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

Manipulating and tailoring the electromagnetic-wave coupling properties, numerous interesting properties of topology driven Mobius Metamaterials Strip is emerging that goes beyond the conventional characteristics and structure functionality relationship. The goal of this paper is 3-folds: (i) to address the key concept of topology and topological notions in a wide class of materials with potential technological applications, (ii) discuss the possibility of application of topology driven negative refractive index composite Metamaterial Mobius strips, and (iii) validation examples (4GHz–12GHz/12GHz–18GHz voltage controlled oscillator circuits for RF/MW applications).

Möbius metamaterial topology: Applications in resonators and tunable oscillator circuits

RF Switches and Attenuators

This paper describes oscillator noise measurement techniques, challenges and associated measurement uncertainty. The cross-correlation method used in modern PN measurement equipments, can present erroneous result, depending upon phase-inversion, harmonics, o/p load mismatch, and cable length. This discussion is imperative for low phase noise signal sources, validated with 2.4 GHz SAW oscillator, and discussed steps for mitigating these issues by using filtering/phase-matching N/W.

Frequency signal source's PN (phase noise) measurements: Challenges and uncertainty

This paper describes a reconfigurable resistive passive FET mixer co-designed with a reconfigurable VCO (voltage controlled oscillator) that acts as a LO (local oscillator), can operate with low noise figure, and high dynamic range without the need of external BALUN (balance-to-unbalance) network. The typical measured input intercept points (IIP 3 ) and conversion loss is 38dBm and 8.5dB with the LO power typically 15dBm for the frequency bands (RF: 700–2300MHz, LO: 650–2100MHz, IF: 50–200MHz).

Reconfigurable and cost-effective FET mixer

A novel adaptive slow-wave mode-coupling technique is incorporated in synthesizer with the intent of lowering size, cost, power-consumption, phase noise, and vibration sensitivity for current and later generation communication systems.

Ulrich L. Rohde

Papers

Möbius metamaterial topology: Applications in resonators and tunable oscillator circuits

RF Switches and Attenuators

Frequency signal source's PN (phase noise) measurements: Challenges and uncertainty

Reconfigurable and cost-effective FET mixer

A novel low cost high performance synthesizer