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

This paper describes STPCR (stubs-tuned planar coupled resonators) that offer user-definable, cost-effective, power-efficient, phase hits insensitive, integrable, compact, and low cost low noise signal source wireless communication systems. The measured phase noise for a carrier frequency 2488 MHz is typically -128 dBc/Hz at 10 kHz offset from the carrier with 40% DC-to-RF conversion efficiency. To our knowledge, this is the best phase noise performance for a given conversion efficiency (RF output power at fundamental frequency 'f0' = 15 dBm, VDC = 5 V, IDC= 15 mA) using STPCR network so far reported.

A Novel Stubs-Tuned Planar Resonator Based Low Noise Signal Source For Wireless Communication Systems

Bei einem Schleifen-Dipol bzw. -Monopol sind die Strahler gegenuber ihrer Soll-Lange stark verkurzt und an ihren Enden durch nichtstrahlende Leitungsstucke elektrisch verlangert.

Verkürzter schleifen-dipol und schleifen-monopol

This paper describes the novel MMS (Mobius Metamaterial Strip) structure, for an example Mobius-Graphene topology for spintronic and Mobius-Metamaterial for VCO applications. For the validation we built 10.24 GHz MMS inspired VCO, MMS Resonator quality factor Q ≅ 25 000. The prototype unit is packaged in a ≅ 2.5in3 connectorized aluminum case1, with 600 mW DC power (5V, 120 mA), measured PN (phase noise) performance is better than −130 dBc/Hz @ 10 kHz offset from the carrier, and delivers +12 dBm at 10.24 GHz.

Möbius-Graphene and Möbius-Metamaterial VCO

Ceramic/SAW (surface acoustic wave) resonators based oscillators are known for their ability to generate high spectral purity signal at microwave frequency but they are not immune to electromagnetic interference (EMI), vibration effects, microphonics, phase hits, and frequency modulation. Moreover, Ceramic/SAW resonators are costly and not suited for fabrication by current integrated circuit (IC) technology. This work is based on innovative and novel approach by using buried multi-mode-coupled planar resonators that offer user-definable, configurable, cost-effective, phase hits insensitive Ceramic/SAW replacement oscillators (CSRO). The typical measured phase noise of CSRO for frequency 2488 MHz is better than -164 dBc/Hz @ 1 MHz offset from the carrier, and is better than the commercial available Ceramic/SAW resonators based oscillators.

User-Defined and Configurable CSRO

Dans un dipole ou monopole cadre, la longueur de consigne des applicateurs est fortement raccourcie et leurs extremites sont electriquement rallongees par des pieces conductrices non rayonnantes.

Ulrich L. Rohde

Papers

A Novel Stubs-Tuned Planar Resonator Based Low Noise Signal Source For Wireless Communication Systems

Verkürzter schleifen-dipol und schleifen-monopol

Möbius-Graphene and Möbius-Metamaterial VCO

User-Defined and Configurable CSRO

Dipole cadre et monopole cadre raccourcis