nalog circuits are fascinating artifacts. They manipulate signals whose informa- Ationcontentisrichcomparedtodigitalsignalsthatcarryminimalamountofinf- mation;theyaredelicateinthatanyperturbationduetoparasiticelements,todelays,to interactionswithotherelementsandwiththeenvironmentmaycauseasigni?cantloss ofinformation. Thedif?cultyindealingwiththeseartifactsistoprotectthemfromall possibleattacks, evenminorones, fromthephysicalworld. Theironyisthattheyare oftenusedtofunnelinformationfromandtothephysicalworldtoandfromtheabstr- tionofthedigitalworldandforthisfunction, theyareirreplaceable. Nowonderthen that analog designers form a club of extraordinary gentlemen where art (or magic?) ratherthanscienceisthesharedtrade. Theyaredif?culttotrainsinceexperienceand intuitionarethetraitsthat characterize them. Andthey have dif?cultiesinexplaining what is the process they use to reach satisfactory results. Tools used for design (s- ulation) are mainly replacing the test benches of an experimental lab. However, the growing complexity of the integrated systems being designed today together with the increasing fragility of analog components brought about by shrinking geometries and reducedpowerconsumptionisposingseverechallengestotraditionalanalogdesigners to produce satisfactory results in a short time. At the same time, the need for expe- enced analog designers has increased constantly since almost all designs, because of integration,docontainanalogcomponents. Thissituationhascreatedastronginterest in developing design methodologies and supporting tools that are based on rigorous, mathematically literate, approaches. Doing so will make it possible to leverage the expertiseofseasonedanalogdesignersandtotrainnewgenerationsfasterandbetter. Inthepast, severalattemptshavebeenmadeinacademia andindustrytocreatethese methodologies and to extend the set of tools available. They have had questionable acceptance in the analog design community. However, recently, a ?urry of start-ups andincreasedinvestmentbyEDAcompaniesinnoveltoolssignalasigni?cantchange inmarketattentiontotheanalogdomain. Ipersonallybelievethattosubstantially- prove quality and design time, tools are simply insuf?cient. A design methodology based on a hierarchy of abstraction layers, successive re?nement between two ad- cent layers, and extensive veri?cation at every layer is necessary. To do so, we need to build theories and models that have strong mathematical foundations. The analog design technology community is as strong as it has ever been.
Foreword. Contributing Authors. Contents. Symbols and Abbreviations. 1 Introduction. 1.1 Structured analysis, a key to successful design. 1.1.1 Electronics, a competitive market. 1.1.2 Analog design: A potential bottleneck. 1.1.3 Structured analog design. 1.1.4 Structured analysis. 1.2 This work. 1.2.1 Main contributions. 1.2.2 Math, it's a language. 1.3 Outline of this book. 2 Modeling and analysis of telecom frontends: basic concepts. 2.1 Models, modeling and analysis. 2.1.1 Models: what you want or what you have. 2.1.2 Good models. 2.1.3 The importance of good models in top-down design. 2.1.4 Modeling languages. 2.1.5 Modeling and analysis: model creation, transformation and interpretation. 2.2 Good models for telecommunication frontends: Architectures and their behavioral properties. 2.2.1 Frontend architectures and their building blocks. 2.2.2 Properties of frontend building block behavior. 2.3 Conclusions. 3 A framework for frequency-domain analysis of linear periodically timevarying Systems. 3.1 The story behind the math. 3.1.1 What's of interest: A designer's point of view. 3.1.2 Using harmonic transfer matrices to characterize LPTV behavior. 3.1.3 LPTV behavior and circuit small-signal analysis. 3.2 Prior art. 3.2.1 Floquet theory. 3.2.2 Lifting. 3.2.3 Frequency-domain approaches. 3.2.4 Contributions of this work. 3.3 Laplace-domain modeling of LPTV systems using Harmonic Transfer Matrices. 3.3.1 LPTV systems: implications of linearity and periodicity. 3.3.2 Linear periodically modulated signal models. 3.3.3 Harmonic transfer matrices: capturing transfer of signal content between carrier waves. 3.3.4 Structural properties of HTMs. 3.3.5 On the Yen -dimensional nature of HTMs. 3.3.6 Matrix-based descriptions for arbitrary LTV behavior. 3.4 LPTV system manipulation using HTMs. 3.4.1 HTMs of elementary systems. 3.4.2 HTMs of LPTV systems connected in parallel or in series. 3.4.3 Feedback systems and HTM inversions. 3.4.4 Relating HTMs to state-space representations. 3.5 LPTV system analysis using HTMs. 3.5.1 Multi-tone analysis. 3.5.2 Stability analysis. 3.5.3 Noise analysis. 3.6 Conclusions and directions for further research. 4 Applications of LPTV system analysis using harmonic transfer matrices. 4.1 HTMs in a nutshell. 4.2 Phase-Locked Loop analysis. 4.2.1 PLL architectures and PLL building blocks. 4.2.2 Prior art. 4.2.3 Signal phases and phase-modulated signal models. 4.2.4 HTM-based PLL building block models. 4.2.5 PLL closed-loop input-output HTM. 4.2.6 Example 1: PLL with sampling PFD. 4.2.7 Example 2: PLL with mixing PFD. 4.2.8 Conclusions. 4.3 Automated symbolic LPTV system analysis. 4.3.1 Prior art. 4.3.2 Symbolic LPTV system analysis: outlining the flow. 4.3.3 Input model construction. 4.3.4 Data structures. 4.3.5 Computational flow of the SymbolicHTM algorithm. 4.3.6 SymbolicHTM: advantages and limitations. 4.3.7 Application 1: linear downconversion mixer. 4.3.8 Application 2: Receiver stage with feedback across the mixing element. 4.4 Conclusions and directions for further research. 5 Modeling oscillator dynamic behavior. 5.1 The story behind the math. 5.1.1 Earth: a big oscillator. 5.1.2 Unperturbed system behavior: neglecting small forces. 5.1.3 Perturbed system behavior: changes in the earth's orbit. 5.1.4 Averaging: focusing on what's important. 5.1.5 How does electronic oscillator dynamics fit in?. 5.1.6 Modeling oscillator behavior. 5.2 Prior art. 5.2.1 General theory. 5.2.2 Phase noise analysis. 5.2.3 Numerical simulation. 5.2.4 Contributions of this work. 5.3 Oscillator circuit equations. 5.3.1 Normalizing the oscillator circuit equations. 5.3.2 Partitioning the normalized circuit equations. 5.4 Characterizing the oscillator's unperturbed core. 5.5 Oscillator perturbation analysis. 5.5.1 Components of an oscillator's perturbed behavior. 5.5.2 Motion xs _ t_ p_ t_ _over the manifold M . 5.5.3 In summary. 5.6 Averaging. 5.7 Oscillator phase (noise) analysis. 5.7.1 Capturing oscillator phase behav
severalattemptshavebeenmadeinacademia andindustrytocreatethese methodologies and to extend the set of tools available. They have had questionable acceptance in the analog design community. However, recently, a ?urry of start-ups andincreasedinvestmentbyEDAcompaniesinnoveltoolssignalasigni?cantchange inmarketattentiontotheanalogdomain. Ipersonallybelievethattosubstantially- prove quality and design time, tools are simply insuf?cient. A design methodology based on a hierarchy of abstraction layers, successive re?nement between two ad- cent layers, and extensive veri?cation at every layer is necessary. To do so, we need to build theories and models that have strong mathematical foundations. The analog design technology community is as strong as it has ever been.
Covers time-varying phase-locked loop stability, noise in mixing circuits, oscillator injection locking, oscillator phase noise behavior, harmonic oscillator dynamics and much more