Noise-shaping successive approximation register (NS-SAR) ADCs combine high resolution with energy efficiency, but their performance degrades at bandwidths in the tens of MHz due to limited oversampling ratios (OSR) and adoption of low-order passive filters. This work introduces a$3{^{\text {rd}}}$-order NS-SAR ADC that leverages a multi-input amplifier and a multi-input comparator, enabling independent optimization and flexible filter coefficient sizing. In addition, a ratio-based floating inverter amplifier ensures remarkable gain stability across process, voltage, and temperature (PVT) variations. Implemented in a 28-nm CMOS process, the prototype achieves 12.3-ENOB over a 20-MHz bandwidth while consuming 1.56 mW, resulting in a Schreier figure-of-merit (FoMS) of 177-dB with robust and consistent performance across PVT corners.

Recent advances in Scientific Machine Learning have shown that second-order methods can enhance the training of Physics-Informed Neural Networks (PINNs), making them a suitable alternative to traditional numerical methods for Partial Differential Equations (PDEs). However, second-order methods induce large memory requirements, making them scale poorly with the model size. In this paper, we define a local Mixture of Experts (MoE) combining the parameter-efficiency of ensemble models and sparse coding to enable the use of second-order training. Our model -- PINN Balls -- also features a fully learnable domain decomposition structure, achieved through the use of Adversarial Adaptive Sampling (AAS), which adapts the DD to the PDE and its domain. PINN Balls achieves better accuracy than the state-of-the-art in scientific machine learning, while maintaining invaluable scalability properties and drawing from a sound theoretical background.

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show how the NTK perspective falls short in the nonlinear scenario. Specifically, we establish that the NTK yields a random matrix at initialization that is not constant during training, contrary to conventional belief. Another significant difference from the linear regime is that, even in the idealistic infinite-width limit, the Hessian does not vanish and hence it cannot be disregarded during training. This motivates the adoption of second-order optimization methods. We explore the convergence guarantees of such methods in both linear and nonlinear cases, addressing challenges such as spectral bias and slow convergence. Every theoretical result is supported by numerical examples with both linear and nonlinear PDEs, and we highlight the benefits of second-order methods in benchmark test cases.

Abstract Generalization is a key property of machine learning models to perform accurately on unseen data. Conversely, in the field of scientific machine learning (SciML), generalization entails not only predictive accuracy but also the capacity of the model to encapsulate underlying physical principles. In this paper, we delve into the concept of generalization for Physics-informed neural networks (PINNs) by investigating the consistency of the predictions of a PINN outside of its training domain. Through the lenses of a novel metric and statistical analysis, we study the scenarios in which a PINN can provide consistent predictions outside the region considered for training and hereinafter assess whether the algorithmic setup of the model can influence its potential for generalizing. Our results highlight why overparametrization is not a crucial component in SciML while encouraging overfitting on the training data. Despite being counterintuitive, the outcome of our analysis serves as a guideline for training PINNs for engineering applications.

This paper analyses for the first time from a quantitative standpoint the effectiveness of redundancy in successive approximation register (SAR) analog-to-digital converters (ADCs) that employ the conventional and monotonic switching algorithms. It is shown that the redundancy tolerance window is one-sided in the case of conventional switching algorithm, thus only underestimations of the input signal can be corrected. Conversely, the monotonic switching algorithm shows a symmetric tolerance window that allows the correction of both underestimations and overestimations of the input signal. Thermal noise due to switches and comparator, and supply bouncing cause both these errors and they can be effectively corrected only with a symmetric redundant window. Behavioral simulations confirm that the monotonic switching algorithm applied to redundant SAR ADCs achieves better performance than the conventional one in terms of signal-to-noise-and-distortion ratio (SNDR).

The paper presents a generalization of the Groszkowski's result in differential oscillators, providing novel equations to describe the oscillation frequency dependence on the harmonic content. The effect of the common-mode oscillation is rigorously included. Moreover, an additional term, arising from the dependence of the transistor current on the drain voltage, which is dominant any time ohmic operation occurs, is disclosed here for the first time. This framework is applied to Van der Pol oscillators, both nMOS and CMOS, designed in a 28-nm bulk CMOS technology. The results correctly match the oscillation frequency dependence derived from detailed circuit simulations. The analysis shows that, when even harmonics are relevant, the classical Groszkowski's result is not able to account for close-in phase noise performance. The novel theoretical framework fully justifies, instead, the simulation results and sheds new light on the flicker noise up-conversion mechanisms in the considered oscillator structures.

This paper describes a simulation method to compute oscillator phase noise which combines transient and periodic-transfer-function analyses, available in most of the commercial circuit simulators. The proposed calculation technique is simple to implement and provides the designer a deep insight into phase noise generation mechanisms for both stationary and cyclostationary sources, thus resulting a powerful tool to perform an optimum design in RF applications.

This work proposes two novel simulation techniques that allow for fast and accurate predictions of phase noise in oscillators even adopting inexpensive software, such as PSpice. The traditional harmonic tone insertion is initially discussed, by applying it to a LC-tuned oscillator taken as benchmark. Then a first, much faster technique based on sensitivity analysis is proposed, which is suitable for the estimation of phase noise due to low-frequency sources, e.g. 1/f noise. Finally, the high-frequency noise sources contributions to SSCR are analyzed through another alternative method based on the frequency demodulation of the carrier. Both of these methods allow the designer to promptly identify the noise sources mainly responsible for the carrier instability and to accomplish the optimization for low phase noise of the synthesizer.