![illustrates both PWM and PWM-2 pulse configuration. It is obvious that output 8 Gbps data stream which passes through the channel with bandwidth restriction parameter BW3dB = 1000 MHz has pulse shaping similar to raised cosine PWM shaping for PWM-2 signal at the channel input; compare pulse shaping in [14] with output data stream in Fig.5. The original idea of using raised cosine shaping for time-domain pre-emphasis techniques was for the first time published in research papers [14], [15].](https://www.researchgate.net/publication/319618500/figure/fig5/AS:668803016970252@1536466473924/illustrates-both-PWM-and-PWM-2-pulse-configuration-It-is-obvious-that-output-8-Gbps-data_Q320.jpg)
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Optimized Signaling Method for High-Speed Transmission Channels with Higher Order Transfer Function
Abstract and Figures
In this paper, the selected results from testing of optimized CMOS friendly signaling method for high-speed communications over cables and printed circuit boards (PCBs) are presented and discussed. The proposed signaling scheme uses modified concept of pulse width modulated (PWM) signal which enables to better equalize significant channel losses during data high-speed transmission. Thus, the very effective signaling method to overcome losses in transmission channels with higher order transfer function, typical for long cables and multilayer PCBs, is clearly analyzed in the time and frequency domain. Experimental results of the measurements include the performance comparison of conventional PWM scheme and clearly show the great potential of the modified signaling method for use in low power CMOS friendly equalization circuits, commonly considered in modern communication standards as PCI-Express, SATA or in Multi-gigabit SerDes interconnects.
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In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew polynomial rings, PBW extensions and skew PBW extensions, etc.) We collect and systematize questions, problems, properties and recent advances in both theories by explicitly developing examples and doing calculations that are usually omitted in the literature. In particular, for Hopf Galois extensions we consider approaches from the point of view of quantum torsors (also known as quantum heaps) and Hopf Galois systems, while for some families of noncommutative rings we present advances in the characterization of ring-theoretic and homological properties. Every developed topic is exemplified with abundant references to classic and current works, so this paper serves as a survey for those interested in either of the two theories. Throughout, interactions between both are presented.
The principal objective of this paper is to provide a torsor theory of physical quantities and basic operations thereon. Torsors are introduced in a bottom-up fashion as actions of scale transformation groups on spaces of unitized quantities. In contrast, the shortcomings of other accounts of quantities that proceed in a top-down axiomatic manner are also discussed. In this paper, quantities are presented as dual counterparts of physical states. States serve as truth-makers of metrological statements about quantity values and are crucial in specifying alternative measurement units for base quantities. For illustration and ease of presentation, the classical notions of length, time, and instantaneous velocity are used as primordial examples. It is shown how torsors provide an effective description of the structure of quantities, systems of quantities, and transformations between them. Using the torsor framework, time-dependent quantities and their unitized derivatives are also investigated. Lastly, the torsor apparatus is applied to deterministic measurement of quantities.
The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system’s ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity’s value into its measuring instrument’s pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument’s indiscernibility relation, manifested by not being able to distinguish the measured system’s topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment.
A novel retimer modeling approach based on IBIS-AMI to capture the performance of a retimer that runs up to 15 Gbps will be presented. The interoperability between retimer and SerDes models and their loss compensation features in full link simulation will be then demonstrated. The retimer CDR tracks low-frequency jitter and filters high-frequency jitter to improve the system jitter rejection ratio
Conjectures play a central role in theoretical physics, especially those that assert an upper bound to some dimensionless ratio of physical quantities. In this paper we introduce a new such conjecture bounding the ratio of the magnetic moment to angular momentum in nature. We also discuss the current status of some old bounds on dimensionless and dimensional quantities in arbitrary spatial dimension. Our new conjecture is that the dimensionless Schuster-Wilson-Blackett number, c{\mu}/JG^{(1/2)}, where {\mu} is the magnetic moment and J is the angular momentum, is bounded above by a number of order unity. We verify that such a bound holds for charged rotating black holes in those theories for which exact solutions are available, including the Einstein-Maxwell theory, Kaluza-Klein theory, the Kerr-Sen black hole, and the so-called STU family of charged rotating supergravity black holes. We also discuss the current status of the Maximum Tension Conjecture, the Dyson Luminosity Bound, and Thorne's Hoop Conjecture.
This paper is concerned with the names and symbols for quantities used to describe oscillatory motion such as for a harmonic oscillator, and the units to be used for the quantity plane angle and phase angle for an oscillator, and related quantities. I draw attention to the need to carefully distinguish the names and symbols for quantities from the names and symbols for their numerical values in any application, and the significance of including units such as radian and cycle for the quantity plane angle. The familiar equations for a harmonic oscillator such as ω = 2πν, and the relation = h/2π for the Planck constant, are shown to hold only if the symbols are taken to represent the dimensionless numerical values of the quantities concerned in particular units, rather than the actual values which are not dimensionless as generally used in the equations of physics. Alternative ways of handling these quantities and units are discussed.
A transmitter pre-emphasis techniques to overcome high-slope losses of printed circuit board (PCB) with higher-order transfer function used in high-speed serial link design is presented. The pre-emphasis technique based on pulse-width modulation (PWM) using timing resolution instead of amplitude resolution to adjust the filter transfer function is analyzed and applied to channel with high-order transfer function. Leading-edge digital silicon manufacturing processes are pushing the maximum swing below 1.0 V and just PWM scheme is a good alternative for these cases. In addition only one coefficient can be used to set equalizer transfer function in depending on channel properties. Standard approaches to transmitter pre-emphasis and novel PWM pre-emphasis are compared in advanced PCB backplane model.
Standards bodies are now examining how to increase the throughput of high-density backplane links to 25 Gbps. One method for achieving this is to construct premium backplane links utilizing advanced materials and connectors. Another approach is to reuse legacy backplanes by employing PAM-4 signaling at half of the baud rate. For PAM-4 to offer an advantage over NRZ, the signal-to-noise ratio (SNR) at the slicer input, i.e. after equalization, must be ∼9.5 dB better than NRZ to overcome loss of separation between signal levels. This paper will examine 25 Gbaud NRZ and 12.5 Gbaud PAM-4 signaling across varying levels of channel insertion loss and crosstalk. Chip parameters such as rise-time and jitter will also be varied. The paper provides a reliable reference for engineers to use when considering when it is appropriate to use NRZ signaling at 25 Gbaud and when it is appropriate to use PAM-4 signaling at 12.5 Gbaud for successful high-density backplane operation.
The term ‘dimension’ as used in the International System of Units (SI) is not well defined. Moreover, the term ‘quantity of dimension one’ (formerly called ‘dimensionless quantity’, a term which is unfortunately still sometimes used) as defined in the International Vocabulary of Metrology (VIM) is mathematically unsound. In order to overcome these difficulties, a new quantity dimension, called ‘dimension number’, will be introduced in this paper. It will be shown that such a dimension necessarily belongs to any system of dimensions, but is not a base dimension.