Circuit extraction via time-domain vector fitting

The finite difference time domain method and finite element methods have proven to be highly effective techniques for the full wave analysis of microwave circuits and resonators. The finite difference time domain (FDTD) method is highly efficient, explicit and parallelizable. Finite element methods have been used in the frequency domain and in the time domain using implicit methods. Implicit methods require a solution of a linear system of equations at each time step. For the finite element time domain (FETD) algorithm to be competitive with the FDTD, the number of time iterations required for a simulation must be significantly less. An unconditionally stable FETD algorithm is used. The variational formulation is based on the vector wave equation. Unconditional stability is achieved by using a modified Newmark-Beta time integration technique. In addition, this algorithm is implemented on parallel message passing computers using a finite element tearing and interconnecting scheme. Some numerical examples based on cavity resonator problems are presented to demonstrate the efficiency and accuracy of the method and the parallel efficiency of the algorithm.

Context. Today, there is a rapid expansion of the range of modern branches of science and technology, which actively use satellite telecommunication systems to receive, process and transmit various information. These radioelectronic systems quite often require an increase of the volumes of information, which they are processing and transmitting. Increase of the volumes of transmitted information in two times can be achieved by using dual-polarization antenna systems and devices. Nowadays, most part of the specialists, who are engaged in the development of various modern polarization-processing microwave devices, carry out their numerical modeling and optimization using variational techniques, methods of integral equations, method of fields matching in partial regions. The methods with division of the internal region of the device into elementary cells are applied most actively. Among them in the time domain the most often used approach is finite difference method with the decomposition at hexagonal mesh, while and in the frequency domain the finite elements method with the adaptive tetrahedral mesh is applied. Therefore, the estimation of the speed and accuracy of these methods with the purpose of determination of more effective among them is a relevant problem. Objective. The goal of the research is comparison of speed and accuracy of the calculations of electromagnetic characteristics of waveguide polarizers using FEM and FDTD methods, as well as the comparison of the convergence of these methods for the analysis of polarization-processing microwave devices with diaphragms. Method. For the calculations and analysis of electromagnetic characteristics in the article we used the method of finite differences in the time domain (FDTD) and the method of finite elements in the frequency domain (FEM). In FEM the volume is split into the tetrahedral mesh cells. In FDTD the computational domain is divided into hexagonal mesh cells. Results. It was found that the convergence of voltage standing wave ratio for the waveguide polarizer is fast for both methods. It was obtained that the convergence of the characteristics of differential phase shift, axial ratio, and crosspolar discrimination of the developed microwave device turned out to be much more sensitive to the number of mesh cells used. Moreover, in the research it was obtained by calculations that the computation time by the finite elements method in the frequency domain is more than 2 times less than the corresponding time required for calculations by the finite difference time domain method. When using the finite elements method in the frequency domain the corresponding number of tetrahedral mesh cells is 10 times less than the number of hexagonal mesh cells, which are used in the finite difference time domain method. Conclusions. Performed investigations have shown that FEM in the frequency domain, which applies an adaptive tetrahedral mesh, is more efficient than the FDTD method for the calculations of phase and polarization characteristics of modern waveguide polarizers and other microwave devices for various applications.

While fractal boundaries and their ability to describe irregularity have been intensively studied, only a few studies are available on wave propagation in a medium where a fractal or quasi fractal pattern is embedded. Acoustical propagation in 1D or 2D domains can be modeled using Time Domain Finite Differences or in Frequency domain with Finite element methods. The fractal object is then considered as a subwavelength set of scatterers, and the problem becomes a multiple scattering one leading to acoustic localization. So, as some important part of the energy remains trapped inside the fractal pattern, imaging such a medium becomes difficult and imaging such complex media with classical tools as B-scan or comparable methods is not sufficient. The resolution of the inverse problem of wave propagation can then be achieved with the help of the more efficient imaging methods related with Time Reversal. Using the concept of topological derivative as defined in Time Domain Topological Energy and Fast Topological Imaging Method, respectively, in Time domain and Frequency domain is powerful in that case. Examples in 1D and 2D will be presented including the image obtained for a sliced sponge.

This paper presents an efficient hybrid method consisting of finite-difference time-domain (FDTD) method, transmission line (TL) equations, and a novel time-domain S -parameter cascade (TD-SC) technique, which can be directly applied in time domain for the EMI analysis of transmission line network (TLN) in shielded electronic device excited by ambient electromagnetic wave. The FDTD method combined with an auto mesh generator is utilized to model the shielded structure of an arbitrary electronic device rapidly, and obtain the excitation fields of the TLN exactly. Then, the TD-SC technique based on TL equations, FDTD method, and S parameter of circuits is proposed for the further EMI analysis of the TLN consisting of multistage TLs and circuits. It has the advantage of without modeling the fine structures of TLs and circuits directly. Numerous examinations exhibit that this hybrid method is an efficient method for the EMI analysis of TLN by comparing with a three-dimensional FDTD method. The computation time and memory cost by this hybrid method is much less than that of the FDTD method, because the hybrid method provides a fast way to compute the transient responses on TLN in which the TLs and circuits do not need to be meshed.

Heart period variability has been considered for clinical assessment of autonomic function, determining the presence of haemorrhage or disease states, and for predicting mortality from traumatic injury. However, for heart period variability to be clinically useful, a number of important methodological issues should be addressed, including the minimum number of R-R intervals (RRI) required for accurate derivation, and the reproducibility of these metrics. ECGs were recorded for > or =10 min in 18 resting, supine subjects (12 M/6 F; 19-55 years). Heart period variability analyses included 21 time, frequency and complexity domain metrics. For assessment of minimum RRIs required, measurements were made from ECG recordings of 5 min down to 30 s for time and frequency domain metrics, and from 800 RRIs down to 100 RRIs for complexity metrics, by methodical truncation of the data set. Inter-subject variability was assessed by calculating the range and co-efficient of variation (%CV) across all subjects. Two independent 30 s or 100 RRI ECG segments were used to assess intra-subject variability via calculation of %CV in each subject. Six time and frequency domain metrics were robust down to 30 s of data, while five complexity metrics were robust down to 100 RRIs. All time and frequency domain metrics (except for RRI) exhibited high inter-subject variability (CVs > or = 30.0%), while five of eleven complexity metrics displayed low inter-subject variability (CVs < or = 8.5%). In the assessment of intra-subject variability in metrics valid with 30 s or 100 RRIs of ECG, only one time domain and four complexity metrics had CVs < 10%. Metrics that are highly reproducible and require few RRIs are advantageous for patient monitoring as less time is required to assess physiological status and initiate early interventions. Based on our analyses from healthy, resting humans, we have identified a select cohort of heart period variability metrics that performed well in regards to these two criteria.

Based on a novel multidimensional deconvolution algorithm (MDA), this paper proposes a time-domain approach to synthesize the broadband SPICE-compatible macromodels of coupled interconnects. The multiple conductor interconnects are excited either experimentally by TDR or numerically by the step-like source in finite difference time domain (FDTD) method. According to the time-domain scattered data, the macromodel of the interconnect can be efficiently extracted by cascading several configuration-oriented coupled transmission lines (CCTL). Two examples are used to demonstrate the validity of the proposed approach. One is the equivalent models for differential pairs crossing an asymmetrical ground slot. The other is the crosstalk behavior prediction for a three-coupled microstrip line. The accuracy in broadband frequency range of the synthesized models of these two examples are checked both in time and frequency domain and compared with the direct-FDTD simulation. The agreement is favorably good.

We review some recent extensions of the Finite Integration Technique (FIT), which is known to be a generalization of the Finite Difference Time Domain (FDTD) method. Some shortcomings of the standard formulation are discussed which limit the applicability or at least the efficiency of the time domain variant of FIT. The novel developments which are proposed in this paper cover both the basic geometrical modeling in space and time and advanced methods to solve the algebraic problems in time and frequency domain. A numerical application is presented to demonstrate the performance of the algorithms in the high frequency regime.KeywordsModel Order ReductionFinite Difference Time DomainCartesian GridTriangular GridImpedance MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Third order time and frequency analysis has exhibited great potential for correlation analysis of multi-sensor datasets, but is usually presented as separate time domain and frequency domain approaches. A combined framework of both frequency domain and time domain has rarely been used. This paper proposes a non-parametric third order time and frequency domain framework which used two dimensional Fourier transforms to bridge the gap between time domain and frequency domain. A unified framework offers flexibility and efficiency to apply to data. In this paper we study neural spike train data treated as stochastic point processes. In time domain direct analysis, third order cumulant densities of spike trains are applied, which need all first-, secondand third order product densities to be calculated before constructing the third order cumulant density, which brings additional challenges. The novelty in this study is that a new framework is proposed which can offer an alternative approach without calculating lower order quantities and can reveal nonlinear relationship between neural recordings. The results show that the present framework provides a novel non-parametric method to estimate both time and frequency domain measurements which is applicable to neural spike trains.

R wave is short for Rayleigh wave. R wave,on which the effect of gravity is generally inevitable,has received considerably extensive attention and been widely used in many fields,such as geological exploration,nondestructive test,etc. The effects of gravity on R wave velocity for elastic parameters were further analyzed based on available R wave velocity function,and the applicable range of the approximate one was given as well. Wave propagation through quasi-half-space isotropic linear elastic medium with gravity,under the excitation of differentiated Gaussian pulse( DGP) was studied by finite difference time domain( FDTD) method with staggered grid discretization,and extended boundary conditions were introduced.Velocity values obtained were closer to the theoretical ones. Meanwhile,the influence of gravity on time domain,frequency domain response was discussed. By analyzing the theoretical and numerical results,it is necessary to take the effect of gravity into account in simulation for more accurate prediction.

Near to Far zone transformation can be performed by integration of the equivalent electric and magnetic currents originating from scattered electric and magnetic fields on a surface enclosing the object. This can be done with finite difference time domain and frequency domain. In this way, near zone fields can be computed by finite difference time domain and conversion of near zone to far zone can be done in frequency domain. This method combines the accuracy of time domain in near zone and speed of computation in frequency domain to convert near zone to far zone.

Summary form only given. Currently High-Power Microwave (HPM) systems make use of antennas to radiate the generated microwave pulse. Typically, HPM sources generate a single or dominant frequency with a pulse duration of several hundred microwave cycles. Typically, these antenna systems are calibrated or verified with a frequency domain technique using a Continuous Wave (CW) signal. The radiating system vacuum window or radome may be designed for the dominant frequency of the HPM source. However, the antenna/radome system may not properly accommodate the finite frequency bandwidth due to the finite pulse length or frequency variation. These finite microwave packet size issues can now be accommodated both computationally and experimentally. We will be presenting data comparing frequency domain and time domain simulations, along with experiments. The frequency domain simulations are done with the High Frequency Structure Simulator (HFSS), while the time domain simulations will be done with a Finite-Difference-Time-Domain (FDTD) code such as ICEPIC or VOLMAX. The experiments will compare the standard frequency domain measurements done with a Vector Network Analyzer, while the time domain measurements will be done with packets generated with a CW oscillator and an Arbitrary Waveform Generator (AWG). An example antenna/radome system is our existing Vlasov Antenna and fiberglass belljars. We will also be making use of a TEM to TM/sub 01/ launcher, which has a measured return loss of -20 dB over the frequency range of 1.1 to 1.6 GHz.

BackgroundIn investigations of the human motor system, two approaches are generally employed toward the identification of common modulating drives from motor unit recordings. One is a frequency domain method and uses the coherence function to determine the degree of linear correlation between each frequency component of the signals. The other is a time domain method that has been developed to determine the strength of low frequency common modulations between motor unit spike trains, often referred to in the literature as 'common drive'.MethodsThe relationships between these methods are systematically explored using both mathematical and experimental procedures. A mathematical derivation is presented that shows the theoretical relationship between both time and frequency domain techniques. Multiple recordings from concurrent activities of pairs of motor units are studied and linear regressions are performed between time and frequency domain estimates (for different time domain window sizes) to assess their equivalence.ResultsAnalytically, it may be demonstrated that under the theoretical condition of a narrowband point frequency, the two relations are equivalent. However practical situations deviate from this ideal condition. The correlation between the two techniques varies with time domain moving average window length and for window lengths of 200 ms, 400 ms and 800 ms, the r2 regression statistics (p < 0.05) are 0.56, 0.81 and 0.80 respectively.ConclusionsAlthough theoretically equivalent and experimentally well correlated there are a number of minor discrepancies between the two techniques that are explored. The time domain technique is preferred for short data segments and is better able to quantify the strength of a broad band drive into a single index. The frequency domain measures are more encompassing, providing a complete description of all oscillatory inputs and are better suited to quantifying narrow ranges of descending input into a single index. In general the physiological question at hand should dictate which technique is best suited.

We describe the main properties of the EQUATOR airborne geophysical system and how the system can be employed to solve some engineering and environmental problems. To date, the EQUATOR system has been used for groundwater search in 2014 and 2015 in Siberia. The name “EQUATOR” originates from the intention to EQUATE, or to balance time and frequency domain approaches in airborne electromagnetics, which is why the system was originally designed. To the best of our knowledge, EQUATOR is the only system to collect electromagnetic data both in time and in frequency domains. We further explain the difference between the two methods on some numerical and field examples. Also we describe some advantages of their coupling. In particular, by virtue of our approach, a numerically more robust solution of the one-dimensional electromagnetic inverse problem may be achieved. The recorded full-time measurements are further converted to in-phase, quadrature and off-time responses, as opposed to standard frequency or time domain solutions, which have been widely adapted within the industry. When inverting the data, our main focus is within the top 100 m of the Earth, which are the most relevant for engineering and environmental studies. We emphasize that a combined use of frequency and time domain data gives more detailed information about geological structures in the near-surface. As an example, we present some case studies obtained over a platform (Siberia) and a crystalline shield (Western Africa) setting. We further suggest using these results in such near-surface studies as sediment thickness estimation, soil state analysis, groundwater search, and geological structural analysis.

This chapter discusses important issues related to the quality of the solutions obtained with a partial element equivalent circuit (PEEC) solver. Issues are considered such as the passivity in both the time and frequency domain responses and their stability in the time domain. Time domain stability has impacted differential equation???based electromagnetic (EM) techniques such as the finite difference time domain (FDTD) or the finite integration technique (FIT) models, as well as FEM methods. The chapter also considers techniques for the improvement of stability as well as passivity for the solution obtained with (EM) PEEC methods. It further summarizes the different relevant assessment, enhancement, and enforcement techniques, including solver stability enhancement, solver passivity enhancement, solution passivity assessment, and solution passivity enforcement. Finally, the chapter considers passivity of quasistatic (QS) PEEC models and general properties of all PEEC models.

In this paper, we propose a reduced-complexity finite difference time domain (FDTD) simulations of modulated metasurfaces with arbitrary unit cells. The three dimensional (3D) physical structure of the metasurface is substituted by a spatially varying surface impedance boundary condition (IBC) in the simulation; as the mesh size is not dictated by sub-wavelength details, considerable advantage in space- and time-step is achieved. The local parameters of the IBC are obtained by numerical simulation of the individual unit cells of the physical structure, in a periodic environment approximation, in the frequency domain. As the FDTD requires an appropriate time domain impulse-response, the latter is obtained by broad-band frequency simulations, and vector fitting to an analytic realizable time response. The approach is tested on metasurface structures with complex unit cells and extending over 10 ××10 wavelengths, using a standard PC with 64GB RAM.