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 discusses the radio monitoring receiver dynamics in conjunction with SDN-SDR (Software Defined Network-Software Defined Radio) for IoT (Internet of Things) applications.

Monitoring Radios: Dynamics And Emerging Trends

This paper presents, for the first time, an integrated method for transistor model parameter extraction by fitting the DC, multi-bias S-parameter and noise measurements simultaneously. The extracted model provides accurate small-signal, large-signal and noise characteristics. This technique is demonstrated for a Raytheon foundry HBT and excellent results are obtained. Self-heating effects are taken into consideration in the parameter extraction procedure.

Transistor parameter extraction using DC, S-parameter and noise data simultaneously

For large-signal operation of oscillators, it is typically necessary to obtain the large signal device parameters of the active two-port network and calculate the external feedback elements for the circuit [1]–[16] Figure 1 shows the simplified circuit diagram for a series feedback oscillator comprising the intrinsic transistor, its package parasitics, and the external feedback circuit Both series and parallel feedback arrangements are common in oscillator circuits [9] The circuit example shown below is based on the series feedback circuit and accounts for all intrinsic parasitic parameters [7]–[9]

MTT-17 Presents: An Analytical Approach for Designing Efficient Microwave Oscillators

This paper describes ITCO (injection-tuned coupled-oscillators) that offers cost-effective, power-efficient, integrable, compact, and low cost spectral pure signal source for wireless communication systems. The measured phase noise for 9.2 GHz ITCO is typically -132 dBc/Hz at 100 kHz offset from the carrier with 18% DC-to-RF conversion efficiency respectively. To our knowledge, this is the best phase noise performance for a given class and DC-to-RF conversion efficiency so far reported.

Injection-Tuned Coupled-Oscillators

The noise cancellation and noise minimization techniques described in this work can satisfy the need of the present demand for low cost, low noise, low power consumption, compact, configurable RF oscillators/VCOs, and also easily amenable for integration in integrated circuit (IC) technology.

Ulrich L. Rohde

Papers

Monitoring Radios: Dynamics And Emerging Trends

Transistor parameter extraction using DC, S-parameter and noise data simultaneously

MTT-17 Presents: An Analytical Approach for Designing Efficient Microwave Oscillators

Injection-Tuned Coupled-Oscillators

Noise reduction techniques for configurable RF signal source