electromagnetic environment of the product. So, like every other aspect of EMC, the standards compliance is no guarantee that the product will actually work in all circumstances. Therefore we may say in the end, that we have some good design guidelines, but there is no way of knowing exactly what will happen in real life of the product. However, it is possible in theory to design the product that will not make or accept any interference from other products, but it will be bulky, expensive and hard to sell. On the other hand, if we design cheap and for electromagnetic interferences sensitive electronic devices, nobody would buy them either. So designing for electromagnetic compatibility may be extremely convoluted, unpredictable and difficult business, and above all, it is always a subject of compromise. Furthermore always keep in mind that a user, manufacturer or even a provider of electrical device that caused material loses or any other harm to a third party due to electromagnetic compatibility, may be prosecuted. 184 J. Trontelj jr.:Design Guidelines for a Robust Electromagnetic Compatibility Operation of Aplication Specific Microelectronic Systems Informacije MIDEM 38(2008)3, str. 180-185 5 References /1/ C. R. Paul, Introduction to Electromagnetic Compatibility, John Wiley & Sons Inc., New Jersey, 2006, ISBN-10:0-471-75500-1. /2/ M. I. Montrose, E. M. Nakauchi, Testing for EMC Compliance, John Wiley & Sons Inc., New Jersey, 2004, ISBN 0-471-43308-X /3/ S. B. Dhia, M. Ramdani, E. Sicard, Electromagnetic Compatibility of Integrated Circuits, Springer US, 2006, ISBN 978-0-38726600-8. Dr. Janez Trontelj jr. University of Ljubljana, Faculty of Electrical Engineering Laboratory of Microelectronics Tržaška 25, SI-1000 Ljubljana, Slovenia Tel.: +386(0)14768471 e-mail: janez.trontelj-jr@fe.uni-lj.si Prispelo (Arrived): 26.06.2008 Sprejeto (Accepted): 15.09.2008 185 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana A MICRO-BOLOMETER FOR FAR INFRARED (FIR) APPLICATIONS BASED ON BORON DOPED POLYCRYSTALLINE SILICONE LAYERS Radko Osredkar1, Marijan Maček .2 1University of Ljubljana, Faculty of Computer and Information Science, Ljubljana, Slovenia 2University of Ljubljana, Faculty of Electrical Engineering, Ljubljana, Slovenia Key words: bolometer, FIR, thin films, doped poly Si, noise, micro electronic technologies Abstract: Sources if noise in moderately doped (rid = 1018 1 020 cm3, r = 0.002 - 1 Wcm) p-type (boron doped) poly Si resistors, used as a bolometer sensing element, at low frequencies are analysed. We demonstrate that the 1/f noise in such resistors is well described by the Hooge relationship, and that parameter sh is linearly proportional to the energy barrier height Eb. The noise generated in the contact areas of the ptype resistors does not contribute significantly to the overall noise of the device. The test bolometer chip characteristics, developed at our laboratory specifically for evaluating the resistor film performance, closely follow the theoretical predictions of the accepted theory, making the design and fabrication of a usefull FIR detector possible. Mikro bolometer namenjen uporabi v daljnem IR območju, zgrajen na osnovi tanke, polikristaline silicijeve plasti dopirane z borom Kjučne besede: bolometer, tanke plasti, popirani polisilicij, šum, mikroelektronske tehnologije Izvleček: V prispevku analiziramo izvore šuma pri nizkih frekvencah v zmerno dopiranem z borom (nd = 1018 - 1020 cm3, r = 0.002 - 1 Wcm) polisilic-ijevem uporniku tipa p, ki je uporabljen kot seznorski element v bolometru. Pokažemo, da šum 1/f v takšnih upornikih dobro opisuje Hoogeova enačba, da je parameter aH v njej linearno odvisen od veliksto energijske bariere Eb med zrni polisilicija. Šum kontaktv upornikov tipa p ne prispeva znatno k skupnemu šumu celotne bolometrske naprave. Lastnosti testnega bolomotra na silicijevi tableti, ki smo ga v laboratoriju razvili posebej z namenom okarakterizirati lastnosti uporovne plasti, dobro opisuje veljavna teorija, kar nam omogoča načrtati in izdelati uporaben detektor za EM valovanja v daljnem IR območju. 1. Introduction Due to the small photon energies photonic detector are unsuitable for detection of electromagnetic (EM) radiation with wavelengths longer than 12 em and therefore can not be used for detection of far infrared (FIR) and terahertz (0.1 to 10 THz, i.e. wavelengths between 10 em to several millimeters) waves. But in this range of the EM spectrum heat detectors are available, offering several advantages: their response is in principle not dependent on the wavelength of the incoming radiation, and are relatively simple to use and maintain as they do not require cooling to low temperatures, if temperature resolution of the order of ~0.1 KHz -1/2 is sought. Such detectors have often been used for remote temperature measurements and in different motion sensors, however, advances in materials science and micromachining technologies have made fabrication of arrays of heat detectors possible that are used in thermo vision systems /1, 2/. All heat detectors absorb IR radiation and consequently their temperature rises. This temperature change is converted by the detector to a change of the output signal /2/ via a change of resistance of the device (e.g. in metal, semiconductor, or ferroelectric bolometers), a change in thermo-voltage, pressure (e.g. Gol- lay cell), pyroelectric effect, etc. In this paper we present a study of the sensing materials for a bolometric type of heat detector, together with an example of the detector. 2. Bolometer parameters The bolometric principle and several devices based on it have been studied in detail /3, 4/. The basic parameter of a bolometric device is its sensitivity (S). It is a function of the temperature coefficient TC of the device, its heat conductivity G, heat capacity C, and the time constant o = C/ G. Under the influence of the incident EM radiation of frequency u and intensity Po, the sensitivity of the bolometer is given by TC-K Po g(i+(cùt)2)12 (1) For a large response of the device to the incident EM radiation thus a material with as large as possible TC, and as low as possible heat conductivity G is needed. These may be conflicting requirements as the TC is determined by the materials used, and G, on the other hand, is basically determined by the fabrication technology employed. Its val- 186 R. Osredkar, M. Maček: A Micro-bolometer for Far Infrared (Fir) Applications Based on Boron Doped Polycrystalline Silicone Layers Informacije MIDEM 38(2008)3, str. 186-190 ue can be lowered if the sensing element of the device is positioned in vacuum, whereby the heat losses are minimized. From (1) it would appear that the sensitivity could be conveniently increased by increasing the voltage drop Vs over the bolometer sensor, however, the signal voltage to noise voltage ratio of the bolometer must be also be considered. Generally, there are three sources of voltage noise present in all types of resistors: the Johnson noise Vj , caused by the thermal motion of the charges in the sensing element, noise due to temperature fluctuations (the so called pho-non noise), and the 1/f noise, due to recombination -generation effects in semiconductors and/or effects on grain boundaries /5/. The first two types of noise are frequency independent (white noise) and also independent of the current through the resistor, but not the 1/f noise. At low frequencies or/and high applied currents the 1/f noise becomes predominant. The Johnson noise is a white noise with a constant spectral distribution S over the entire frequency range. It is described by the well known equation Sj =4kTR (2) where k is the Boltzmann constant, 1.38 10-23 J/K. The spectral density of phonon noise is given /1/ by the equation ST2 = I(TC)R.. kT2 ~G (3) and is linear with respect to the current through the bolometer structure. If the heat conductance G of the device is sufficiently small (below 0.1 mW/K), the phonon noise of the device approaches the Johnson noise. A much more serious source of noise in bolometers is the 1/f noise as the devices usually operate at frequencies of several 10 Hz and a relatively high voltage over the device. This contribution to the noise is described by the Hooge semi-empirical equation 1 (4) sH yl h f-N where ¿h is the Hooge constant, f the frequency and N the number of charge carriers. The total noise spectral density (energy) is the sum of all 3 contributions, S„=Sj +ST+SH (5) The measured noise Vn is therefore the integral of spectral density Sn over the frequency range of interest 3. Experimental: polycrystalline silicone film properties In designing a bolometric device with a polycrystalline silicon (poly Si) resistor the properties of the resistor film should be understood in extensive detail. Poly Si has been used in semiconductor manufacturing for decades as material for transistor gates, resistors, capacitors, etc. Due to its well established technology, and its electrical and mechanical properties it is also a very attractive material for a wide range of micro-machined devices and sensors. Unfortunately, there is a serious draw back in poly Si properties, if used in a bolometric device: its 1/f noise /6, 7/ is large. Excessive 1/f noise can seriously degrade sensor properties, especially in case of bolometers, where heating and sensing are combined in the same material. For instance, detectivity of bolometers fabricated on n-doped poly Si, as reported in /8, 9/, was by an order of magnitude lower than expected. Poly Si films in this study were deposited on the top of an oxidized (50 nm) 100 mm Si wafers. The poly Si deposition was performed in a commercial LPCVD reactor by the decomposition of SiH4 at the standard conditions, T = 625°C, p = 350 mtorr. Doping of 0.38 mm and 1.0 mm thick films was performed by ion implantation of boron (Da = 31014 - 51015 cm-2, E = 40 keV). After poly Si patterning (two resistors geometries: 375 ■ 75 mm2, and 375 ■ 5 mm2) wafers underwent process steps typical for the standard CMOS processing with 2 mm minimal geometry, including annealing at 920°C and a 1000°C reflow. The final step was alloying in the forming gas at 420°C. The noise measurements were performed according to the technique described in ref. /10/, using a low noise spectrum analyzer HP 3585A. It is known that the energy barrier between small Si grains in the poly Si film is a function of dopant concentration. As a first approximation the dopant concentration nd is proportional to the ratio of the dose to the poly Si film thickness. In Fig. 1 we demonstrate that the energy barrier (Eb) in boron doped (ptype) poly Si is proportional to nd _0,59 while in phosphorous doped (ntype) the Eb m nd _0,85. According to ref. /8/ the power of the concentrations above the critical concentration, ~5x1017 cm-3, should be be- r>d ~ dose/polySi thickness [cm Fig. 1: FigEbConc:: Energy barrier height Eb as a function of doping for p- and n-type poly Si. Concentration of dopant is defined as: nd H" Dose/poly thickness. 187 R. Osredkar, M. Maček: A Micro-bolometer for Far Infrared (Fir) Informacije MIDEM 38(2008)3, str. 186-190 Applications Based on Boron Doped Polycrystalline Silicone Layers tween -0.85 and -1. Our measured values for the Eb of p-type correspond to the values given in /8/. On the other hand, the relationship between the resistivity r and the barrier Eb shows the same relationship for both types of poly Si. The noise measured in a poly Si resistor, as described above, is the sum of the thermal and Johnson noise, 1/f noise, and the noise of the measuring system. Spectral density Si/f of the noise is proportional to the square of the applied bias voltage or current Io flowing trough the resistor. This relationship is demonstrated in Fig. 2, where the Sv1/2 vs. Io is plotted for convenience. For the particular resistor (nd ~ 31018 cm-3, R = 29.2 kW, ??f = 75 Hz) the power of the current was 2.02, which is close to theoretical value /7/. This indicates that the noise is mainly generated in the depletion barrier region of poly Si. If the noise were generated in the grain bulk region the relationship would involve a higher power of Io. 1000 - 100 - Fig. 2: Measured noise spectral density Sv and its Si/f component at f = 75 Hz as a function of the current flowing trough the resistor with R = 29.2 kW According to the theory the noise spectral density Si/f is inversely proportional to the frequency, Si/f m f 1. This is demonstrated in Fig. 3, where the frequency dependence of the same resistor as in Fig. 2 is plotted. The measured Si/f is proportional to f-109, which is reasonably close to the theoretical value and published experimental data /10/: for ptype resistors the reported values are -1 and -0.85 for p and ntype poly Si respectively. Indeed, we have measured values about -0.9 for n-type poly Si bolometers /9/. The dependence of the measured 1/f noise on the current and frequency confirms the accepted notion that the noise is generated within the depletion barrier region of poly Si and not in the bulk of the grain. Data for thin 0.38 mm and thick 1 mm layers demonstrate that the noise is also independent of the geometry, and is influenced by the carrier number only. The main difference between the p and ntype materials is the different energy barriers. Gen- „ io4. > (O f[s"1] Fig. 3: Measured noise spectral density Sv and S1/f component as a function of the frequency for the same resistor as in Fig. at Io = 200 mA. erally, the energy barrier in ntype semiconductor is higher than in the ptype for the same doping. And the same is valid for poly Si at low and medium doping levels (<1020 cm-3), as indicated by our previous work /11/. Therefore the 1/f noise is much more pronounced in ntype material, unless the doping is so high that the segregation of the dopant on the grain boundaries occurs. For illustration, the specific resistively n of the poly Si film as function of the dopant concentration is shown in Fig. 4. Cone [m ] Fig. 4: The dependence of the specific resistivity of the poly Si layer on the the boron concentration, C = Dii/debSi-Cout. During the heat treatment, approximately 6-1023 m3 boron is lost. (% samples run # 1, f& sample run #2, % bolometer test chip, solid line - theory) For the bolometer applications significant Hooge parameter <3h, which controls the 1/f noise of the poly Si, can now be conveniently presented as a function of the specific resistivity of the boron doped poly Si film (Fig. 5). 188 R. Osredkar, M. Maček: A Micro-bolometer for Far Infrared (Fir) Applications Based on Boron Doped Polycrystalline Silicone Layers Informacije MIDEM 38(2008)3, str. 186-190 Fig. 5: The dependence of the Hooge parameter ¿h on the specific resistivity of the boron doped poly Si layer (% samples run # 1, f& sample run #2, % bolometer test chip, solid line - theory). In step with the dopant concentration, the TC of the film is also changing with its specific resistance. The flow of the current through the film is associated with the tunneling of the charge carriers through the grain boundaries, where, n ~ exp(qEb/kT), and Eb is the height of the barrier. In Fig. 6 the dependence of the TC, measured at 25 °C, is shown as a function of the specific resistivity of the boron doped polysilicon. Fig. 6: The dependence of the TC on the specific resistivity of the boron doped poly Si layer. (% samples run # 1 at 25 °C, % bolometer test chip, solid line - theory) Our measurements on contact chains indicate that the noise in the contact area to the n-type poly Si is extremely sensitive to the doping (Si/f m nd-4) but not in the p-type (rc nd ~08). This indicates that medium and high resistivity ptype resistors can be fabricated without additional doping of the contacts, contrary to the ntype poly Si, where the contacts should be doped above 21020 cm-3 which is typically done from a POCl3 source. 4. Absorption of the EM radiation by the bolometer An important consideration in evaluating a bolometer resistor performance is the absorption of the EM radiation by the active surface of the device. In the FIR domain a satisfactory absorptivity of the bolometer surface can be achieved by covering it with passivation films which are standard in the microelectronic fabrication technologies. Such an absorption film is formed by a LPCVD deposited PSG (refractive index n = 1.46) film, and a mixed SiON (n ~1.75) and SiN (n ~ 2) film, deposited by the PECVD method /12/. At longer incident radiation wavelengths a different approach is indicated, combining dielectric films with conducting films. The calculated absorption coefficients for PECVD SiON films of different thicknesses are shown in Fig. 7. Absorption at even higher wave lengths can be achived (up to 35 mm for PECVD a-Si with n=3.4) by increasing the index of refraction. Fig. 7: The absorption of the bolometer surface as a function of the incident EM radiation wavelength at sheet resistance Zo = 377 Ù/ square for PECV SiON, n = 1.75, for 1 ëm to 2 em film thicknesses (in increments of 0.2 ëm). 5. Bolometer fabrication In the test bolometer fabrication, designed to analyze the poly Si films performance, special care was taken to consider only fabrication steps that are compatible with a standard CMOS technology with 2(3) layers of the poly Si. The fabricated test IC is shown on Fig. 8. The test chip enabled us to characterize the poly Si properties as described above. 6. Conclusion Noise in moderately doped (nd = 10181020 cm-3, r = 0.002 - 1 Wcm) p-type (boron doped) poly Si resistors at low frequencies is dominated by 1/f noise. Its spectral density Si/f is proportional to the square of the current flowing through the resistor, and we conclude that the 1/f noise is generated within the depletion barrier region, not in the 189 R. Osredkar, M. Maček: A Micro-bolometer for Far Infrared (Fir) Informacije MIDEM 38(2008)3, str. 186-190 Applications Based on Boron Doped Polycrystalline Silicone Layers Fig. 8: The test bolometer device, comprising of three, 40-40, 50-50, and 70-70 em2 bolometers. The resistor is supported by 2 em wide supports; the holes in the detector areas enable consistent under-etching of the structure during fabrication. bulk of grains or in the contact areas. Spectral density Si/ f is also inversely proportional to the frequency, and frequency dependent noise is well described by the Hooge relationship. Parameter an is linearly proportional to the energy barrier height Eb which itself is proportional to the doping, Eb p nd-059. Its values are from 10-2 to 310-3 for doping levels 1018 to 1020 cm-3. Measured values for aw are similar to the reported values for p-type boron doped poly SiGe /13/ and lower than reported for the n-type poly Si /7, 10/. The noise generated in the contact areas of ptype resistors does not contribute significantly to the overall noise of the resistors. Therefore there is no need for additional doping of the contacts. The test bolometer chip characteristics, developed at our laboratory specifically for evaluating the resistor film performance, closely follow the theoretical predictions of the accepted theory, thus assuring us that the design and fabrication of a usefull FIR detector is within our reach. 7. Acknowledgement This work was supported by the Ministry of Education, Science and Sports of the Republic of Slovenia. 8. References /1/ P.W. Kruse, Design of Uncooled Infrared Imaging Arrays, SPIE 2746 Infrared Detectors and Focal Plane Arrays IX, Orlando, FL. April 1996 /2/ P.W. Kruse, Uncooled IR Focal Plane Arrays, AeroSense 1996, Los Angeles 10.Apr.1998 /3/ M. Maček, Inf. MIDEM, 1998, 86, pp. 77-89 (1998) /4/ P.L. Richards, J. Appl. Phys, 76 (1), 1994, pp. 1-24 /5/ F.N.Hooge, T.G.M. Kleinpenning, L.K.J. Vandamme, Rep.Prog.Phys, 44, 479(1981) /6/ H.C. de Graff, M.T.M. Huybers, J.Appl.Phys, 54, pp. 25042507, (1983) /7/ M.Y. Luo, G. Bosman, IEEE Trans.Electro Devices, 37, pp. 768774 (1990) /8/ J.Y.W. Seto, J.Appl.Phys, 46, 5247-5254 (1975) /9/ M. Maček, Inf. MIDEM, 1998, 86, pp. 77-89 (1998) /10/ M.J. Dean, S. Rumyantsev, J. Orchard-Webb, J.Vac.Sci.Tecnol.B, 16, pp.1881-1884(1998) /11/ M. Maček, 40th International Conference on Microelectronics, September 29. - October 01. 2004, Maribor, Slovenia. Proceedings. MIDEM - Society for Microelectronics, Electronic Components and Materials, 2004, str. 81-85 /12/ M. Maček, Inf. MIDEM, 1998, let. 28, 86, pp. 81-89 /13/ X.Y. Chen, C. Salm, Appl. Phys. Lett. 75, pp. 516-518 Radko Osredkar University of Ljubljana, Faculty of Computer and Information Science Tržaška 25, 1000 Ljubljana, Slovenia Tel:01/4768-358; Email: radko.osredkar@fri.uni-lj.si Marijan Maček University of Ljubljana, Faculty of Electrical Engineering Tržaška 25, 1000 Ljubljana, Slovenia Tel:01/4768-473; Email: marijan.macek@fe.uni-lj.si Prispelo (Arrived): 08.05.2008 Sprejeto (Accepted): 15.09.2008 190 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana TEMPERATURE BEHAVIOUR OF CAPACITIVE PRESSURE SENSOR FABRICATED WITH LTCC TECHNOLOGY Darko Belavič, Marina Santo Zarnik, Marko Hrovat*, Srečko Maček*, Marija Kosec* HIPOT-RR d.o.o., 8310 Šentjernej, Slovenia Jožef Stefan Institute, 1000 Ljubljana, Slovenia Key words: sensor, pressure sensor, capacitive pressure sensor, thick-film technology, temperature behaviour Abstract: This work is focused on capacitive pressure sensors designed as ceramic capsules, made with low-temperature cofired ceramic (LTCC), consisting of a circular edge-clamped deformable diaphragm that is bonded to a rigid ring and the base substrate. This construction forms the cavity of the pressure sensor. The diaphragm, with a diameter of 9.0 mm has a thickness of 200 ém, and the depth of the cavity is from about 70 ^m. The principle of capacitive pressure sensor is based on changes of the capacitance values between two electrodes. One thick-film electrode is deposited on the diaphragm and the other on the rigid substrate. The distance between electrodes and the area of electrodes define the initial capacitance of the capacitive pressure sensor, which is around 10 pF. The distance between electrodes and together with the geometry and flexibility of the diaphragm define the sensitivity of the sensor, which is about 4 fF/kPa. We investigated the temperature dependence of the sensors' characteristics of capacitive thick-film pressure sensors. The sensor is based on changes the capacitance values between two electrodes: one electrode is fixed and the other is movable. The displacement of the movable electrode depends on the applied pressure. The main influence on the temperature dependence of the sensor characteristics is from the temperature coefficient of the elasticity and sensors geometry, while the temperature coefficient of the Poisson's ratio and the temperature expansion coefficient have only a minor effect. Temperaturne lastnosti kapacitivnega senzorja tlaka narejenega v LTCC tehnologiji Kjučne besede: senzor, senzor tlaka, kapacitivni senzor tlaka, debeloplastna tehnologija, temperaturna odvisnost Izvleček: V prispevku so prikazani raziskovalni rezultati na kapacitivnem senzorju tlaka narejenemu v LTCC tehnologiji. LTCC (Low Temperature Cofered Ceramic) je keramika z nizko temperaturo žganja. Ta keramika se žge pri temperaturah med 850 in 950°C. Da se pri teh razmeroma nizkih temperaturah zasintra, vsebuje precej steklene faze. LTCC tehnologija temelji na tankih keramičnih folijah, ki se jih sestavlja v večplastne strukture. Na ta način je možno zgraditi tridimenzionalno strukturo za kapacitivni senzor tlaka. Osnovo take strukture predstavlja tanka okrogla in upogljiva membrana. Rob membrane je pritrjen na obroč, ta pa na trdo (neupogljivo) podlago. Ena elektroda kondenzatorja je na membrani, druga pa na podlagi. Merjeni tlak upogne membrano, kar spremeni razdaljo med elektrodama. S tem dobimo spremembo kapacitivnosti. Senzor tlaka za tlačno področje do 100 kPa ima membrano s premerom 9,0 mm in debelino 200 mm. Pri razmaku med elektrodama okoli 70 mm je začetna kapacitivnost približno 10 pF. Razmak med elektrodama ter geometrija in fleksibilnost membrane določata občutljivost senzorja na merjeni tlak. Raziskovali smo temperaturno odvisnost karakteristik kapacitivnega senzorja tlaka. Na njo v glavnem vpliva temperaturna odvisnost modula elastičnosti LTCC materiala, delno pa tudi temperaturni razteznostni koeficient LTCC materiala ter konstrukcija in dimenzije tridimenzionalne LTCC strukture. Na temperaturno odvisnost začetne kapacitivnosti pa je znatno vplivajo zaostale mehanske napetosti v membrani in eventualna predhodna ukrivljenost membrane. 1 Introduction Pressure is a mechanical quantity defined as the ratio of force to the surface area over which it is exerted. A complete pressure-measurement system consists of a series of components. One of them is the sensing element (a transducer) that responds to the pressure applied to it and converts the pressure into a measurable signal, which in most cases is an electrical signal. In most cases the sensing elements in pressure sensors are based on strain-gauge, capacitive, piezoelectric or optical principles to convert the physical quantity (pressure) into an electrical signal. The majority of pressure sensors on the market is based on piezoresistive principle. This is mainly due to the fact that that the piezoresistive pressure sensors are relatively sensitive to an applied pressure and their analogue output is linear in a wide pressure range while the output impedance is low. For capacitive pressure sensors the pressure sensitivity is essentially higher than that of piezoresistive pressure sensors, and the power consumption is much lower. The major disadvantages are their small sensing capacitance, high output impedance and nonlin-earity of the sensors response. The small capacitance makes them highly susceptible to parasitic effects. Most pressure sensors are made by micro-machining silicon /1,2/. On the other hand, complex sensor systems combine different materials (silicon, ceramic, metal, polymer, etc.) and technologies (semiconductor, thin and thick film, etc.). In some demanding applications thick-film technology and ceramic materials are a very useful alternative /3-6/. In many cases low-temperature cofired ceramic (LTCC) is used for the fabrication of thick-film pressure sensors. In comparison with semiconductor sensors they are larger, more robust and have a lower sensitivity, but they operate over a wider operating-temperature range /3,5/. 191 D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Informacije MIDEM 38(2008)3, str. 191-196 Temperature Behaviour of Capacitive Pressure Sensor Fabricated ... This contribution includes the study of sensing principle, investigated materials, and designing a capacitive pressure sensor using thick-film and LTCC materials and technology. The special attention is focused on the temperature dependence of sensor's characteristics 2 LTCC materials The low-temperature cofired ceramic (LTCC) technology is a rapidly growing segment of the hybrid electronic-module market. The LTCC technology is a three-dimensional ceramic technology utilizing the third dimension (z) for the interconnects-layers, the electronic components, and the different three-dimensional (3D) structures, such as cantilevers, bridges, diaphragms, channels and cavities. It is a mixture of thick-film and ceramic technologies. Thick-film technology contributes the lateral and vertical electrical interconnections, and the embedded and surface passive electronic components (resistors, thermistors, inductors, capacitors). Ceramic technology contributes the electrical, mechanical and dielectric properties as well as different 3D structures /6,7/. LTCC materials in the green state (called green tapes, before sintering) are soft, flexible, and easily handled and mechanically shaped. A large number of layers can be laminated to form high-density interconnections and three-dimensional structures. The fabrication process of LTCC structures includes several steps, which are named LTCC technology. The separate layers are the mechanical shaping of meso-size features (0.1-15 mm), and then the thick-film layers are the screen-printed. All the layers are then stacked and laminated together with hot pressing. This laminates are sintered in a one-step process (cofiring) at relatively low temperatures (850-900°C) to form a rigid monolithic ceramic multilayer circuit (module). Some thick-film materials need to be post-fired; thick-film pastes are screen-printed on the pre-fired laminate and have to be fired again. The whole LTCC process saves time, money and reduces the circuit's dimensions compared with conventional hybrid thick-film technology. The important advantage for pressure sensors applications is the lower Young's modulus (about 100 GPa) of LTCC materials in comparison with alumina (about 340 GPa). As example Figure 1 shows the comparison of deflections of the diaphragms made with alumina and LTCC materials. The calculated deflections as a function of the distance from the diaphragm centre (r) are presented for the pressure sensors with the same dimensions at an applied pressure of 100 kPa. The diameter of the circular edge-clamped diaphragm is 9.0 mm, and the thickness is 200mm. The biggest deflection, of 8.5 |jm in the middle of the circular diaphragm, was observed for the LTCC, and the lowest deflection, of 2.7 jm, was exhibited by the alumina diaphragm. The LTCC tapes consist of ceramic and glass particles suspended in an organic binder. The materials are either -e- Alumina -LTCC 1 2 ? 3 3 > 4 c ^ o 5 I 6 § - 7 8 5 - 4 - 3-2-101 Distance from the centre r 2 (mm] I r y Fig. 1: The calculated deflections of diaphragms made with alumina and LTCC materials at an applied pressure of 100 kPa. based on crystallisable glass or a mixture of glass and ceramics, for example, alumina, silica or cordierite (Mg2AUSi5Oi8) /8/. The composition of the inorganic phases in most LTCC tapes is similar to, or the same as, materials in thick-film multilayer dielectric pastes. To sinter to a dense and non-porous structure at these, rather low, temperatures, it has to contain some low-melting-point glass phase. This glass could presumably interact with other thick-film materials, leading to changes in the electrical characteristics /8,9/. The composition of a typical LTCC material is shown in Figure 2. Fig.2: The composition of a typical green LTCC material (wt.%). The disadvantages of LTCC technology as compared with an alumina are a lower thermal conductivity (about 2.5 to 4 W/mK) in comparison with alumina and the shrinking (about 10 to 15% in x/y-axis and about 10 to 45% in z-axis) of the tapes during firing. Some of the characteristics of alumina substrates and fired LTCC laminates are presented in Table 1. 192 D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Temperature Behaviour of Capacitive Pressure Sensor Fabricated Informacije MIDEM 38(2008)3, str. 191-196 Table 1: Some characteristics of LTCC material in comparison with AhO3 ceramics Characteristics ai2o3 (94-99.5%) LTCC Thermal expansion coefi. (10"6/K) 7.6-8.3 5.8-7.0 Density (g/cm2) 3.7-3.9 2.5-3.2 Flexural strength (MPa) 300-460 170-320 Young's modulus (GPa) 215-415 90-110 Thermal conductivity (Wm/K) 20-26 2.0-4.5 Dielectric constant 9.2-9.8 7.5-8.0 Loss tg (xlO"3) 0.5 1.5-2.0 Resistivity (ohm.cm) 1012-1014 1012-1014 Breakdown (V/100 urn) 3000-4000 >4000 3 LTCC Structure Most ceramic pressure sensors are made with deforma-ble diaphragms /5/. The deformation is induced by the applied pressure and then converted into an electrical signal. LTCC technology and materials are suitable for forming a three-dimensional (3D) construction, consisting of a circular edge-clamped deformable diaphragm that is bonded to a rigid ring and a base substrate /3,6,7/. These elements form the cavity of the pressure sensor. The cross-section of ceramic pressure sensor is shown in Figures 3 and 4. Cross-section (not to scale) r Diaphragm with thickness (t) and radius (R) / /"" Rigid ring Fig.3: The schematic cross-section of the LTCC structure of a pressure sensor (not to scale). Fig.4: The cross-section of 3D LTCC structure for the pressure sensor. 4 LTCC Capacitive Pressure SENSOR The LTCC capacitive pressure sensor is based on the fractional change in capacitance (DC/C) induced by the applied pressure. The capacitance change can be due to changes of the distance between the electrodes of the capacitor, to changes of the permittivity of the dielectric materials, or changing both. In this contribution we present the capacitive pressure sensor based on changes of the distance between the electrodes of the air capacitor. The construction of the thick-film capacitive sensor is very similar to other thick-film pressure sensors /10-13/. The difference is that the distance between the deformable diaphragm and the rigid base substrate is smaller and must be very well defined. The bottom electrode of the capacitor is on the rigid substrate and the upper electrode is on the deformable diaphragm. Therefore, the area of the electrode and the distance between them define the value of the initial capacitance of the pressure sensor. The principle of the construction is shown in Figure 5. Fig.5: The cross-section of a capacitive pressure sensor without (above) and with (bottom) applied measuring pressure (schematic, not to scale). The capacitive pressure sensors' characteristics depend on the construction, the dimensions and the material properties (Table 1) of the sensor body and sensing capacitor /10-15/. The influence of the geometry and the material properties of the LTCC structure on the deflection of an edge-clamped deformable diaphragm under an applied pressure is described by equation (1) 193 D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Informacije MIDEM 38(2008)3, str. 191-196 Temperature Behaviour of Capacitive Pressure Sensor Fabricated ... 16 Et3 (1) where the deflection y at the position r from the centre of the diaphragm is a function of the applied pressure, P, the material characteristics (elasticity, E, and Poisson's ratio, n) of the diaphragm, and the dimensions (thickness, t, and radius, R) of the diaphragm (Figures 3 and 5). The value of initial capacitance (Co) of the capacitive pressure sensor is defined with the areas of the electrodes and the distance between them. The distance between the electrodes (D) is subtracted from cavity depth and the thickness of both electrodes. When the deflection of the diaphragm y(r=0) under an applied pressure is much smaller than the thickness of the diaphragm and the separation of the electrodes than the capacitance between electrodes is given by equation (2) C(P)=e0 -e, J 2-71 •r-dr J D0-y(r) (2) where C is the capacitance under an applied pressure P, lo is the permittivity in vacuum, ir is the relative permittivity, R is the radius of the electrode, r is the current radius, Do is the distance between the electrodes at zero applied pressure and y(r) is the deflection at the current radius r when the pressure P is applied. The air capacitor of the test samples of the LTCC capacitive pressure sensor was designed as a cavity with a diameter of 9.0 mm and a height of about 80 pm. The thickness of the diaphragm is 200 em, and the dimensions of the whole LTCC structure are 18.0 * 12.5 * 1.4 mm. The diameter of the upper and bottom electrodes is 8.6 mm. The test samples of the sensors were fabricated with LTCC materials Du Pont 951. The diaphragm has a thickness of 200 em. The fabricated samples, which are shown in Figure 6, were tested in the range from 0 to 70 kPa, where the sensor's response is linear. The test samples were measured at five different temperatures (-25°C, 0°C, 25°C, 50°C and 75°C). 5 Results and discussion All the test samples were tested at different applied pressures and at different temperatures. The initial capacitances (C0) of the pressure sensors are between 8 and 10 pF. The relative changes in the initial capacitance of the pressure sensors M2/1 and M3/1) versus the different temperatures are shown in Figures 7 and 8. The calculate temperature coefficients of initial capacitances for two samples M2/1 and M3/1 calculated from experimental results presented in Figures 7 and 8 are about -350*10-6/K and +300*10-6/K respectively. Those selected test samples have extreme values (maximum and minimum) of temperature coefficients of initial capacitances. Other fabricated samples have lower values and mostly located in two Fig.6: The capacitive pressure sensors made in a 3D LTCC structure. groups. The first group has average value about -250*10-6/K and the second about +200x10-6/K. dC/C Relative capacitance at different temperature 2,5% XM2/1 Fig.7: 25 Temerature [°C] The relative change of initial capacitance at different temperatures for the capacitive pressure sensor M2/1. The capacitance of the pressure sensors versus negative applied pressure is shown in Figure 9 and the calculated pressure sensitivities from the measured data are between 3.5 and 5.0 fF/kPa. The temperature dependences of sensitivity are not linear and relative high from -700 to 2000 *10-6/K. 194 D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Temperature Behaviour of Capacitive Pressure Sensor Fabricated Informacije MIDEM 38(2008)3, str. 191-196 dC/C Relative capacitance at different temperature 2,0% 1,5% 1,0% 0,5% 0,0% -0,5% -1,0% -25 0 25 50 75 Temerature [°C] Fig.8: The relative change of initial capacitance at different temperatures for the capacitive pressure sensor M3/1. Fig.9: The capacitance versus the negative applied pressure of the capacitive pressure sensor. The temperature has a noticeable influence on the material characteristics (elasticity and Poisson's ratio) and the fractional changes in the dimensions /8/. The data on the temperature dependence of elasticity of LTCC materials are not available. For this study we presumed that the values of the temperature coefficients of elasticity (TCE) of the LTCC are between the TCE of alumina and the TCE of glass. Therefore, we used a value of -250x10-6/K in our calculations. The data on temperature dependence of the Poisson's ratio of LTCC materials is also not available. The temperature dependence of the Poisson's ratio of alumina is 68*10-6/ K. Therefore, 100x10-6/K was used as a rough estimation for the temperature coefficient of the Poisson's ratio of the glassy-alumina-filled LTCC material. The temperature expansion coefficient (TEC) of LTCC materials is 5.8x10"6/K. Some analytically calculated and experimental values of the characteristics of the LTCC capacitive pressure sensor are presented in Table 2. The main influence on the temperature dependence of the sensor characteristics is from the temperature coefficient of the elasticity, while the temperature coefficient of the Poisson's ratio and the temperature expansion coefficient have only a minor, and opposite, effect on the temperature coefficient of capacitance and the temperature coefficient of sensitivity. Table 2: Analytically calculated and experimental values of the characteristics of the LTCC capacitive pressure sensor Characteristics Calculated Value Experimental Value Initial capacitance (pF) 8.7 8+10 Sensitivity (fF/kPa) 4.0 3.5+5.0 Temperature coefficient of initial capacitance (x10®/K) 5.3 -200+300 Temperature coefficient of sensitivity (*1ff6/K) 260 700+2000 We presume that the significant differences between the experimental and the analytical results of temperature dependences of sensors characteristics lies in the residual stresses and diaphragm pre-bending. Those two effects are not included into the analytical analyses although they have significant influence on the temperature dependences of sensors characteristics. This defectiveness can be corrected by electronic conditioning circuit. For this reason we made the capacitive pressure sensor as the part of the electronic conditioning circuit with the frequency output. The typical output frequency is between 10 and 14 kHz, and depends on the applied pressure. The output frequency versus applied pressure is shown in Figure 10. The calculated pressure sensitivities from the measured data are between 2.5 and 3.5 Hz/kPa. The relative output frequency versus applied pressure at different temperatures is shown in Figure 11. The temperature dependence of initial frequency is relatively high and must be compensated, while the temperature dependence of sensitivity is form -200 to 350 x10-6/K. Fig.10: The output frequency versus the applied pressure of the capacitive pressure sensor with the electronic conditioning circuit. 195 D. Belavič, M. Santo Zarnik, M. Hrovat, S. Maček, M. Kosec: Informacije MIDEM 38(2008)3, str. 191-196 Temperature Behaviour of Capacitive Pressure Sensor Fabricated ... Fig. 11 : The relative output frequency at different temperatures versus the applied pressure of the capacitive pressure sensor with the electronic conditioning circuit. Conclusion The fabrication of capacitive pressure sensors using thick-film and LTCC materials and technology is challenging opportunity for pressure sensors market. The applied pressures generate a relatively small deflection of ceramic diaphragm. This is suitable to use in capacitive pressure sensor because it means that the response of sensors is usefully linear. However, special attention during the fabrication process must be paid to the parallelism of the capacitor electrodes and the repeatability of capacitor dimensions' (areas of electrodes and s distance between them). For the use in the wide temperature ranges the temperature dependences of the sensors characteristics must be compensated by the electronic circuits. The electronic circuits must be used also to minimize the problem of very high output impedance of the pressure sensor. The output capacitance is small, of the order of a few 10 pF, and the changes in this capacitance are of the order of a few fF. This makes it very susceptible to parasitic effects. For capacitive measuring circuits, it is therefore important to minimize the physical separation between the sensing element, i.e. capacitor, and the rest of the circuit. Acknowledgements The financial support of the Slovenian Research Agency and the company HYB d.o.o. in the frame of the project L2-7073 is gratefully acknowledged. The authors wish to thank Mr. Mitja Jerlah (HIPOT-RR) for fabricate test samples. The paper is dedicated to Professor Lojze Trontelj, Faculty of Electrical Engineering, University of Ljubljana, because of his outstanding and significant contribution in the field of microelectronics and electronic components in Slovenia. References /1/ N. M. White, J. D. 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HIPOT-RR d.o.o. c/o Jožef Stefan Institute Jamova 39, 1000 Ljubljana, Slovenia Phone: +386 1 4773 479 E-mail: darko.belavič@ijs.si Prispelo (Arrived): 08.05.2008 Sprejeto (Accepted): 15.09.2008 196 UDK621.3:(53+54+621+66), ISSN0352-9045 Informacije MIDEM 38(2008)3, Ljubljana CALIBRATION YIELD IMPROVEMENT AND QUALITY CONTROL OF SMART SENSORS Matej Možek, Danilo Vrtačnik, Drago Resnik, Slavko Amon Laboratory of Microsensor Structures and Electronics (LMSE), Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, Slovenia Key words: smart sensor, failure analysis, digital temperature compensation, adaptive calibration Abstract: Concept and realization of an adaptive closed loop system for calibration of smart pressure sensors is presented. Closed loop concept enables the analysis of sensor properties and optimization of calibration procedure. System quality control mechanisms enable automatic sensor classification. Statistical data enable sensor quality information for failure analysis and quality control of calibrated sensors. System enables optimal digital temperature compensation based on sensor data acquisition and digital evaluation of sensor characteristic. Proposed digital temperature compensation reduces typical sensor temperature error after calibration to 0.05%FS, based on calibration of a lot with 34422 MAP sensors. Calibration yield was improved from 93.7% to 96.8%, achieved by adaptive evaluation of sensor properties such as offset and sensitivity. Proposed calibration system shortens the total time for calibration of smart sensors, by implementing the input testing of sensor parameters as well as final testing of the calibrated sensors, achieving calibration time of 42 seconds per sensor in system current calibration capability. Izboljšava izplena umerjanja in nadzor kakovosti pametnih senzorjev Kjučne besede: pametni senzor, analiza napak, digitalna temperaturna kompenzacija, adaptivno umerjanje Izvleček: V prispevku sta predstavljeni zasnova in realizacija adaptivnega zaprtozančnega sistema za umerjanje pametnih senzorjev tlaka. Predstavljeni zaprtozančni koncept omogoča analizo lastnosti senzorjev in optimizacijo postopka umerjanja. Mehanizmi za nadzor kakovosti senzorjev omogočajo avtomatsko klasifikacijo umerjenih senzorjev. Pridobljeni statistični podatki sistema za umerjanje nudijo vpogled v kvaliteto izdelanih senzorjev, obenem pa omogočajo analizo napak umerjanja senzorjev. Sistem zagotavlja optimalno digitalno temperaturno kompenzacijo na osnovi digitalnega opisa senzorske karakteristike. Na podlagi rezultatov umerjanja serije 34422 MAP senzorjev smo dosegli tipično temperaturno napako senzorjev 0.05%FS. Izkoristek umerjanja se ob uporabi zaprtozančne strukture sistema za umerjanje poveča z 93.7% na 96.8%, kar smo dosegli z adaptivnim ovrednotenjem senzorskih lastnosti kot sta ničelna napetost in občutljivost. Predlagana izvedba skrajša čas umerjanja na 42 s na senzor pri trenutni kapaciteti sistema, kar smo dosegli z vključevanjem testnih parametrov senzorja v zaprtozančno strukturo sistema za umerjanje. 1 Introduction Smart sensors represent an attractive approach in sensor applications due to their adaptability, achieved by means of digital signal processing. Sensor adaptability can be further turned into a major advantage by introduction of smart calibration systems. Smart sensors are generally integrated with signal conditioning circuits. Signal conditioning circuits are needed to adjust the offset voltage and span, for compensation of temperature effects of both offset voltage and span, as well as to provide an appropriately amplified signal. The proposed approach is based on a special case of smart pressure sensors, but the developed calibration system is generally applicable for any kind of smart sensor. In manufacturing of modern electronic devices achieving and maintaining high yield level is a challenging task, depending primarily on the capability of identifying and correcting repetitive failure mechanisms. Yield enhancement is defined as the process of improving the baseline yield for a given technology generation from R&D yield level to mature yield. Yield enhancement is one of the strategic topics of ITRS (International Technology Roadmap for Sem- iconductors) /1/. This iterative improvement of yield is based on yield learning process, which is a collection and application of knowledge of manufacturing process in order to improve device yield through the identification and resolution of systematic and random manufacturing events /2/. Yield improvement process will consequentially increase the number of test parameters and hence the calibration system complexity. One of advantages of increasing system complexity is the ability to integrate the input testing processes and output final testing processes into the calibration process itself, thus shortening the total time for calibration. Several types of smart sensors with integrated signal conditioning have been presented over the past few years /3, 4/. The calibration processes and temperature compensating methods for these sensors are based either on analog, digital or mixed approaches. Analog approach usually comprises an amplifier with laser trimmable thin film resistors /5, 6/ or off-chip trimmable potentiometers /7, 8/ , to calibrate the sensor span and offset voltage and to compensate for their temperature drift. Analog compensation techniques are relatively slow, inflexible and cost-ineffective. In digital approach, sampling for raw digital pressure and temperature values is first performed, followed 197 M. Mozek, D. Vrtacnik, D. Resnik, S. Amon: Informacije MIDEM 38(2008)3, str. 197-205 Calibration Yield Improvement and Quality Control of Smart Sensors by an evaluation of the output digital values via polynomials for describing sensor characteristic, and finally converting the computed pressure values to according analog voltages /9, 10/. Mixed approach retains strictly the analog signal conversion path, while smart sensor offset and span are adjusted by setting of operational amplifiers by digital means /11/. This paper will focus on the problem of adaptive calibration any quality control of smart sensors with digital temperature compensation, which is one of the most time consuming steps in sensor production. In order to advance calibration system performance, smart calibration system is conceived as a digitally controlled closed loop system capable of adaptive learning. Presented concept of calibration system is directly implemented in the iterative yield enhancement process in the production of piezoresistive pressure sensors for automotive applications. The calibration system operation and quality control is illustrated on the case of Manifold Absolute Pressure (MAP) sensors. The emphasis will be on MAP sensors, although the proposed approach can be implemented in other fields of application. 2 Calibration procedure Main calibration procedure starts with measurement of sensor coarse gain and offset and optimization of sensor parameters to the sensor signal conditioner front end stage. After initial optimization procedure the calibration conditions are set according to calibration scenario. Raw sensor readouts of supplied reference quantities are acquired at each calibration point. After acquisition, digital description of sensor characteristic is evaluated and the results are stored back to sensor. A detailed description of calibration procedure is given in /12/. Calibration scenario defines the sequence of reference quantities, which are applied to sensors under calibration. In case of temperature compensation of pressure sensor, the reference quantities are pressure and temperature. Minimal number of calibration points is 4. This is defined by using the lowest (i.e. linear) degree of polynomial for sensor characteristic description /9, 10/ in the temperature and pressure direction. Maximal number of calibration points is primarily limited by total calibration time. In case of pressure sensors, both calibration axes consist of three calibration points, thus enabling compensation of second order non-linearity in both directions, as depicted in Figure 1. Maximal number of calibration points for pressure sensor can cover nonlinearities up to third order in pressure direction. Actual number of calibration points is a compromise between calibration precision and total calibration time. To shorten total calibration time, the slower settling axis should be used for definition of the calibration points order. In case of MAP sensor, the temperature axis defines the calibration scenario. PMAX...... ......©- ....... \L> 4» "-O 1» S TCS3 [ppm of (mV/V/bar/°C)] Fig. 2: Input temperature coefficient of sensitivity. 3 Results Presented results are based on 34422 calibrated manifold absolute pressure sensors. Results comprise analysis of operation of two calibration systems. Input sensor properties investigation is presented on ZMD31020 signal conditioner /9/. Output properties analysis and failure analysis was performed on ZMD31050 signal conditioner /10/. 3.1 Input properties of calibrated sensors Based on described statistical analysis of sensor properties a histogram, which sets the sensor validity interval was plot. The input temperature coefficient of pressure sensitivity at calibration point 3 in Figure 1 is in the range of /-8% ... -0.2%/, which represents a insurmountable span of temperature coefficients, if analog calibration was to be made upon such sensors. Average value of input temperature coefficient of pressure sensitivity in the histogram, depicted in the Figure 2 is -4.9% (mV/V/bar). Standard deviation from this value is 0.51% of (mV/V/bar). Sensors, based on analog signal conditioners with operational amplifiers /7/, can compen- sate temperature coefficient of sensitivity up to 0.2%/°C. The latter clearly demonstrates the advantage of the digital temperature compensation based signal conditioners. Input temperature coefficient of offset voltage is depicted in Figure 3. Again, the plotted histogram depicts large variations for temperature coefficient of offset voltage. Analog calibration system could not calibrate the sensor with temperature coefficient of offset voltage in the range of 1mV/°C. 3.2 Output properties of calibrated sensors In case of calibration of ZMD31050 based MAP sensors, further 11 test points were introduced to calibration scenario. Output temperature error histograms were evaluated at 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80% and 90% of power supply voltage pressure response at 85°C and 20°C upon a set of 5828 sensors. From initial 5828 sensors, 366 were evaluated as bad. Among them were 182 sensors, lacking the results from testing at 20°C. Calculated histograms are a clear demonstration of effectiveness of digital temperature compensation. The histogram in Figure 4 depicts the magnitude of temperature error in test point 1 (T=85°C, P=17kPa, Vout=5%VCC). Presented result was subtracted with an ideal value and 100000 10000 1000 H 100 [-347...-194) [-194...-41) [-41...112) [112...265) [265...418) [418...571) (571...724) (724...877) (877...1030) [1030...1192] TCOF3 [uV/°C] Fig. 3: Input temperature coefficient of offset voltage. 200 M. Možek, D. Vrtačnik, D. Resnik, S. Amon: Calibration Yield Improvement and Quality Control of Smart Sensors Informacije MIDEM 38(2008)3, str. 197-205 2500 2000 1500 1000 500 0 3 7 16 192 w ?L 1. r t a rx> i. 223 \\> 21 6 2 m "SB