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

Oscillators/VCOs phase noise is an important concern in RF design. Ultra low noise oscillator sources are crucial for the development of high bit rate wireless link system such as point-to-point radios or multipoint radios. This paper presents an analytical method to optimize phase noise of high Q autonomous circuits (oscillators/VCOs). The key point of this approach is to optimize the conduction angle of the RF current leading to minimum phase noise for a given transistor and resonator. The optimization technique is demonstrated through a design example, leading to an ultra low noise oscillator at 2.4 GHz. The measured phase noise at 1 KHz offset frequency is better than -108 dBc/Hz, and to our knowledge this is best phase noise using ceramic resonator so far reported

A unifying theory and characterization of microwave oscillator/VCO

RF-MEMS based components such as inductors, variable capacitors, transmission line, filter, switches, phase-shifter, and resonators are superior in performances in term of quality factor, noise, linearity, power consumption, size, and cost, which cannot be achieved by conventional approach, thereby, prime candidate for ubiquitous connectivity. This work discusses the recent trends in wireless connectivity and gives the brief overview of the RF-MEMS enabled front ends, especially, RF signal source (VCOs) that can be extended to microwave, and is also amenable for integrated circuit (IC) fabrication.

RF-MEMS Enabled RF-Signal Source For Low-Power Consumption Ultrawideband Communication Systems

This paper describes the applications of SDR (Software Defined Radio) and SDN (Software Defined Network) technology in the next generation radios.

Next generation radios: SDR and SDN

This paper discusses the expectations, challenges, and uncertainties of the next generation 5G radio communication networks. The acknowledged high expectations for new radios place challenges on designers and uncertainties on the selection of the frequency spectrum. Although, research community and industry leaders are engaged towards figuring out the dynamics of 5G (fifth generation), expectation continue high for the next-generation radio standard, which will require higher data rates, massive device connectivity, more system capacity, reduced latency, energy savings, and inexpensive solution. The transition from 4G to 5G can lead to significant augmentation in data rates and latency. Designers are engaged in cope with the needed dimension of time t in 5G, which aims at air latency of 10 Gbps at millimeter wave frequencies. Therefore, considerable design challenges stretch out ahead for system engineers to integrate novel technologies (CR, SDN, SDR), into interoperable platforms that intelligently connect to local and global NW and offers affordable solutions.

Next generation 5G radio communication NW

In this paper tunable active inductor (TAI) based oscillator topologies are presented. The reported TAI oscillator circuit uses dynamic phase-injection and feed-forward mechanism for improving the phase noise performance and dynamic ranges. The measured phase noise for carrier frequency 11.8 GHz is better than −110dBc/Hz at 1MHz offset with 200 MHz tuning and DC bias of 3V, 30 mA.

Ulrich L. Rohde

Papers

A unifying theory and characterization of microwave oscillator/VCO

RF-MEMS Enabled RF-Signal Source For Low-Power Consumption Ultrawideband Communication Systems

Next generation radios: SDR and SDN

Next generation 5G radio communication NW

Tunable active inductor oscillator