Digital waveguide modeling for wind instruments: building a state-space representation based on the Webster-Lokshin model

This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations for the refined acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature). The purpose of this work is to build low-cost digital simulations in the time domain based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a Kelly-Lochbaum network of input/output systems and delays. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in the time domain. The method is applied to a real trombone, and results of simulations are presented and compared with measurements. This method seems to be a promising approach in term of modularity, complexity of calculation and accuracy, for any acoustic resonators based on tubes

Efficient Synthesis of Room Acoustics via Scattering Delay Networks

An acoustic reverberator consisting of a network of delay lines connected via scattering junctions is proposed. All parameters of the reverberator are derived from physical properties of the enclosure it simulates. It allows for simulation of unequal and frequency-dependent wall absorption, as well as directional sources and microphones. The reverberator renders the first-order reflections exactly, while making progressively coarser approximations of higher-order reflections. The rate of energy decay is close to that obtained with the image method (IM) and consistent with the predictions of Sabine and Eyring equations. The time evolution of the normalized echo density, which was previously shown to be correlated with the perceived texture of reverberation, is also close to that of IM. However, its computational complexity is one to two orders of magnitude lower, comparable to the computational complexity of a feedback delay network (FDN), and its memory requirements are negligible

An Early History of Optimization Technology for Automated Design of Microwave Circuits

This paper outlines the early history of optimization technology for the design of microwave circuits—a personal journey filled with aspirations, academic contributions, and commercial innovations. Microwave engineers have evolved from being consumers of mathematical optimization algorithms to originators of exciting concepts and technologies that have spread far beyond the boundaries of microwaves. From the early days of simple direct search algorithms based on heuristic methods through gradient-based electromagnetic optimization to space mapping technology we arrive at today’s surrogate methodologies. Our path finally connects to today’s multi-physics, system-level, and measurement-based optimization challenges exploiting confined and feature-based surrogates, cognition-driven space mapping, Bayesian approaches, and more. Our story recognizes visionaries such as William J. Getsinger of the 1960s and Robert Pucel of the 1980s, and highlights a seminal decades-long collaboration with mathematician Kaj Madsen. We address not only academic contributions that provide proof of concept, but also indicate early formative milestones in the development of commercially competitive software specifically featuring optimization technology.ITESO, A.C

Design Optimization of Full-Wave EM Models by Low-Order Low-Dimension Polynomial Surrogate Functionals

A practical formulation for EM-based design optimization of high-frequency circuits using simple polynomial surrogate functionals is proposed in this paper. Our approach starts from a careful selection of design variables and is based on a closed-form formulation that yields global optimal values for the surrogate model weighting factors, avoiding a large set of expensive EM model data, and resulting in accurate low-order low-dimension polynomials interpolants that are used as vehicles for efficient design optimization. Our formulation is especially suitable for EM-based design problems with no equivalent circuital models available. The proposed technique is illustrated by the EM-based design optimization of a Ka-band substrate integrated waveguide (SIW) interconnect with conductor-backed coplanar waveguide (CBCPW) transitions, a low crosstalk PCB microstrip interconnect structure with guard traces, and a 10-40 GHz SIW interconnect with microstrip transitions on a standard FR4-based substrate. Three commercially available full-wave EM solvers are used in our examples: CST, Sonnet and COMSOL

Physical Layer Modeling and Optimization of Silicon Photonic Interconnection Networks

The progressive blooming of silicon photonics technology (SiP) has indicated that optical interconnects may substitute the electrical wires for data movement over short distances in the future. Silicon Photonics platform has been the subject of intensive research for more than a decade now and its prospects continue to emerge as it enjoys the maturity of CMOS manufacturing industry. SiP foundries all over the world and particularly in the US (AIM Photonics) have been developing reliable photonic design kits (PDKs) that include fundamental SiP building blocks such as wavelength selective modulators and tunable filters. Microring resonators (MRR) are hailed as the most compact devices that can perform both modulation and demodulation in a wavelength division multiplexed (WDM) transceiver design. Although the use of WDM can reduce the number of fibers carrying data, it also makes the design of transceivers challenging. It is probably acceptable to achieve compactness at the expense of somewhat higher transceiver cost and power consumption. Nevertheless, these two metrics should remain close to their roadmap values for Datacom applications. An increase of an order of magnitude is clearly not acceptable. For example costs relative to bandwidth for an optical link in a data center interconnect will have to decrease from the current $5/Gbps down to <$1/Gbps. Additionally, the transceiver itself must remain compact. The optical properties of SiP devices are subject to various design considerations, operation conditions, and optimization procedures. In this thesis, the general goal is to develop mathematical models that can accurately describe the thermo-optical and electro-optical behavior of individual SiP devices and then use these models to perform optimization on the parameters of such devices to maximize the capabilities of photonic links or photonic switch fabrics for datacom applications. In Chapter 1, Introduction, we first provide an overview of the current state of the optical transceivers for data centers and datacom applications. Four main categories for optical interfaces (Pluggable transceivers, On-board optics, Co-packaged optics, monolithic integration) are briefly discussed. The structure of a silicon photonic link is also briefly introduced. Then the direction is shifted towards optical switching technologies where various technologies such as free space MEMS, liquid crystal on silicon (LCOS), SOA-based switches, and silicon-based switches are explored. In Chapter 2, Silicon Photonic Waveguides, we present an extensive study of the silicon-on-insulator (SOI) waveguides that are the basic building blocks of all of the SiP devices. The dispersion of Si and SiO2 is modeled with Sellmiere equation for the wavelength range 1500–1600 nm and then is used to calculate the TE and TM modes of a 2D slab waveguide. There are two reasons that 2D waveguides are studied: first, the modes of these waveguides have closed form solutions and the modes of 3D waveguides can be approximated from 2D waveguides based on the effective index method. Second, when the coupling of waveguides is studied and the concept of curvature function of coupling is developed, the coupled modes of 2D waveguides are used to show that this approach has some inherent small error due to the discretization of the nonuniform coupling. This chapter finishes by describing the coefficients of the sensitivity of optical modes of the waveguides to the geometrical and material parameters. Perturbation theory is briefly presented as a way to analytically examine the impact of small perturbations on the effective index of the modes. In Chapter 3, Compact Modeling Approach, the concept of scattering matrix of a multi-port silicon photonic device is presented. The elements of the S-matrix are complex numbers that relate the amplitude and phase relationships of the optical models in the input and output ports. Based on the scattering matrix modeling of silicon photonics devices, two methods of solving photonic circuits are developed: the first one is based on the iteration for linear circuits. The second approach is based on the construction of an equivalent signal flow graph (SFG) for the circuit. We show that the SFG approach is very efficient for circuits involving microring resonator structures. Not only SFG can provide the solution for the transmission, it also provides the signal paths and the closed-form solution based on the Mason’s graph formula. We also show how the SFG method can be utilized to formulate the backscattering effects inside a ring resonator. In Chapter 4, Scalability of Silicon Photonic Switch Fabrics, we develop the models for electro-optic Mach-Zehnder switch elements (2×2). For the electro-optic properties, the empirical Soref’s equations are used to characterize how the loss and index of silicon changes when the charge carrier density is changed. We then use our photonic circuit solver based on the iteration method to find accurate result of light propagation in large-scale switch topologies (e.g. 4×4, and 8×8). The concept of advanced path mapping based on physical layer evaluation of the switch fabric is introduced and used to develop the optimum routing tables for 4×4 and 8×8 Benes switch topologies. In Chapter 5, Design space of Microring Resonators, we introduce the concept of curvature function of coupling to mathematically characterize the coupling coefficient of a ring resonator to a waveguide as a function of the geometrical parameters (ring radius, coupling gap, width and height of waveguides) and the wavelength. Extensive 2D and 3D FDTD simulations are carried out to validate our modeling approach. Experimental demonstrations are also used to not only further validate our modeling of coupling, but also to extract an empirical power-law model for the bending loss of the ring resonators as a function the radius. By combining these models, we for the first time present a full characterization of the design space of microring resonators. Moreover, the value of this discussion will be further apparent when the scalability of a silicon photonic link is studied. We will show that the FSR of the rings determines the optical bandwidth but it also impacts the properties of the ring resonators. In Chapter 6, Thermo-optic Efficiency of Microheaters, we develop analytical models for the thermo-optic properties of SiP waveguides. For the thermo-optic properties, the concept of thermal impulse response is mathematically developed for integrated micro-heaters. The thermal impulse response is a key function that determines the tradeoff between heating efficiency and heating speed (thermal bandwidth), as well as allows us to predict the pulse-width-modulation (PWM) optical response of the heater-waveguide system. One of the motivations behind this study was to find the highest possible efficiency for thermal tuning of microring resonators to use it in the evaluation of the energy consumption of a photonic link. The results indicate 2 nm/mW which is in agreement with the trends that we see in the literature. In Chapter 7, Crosstalk Penalty, we theoretically and experimentally investigate the optical crosstalk effects in microring-based silicon photonic interconnects. Both inter-channel crosstalk and intra-channel crosstalk are investigated and approximate equations are developed for their corresponding power penalties. Inclusion of the inter-channel crosstalk is an important part of our final analysis of a silicon photonic link. In Chapter 8, Scalability of Silicon Photonic Links, we present the analysis of a WDM silicon photonics point-to-point link based on microring modulators and microring wavelength filters. Our approach is based on the power penalty analysis of non-return-to-zero (NRZ) signals and Gaussian noise statistics. All the necessary equations for the optical power penalty calculations are presented for microring modulators and filters. The first part of the analysis is based on various ideal assumptions which lead to a maximum capacity of 2.1 Tb/s for the link. The second part of the analysis is carried out with more realistic assumptions on the photonic elements in the link, culminating in a maximum throughput of 800 Gb/s. We also provide estimations of the energy/bit metric of such links based on the optimized models of electronic circuits in 65 nm CMOS technology

Advanced RF and Microwave Design Optimization: A Journey and a Vision of Future Trends

In this paper, we outline the historical evolution of RF and microwave design optimization and envisage imminent and future challenges that will be addressed by the next generation of optimization developments. Our journey starts in the 1960s, with the emergence of formal numerical optimization algorithms for circuit design. In our fast historical analysis, we emphasize the last two decades of documented microwave design optimization problems and solutions. From that retrospective, we identify a number of prominent scientific and engineering challenges: 1) the reliable and computationally efficient optimization of highly accurate system-level complex models subject to statistical uncertainty and varying operating or environmental conditions; 2) the computationally-efficient EM-driven multi-objective design optimization in high-dimensional design spaces including categorical, conditional, or combinatorial variables; and 3) the manufacturability assessment, statistical design, and yield optimization of high-frequency structures based on high-fidelity multi-physical representations. To address these major challenges, we venture into the development of sophisticated optimization approaches, exploiting confined and dimensionally reduced surrogate vehicles, automated feature-engineering-based optimization, and formal cognition-driven space mapping approaches, assisted by Bayesian and machine learning techniques.ITESO, A.C

Contributions to discrete-time methods for room acoustic simulation

The sound field distribution in a room is the consequence of the acoustic properties of radiating sources and the position, geometry and absorbing characteristics of the surrounding boundaries in an enclosure (boundary conditions). Despite there existing a consolidated acoustic wave theory, it is very difficult, nearly impossible, to find an analytical expression of the sound variables distribution in a real room, as a function of time and position. This scenario represents as an inhomogeneous boundary value problem, where the complexity of source properties and boundary conditions make that problem extremely hard to solve. Room acoustic simulation, as treated in this thesis, comprises the algebraical approach to solve the wave equation, and the way to define the boundary conditions and source modeling of the scenario under analysis. Numerical methods provide accurate algorithms for this purpose and among the different possibilities, the use of discrete-time methods arises as a suitable solution for solving those partial differential equations, particularized by some specific constrains. Together with the constant growth of computer power, those methods are increasing their suitability for room acoustic simulation. However, there exists an important lack of accuracy in the definition of some of these conditions so far: current frequency-dependent boundary conditions do not comply with any physical model, and directive sources in discrete-time methods have been hardly treated. This thesis discusses about the current state-of-the-art of the boundary conditions and source modeling in discrete-time methods for room acoustic simulation, and it contributes some algorithms to enhance boundary condition formulation, in a locally reacting impedance sense, and source modelling in terms of directive sources under a defined radiation pattern. These algorithms have been particularized to some discrete-time methods such as the Finite Difference Time Domain and the Digital Waveguide Mesh.Escolano Carrasco, J. (2008). Contributions to discrete-time methods for room acoustic simulation [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8309Palanci

The Telecommunications and Data Acquisition Report

This quarterly publication provides archival reports on developments in programs in space communications, radio navigation, radio science, and ground-based radio and radar astronomy. It reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standardization activities at the Jet Propulsion Laboratory for space data and information systems

Gradient Optics of subwavelength nanofilms

Propagation and tunneling of light through subwavelength photonic barriers, formed by dielectric layers with continuous spatial variations of dielectric susceptibility across the film are considered. Effects of giant heterogeneity-induced non-local dispersion, both normal and anomalous, are examined by means of a series of exact analytical solutions of Maxwell equations for gradient media. Generalized Fresnel formulae, visualizing a profound influence of gradient and curvature of dielectric susceptibility profiles on reflectance/transmittance of periodical photonic heterostructures are presented. Depending on the cutoff frequency of the barrier, governed by technologically managed spatial profile of its refractive index, propagation or tunneling of light through these barriers are examined. Nonattenuative transfer of EM energy by evanescent waves, tunneling through dielectric gradient barriers, characterized by real values of refractive index, decreasing in the depth of medium, is shown. Scaling of the obtained results for different spectral ranges of visible, IR and THz waves is illustrated. Potential of gradient optical structures for design of miniaturized filters, polarizers and frequency-selective interfaces of subwavelength thickness is considered