There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

Phase noise is a topic of theoretical and practical interest in electronic circuits, as well as in other fields, such as optics. Although progress has been made in understanding the phenomenon, there still remain significant gaps, both in its fundamental theory and in numerical techniques for its characterization. In this paper, we develop a solid foundation for phase noise that is valid for any oscillator, regardless of operating mechanism. We establish novel results about the dynamics of stable nonlinear oscillators in the presence of perturbations, both deterministic and random. We obtain an exact nonlinear equation for phase error, which we solve without approximations for random perturbations. This leads us to a precise characterization of timing jitter and spectral dispersion, for computing of which we have developed efficient numerical methods. We demonstrate our techniques on a variety of practical electrical oscillators and obtain good matches with measurements, even at frequencies close to the carrier, where previous techniques break down. Our methods are more than three orders of magnitude faster than the brute-force Monte Carlo approach, which is the only previously available technique that can predict phase noise correctly.

Phase noise in oscillators: a unifying theory and numerical methods for characterization

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Design Of Analog Cmos Integrated Circuits

For professional-level information, this classic work has long been considered the definitive guide to both theory and design of all types of communications receivers including shortwave, military, broadcast, and direction-finding.Now the new edition builds on the reputation of its best-selling predecessor. Completely revised throughout, it features the latest advances in cellular and digital systems ... basic discussions of selectivity and dynamic range ... specifics on design approaches, circuitry, and components ... details on the use of microprocessors and logic devices ... coverage of special modes such as pulse and data ... and more.

Communications Receivers: Principles and Design

Digital PLL frequency synthesizers

Noise is associated with all the components of the oscillator circuit; however, the major contribution of the noise in an oscillator is from the active device, which introduces amplitude modulation (AM) and phase modulation (PM) noise. The conventional wisdom is to ignore AM component of the noise because the gain limiting effects of the active device operating under saturation, allowing only little variation in the output amplitude due to the noise in comparison to PM noise component, which directly affects the frequency stability of the oscillator and creates noise sidebands. But in reality, many oscillator topologies create significant AM noise, therefore effective noise contribution is the combination of 1/f spectrum with the 1/f 2 effect in all PM, makes the low-frequency noise much greater, and that's where the information in most modulated signals resides.

How Low Can They Go?: Oscillator Phase Noise Model, Theoretical, Experimental Validation, and Phase Noise Measurements

A novel forced oscillation technique is discussed for the phase noise reduction of electrical and optoelectronic oscillators. This paper features self-injection locking using single and dual long fiber-optic delay loops and provides analysis for the phase noise of oscillators employing this technique under various operating conditions. Experimental results are also provided to verify the analytical modeling and to identify techniques to further enhance spectral purity of oscillators.

Analytical and Experimental Evaluation of SSB Phase Noise Reduction in Self-Injection Locked Oscillators Using Optical Delay Loops

Introduction Radio Reception Principles Characteristics and Requirements of Software Radio Systems Radio Receiver Characteristics Receiver System Planning Antennas and Antenna Coupling Amplifiers and Gain Control Mixers Frequency Control and Local Oscillators Demodulation and Demodulators Digital Signal Processing Receiver Design Trends Appendices

Ulrich L. Rohde

Papers

Communications Receivers: Principles and Design

Digital PLL frequency synthesizers

How Low Can They Go?: Oscillator Phase Noise Model, Theoretical, Experimental Validation, and Phase Noise Measurements

Analytical and Experimental Evaluation of SSB Phase Noise Reduction in Self-Injection Locked Oscillators Using Optical Delay Loops

Communications Receivers: DSP, Software Radios, and Design