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.

/pdf/science-and-technology-roadmap-for-graphene-related-two-4q9m7czlkc.pdf

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 the super-regenerative receiver (SRR); a device widely used in short distance telemetry and remote control applications. The difficulty in modeling the regenerative behavior served as the basis for "cut and try" methodology based on results obtained from the simplified model using conventional approach. This work presents the SRR behavior to practical implementations by dynamically controlling the injection-mode levels of the super-regenerative oscillator (SRO) for optimum sensitivity and dynamic ranges.

Super-Regenerative Receiver

In this paper, we show that two back to back coplanar waveguide (CPW) in the form of Mobius strip has resulted in an infinite transmission line capable of retaining a large bandwidth of frequencies that can be useful for real time signal retention device (RTRD). By providing Mobius twist to CPW, a continuous phase change reported instead of abrupt phase change by using shorting pins between two parallel transmission lines. It is observed that the device retains the injected signal in time domain over a broad band of frequencies. The signal can also be a pulsed signal as in Ultra Wide Band (UWB), or a modulated microwave signal, can retain transient signals encountered in Radio Astronomy, Medical applications and many more exciting applications.

Real time signal retention device using co-planar waveguide (CPW) as Mobius strip

Manipulating and tailoring the electromagnetic wave coupling properties, several interesting properties of Metamaterials Mobius Strips (MMS) envisage, such as reduction in the size for a given operating frequency and suppression of spurious resonance modes, thereby improving the overall performances including reducing the power consumption; validated with the examples of 6 GHz VCO, measured phase noise @ 10 kHz offset is -120 dBc/Hz with more than 10 MHz tuning for compensating the frequency drift over operating temperature (-40 degree C to +85 degree C), typical power consumption of 100 milli Watt (5V, 20mA) and output power is more than 2 dBm.

http://ieeexplore.ieee.org/iel7/6850264/6859834/06859924.pdf

Metamaterial Möbius Strips (MMS): Application in resonators for oscillators and synthesizers

Super-regenerative receiver (SRR) has been been widely used for many decades in short- range wireless communications due to it's simplicity, low cost, low power consumption, and small number of components that improves the reliability of the systems. This paper describes brief theory of the SRR and also gives insights about the dynamic mode- coupled planar resonator used for regenerative actions, thereby, cost-effective and power-efficient alternative of expensive SAW based SRR.

Super-Regenerative Receiver (SRR)

Crystal oscillators are commonly used as reference frequency standards for synthesis of the harmonic signal required for their operation in synthesizer and timing devices. The phase noise of these reference frequency standards limits the noise floor and electromagnetic interference susceptibility that affects the dynamic range, selectivity, and sensitivity of a receiver. This contribution is devoted to design guidelines for selecting the low-phase-noise topology of crystal oscillator circuits for the applications in modern communication systems. Numerous practical examples are demonstrated and validated with computer-assisted design (CAD) simulation and measured results, which allows for the realization of high-performance stable reference frequency standards.


Keywords:

crystal oscillator;
crystal resonator;
drive level;
EMI;
output power;
mode-coupling;
phase noise;
FOM;
sensitivity;
Q-factor;
noise model

Ulrich L. Rohde

Papers

Super-Regenerative Receiver

Real time signal retention device using co-planar waveguide (CPW) as Mobius strip

Metamaterial Möbius Strips (MMS): Application in resonators for oscillators and synthesizers

Super-Regenerative Receiver (SRR)

Crystal Oscillator Design