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

A high intercept points, cost-effective, and power-efficient switching FET double balanced mixer (DBM) is reported. The Switching FET DBM demonstrated in this work offers input intercepts points (IIP3) and conversion loss typically 43 dBm and 9 dB respectively with 16 dBm LO power for the frequency band (RF: 900-2650 MHz, LO: 850-2450 MHz, IF: 50-200 MHz). The measured interport isolation is typically better than 30 dB for broadband applications, and the circuit topology is not limited to these frequencies, and can be easily extended 3rd and later generation of communication systems.

Brroadband, High Intercept Points, Cost-Effective Power-Efficient Double Balanced Mixer (DBM)

T-filter circuits (F1-Fn), designed regarding output as serial acceptor circuits (SE1-SEn) and connected to an input (E) and output (A) switch on or off by switches (D1-Dn) fitted to the side opposite the input for the serial acceptor circuits. One of the filter circuits acts as a parallel acceptor circuit.

Pre-selection filter layout for high frequency receivers

Optoelectronic oscillators with their demonstrated low phase noise are popular due to the increasing demand of very clean local oscillator and clock signal sources. Forced techniques are applied on an OEO system reducing the phase noise and suppresses side mode observed in standard OEO with long delays. A frequency synthesizer working at X-band is demonstrated using dispersive optical transversal filter cascaded with YIG filter to electronically fine and coarse tune the oscillation frequency of the synthesized frequency, as a replacement for fixed frequency high Q metallic filter. Close-in to carrier phase noise of −135 dBc/Hz at 10 kHz are reported by V π/2 operation of a Mach-Zehnder (MZM) over 9 GHz to 11 GHz with frequency tuning step as small as 10 kHz/pm.

High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators

Injection mode-coupled voltage-controlled SAW oscillators (VCSOs) are versatile performers in low-noise frequency synthesizers, both as high-frequency sources and as reference oscillators. A novel high frequency digital synthesizer is reported with the intent of lowering following: size, cost, power-consumption, phase noise, jitter, and vibration sensitivity. The measured phase noise is typically better than −100 dBc/Hz, −115 dBc/Hz, −129 dBc/Hz, −133 dBc/Hz at 100 Hz, 1 kHz, 10 kHz, and 100 kHz offset frequencies respectively from the carrier frequency of 5200 MHz. The reported synthesizer can generate frequencies from 5 GHz to 5.3 GHz in steps of 100 kHz with typical spurious of −65 dBc and the power consumption is less than 300 mill watt for a given 5 dBm output power.

A novel high frequency synthesizer using adaptive injection mode-coupled VCSO for low jitter and low noise applications

A 2D, volumetric (i.e., non-planar), structure consisting of two dielectric layers, loaded by various metal inclusions on multiple-periodic grids and closed by two confining metal planes is introduced in view of advanced dispersion engineering related applications. Full-wave simulation has been used to demonstrate that, for axial propagation, the structure presents (i) a large electromagnetic band-gap and (ii) two modes that have anti-parallel phase and group velocities in different frequency bands where they do not interact with other modes.

Ulrich L. Rohde

Papers

Brroadband, High Intercept Points, Cost-Effective Power-Efficient Double Balanced Mixer (DBM)

Pre-selection filter layout for high frequency receivers

High-resolution frequency synthesizers over X-band using SILPLL opto-electronic oscillators

A novel high frequency synthesizer using adaptive injection mode-coupled VCSO for low jitter and low noise applications

2D periodic structure featuring negative group velocity of bloch waves