![FOOTNOTES.
[161] “Our Gipsy Children.—(To the Editor of the Daily News.)—Sir, I
counted to-day at the great Oxford Fair over two hundred and
twenty vans and covered carts, in each of which there would be an
average of four children and two men and women living and
huddling together regardless of every principle of decency. In many
cases filth, dirt, and ignorance prevailed to an alarming extent. Not
a few of the poor women and children exhibited signs of their having
been in close warfare with rough treatment. Not five per cent. of
the thousand human beings could read and write a sentence. What
a farce upon our Christianity and civilization it is to have this mass of
human beings living actually in the centre of learning, religious
influences, and civilization. We have Bibles, ministers, colleges,
sanitary officers, and education inspectors on every hand, and no
power but the police-man exerting any influence over our poor lost
wanderers. What I want is that their thirty thousand children should
receive a free education—as I propose in an amending Bill to meet
the case of the canal children—and their vans registered and
brought under the influence of the sanitary officers on a simple
plan. The gipsies themselves will hail a measure of this kind with
considerable delight.”
This letter brought forth a reply, to which I rejoined as follows:
“Your correspondent’s repudiation of my statements in your issue of
the 5th inst. does not alter the facts—not ‘ideas’—which were given
to me by the travellers themselves in broad daylight in the midst of a
pouring rain, with the object of getting their condition improved, not
by winking and blinking at the evil and allowing it to grow into a](https://image.slidesharecdn.com/91758-250728000509-4532cb19/85/Nonlinear-Transistor-Model-Parameter-Extraction-Techniques-1st-Edition-Matthias-Rudolph-39-320.jpg)
![more dangerous sore, to be dealt with by the policeman, but to be
faced by extending the blessings of a free education to all travelling
children, and bringing sanitation to their homes. His statements
about immorality have been manufactured by himself; but as he has
been good enough to take my references and weave them into a cap
which fits, I must allow him the pleasure of wearing it. The sad
facts, seen by myself, in my possession, in addition to those
published in my ‘Gipsy Life,’ will most assuredly come to light some
day. With reference to his remarks about no gipsy vans being at
Oxford fair, this is absolutely untrue. I look upon all as gipsies who,
with gipsy blood in their veins, are tramping the country, hawking
and adopting gipsy usages, customs, slang, and ‘rokering,’ if only
slightly. The fact is the old-fashioned gipsies are dead, and their
places are being taken by increasing numbers of travellers who are
not so romantic, living in covered carts and waggons, whose wives
sometimes scrape together a little money in the summer to keep
many of the men in idleness in the winter. Your correspondent takes
credit for the education of the children in the winter. This he knows
perfectly well is what the law requires of those who have settled
homes, but he is silent about the worse than undoing the teachers’
work in the summer; thereby placing the poor gipsy children upon
the vagabond’s path to ruin. Of course all are not alike. There are
the usual good, bad, and indifferent among them. The sad
condition, morally, socially, and religiously, of many of the poor gipsy
and other travelling women and children is truly horrible, and no
amount of wincing at the shadow of redeeming features which are
to follow will stop me till the 70,000 canal and gipsy children are
educated by means of a free pass book, the hard lot of the women
lightened, and their travelling homes made more happy and
conformable with civilized notions and ideas; and if he is wise he will
help forward the work, with a willing hand.”
[215] It is said that Lord Beaconsfield in his youthful days attended
the place of worship to which the poor girl referred; and it is also
stated that the bones of one of Cromwell’s generals lie smouldering](https://image.slidesharecdn.com/91758-250728000509-4532cb19/85/Nonlinear-Transistor-Model-Parameter-Extraction-Techniques-1st-Edition-Matthias-Rudolph-40-320.jpg)
![in the dust within or near the sacred precincts. Extremes meet
sometimes.
[329] On March the 5th, within three months of my visit to Yetholm,
Mr. Laidlaw writes me to say that the Yetholm gipsies are taking to
settled and constant employment at the farmers’ in the
neighbourhood. This is cheering news, and shows most clearly that
my plans will work out rightly, as I have told the gipsies at Yetholm
and other places, without any inconvenience to them worth naming.
[339] I am much indebted to Mr. Joyce, Mr. F. W. Chesson, Mr.
George Bettany, Rev. A. E. Gregory, Mr. H. E. Duke, Mr. T. S.
Townend, Mr. Mallet, Mr. Guy, Mr. Fisher, Mr. W. H. Lucy, Messrs.
Joshua and Joseph Hatton, Mr. M. E. Stark, Mr. D. Gorrie, Mr. R. W.
Boyle, Mr. W. Saunders, Mr. E. Robbins, Emma Leslie, Mr. S. R.
Bennett, Mr. B. G. Burleigh, Rev. W. L. Lang, Mr. J. Moore, Mr. J. B.
Marsh, Mr. J. D. Shaw, Mr. J. H. Thomas, Mr. Kinnear, Rev. B.
Burrows, Mr. G. J. Stevenson, M.A., Mr. J. Tod, Rev. Mark Guy Pearse,
L. T. Meade, Rev. Chas. Bullock, B.A., Mr. F. Sherlock, Rev. Earnest
Boys, M.A., Dr. Grosart, Mr. A. Locker, Rev. R. Spears, Mr. B. Clarke,
Mr. James Clarke, Mr. Clayden, Mr. W. Binns, Mr. E. Walford, M.A., Mr.
Lobb, Rev. J. Duncan, M.A. Messrs. Morgan and Scott, Mr. Jean, Mr.
R. Albery, Rev. B. Waugh, Dr. Parker, Mr. G. A. Sala, Mr. W. Bradshaw,
Mr. J. Lloyd, Dr. Westby Gibeon, Mr. Alex. H. Grant, M.A., Dr. J. H.
James, Mr. Ewing Ritchie, Mr. J. Hind, Mr. G. Howell, Mr. J. Hutton,
Mr. J. Latey, Mr. Maurice Adams, Mr. J. L. Nye, Revs. E. Weldon, M.A.,
and Colin McKecknie, W. Y. Fullerton, C. H. Kelly, G. Holden Pike, C.
H. Spurgeon, Dr. Gregory, Rev. G. W. Weldon, M.A., Rev. D. Darnell,
M.A., Rev. Dr. Stephenson, Rev. Vernon J. Charlesworth, Dr.
Barnardo, Mr. Edward Lloyd, Mr. W. T. Stead, Miss Fredricks, Mr. G.
Barnet Smith, Mr. G. F. Millin, Mr. J. F. Rolph, Mr. W. T. E. Boscawen,
Mr. A. Watson, Mr. J. Russell, Mr. E. Step, Mr. Austin, Mr. Harry Hicks,
Dr. Griffith, Mr. Morrison Davidson, Mr. Massingham, Mr. S. Reeve,
Rev. W. M. Burnet, M.A., Rev. Ponsonby A. Lyons, Miss Nellie Hellis,
Miss J. Gordon Sutherland, “Una.”](https://image.slidesharecdn.com/91758-250728000509-4532cb19/85/Nonlinear-Transistor-Model-Parameter-Extraction-Techniques-1st-Edition-Matthias-Rudolph-41-320.jpg)
Nonlinear Transistor Model Parameter Extraction Techniques 1st Edition Matthias Rudolph
- 1. Nonlinear Transistor Model Parameter Extraction Techniques 1st Edition Matthias Rudolph - PDF Download (2025) https://ebookultra.com/download/nonlinear-transistor-model- parameter-extraction-techniques-1st-edition-matthias-rudolph/ Visit ebookultra.com today to download the complete set of ebooks or textbooks
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- 5. Nonlinear Transistor Model Parameter Extraction Techniques 1st Edition Matthias Rudolph Digital Instant Download Author(s): Matthias Rudolph, Christian Fager, David E. Root ISBN(s): 9780521762106, 0521762103 Edition: 1 File Details: PDF, 13.53 MB Year: 2011 Language: english
- 8. Nonlinear Transistor Model Parameter Extraction Techniques Achieve accurate and reliable parameter extraction using this complete survey of state- of-the-art techniques and methods. A team of experts from industry and academia provides you with insights into a range of key topics, including parasitics, instrinsic extraction, statistics, extraction uncertainty, nonlinear and DC parameters, self-heating and traps, noise, and package effects. Learn how similar approaches to parameter extraction can be applied to different technologies. A variety of real-world industrial examples and measurement results show you how the theories and methods presented can be used in practice. Whether you use transistor models for evaluation of device processing, need to understand the methods behind the models you use in circuit design, or you want to develop models for existing and new device types, this is your complete guide to parameter extraction. Matthias Rudolph is the Ulrich-L.-Rohde Professor for RF and Microwave Techniques at Brandenburg University of Technology, Cottbus, Germany. Prior to this, he worked at the Ferdinand-Braun-Institut, Leibniz-Insitut für Höchstfrequenztechnik (FBH), Berlin, where he was responsible for the modeling of GaN HEMTs and GaAs HBTs and for heading the low-noise components group. Christian Fager is an Associate Professor at Chalmers University of Technology, Sweden, where he leads a research group focussing on energy efficient transmitters and power amplifiers for future wireless applications. In 2002 he received the Best Student Paper Award at the IEEE International Microwave Symposium for his research on uncertainties in transistor small-signal models. David E. Root is Agilent Research Fellow and Measurement and Modeling Sciences Architect at Agilent Technologies, Inc., where he works on nonlinear device and behav- ioral modeling, large-signal simulation, and nonlinear measurements for new techni- cal capabilities and business opportunities. He is a Fellow of the IEEE and he was a co-recipient of the 2007 IEEE ARFTG Technology Award.
- 9. The Cambridge RF and Microwave Engineering Series Series Editor Steve C. Cripps, Distinguished Research Professor, Cardiff University Peter Aaen, Jaime Plá, and John Wood, Modeling and Characterization of RF and Microwave Power FETs Dominique Schreurs, Máirtı́n O’Droma, Anthony A. Goacher, and Michael Gadringer, RF Amplifier Behavioral Modeling Fan Yang and Yahya Rahmat-Samii, Electromagnetic Band Gap Structures in Antenna Engineering Enrico Rubiola, Phase Noise and Frequency Stability in Oscillators Earl McCune, Practical Digital Wireless Signals Stepan Lucyszyn, Advanced RF MEMS Patrick Roblin, Nonlinear RF Circuits and the Large-Signal Network Analyzer John L.B. Walker, Handbook of RF and Microwave Solid-State Power Amplifiers Forthcoming Sorin Voinigescu, High-Frequency Integrated Circuits David E. Root, Jason Horn, Mihai Marcu and Jan Verspecht, X-Parameters Richard Carter, Theory and Design of Microwave Tubes Anh-Vu H. Pham, Morgan J. Chen, and Kunia Aihara, LCP for Microwave Packages and Modules Nuno Borges Carvalho and Dominique Scheurs, Microwave and Wireless Measurement Techniques
- 10. Nonlinear Transistor Model Parameter Extraction Techniques Edited by MATTHIAS RUDOLPH Brandenburg University of Technology, Cottbus, Germany CHRISTIAN FAGER Chalmers University of Technology, Sweden DAVID E. ROOT Agilent Technologies, Inc.
- 11. CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Tokyo, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521762106 C Cambridge University Press 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Printed in the United Kingdom at the University Press, Cambridge A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Nonlinear transistor model parameter extraction techniques / edited by Matthias Rudolph, Christian Fager, David E. Root. p. cm. – (Cambridge RF and microwave engineering series) Includes bibliographical references and index. ISBN 978-0-521-76210-6 (hardback) 1. Transistors – Mathematical models. 2. Electronic circuit design. I. Fager, Christian. II. Root, David E. III. Rudolph, Matthias, 1969– IV . Title. V . Series. TK7871.9.N66 2011 621.381528 – dc23 2011027239 ISBN 978-0-521-76210-6 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
- 12. For Katrin, Elisabeth and Jakob M.R For Maria and Sonja C.F For Marilyn, Daniel, and Alex D.E.R
- 13. Modeling is at the heart of any modern design process and improvements in transistor modeling have made a significant, but often unrecognized, contribution to the wireless revolution impacting our daily lives. The authors and contributors have collaborated across academic and company boundaries to bring together the latest techniques in a comprehensive and practical review of transistor modeling. This book is destined to become the “go to” reference on the subject. Mark Pierpoint, Agilent Technologies Without accurate component models, even the most powerful circuit simulator cannot provide meaningful results. The old saying, “Junk in-Junk out,” summarizes the process. The textbook, Nonlinear Transistor Model Parameter Extraction Techniques, contains a wealth of theoretical and practical information. It should be read by every designer of active RF/microwave circuits and devices. Les Besser, Author of COMPACT and Founder of Besser Associates Nonlinear Transistor Model Parameter Extraction Techniques is an excellent book that covers this extremely important topic very well . . . the editors have done a thorough job in putting together a complete summary of the important issues in this area. For a range of device technologies, the main themes that need to be addressed including measurement, extraction, DC and non-linear modelling, noise modelling, thermal issues and package modelling are covered in a clear but detailed manner, by experts in each area. I would highly recommend this title. John Atherton, WIN Semiconductors
- 14. Contents List of contributors page x Preface xiii 1 Introduction 1 Matthias Rudolph 1.1 Model extraction challenges 2 1.2 Model extraction workflow 15 References 17 2 DC and thermal modeling: III–V FETs and HBTs 18 Masaya Iwamoto, Jianjun Xu, and David E. Root 2.1 Introduction 18 2.2 Basic DC characteristics 19 2.3 FET DC parameters and modeling 21 2.4 HBT DC parameters and modeling 25 2.5 Process control monitoring 27 2.6 Thermal modeling overview 28 2.7 Physics-based thermal scaling model for HBTs 31 2.8 Measurement-based thermal model for FETs 32 2.9 Transistor reliability evaluation 36 Acknowledgments 40 References 41 3 Extrinsic parameter and parasitic elements in III–V HBT and HEMT modeling 43 Sonja R. Nedeljkovic, William J. Clausen, Faramarz Kharabi, John R.F. McMacken, and Joseph M. Gering 3.1 Introduction 43 3.2 Test structures with calibration and de-embedding 43 3.3 Methods for extrinsic parameter extraction used in HBTs 49 3.4 Methods for extrinsic parameter extraction used in HEMTs 60 3.5 Scaling for multicell arrays 72 References 83
- 15. viii Contents 4 Uncertainties in small-signal equivalent circuit modeling 86 Christian Fager, Kristoffer Andersson, and Matthias Ferndahl 4.1 Introduction 86 4.2 Uncertainties in direct extraction methods 88 4.3 Optimizer-based estimation techniques 97 4.4 Complexity versus uncertainty in equivalent circuit modeling 116 4.5 Summary and discussion 120 References 120 5 The large-signal model: theoretical foundations, practical considerations, and recent trends 123 David E. Root, Jianjun Xu, Jason Horn, and Masaya Iwamoto 5.1 Introduction 123 5.2 The equivalent circuit 123 5.3 Nonlinear model constitutive relations 127 5.4 Table-based models 130 5.5 Models based on artificial neural networks (ANNs) 135 5.6 Extrapolation of measurement-based models 137 5.7 Charge modeling 139 5.8 Terminal charge conservation, delay, and transit time for HBT models 153 5.9 FET modeling in terms of a drift charge concept 156 5.10 Parameter extraction of compact models from large-signal data 158 5.11 Conclusions 166 References 166 6 Large and packaged transistors 171 Jens Engelmann, Franz-Josef Schmückle, and Matthias Rudolph 6.1 Introduction 171 6.2 Thermal modeling 175 6.3 EM simulation 178 6.4 Equivalent-circuit package model 187 References 204 7 Nonlinear characterization and modeling of dispersive effects in high-frequency power transistors 206 Olivier Jardel, Raphael Sommet, Jean-Pierre Teyssier, and Raymond Quéré 7.1 Introduction 206 7.2 Nonlinear electrothermal modeling 207 7.3 Trapping effects 215 7.4 Characterization tools 243 7.5 Conclusions 249 Acknowledgment 250 References 250
- 16. Contents ix 8 Optimizing microwave measurements for model construction and validation 257 Dominique Schreurs, Maciej Myslinski, and Giovanni Crupi 8.1 Introduction 257 8.2 Microwave measurements and de-embedding 258 8.3 Measurements for linear model construction 264 8.4 Measurements for model validation 266 8.5 Measurements for nonlinear model construction 274 References 284 9 Practical statistical simulation for efficient circuit design 287 Peter Zampardi, Yingying Yang, Juntao Hu, Bin Li, Mats Fredriksson, Kai Kwok, and Hongxiao Shao 9.1 Introduction 287 9.2 Approach, model development, design flow 289 9.3 Examples of application to real circuits 312 9.4 Summary 314 Acknowledgments 315 References 316 10 Noise modeling 318 Manfred Berroth 10.1 Fundamentals 318 10.2 Noise sources 325 10.3 Noise analysis in linear network theory 331 10.4 Noise measurement setups 336 10.5 Transistor noise parameter extraction 339 10.6 Summary 348 References 348 Index 350
- 17. List of contributors Kristoffer Andersson Chalmers University of Technology Manfred Berroth University of Stuttgart William J. Clausen RFMD, Greensboro Giovanni Crupi University of Messina, Italy Jens Engelmann Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik Christian Fager Chalmers University of Technology Matthias Ferndahl Chalmers University of Technology Mats Fredriksson Skyworks Solutions, Inc. Joseph M. Gering RFMD, Greensboro Jason Horn Agilent Technologies, Inc. Juntao Hu Skyworks Solutions, Inc. Masaya Iwamoto Agilent Technologies, Inc. Olivier Jardel 3–5 Labs, France Faramarz Kharabi RFMD, Greensboro Kai Kwok Skyworks Solutions, Inc. Bin Li Skyworks Solutions, Inc. John R.F. McMacken RFMD, Greensboro Maciej Myslinski K.U.Leuven, Belgium Sonja R. Nedeljkovic RFMD, Greensboro Raymond Quéré University of Limoges, France David E. Root Agilent Technologies, Inc. Matthias Rudolph Brandenburg University of Technology
- 18. List of contributors xi Franz-Josef Schmückle Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik Dominique Schreurs K.U.Leuven, Belgium Hongxiao Shao Skyworks Solutions, Inc. Raphael Sommet CNRS-University of Limoges, France Jean-Pierre Teyssier University of Limoges, France Jianjun Xu Agilent Technologies, Inc. Yingying Yang Skyworks Solutions, Inc. Peter Zampardi Skyworks Solutions, Inc.
- 20. Preface Designing microwave circuits today means relying on numerical circuit simulation. While not a substitute for one’s own skills, knowledge, and experience, a designer must be able to count on the adequacy of circuit simulation tools to accurately simulate the circuit performance. Circuit simulators themselves are generally up to the challenge. However, there is a perpetual quest for good transistor models to use with the simulator, because models are usually the limiting factor in the accuracy of a simulated design. This is due to the continuous evolution of transistor technology, requiring the models to keep up, and also to the increasing demands placed on the models to perform with respect to wider classes of signals, operating conditions (e.g., temperature), and statistical variation. Circuit designers therefore often face the challenge of adapting the models that are provided with simulators to better describe the actual transistor that is being used in the design. This is achieved by characterizing the transistor, mainly by measurement, but also by electromagnetic and/or thermal simulation. Finally, model parameter values must be extracted from this data before the model can be used at all in a design. As transistor modeling is a key to circuit design, many publications are available on the models for any type of transistor, ranging from model documentation in simulator products, to application notes and scientific papers in technical conferences and journals; but it seems that much less is published on how the respective model parameters can be determined. It is the aim of this book to provide a comprehensive overview of transistor model parameter extraction. The basic premise is that parameter extraction, on one hand, is at least as important as the physics-based development of the model formulation itself. On the other hand, extraction approaches, even for quite different technologies, are often based on the same ideas and assumptions. Therefore, the book is intended to give a broad perspective, focusing on one issue and concept after the other, but not restricting any particular concept to a single type of transistor. The book is based on a workshop presented at the IEEE Microwave Theory and Techniques Society International Microwave Symposium in 2009, organized by the editors. Each chapter of the book corresponds to an individual talk at the workshop. The range of the topics presented covers almost all challenges in parameter extraction, from DC to small-signal parameters, how to integrate small-signal parameters to obtain large-signal quantities such as charge and current, how to determine extrinsic element values, transistor package modeling and self-heating, dispersion effects, noise, statistics
- 21. xiv Preface of a transistor process, and an overview of measurement techniques for extraction and validation. The editors would like to thank all the authors for their contributions. We enjoyed the workshop presentations very much and felt that publishing this knowledge in an appropriate way would constitute a valuable contribution to the field. The estimate of the workload to transform a talk into a book chapter turned out to be initially a little optimistic, so we especially appreciate the authors’ extra efforts. We would also like to thank Cambridge University Press, especially Dr. Julie Lan- cashire and Ms. Sarah Matthews, for their support of the project. It was always a pleasure to work with the staff at Cambridge. Cottbus, Germany; Göteborg, Sweden; and Santa Rosa, CA, USA M.R., C.F., D.E.R.
- 22. 1 Introduction Matthias Rudolph Brandenburg University of Technology If one is about to design a circuit, one certainly relies on a circuit simulation tool that provides us with the capability to determine circuit performance with high accuracy without even fabricating a prototype. We expect the simulation to provide us with the numerical algorithm that is capable of accurately calculating the relevant variables, such as currents, voltages, noise, distortion products, etc. At least as important is the description of the components that will be used, since ultimately the simulation can never be more accurate than the models of the components used. Component models commonly are provided as drag-and-drop components in modern circuit simulators. At least for established technologies, accurate models are available for passive and active components. All problems solved? Unfortunately not. The models, especially compact transistor models, are parametrized. It is a big step from the general-purpose model that is capable of describ- ing, say, SiGe heterojunction bipolar transistors (HBTs) in general to the specific model for a specific transistor of a specific size, from a specific foundry, that one plans to use in the actual design. But why bother? One would expect the foundry selling the transistor also to provide us with a valid model. In reality the situation is more like the following: 1. Some vendors simply do not provide their customers with appropriate models. Either one gets just plain data sheets providing some figures of merit and printed S-parameters. Or quite often, even for the most advanced transistors, only very basic SPICE-type model parameters are provided. While these models are available in lit- erally all circuit simulators, their accuracy is often quite limited, since these models only describe the very basic transistor behavior. 2. If one deals with the most advanced generation of devices, the model might not yet be determined. This happens frequently in research. 3. Often, it turns out that the model provided by the device manufacturer is generally of good accuracy, but unfortunately not for the special application one is aiming at. Therefore, a model parameter refinement is required. This book presents an overview of the different aspects and methods of model param- eter extraction. In this context, we assume and take for granted that the model chosen is, in general, accurate. This means that the underlying mathematical formulation is able to account for all effects that are observed. The method behind how a parameter for
- 23. 2 Introduction a specific model is extracted depends on which physical effect it describes rather than what specific model is used. This holds even for different types of device. Hence, the chapters in this book address the relevant issues in parameter extraction topic by topic. Specific device technologies are only addressed in order to provide examples, while the methods in general can be applied also to other transistor technologies. 1.1 Model extraction challenges Before parameter extraction is discussed in detail, some basic issues shall be addressed: first, what it means that a model is accurate. To state that a model possibly predicts device performance very well is, however, not sufficient. It needs to do so under realistic working conditions. Simulation of realistic cases is usually numerically much more challenging than the standard test cases commonly used to judge model accuracy. Whether or not a simulation converges depends not only on the numerical solver the simulator uses, but also model description and model parameter values extracted. These aspects, which parameters to determine, and which ranges of values are advisable therefore also need to be discussed in this introduction. The final section will address how to choose a suitable type of transistor for the modeling procedure. 1.1.1 Accuracy If one asks for the model of a specific transistor, this is what one usually gets: a set of parameters, and, hopefully, some comparison between the simulation results with mea- surement. Typically, output IV-curves, and S-parameters at a few bias points are shown. Is it safe to trust the model, provided that the agreement of simulated and measured data we have seen is perfect? The obvious answer: not necessarily. Whether the model parameter set is valid depends on a number of questions that will be discussed in the following in more detail: what is the application one wants to simulate? How accurate is the measurement? How about performance variations of nominally identical transistors? 1.1.1.1 Circuit application So far, we spoke of an accurate model, but, as with everything on earth, a model cannot be just completely accurate. All we will get is a model that is accurate within certain limits. Model validity can only be guaranteed within a certain range of, e.g., bias points, frequencies, temperatures, or output power levels. These limits need to match the targeted circuit type. Some examples: 1. True small-signal operation requires only the bias point to be predicted well, together with the S-parameters in the respective frequency range. Of course, this model is restricted to one bias point. If another bias point is to be simulated (e.g., in order to minimize power consumption or to improve noise performance), accuracy cannot be assumed a priori without proving first how well the model will match. 2. Weakly nonlinear operation can be assumed in the case of a low-noise amplifier. The transistor will only be subject to low-power signals, but the small-signal condition
- 24. 1.1 Model extraction challenges 3 Pout TOI Im3 t (ns) 80 90 100 110 120 −4 4 2 −2 0 V out (V) weakly nonlinear two-tone measurement V (V) ce I c (A) switch-mode PA 6 5 4 3 2 1 0 0.1 0.2 0.3 0.4 0.5 P out (dBm) −60 −40 −20 0 20 40 −15 −10 −5 0 5 10 15 20 Pin (dBm) Figure 1.1 Depending on the circuit application, a model is required to be accurate in different operation areas, while others can be neglected. Shown here are two extreme cases: slightly nonlinear class-A operation, and switching operation. might be violated which calls for a nonlinear model. The common two-tone mea- surement for the determination of the third-order intercept points characterizes this operation condition. Besides the bias point, S-parameters also need to be predicted well within a limited operating area around the quiescent bias point. This area is shown in gray in Figure 1.1. While high accuracy is required here, no specific accu- racy requirements apply outside. Again: if the bias point is shifted, the model needs to be re-examined and possibly the parameters need to be adjusted. 3. Power compression results from output voltages reaching the minimum, or currents approaching the maximum. Starting from the weakly nonlinear operation, the voltage and current swings increase with increasing transistor output power. The range of currents and voltages, where the model needs to be accurate, therefore increases. However, things change significantly once the voltage dynamically drops below the knee voltage, and the current swings into the saturation (bipolar transistors) or linear (field-effect transistors) region. In this region, the transistor is working in a different mode than in class A, and a different subset of parameters is used to describe it in the model. Therefore, a model that is very accurate in class-A operation can completely fail to predict the compression behavior. 4. In order to extend the last statement: if any additional nonideal effect comes into play, for example breakdown or self-heating, the respective model parameters need to be determined and the model is to be verified by appropriate measurements. No compact
- 25. 4 Introduction reverse operation knee region self-heating breakdown I d (mA) Vds (V) −5 0 5 10 15 20 25 30 0 100 80 60 40 20 −20 −40 −60 −80 Figure 1.2 Schematic output-IV curves of a FET. Some critical areas are highlighted where the electrical behavior is dominated by physical effects that are not significant elsewhere. model can be expected to predict all physical effects. All need to be characterized first and the respective model parameters need to be determined. 5. A special case are switch-mode power amplifiers, such as class-E power amplifiers. For this application, the transistor model needs to be highly accurate in on and off states. The common class-A operation area is in the switch-mode case only shortly touched during the switching event. A gray area in Figure 1.1 shows the area where high model accuracy is required for this operation condition. 6. Another special case is the resistive mixer. The field effect transistor (FET) is biased at a drain-source voltage of zero. The model therefore needs to describe the transistor performance in forward and in reverse mode. It needs to be accurate not only for a certain voltage swing at the gate, but also for a certain voltage swing at the drain around zero volts. At negative drain voltages, drain and source terminals exchange their functionality, with drain becoming the effective source and vice versa. This reverse operation condition is commonly ignored completely during model parameter extraction. At this point, it is pretty obvious that a semiconductor manufacturer who provides us with a model parameter set cannot be expected to anticipate all possible modes of operation. Commonly, the parameter sets are determined for the generic case of class-A types of operation at the optimum bias point of the respective device. Therefore, without careful assessment of model accuracy, no more than an estimate of circuit performance can be expected from using the model. If the mode of operation is too far from class A, such as in the cases of resistive mixer or switch-mode amplifier, the model might even fail to provide a rough estimate. Figure 1.2 illustrates possible sources of error. Depending on the mode of operation, different physical effects come into play such as breakdown or self-heating. These might not be present during parameter extraction, but the model cannot extrapolate
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- 39. FOOTNOTES. [161] “Our Gipsy Children.—(To the Editor of the Daily News.)—Sir, I counted to-day at the great Oxford Fair over two hundred and twenty vans and covered carts, in each of which there would be an average of four children and two men and women living and huddling together regardless of every principle of decency. In many cases filth, dirt, and ignorance prevailed to an alarming extent. Not a few of the poor women and children exhibited signs of their having been in close warfare with rough treatment. Not five per cent. of the thousand human beings could read and write a sentence. What a farce upon our Christianity and civilization it is to have this mass of human beings living actually in the centre of learning, religious influences, and civilization. We have Bibles, ministers, colleges, sanitary officers, and education inspectors on every hand, and no power but the police-man exerting any influence over our poor lost wanderers. What I want is that their thirty thousand children should receive a free education—as I propose in an amending Bill to meet the case of the canal children—and their vans registered and brought under the influence of the sanitary officers on a simple plan. The gipsies themselves will hail a measure of this kind with considerable delight.” This letter brought forth a reply, to which I rejoined as follows: “Your correspondent’s repudiation of my statements in your issue of the 5th inst. does not alter the facts—not ‘ideas’—which were given to me by the travellers themselves in broad daylight in the midst of a pouring rain, with the object of getting their condition improved, not by winking and blinking at the evil and allowing it to grow into a
- 40. more dangerous sore, to be dealt with by the policeman, but to be faced by extending the blessings of a free education to all travelling children, and bringing sanitation to their homes. His statements about immorality have been manufactured by himself; but as he has been good enough to take my references and weave them into a cap which fits, I must allow him the pleasure of wearing it. The sad facts, seen by myself, in my possession, in addition to those published in my ‘Gipsy Life,’ will most assuredly come to light some day. With reference to his remarks about no gipsy vans being at Oxford fair, this is absolutely untrue. I look upon all as gipsies who, with gipsy blood in their veins, are tramping the country, hawking and adopting gipsy usages, customs, slang, and ‘rokering,’ if only slightly. The fact is the old-fashioned gipsies are dead, and their places are being taken by increasing numbers of travellers who are not so romantic, living in covered carts and waggons, whose wives sometimes scrape together a little money in the summer to keep many of the men in idleness in the winter. Your correspondent takes credit for the education of the children in the winter. This he knows perfectly well is what the law requires of those who have settled homes, but he is silent about the worse than undoing the teachers’ work in the summer; thereby placing the poor gipsy children upon the vagabond’s path to ruin. Of course all are not alike. There are the usual good, bad, and indifferent among them. The sad condition, morally, socially, and religiously, of many of the poor gipsy and other travelling women and children is truly horrible, and no amount of wincing at the shadow of redeeming features which are to follow will stop me till the 70,000 canal and gipsy children are educated by means of a free pass book, the hard lot of the women lightened, and their travelling homes made more happy and conformable with civilized notions and ideas; and if he is wise he will help forward the work, with a willing hand.” [215] It is said that Lord Beaconsfield in his youthful days attended the place of worship to which the poor girl referred; and it is also stated that the bones of one of Cromwell’s generals lie smouldering
- 41. in the dust within or near the sacred precincts. Extremes meet sometimes. [329] On March the 5th, within three months of my visit to Yetholm, Mr. Laidlaw writes me to say that the Yetholm gipsies are taking to settled and constant employment at the farmers’ in the neighbourhood. This is cheering news, and shows most clearly that my plans will work out rightly, as I have told the gipsies at Yetholm and other places, without any inconvenience to them worth naming. [339] I am much indebted to Mr. Joyce, Mr. F. W. Chesson, Mr. George Bettany, Rev. A. E. Gregory, Mr. H. E. Duke, Mr. T. S. Townend, Mr. Mallet, Mr. Guy, Mr. Fisher, Mr. W. H. Lucy, Messrs. Joshua and Joseph Hatton, Mr. M. E. Stark, Mr. D. Gorrie, Mr. R. W. Boyle, Mr. W. Saunders, Mr. E. Robbins, Emma Leslie, Mr. S. R. Bennett, Mr. B. G. Burleigh, Rev. W. L. Lang, Mr. J. Moore, Mr. J. B. Marsh, Mr. J. D. Shaw, Mr. J. H. Thomas, Mr. Kinnear, Rev. B. Burrows, Mr. G. J. Stevenson, M.A., Mr. J. Tod, Rev. Mark Guy Pearse, L. T. Meade, Rev. Chas. Bullock, B.A., Mr. F. Sherlock, Rev. Earnest Boys, M.A., Dr. Grosart, Mr. A. Locker, Rev. R. Spears, Mr. B. Clarke, Mr. James Clarke, Mr. Clayden, Mr. W. Binns, Mr. E. Walford, M.A., Mr. Lobb, Rev. J. Duncan, M.A. Messrs. Morgan and Scott, Mr. Jean, Mr. R. Albery, Rev. B. Waugh, Dr. Parker, Mr. G. A. Sala, Mr. W. Bradshaw, Mr. J. Lloyd, Dr. Westby Gibeon, Mr. Alex. H. Grant, M.A., Dr. J. H. James, Mr. Ewing Ritchie, Mr. J. Hind, Mr. G. Howell, Mr. J. Hutton, Mr. J. Latey, Mr. Maurice Adams, Mr. J. L. Nye, Revs. E. Weldon, M.A., and Colin McKecknie, W. Y. Fullerton, C. H. Kelly, G. Holden Pike, C. H. Spurgeon, Dr. Gregory, Rev. G. W. Weldon, M.A., Rev. D. Darnell, M.A., Rev. Dr. Stephenson, Rev. Vernon J. Charlesworth, Dr. Barnardo, Mr. Edward Lloyd, Mr. W. T. Stead, Miss Fredricks, Mr. G. Barnet Smith, Mr. G. F. Millin, Mr. J. F. Rolph, Mr. W. T. E. Boscawen, Mr. A. Watson, Mr. J. Russell, Mr. E. Step, Mr. Austin, Mr. Harry Hicks, Dr. Griffith, Mr. Morrison Davidson, Mr. Massingham, Mr. S. Reeve, Rev. W. M. Burnet, M.A., Rev. Ponsonby A. Lyons, Miss Nellie Hellis, Miss J. Gordon Sutherland, “Una.”
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