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 a novel 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. In this approach, dynamic slope optimizer network, which drives and resonates the gates of the mixing cell (Dual-FETs) for a given conduction angle of the differential (180deg phase shift) VCO output is adapted to meet the challenge of the conflicting requirements such as linearity, conversion loss, and noise figure. By introducing dynamic feedback mechanism by incorporating series resistor and capacitor between the drain and gate of the mixing cell (Dual-FETs) network, impedance level can be optimized for minimum loss of the RF signal, thereby; it improves the flatness of the conversion loss over the operating frequency band. The typical measured input intercept points (IIP3) and conversion loss is 39 dBm and 8.5 dB with the LO power typically 15dBm for the frequency bands (RF: 1150-2450 MHz, LO: 1200-2650 MHz, IF: 50-200 MHz).

Low Cost, Power-Efficient Reconfigurable Passive FET Mixers

RF signals in VCOs, PLLs and synthesizers are characterized by signal power, harmonic content and phase noise. These parameters have to be accurately measured in order to guarantee the system performance. This paper focuses on the relationship between the signal's harmonic content and the precision of the phase noise measurement in test equipment. The phase noise measurement's accuracy is degraded when the measured signal has high harmonics. We demonstrate a case in which a 3rd harmonic level of −7dBc results in a 12dB variation in the phase noise measurement's accuracy. Based on our studies, the phase noise test setup should include filters between the source and the test equipment to bring down the harmonic level to −20 dBc max.

Harmonics induced uncertainty in phase noise measurements

Forced opto-electronics oscillator (OEO) is a very promising way to build low phase noise oscillators. Forced techniques of self-injection locking phase locking (SILDPLL) are integrated with narrowband tunable RF filters to build OEO system to further reduce the phase noise and suppress side mode generated among standard OEOs because of long fiber delays. The narrowband tunable RF filter is based on an optical wavelength tuned transversal filter using a fiber Bragg grating as delay element cascaded with current tuned YIG filter to accomplish a 2kHz frequency resolution over K-band. Second harmonic generated frequency synthesized signals with close-in to carrier phase noise of −127 dBc/Hz at 10 kHz offset are reported by Vπ operation of a Mach-Zehnder (MZM) over 18 GHz to 22 GHz. 19” rack mount system is also constructed and long-term stability of 4.5 kHz over 60 min is measured at K-band, while a 3.5 kHz drift is measured for a tabletop realization.

K-Band High Stablity and Resolution Frequency Synthesizers Using Forced Opto-Electronic Oscillators

The coexistence of second and third generation wireless system requires multi-mode, multi-band and multi-standard mobile communication systems, therefore, requiring a configurable RF signal source (VCO) that may replace several narrow band VCO modules by a single low noise ultrawideband (UWB) adaptable RF signal source. The performance of the wireless communication systems strongly depends on the speed of devices, and technological scaling has driven this momentum towards achieving faster speed and high level of integration. This paper investigates the impact of device scaling on phase noise of the UWB (2-8GHz) configurable coupled N-Push voltage controlled oscillator (VCO) in SiGe HBT, which has recently emerged as a strong contender for RF and mixed signal applications.

Technological Scaling and Impact on UWB Configurable RF Signal Source

The performance of the electronic system strongly depends on the speed of devices, and device scaling has driven this momentum towards achieving faster speed and high level of integration. This paper describes the impact of phase noise in scaled SiGe HBTs coupled mode oscillators topology, which has recently emerged as a strong contender for RF and mixed signal applications. The relative contribution of the broadband (thermal and shot noise) and low frequency (1 / f noise) noise sources are examined with respect to the device scaling. A method of minimizing the phase noise with respect to the device scaling is discussed, and demonstrated for planar coupled resonators based VCO. The circuit topology is not limited to these frequencies, and easily amenable for integration in MMIC form.

Ulrich L. Rohde

Papers

Low Cost, Power-Efficient Reconfigurable Passive FET Mixers

Harmonics induced uncertainty in phase noise measurements

K-Band High Stablity and Resolution Frequency Synthesizers Using Forced Opto-Electronic Oscillators

Technological Scaling and Impact on UWB Configurable RF Signal Source

Minimization of phase noise in scaled device coupled mode oscillators