Design Method for High-Order Sigma–Delta Modulator Stabilized by Departure Angles Designed to Keep Root Loci in Unit Circle

In this brief, a systematic method to design stable single-stage high-order sigma-delta modulators (SDMs) without the need of stability-recovery mechanisms is proposed. It is shown that if the critical root loci of an SDM transfer function are all located inside a unit circle, then the SDM is guaranteed to be stable. Instead of basing the design on noise transfer function as in previous designs, the presented method bases the design on proper choice of open-loop transfer function departure angles so as to keep the critical root loci within the unit circle. A stable fourth-order SDM with the critical root loci inside the unit circle is given as a design example. Simulation results reveal that based on the presented design method, stable single-stage high-order SDMs can be free from overload instability even with full-scale input magnitude. Tradeoffs between stability and performance of the SDMs are presented. By allowing parts of the critical root loci to be located outside the unit circle, this method can be extended for SDM designs with higher signal-to-noise ratio but smaller stable input range     

Modeling Harmonic Distortions Caused by Nonlinear Op-Amp DC Gain for Switched-Capacitor Sigma–Delta Modulators

Op-amps are crucial components in sigma-delta modulators (SDMs). As device dimensions and supply voltages continue to scale down, it is increasingly critical to determine a suitable op-amp dc gain. If the dc gain is set too high, then the op-amp consumes too much power; if the dc gain is too small, then nonlinear distortion becomes serious. However, there exists no efficient approach for selecting dc gains. In this brief, we propose to use a nonlinear function to model nonlinear op-amp dc gain curves. Then, this nonlinear function is employed to derive an SDM nonlinear distortion model as a function of SDM system parameters. The obtained SDM nonlinear distortion model can subsequently be used to compute the minimum required op-amp dc gain such that nonlinear distortions are kept under a tolerable value. The nonlinear dc gain curve model and the SDM nonlinear distortion model proposed in this brief are verified by behavior simulations and transistor-level simulations.     

On the uniform-traffic capacity of single-hop interconnectionsemploying shared directional multichannels

A shared directional multichannel (SDM) consists of a set of inputs and a set of outputs to which transmitters and receivers respectively, are connected. A signal placed at any given input reaches a subset of the outputs, and a channel is specified by the sets of outputs that are reachable from each input. A message is received successfully at an output of the channel if and only if it is addressed to the receiver connected to that output and no other signals reach that output at the same time. Constructive lower bounds as well as some upper bounds on the uniform-traffic capacity of SDM-based single-hop interconnections between a set of multitransmitter source stations and a set of multireceiver destination stations are derived. A bidirectional interconnection among a set of stations can be obtained by representing each station as one source station and one destination station. It is shown that with randomized transmissions, SDMs that can be described as a collection of buses can perform as well as any other channels. With deterministic scheduling, however, the use of certain non-bus-oriented SDMs yields a much higher interconnection capacity     

Liquid Crystal Enabled Early Stage Detection of Beta Amyloid Formation on Lipid Monolayers

Liquid crystals (LCs) can serve as sensitive reporters of interfacial events, and this property has been used for sensing of synthetic or biological toxins. Here it is demonstrated that LCs can distinguish distinct molecular motifs and exhibit a specific response to beta‐sheet structures. That property is used to detect the formation of highly toxic protofibrils involved in neurodegenerative diseases, where it is crucial to develop methods that probe the early‐stage aggregation of amyloidogenic peptides in the vicinity of biological membranes. In the proposed method, the amyloid fibrils formed at the lipid–decorated LC interface can change the orientation of LCs and form elongated and branched structures that are amplified by the mesogenic medium; however, nonamyloidogenic peptides form ellipsoidal domains of tilted LCs. Moreover, a theoretical and computational analysis is used to reveal the underlying structure of the LC, thereby providing a detailed molecular‐level view of the interactions and mechanisms responsible for such motifs. The corresponding signatures can be detected at nanomolar concentrations of peptide by polarized light microscopy and much earlier than the ones that can be identified by fluorescence‐based techniques. As such, it offers the potential for early diagnoses of neurodegenerative diseases and for facile testing of inhibitors of amyloid formation.     

Spectral modeling of switched-mode power converters

A new modeling approach for the spectral analysis of pulsewidth modulated (PWM) converters with independent inputs is developed. The key of this approach is to extend the Volterra functional series to nonlinear systems with multiple independent inputs. After formulating the state-space equations describing the dynamical behavior of PWM converters, the Volterra transfer function characterizing the output frequency response can be obtained, which is then symmetrised to form the spectral model. Since the model is developed in a closed form, it is suitable for computer analysis. The modeling approach has been applied to various PWM converters, and the results are verified. The spectral models of different power converters can readily be obtained by using this general approach     

Local stability of the median LMS filter

Local stability properties of the median LMS adaptive filter are investigated by relating the behavior of the algorithm to the behavior of an associated ordinary differential equation. With independent inputs, the differential equation and the algorithm are shown to be locally stable. On the other hand, several classes of (periodic, nonindependent) inputs are described which cause the differential equation and the algorithm to be unstable about its equilibrium, even in the no disturbance case. This will help delineate those applications for which the median LMS is an appropriate adaptive algorithm     

Detection and Removal of Limit Cycles in Sigma Delta Modulators

Sigma delta modulation is a popular method for converting signals from analog to digital and vice-versa. However, sigma delta modulators (SDMs) may suffer from limit cycles, where the output bits may enter a repeating pattern. Current methods of preventing this phenomenon introduce unwanted noise, do not always succeed, and are often implemented when not needed. We present a more effective method for detecting and removing unwanted limit cycles. This method includes adding a small disturbance to the input, which destroys the periodicity of sigma-delta analog-to-digital conversion (ADC) modulator's output sequence and thereby removes the limit cycles. Compared with conventional methods this method is simpler to implement, and the SDM has less signal-to-noise ratio (SNR) penalty and a higher allowed input dynamic range. Various implementations of the limit cycle detection and removal schemes are described for feedforward SDMs. Results are reported which demonstrate the success of these methods.      

Quantizer Nonoverload Criteria in Sigma–Delta Modulators

A simple method to guarantee absolute stability in multibit sigma-delta modulators (SDMs) is to ensure that the quantizer never overloads. This applies to any SDM. Derivation of the requirements for nonoverload have previously been shown for different types of modulators; the sigma-delta or output-feedback modulator with rounding quantizer as well as the error-feedback modulator using truncation. Here, these nonoverload requirements will be clarified and a unified formulation is presented that is not limited with regard to modulator topology or quantizer function     

COMPARISON OF SIGMA-DELTA MODULATOR FOR FRACTIONAL-N PLL FREQUENCY SYNTHESIZER

This paper investigates the design of digital Sigma-Delta Modulator （SDM） for fractional-N frequency synthesizer. Characteristics of SDMs are compared through theory analysis and simulation. The curve of maximum-loop-bandwidth vs. maximum-phase-noise is suggested to be a new criterion to the performance of SDM, which greatly helps designers to select an appropriate SDM structure to meet their real application requirements and to reduce the cost as low as possible. A low-spur 3-order Multistage Noise Shaping （MASH）-1-1-1 SDM using three 2-bit first-order cascaded modulators is proposed, which balances the requirements of tone-free and maximum operation frequency.     

Alignment of liquid crystals on a topographically nano-patterned polymer surface prepared by a soft-imprint technique

In this study, we have fabricated polyacrylate substrates having a nano-patterned surface topography using a soft-imprint technique. The planar alignment of liquid crystals (LCs) along the direction of nanogrooves has been generated. Twisting behavior of nematic LCs has been also observed with a perpendicularly assembled LC cell and the cell parameters can be estimated by using the Soutar and Lu method. By comparing the anchoring energies obtained, accordingly, it has been demonstrated that the polymer nanogroove pattern has a comparable influence on LC alignment to the conventional rubbing process. It has been also shown that the artificial topography of the line grooves on the conventionally rubbed surface has a significant influence on the anchoring stability of the LC molecules.     

Preparation of poly (N-vinylcarbazole)-co-poly(2-(dimethylamino)ethyl methacrylate) based hydrogen bonded side-chain liquid crystal copolymer

In this study, new side chain liquid crystalline copolymers were prepared from N-vinyl carbazole (NVC) and 2-(Dimethylamino)ethyl methacrylate) (DMAEM) as a hydrogen bond acceptor copolymer and 8-(4-cyanobiphenyl-4′-oxy)octan-1-ol (LC8) by molecular self-assembly processes via hydrogen bond formation between nitrogen of (DMAEM) and hydroxyl group of the LC8. The formation of H bond was confirmed by using FTIR spectroscopy. The liquid crystalline behavior of the copolymers and homopolymer of the (DMAEM) was investigated using a differential scanning calorimeter (DSC) and polarized optical microscopy. The dielectric relaxation properties of H-bonded Side Chain LC Copolymers (HB-LCP) doped 8-(4-cyanobiphenyl-4′-oxy)octan-1-ol (LC8) and pure LC8 liquid crystals have been investigated by the dielectric spectroscopy (DS) method. The dielectric behavior of the LCs shows a dielectric relaxation process. The relaxation frequency of the LCs was changed by the addition of HB-PLC. It is evaluated that the dielectric strength and relaxation properties of LC8 and LC8/HB-PLC LCs can be controlled by 1% HB-PLC dopant.     

Analysis of 2-D state-space periodically shift-variant discrete systems

Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.This work was supported in part by a grant from the Colorado Advanced Software Institute.     

Digital Modeling and PID Controller Design for MIMO Analog Systems with Multiple Delays in States, Inputs and Outputs

This paper presents a discrete-time state-space methodology for the digital modeling and design of an optimal digital proportional-integral-derivative (PID) plus state-feedback controller for multiple-input, multiple-output (MIMO) continuous-time systems with multiple time delays in states, inputs and outputs. To implement the digital design, first the Chebyshev quadrature formula together with a linear interpolation method is employed to obtain an extended discrete-time state-space model from the continuous-time multiple time-delay system. Then, a partially predetermined digital PID controller and the extended discrete-time state-space model are formulated as an augmented discrete-time state-space system utilizing state-feedforward and state-feedback linear-quadratic regulator (LQR) design. As a result, the parameters of the optimal PID controller and its associated state-feedback controller can be determined by tuning the weighting matrices in the LQR performance criteria. Further, an optimal discrete-time observer is jointly constructed for the multivariable system with multiple delays in states, inputs and outputs. The proposed design methodology can be applied to general MIMO continuous-time multiple time-delay systems for performance improvement and disturbance rejection. An illustrative example is given to demonstrate the effectiveness of the developed method. This work was supported in part by U.S. Army Research Office under Grant W911NF-06-1-0507, the National Science Foundation under Grant NSF0717860, and Research Contract 1440234.     

Smectic Liquid Crystal Defects for Self‐Assembling of Building Blocks and Their Lithographic Applications

Recently, it has been reported that liquid crystal (LC) defects can be used to create highly periodic templates by controlling the surface anchoring and the elastic properties of LC molecules. The self‐assembled defect ordering of the LC materials takes advantage of the ability to achieve fast stabilization of molecular ordering and structure due to the reversible and non‐covalent interactions of the LC molecules. In this Featre Article, the defect structures of liquid crystalline materials will be demonstrated by the surface anchoring and elastic properties. A particular focus are the focal conic domains (FCDs) that are commonly observed in SmA liquid crystals and their lamellar lyotropic counterparts, which form periodic defect ordered structures. In addition, methodologies for creating lithographic templates from the defect order will be described. Finally, the review closes with a discussion of toric focal conic domain arrays that have been fabricated in this manner and used for various applications.     

A wideband CMOS sigma-delta modulator with incremental dataweighted averaging

A low-complexity high-speed circuit is proposed for the implementation of an incremental data weighted averaging (IDWA) technique used for reducing digital-to-analog converter (DAC) noise due to component mismatches. IDWA can achieve very good performance even when it is used with a low oversampling ratio (OSR), which reduces demands on circuit speed and power consumption. Therefore, the IDWA is highly suitable for wideband, low-power and small-area sigma-delta modulator (SDM) implementation. Incorporating the IDWA technique, a fourth-order feedforward (FF) SDM with an OSR of 12 and a 4-bit internal quantizer is implemented with a 2.5-V 0.25-μm CMOS process. Measurement results show that the SDM operating from a 2.5-V supply voltage can achieve respective dynamic ranges (DRs) of 84/80 dB and spurious-free dynamic ranges (SFDRs) of 90/85 dB with signal bandwidths of 1.25/2 MHz at sampling frequencies of 30/48 MHz. The power dissipation is less than 105 mW and the active area is 2.6 mm². Wider bandwidth, lower OSR, less power, and lower supply voltage are achieved compared with two recently published 3.3-V/3-V CMOS wideband SDMs with comparable SNDR performance     

Magnetic and Transparent Composites by Linking Liquid Crystals to Ferrite Nanoparticles through Covalent Networks

The fabrication of transparent, flexible, and optically homogeneous magnetic composites containing ferrite (Fe₃O₄) nanoparticles, liquid crystals (LCs), and siloxane backbones is reported. The transparent magnets are achieved by covalently bonding LCs to the siloxane backbones and then linking them to dopamine‐functionalized ferrite nanocrystals. They exhibit simultaneous high transparency and strong magnetic properties. A remarkable feature of these films is that the surface morphology of the LC‐attached ferrite films can be tuned by an external magnetic field, demonstrating a striped surface in the direction of the field. We show that the LC‐attached film can act as an alignment layer to orient LCs, enabling the development of LC alignment surfaces on the basis of these nanomagnet–LC polymer composites.     

Discotic Liquid Crystal‐Functionalized Gold Nanorods: 2‐ and 3D Self‐Assembly and Macroscopic Alignment as well as Increased Charge Carrier Mobility in Hexagonal Columnar Liquid Crystal Hosts Affected by Molecular Packing and π–π Interactions

Gold nanorods functionalized with triphenylene‐based discotic liquid crystal (LC) motifs show striking self‐assembly behavior both on transmission electron microscopy (TEM) grids as well as in the bulk enforced by the π–π‐stacking of triphenylene groups of adjacent nanorods. TEM images confirm that these discotic LC nanorods form ribbons of parallel‐stacked nanorods several hundred nanometer long. The pursued silane conjugation approach to decorate the nanorods allows for the preparation of dispersions of the nanorods in the hexagonal columnar phases of parent discotic LCs, where the nanorods can be macroscopically aligned with almost 80% efficiency by a simple shearing protocol. Doping the parent host materials with about 1% by weight of the discotic LC‐capped nanorods also reduces the lattice parameter and the intracolumnar packing, which gives rise to enhanced charge carrier mobility in these hosts as determined by time‐of‐flight measurements.     

Unprecedented Dual Alignment Mode and Freedericksz Transition in Planar Nematic Liquid Crystal Cells Doped with Gold Nanoclusters

We demonstrate that alkylthiol‐capped gold nanoclusters doped into nematic liquid crystals (N‐LCs) with positive dielectric anisotropy give rise to an unprecedented dual alignment mode and electro‐optical response, which has a potential impact on current liquid crystal (LC) display technologies and N‐LC optical‐biosensor design. By fine‐tuning experimental conditions (temperature, electric field, and alignment), N‐LCs doped with gold nanoclusters can be aligned and electrically reoriented either like N‐LCs with a positive dielectric anisotropy in a planar cell or, alternatively, as N‐LCs with a negative dielectric anisotropy in a homeotropic cell, both at lower threshold voltages than the pure N‐LC.     

Monotone Span Program vs.Linear Code

Monotone span program(MSP) and Linear code(LC) are efficient tools to construct Linear secret sharing scheme (LSSS) for a given access structure.Since the size of an MSP or the length of an LC corresponds to the communicational complexity of an LSSS,one main motivation to study MSPs or LCs is the lower bound for their sizes or lengths.Therefore,it is one of the most important open problems how to efficiently construct an MSP or LC for a given access structure Γ with the smallest sizes or shortest length.Our contributions are:We extend TANG et al.'s result,showing that,for any given access structure Γ,there exists an MSP or an LC to realizeΓ if and only ifa system of quadratic equations has solutions;We utilize the relationship between LCs and MSPs to obtain the greatest lower bound on the row size and the column size of MSPs realizing a given Γ,as well as an upper bound on the column size of MSPs;We give an algorithm to construct an MSP with the smallest sizes.