This book is intended to fill in a missing link between two well-established disciplines, namely modelling and circuit design. From the perspective of circuit designers, simulation times have increased beyond what is practical with the ever-increasing complexity of circuits, even though computers have also got faster. Modelling systems, especially at higher levels of design abstraction, has become a necessity. On the other hand, the designer is faced with a bewildering array of choices in models. In order to make a feasible choice, the circuit designer has to understand the underlying mathematics of each model as well as its limitations.

In this chapter, we discuss several state-of-the-art RSM methods for performance modeling of analog and AMS circuits. RSM aims to approximate a given PoI by the linear combination of a set of basis functions. If the number of training samples is much larger than the number of adopted basis functions, the model coefficients can be accurately estimated by using LS regression. To reduce the number of required training samples and, hence, the modeling cost, we can explore the sparsity of model coefficients and, next, cast performance modeling to an L₀-norm regularization problem. Both OMP and L₁-norm regularization can be used to efficiently approximate the sparse solution of L₀-norm regularization. Alternatively, based on the observation that today's AMS circuits are often designed via a multistage fl ow, BMF attempts to reduce the modeling cost by fusing the early -stage and late -stage data together through Bayesian inference. As an important aspect of future research, a number of recently developed machine learning techniques, such as deep learning, maybe further adopted for RSM for AMS applications.

Today, with the advances in the hardware technologies, it is possible to store, process, and output large amount of data. With the increase in the size of data, explaining it, that is, extracting meaningful information from it, becomes a bottleneck. Machine learning, i.e., the science of extracting useful information from data comes as an aid. Empowered with concepts from mathematics, statistics, and computer science, machine learning is arguably the solution for all of our information extraction problems.

Utilization of computer simulations has become ubiquitous in contemporary engineering design. Accurate simulations can provide a reliable assessment of components and devices, thereby replace the need for prototyping, reduce the cost of the design cycle, as well as its cost. At the same time, the computational cost of computer simulations (e.g., full -wave electromagnetic (EM) analysis in microwave or antenna engineering) maybe considerable or even unmanageable, particularly for complex structures. This is usually not a problem for design verification or even simple simulation -driven design procedures based on parameter sweeping; however, it becomes problematic for procedures that require numerous analyses, such as parametric optimization, statistical analysis, or tolerance -aware design.

In this chapter we concentrated on checking the correctness or accuracy of analog behavioral models. The authors presented some approaches to judge the verification process using metrics like code or state-space coverage. These coverage methods are new for the analog domain and can be used to substantially increase the confidence in the verification setup and following in the model. Additionally, the authors presented a methodology to generate a model in a complete formal way due to the consideration of the whole reachable state space of the original circuit. This approach reaches a big abstraction in combination with a high speed-up comparable with manually written behavioral models.

Analog circuit modeling is the procedure through which analog circuit operation and performance are described by a succinct, comprehensive yet accurate representation. Circuit modeling has application in numerous design-related activities, like getting insight into circuit operation, circuit topology synthesis and improvement, circuit parameter optimization, fast simulation, design centering and yield improvement, test and validation, and design knowledge representation. This chapter offers an overview of some of the main methodologies and algorithms for analog circuit modeling without claiming that it exhaustively summarizes the entire research domain. It would be very hard considering the large number of publications on analog circuit modeling. This chapter mainly focuses on three main categories of automated circuit modeling techniques: symbolic methods, neural network (NN)-based approaches, and macromodeling. The related techniques are grouped depending on the similarity of their pursued goals and concepts. The chapter refers to close to 100 papers to present the capabilities, strengths, and limitations of the different methods.

This chapter describes an inductor modeling strategy based on machine-learning techniques. The model developed is based on Kriging functions and uses a novel modeling technique based on a two-step strategy, which is able to obtain an extremely accurate model with less than 1% error when compared to electromagnetic (EM) simulations. Due to its extreme accuracy and efficiency, the model can be used in inductor synthesis processes using single- or multi-objective optimization algorithms in order to obtain a single design or a Pareto-optimal front. Also, the model can describe the inductor behavior in frequency and therefore can also be used in circuit design using modern electrical simulators. This chapter discusses both applications (inductor synthesis and circuit design), performing several singleand multi-objective inductor optimizations, using different inductor topologies and operating frequencies. Furthermore, the model is also used in order to accurately model inductors during the design of a voltage-controlled oscillator (VCO) and a low-noise amplifier (LNA).

This chapter is divided into four sections. In Section 8.1, the probabilistic defect occupancy (PDO) model, a physics-based compact model, is introduced, which can be easily implemented into circuit simulators. Section 8.2 describes a purposely designed IC which contains suitable test structures, together with a full instrumentation system for the massive characterization of TZV and TDV in CMOS transistors, from which aging of the technology under study can be statistically evaluated. Section 8.3 is devoted to a smart methodology, which allows extracting the statistical distributions of the main physical parameters related to TDV from the measurements performed with the instrumentation system. Finally, Section 8.4 describes CASE, a new reliability simulation tool that accounts for TZV and TDV in analog circuits, covering important aspects, such as the device degradation evaluation, by means of stochastic modeling and the link between the device biasing and its degradation. As an example, the shifts of the performance of a Miller operational amplifier related to the device TDV is evaluated using CASE. Finally, in Section 8.5 the main conclusions are summarized.

During the design of mixed signal circuits and systems, engineers often begin with high-level behavioral descriptions of the target system. The main appeal of this approach is to reveal theoretical limits and impact of nonidealities before starting transistor level design. This method becomes especially valuable during the design of high-performance and high-resolution circuits. Therefore, behavioral models of mixed signal systems, such as analog-to-digital converters (ADCs), have become a popular research topic. Using such models, the design parameters can be explored based on fast, high-level simulations. As will be described in this chapter, behavioral models of the circuit nonidealities can reveal many issues early in the design. Hence, nonidealities of the circuits should be described and modeled carefully. Sections 9.1 and 9.2 briefly explain the structure of the pipeline ADC and flash ADC, respectively. Section 9.3 describes an ideal model for a pipeline ADC. Next, in Section 9.4, circuit nonidealities are analyzed and modeled in MATLAB^® and Simulink^TM environments. Finally, the model of whole ADC with nonideality models are simulated and results are presented in Section 9.5.

An introduction to the topic of power systems modelling has been given. There are many aspects of power systems that make their modelling different from other analogue systems; however, constructing a small -signal model provides fast analysis of the behaviour, subject to certain limitations as having been discussed. The efficiency of a power system is determined by many parasitic components not just in the core converter but many times also in the external components. An insight into the nonideal behaviours and lossy mechanisms of capacitors and inductors has been given. Battery modelling is an area of active research driven by the plethora of low power wireless applications and electric vehicle adoption, and the reader is referred to the references for further reading on this topic.

For several years, micro-electro-mechanical systems (MEMS) have been experiencing dynamic and sustained growth. This development is mainly driven by the automotive industry. One example of such a growing market is tire pressure monitoring systems (TPMS). Initiated by legal regulations in the USA and the EU (in China, laws on the mandatory use of TPMS will apply from 2020), the market has experienced its own momentum as a result of the continuous development of TPMS. In addition, the positive market development is reinforced by the continuously decreasing costs of sensors. Costs related to sensor development are the development costs, which are reflected in the time from the customer inquiry or specification to the tape out. Although the design of MEMS has been the subject of research and development activities for years, there is still a gap compared to a typical IC design environment. This chapter provides an overview of the current state of MEMS design. Using the example of a three-dimensional (3D) acceleration sensor, new approaches for efficient design and layout are shown.

In this chapter, we discuss the physical principles of spintronic devices and their sensing challenges and compare the different sensing schemes withing terms of the power and speed constraints. Moreover, the circuit operation and its benefits over other implementations of the proposed sensing scheme are clarified.

Analogue integrated circuit design started with primitive transistor models that were able to capture the operation of solid-state devices. Only simple functionality could be accomplished through the circuits designed. Via aggressive scaling, however, the number of transistors that could be integrated has dramatically increased, thereby boosting the capability of circuits to achieve diverse and complex tasks. At first, more transistors meant an augmented computational cost only, since a large number of equations had to be solved concurrently to determine the circuit response. The time to find out the transistor operating points became crucial. Transistor models should be both accurate and easy to evaluate. Thus, alternative approaches have been proposed to characterize the device physics mathematically, some of which have led to the development of well-known transistor models, such as BSIM, EKV, and PSP, over the years. As the scaling continued in its unprecedented pace, novel modelling issues started to arise. Simulations using primitive device models with few parameters were not sufficient to predict the outcomes of measurements. There were different reasons for this observation: smaller transistor sizes were triggering quantum mechanical effects, such as quantum tunnelling as well as entailing models with more complex underlying equations. Moreover, with shorter geometries, device-todevice variation of transistor parameters significantly increased. There was a need to characterize the changes induced by manufacturing steps with a separate set of parameters. Finally, devices were failing after prolonged usage due to the high vertical and lateral electric fields they undergo during regular operation. These were basically reliability issues occurring towards the end of the device lifetime. Thus, reliability phenomena needed to be described with dedicated models, as well.