Construction of isodual codes from polycirculant matrices

Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can only occur over \F_2 in the double circulant case. Building on an explicit infinite sequence of irreducible trinomials over \F_2, we show that binary double polycirculant codes are asymptotically good

Estimating the Power Bus Impedance of Printed Circuit Boards with Embedded Capacitance

Embedded capacitance is an alternative to discrete decoupling capacitors and is achieved by enhancing the natural capacitance between closely spaced power and return planes. This paper employs a simple cavity model to investigate the features affecting the power bus impedance of printed circuit boards with embedded capacitance

The Development of a Closed-form Expression for the Input Impedance of Power-return Plane Structures

In multilayer printed circuit boards, the noise on the power bus is influenced by the impedance between the power and ground planes. Power-bus noise estimates require an accurate estimate of the power-bus input impedance. This paper develops a closed-form estimate of the input impedance for circular power-return plane structures. When the structure is lossy (e.g., boards employing embedded capacitance or densely populated boards), the energy reflected from the board edge does not significantly affect the input impedance. In general, the expressions developed here for circular structures can be used to estimate the impedance of lossy power-return plane structures of any shape

Application of the Cavity Model to Lossy Power-Return Plane Structures in Printed Circuit Boards

Power-return plane pairs in printed circuit boards are often modeled as resonant cavities. Cavity models can be used to calculate transfer impedance parameters used to predict levels of power bus noise. Techniques for applying the cavity model to lossy printed circuit board geometries rely on a low-loss assumption in their derivations. Boards that have been designed to damp power bus resonances (e.g., boards with embedded capacitance) generally violate this low-loss assumption. This paper investigates the validity of the cavity model when applied to printed circuit board structures where the board resonances are significantly damped. Cavity modeling results for sample lossy power-return plane structures are validated using a three-dimensional full wave numerical code. A simple method is also established to check the validity of the cavity model for a power-return plane structure with imperfect conductors and lossy dielectric substrates

LCD Codes from tridiagonal Toeplitz matrice

Double Toeplitz (DT) codes are codes with a generator matrix of the form $(I,T)$ with $T$ a Toeplitz matrix, that is to say constant on the diagonals parallel to the main. When $T$ is tridiagonal and symmetric we determine its spectrum explicitly by using Dickson polynomials, and deduce from there conditions for the code to be LCD. Using a special concatenation process, we construct optimal or quasi-optimal examples of binary and ternary LCD codes from DT codes over extension fields.Comment: 16 page

Impedance Boundary Conditions in a Hybrid FEM/MOM Formulation

When numerically modeling structures with imperfect conductors or conductors coated with a dielectric material, impedance boundary conditions (IBCs) can substantially reduce the amount of computation required. This paper incorporates the IBC in the finite-element method (FEM) part of a FEM/method of moments (FEM/MoM) modeling code. Properties of the new formulation are investigated and the formulation is used to model three practical electromagnetic problems. Results are compared to either measured data or other numerical results. The effect of the IBC on the condition number of hybrid FEM/MoM matrices is also discussed

DEVELOPMENT OF A LOADING DEVICE FOR IMAGING RABBIT MCL ENTHESES WITH SECOND HARMONIC GENERATION MICROSCOPY

INTRODUCTION Entheses are transitional structures in the body between a flexible material and a much stiffer material: ligament and bone, respectively. A gradual transition of mineral content and collagen fibre organization enables the enthesis to dissipate stress concentrations and transfer load between the adjoining elements, contributing to normal joint function [1]. Damage to this small region is associated with conditions like tennis elbow and jumper’s knee. Enthesis tears do not repair well, causing long term weakness. To date, the challenge of observing entheses under applied load has inhibited understanding of their mechanical behaviour. Second Harmonic Generation (SHG) microscopy is a technology that can be used to image highly polarizable proteins like collagen without the need for section fixation or molecular excitation [2]. Given that collagen fibre structure affects load transfer at entheses, SHG microscopy is an ideal tool to elucidate the fibre structure at MCL entheses. The purpose of the project described was to develop a custom device to allow observation of the collagen fibre network of the rabbit medial collateral ligament (MCL) enthesis in the SHG microscope as tensile load is applied. METHODS After generating a morphological chart of alternative solutions, the optimal option was chosen based on project requirements. The design was created with CAD software (SolidWorks 2015) and where possible, the proposed design was modified to optimize objectives— minimizing cost and maximizing movement accuracy. With CAD, it is easy to modify components of a model while assessing its impact on the model as a whole. RESULTS In the final design, the rabbit bones can be secured to bone pots at a physiological angle of 70°, with the MCL in the line of action of the applied force. One bone pot remains stationary as the other, sliding on rail guides which constrain pot movement, is pulled by a linear actuator. A custom load cell will collect force data as the load is applied. For its light-weight property and potential to be scanned using MRI, Perspex is the material of choice for the device. The completed design, shown in Figure 1, satisfies all the requirements previously established and requires only one hand for operation. This model allows for a testing procedure simulating physiological conditions while maximizing accuracy of the recorded data through incorporating rail guides and making use of a linear actuator. DISCUSSION AND CONCLUSIONS With some minor modifications to the bone pots, this device can be used as a reference product for the study of other tissues under load. However, it would be worthwhile to consider interchanging the bone pots between uses since the bone cement is difficult to remove. The small size of entheses has stymied researchers’ efforts to characterize their inhomogeneous material behavior. However, this device will enable the observation of collagen fibre behaviour under load, which will provide insight into mechanisms of load transfer in the enthesis and in time, contribute to improved surgical attachment procedures

Redesigning spectroscopic sensors with programmable photonic circuits

Optical spectroscopic sensors are a powerful tool to reveal light-matter interactions in many fields, such as physics, biology, chemistry, and astronomy. Miniaturizing the currently bulky spectrometers has become imperative for the wide range of applications that demand in situ or even in vitro characterization systems, a field that is growing rapidly. Benchtop spectrometers are capable of offering superior resolution and spectral range, but at the expense of requiring a large size. In this paper, we propose a novel method that redesigns spectroscopic sensors via the use of programmable photonic circuits. Drawing from compressive sensing theory, we start by investigating the most ideal sampling matrix for a reconstructive spectrometer and reveal that a sufficiently large number of sampling channels is a prerequisite for both fine resolution and low reconstruction error. This number is, however, still considerably smaller than that of the reconstructed spectral pixels, benefitting from the nature of reconstruction algorithms. We then show that the cascading of a few engineered MZI elements can be readily programmed to create an exponentially scalable number of such sampling spectral responses over an ultra-broad bandwidth, allowing for ultra-high resolution down to single-digit picometers without incurring additional hardware costs. Experimentally, we implement an on-chip spectrometer with a fully-programmable 6-stage cascaded MZI structure and demonstrate a 200 nm bandwidth using only 729 sampling channels. This achieves a bandwidth-to-resolution ratio of over 20,000, which is, to our best knowledge, about one order of magnitude greater than any reported miniaturized spectrometers to date. We further illustrate that by employing dispersion-engineered waveguide components, the device bandwidth can be extended to over 400 nm

Development of a Closed-Form Expression for the Input Impedance of Power-ground Plane Structures

This paper analyzes the fundamental behavior of PCB power bus structures using the modal expansion method. The results are validated by experiments and full-wave numerical modeling. It is shown that the power bus can be modeled as a series LeC circuit below the first board resonance frequency. C is the interplane capacitance and Le is an effective inductance contributed by all the cavity nodes. The effects of the layer thickness, port location, board size and the feeding wire radius on the value of Le are discussed in this study. Le can be estimated from the geometry parameters of the test board. The goal is to obtain a simple model that can be used to analyze the power bus impedance below the first board resonance

Power-Bus Decoupling with Embedded Capacitance in Printed Circuit Board Design

This paper experimentally investigates the effectiveness of embedded capacitance for reducing power-bus noise in high-speed printed circuit board designs. Boards with embedded capacitance employ closely spaced power-return plane pairs separated by a thin layer of dielectric material. In this paper, test boards with four embedded capacitance materials are evaluated. Power-bus input impedance measurements and power-bus noise measurements are presented for boards with various dimensions and layer stack ups. Unlike discrete decoupling capacitors, whose effective frequency range is generally limited to a few hundred megahertz due to interconnect inductance, embedded capacitance was found to efficiently reduce power-bus noise over the entire frequency range evaluated (up to 5 GHz)