Analytical Transfer Function Research Articles

A modified zone model for estimating equivalent room thermal capacity

The zone model has been widely applied in control analysis of heating, ventilation and air conditioning (HVAC) systems to achieve a high building efficiency. This paper proposed a modified zone model which is much simpler in the HVAC system simulation and has the similar accuracy to the complicated simulation model. The proposed model took into consideration the effect of envelop heat reservoir on the room indoor temperature by introducing the thermal admittance of the inner surfaces of the building enclosure. The thermal admittance for the building enclosure was developed based on the building thermal network analytical theory and transfer function method. The efficacy of the proposed model was demonstrated by comparing it with the complicated model — heat balance method (HTB2 program). The predicted results from the proposed model well agreed with those from the complicated simulation. The proposed model can then make the HVAC system dynamic simulation much faster and more acceptable for control design due to its simplicity and efficiency.

Analytical Transfer Functions Relating Power and Ground Voltage Fluctuations to Jitter at a Single-Ended Full-Swing Buffer

The transfer functions relating supply voltage fluctuations to jitter are analytically derived in closed form expressions for a single-ended buffer. The analytic transfer functions are derived from a linear differential equation obtained from asymptotic linear inverter I-V curves. The transfer functions are validated by comparison with HSPICE simulations. The estimated jitter is compared with the simulated jitter using eye diagrams with single-frequency and multitone supply voltage fluctuations.

Impacts of Wetting Layer and Excited State on the Modulation Response of Quantum-Dot Lasers

The modulation response of quantum-dot (QD) lasers is studied. Based on a set of four rate equations, a new analytical modulation transfer function is developed via a small-signal analysis. The transfer function can clearly describe the impacts of the wetting layer and the excited states: finite carrier capture and carrier relaxation times as well as the Pauli blocking limits the modulation bandwidth. The definitions of the resonance frequency and the damping factor of QD lasers are also improved. From the analysis, it is demonstrated that carrier escape from the ground state to the excited states leads to a nonzero resonance frequency at low bias powers associated to a strong damping factor.

Memory Speed Analysis of Optical RAM and Optical Flip-Flop Circuits Based on Coupled SOA-MZI Gates

We demonstrate analytical frequency-domain transfer function expressions for an optical random access memory (RAM) cell that employs two SOA-based ON/OFF switches and two coupled SOA-MZI gates forming an optical flip-flop. Our theoretical model relies on first-order perturbation theory approximations applied for the first time to coupled optical switching structures, resulting to an optical RAM cell frequency response that allows for a qualitative and quantitative analysis of optical RAM memory speed and performance characteristics and their dependence on certain RAM cell device parameters. We show that the transfer function of an optical RAM cell and its incorporated flip-flop device exhibits periodic resonance frequencies resembling the behavior of optical ring resonator configurations. Its free spectral range is mainly dictated by the length of the waveguide that enables the coupling of the two SOA-MZI gates, yielding this coupling length as the dominant memory speed determining factor. The obtained results are in close agreement with experimental observations, demonstrating that optimized RAM cell designs with waveguide coupling lengths lower than 5 mm can enable RAM operation at memory speeds well beyond 40 GHz.

Direct estimation of the distribution of relaxation times from induced‐polarization spectra using a Fourier transform analysis

ABSTRACTThe analysis of low‐frequency spectral induced polarization data involves the determination of the distribution of relaxation times either from time‐domain or frequency domain measurements. The classical approach is to assume a simple transfer function (e.g., a Cole‐Cole function) and to determine, by a deterministic or a stochastic fitting procedure, the parameters of this transfer function (for instance the four Cole‐Cole parameters). Some other methods (based on optimization) have been developed recently avoiding the choice of a specific transfer function that can bias data interpretation. We have developed a new approach based on the Fourier transform also avoiding the use of a specific analytical transfer function. The use of the Fourier transform is a classical approach to retrieve the kernel of a Fredholm integral equation of the first kind (especially in potential field theory) and this corresponds exactly to the problem we want to solve. We adapt the Fourier transform approach to retrieve the distribution of the relaxation times (for instance to process low‐frequency induced polarization data). Problems resulting from the use of this approach with noisy data are prevented by using Wiener filtering. As far as induced polarization is concerned, we found that it is necessary to fit the high‐frequency dielectric contribution of the spectra and to remove this contribution from the quadrature conductivity data before inverting the distribution of the relaxation times. Our approach is benchmarked with analytical pair solutions and then tested by using synthetic and experimental data sets.

An approximate causal Green’s function for the Stokes wave equation.

A causal analytical approximation is derived for the time‐domain Green’s function of the Stokes wave equation. This causal approximation, which contains a modified Bessel function of the first kind, is the exact analytical time‐domain Green’s function for a related wave equation that approaches the Stokes wave equation in the low frequency limit. An asymptotic expression is also obtained for this approximate Green’s function. The causal approximation and the asymptotic expression are evaluated and compared to the numerically computed time‐domain Green’s function and the analytical frequency‐domain transfer function of the Stokes wave equation and to other causal and noncausal approximations. The results show that this approximate Green’s function closely matches the numerically computed Green’s function and the analytical frequency domain transfer function of the Stokes wave equation near the source, and at greater distances, the asymptotic expression accurately represents the time‐ and frequency‐domain behavior of the Stokes wave equation. Time‐domain analysis demonstrates that the analytical approximation and the asymptotic expression are dispersive, whereas causality is verified in the time‐domain and in the frequency‐domain. The differences and similarities between these causal approximations and other causal and noncausal approximations are also identified and discussed. [Work supported in part by NIH Grant No. EB012079.]

Approximate analytical optical transfer function for a wavefront-coded imaging system with two-dimensional rectangularly separable phase masks

Wavefront coding can be used to extend the depth of field of incoherent imaging systems and is a powerful system-level technique. In order to assess the performance of a wavefront-coded imaging system, defocused optical transfer function (OTF) is the metric frequently used. Unfortunately, to the best of our knowledge, among all types of phase masks, it is usually difficult to obtain the analytical OTF except the cubic one. Although numerical computation seems good enough for performance evaluation, the approximate analytical OTF is still indispensable because it can reflect the relationship between mask parameters and system frequency response in a clearer way. Thus, a method is proposed to derive the approximate analytical OTF for two-dimensional rectangularly separable phase masks. The analytical results are well consistent with the direct numerical computations, but the proposed method can be accepted only from engineering point of view and needs rigorous proof in future.

Probabilistic Analysis of a Comb-Drive Actuator

In the present paper, we discuss about design methodology to study the reliability of a microelectromechanical systems device. The proposed methodology was illustrated for design of a comb-drive actuator. In particular, effect of variations introduced in the design parameters due to the fabrication process and their impact on reliability of a comb-drive actuator is reviewed in detail. We use Crystal Ball® (Decisioneering, Inc., 2000), a probabilistic analysis tool to analyze the performance of comb-drive actuator. The present method requires an analytical model or transfer function derived using experimental data to study the variation in output due to variations in input parameters. We developed an analytical model for displacement of actuator and verified the analytical model using finite element model. This analytical model was used to study the variation in displacement of comb-drive actuator. This methodology uses a combination detailed experimental studies done to establish fabrication limitations or capabilities. The analysis and final design selection was based on a combination of Crystal Ball® studies and fabrication constraints. The same methodology could be extended to study the reliability of MEMS sensors and actuators due to variations on process parameters.

Improved analytical modulation transfer function for image intensified charge coupled devices*

The basic problem of simulation and modeling of Image Intensified Charge Coupled Device (ICCD) is the difference between the analytical Modulation Transfer Function (MTF) formulation used in the model and the experimentally obtained MTF. An investigation into the MTF of ICCD sub-components reveal that the MTF of the Image Intensifier Tube (IIT) is the main factor in this deviation. In this study, a regulation factor for the MTF of 3^{rd} generation IITs has been developed. A commonly used MTF formulation for IITs has been modified to include a regulation factor which has helped produce more precise MTF values for the Night Vision Sight (NVS) device. The results obtained through the new formulation have been compared with the experimental results and it is revealed that the proposed formulation yields MTF values within 3% of the experimental results, on average, while the most commonly used formulation produces approximately 29.5% difference, which amounts to almost 10% improvement in analytical analysis. The analysis is then extended to other generations of IITs where similar improvements have been achieved.

가진입력의 크기에 따른 동조액체기둥감쇠기의 비선형 특성

The objective of this study is to investigate design parameters of a tuned liquid column damper(TLCD), which is affected by various excitation amplitude, through shaking table test. Design parameters of a TLCD are examined based on the equivalent tuned mass damper(TMD) model of a TLCD, in which the nonlinear damping of a TLCD is transposed to equivalent viscous damping. Shaking table test is carried out for a TLCD specimen subjected to harmonic waves with various amplitude. Transfer functions are ratios of liquid displacement of TLCD and control force produced by a TLCD, respectively, with respect to the acceleration excited by a shaking table. They are derived based on the equivalent TMD model of a TLCD. Then, the variation of design parameters according to the excitation amplitude is examined by comparing analytical transfer functions with experimental ones. Finally, the dissipation energy due to the damping of a TLCD, which is experimentally observed from the shaking table test, is examined according to the excitation amplitude. Comparisons between test results and analytical transfer functions showed that natural frequencies of TLCD and the ratio of the liquid mass in a horizontal column to the total liquid mass do not depend on the excitation amplitude, while the damping ratio of a TLCD increases with larger excitation amplitude.

Determination of an Empirical Transfer Function of a Solid Oxide Fuel Cell Gas Turbine Hybrid System Via Frequency Response Analysis

This paper presents the study of the effect variations in the heat effluence from a solid oxide fuel cell (SOFC) has on a gas turbine hybrid configuration. The SOFC is simulated through hardware at the U.S. Department of Energy, National Energy Technology Laboratory (NETL). The gas turbine, compressor, recuperative heat exchanger, and other balance of plant components are represented by actual hardware in the Hybrid Performance Test Facility at NETL. Fuel cell heat exhaust is represented by a combustor that is activated by a fuel cell model that computes energy release for various sensed system states System structure is derived by means of frequency response data generated by the sinusoidal oscillation of the combustor fuel valve over a range of frequencies covering three orders of magnitude. System delay and order are obtained from Bode plots of the magnitude and phase relationships between input and output parameters. Transfer functions for mass flow, temperature, pressure, and other states of interest are derived as a function of fuel valve flow, representative of fuel cell thermal effluent. The Bode plots can validate existing analytical transfer functions, provide steady state error detection, give a stability margin criterion for the fuel valve input, estimate system bandwidth, identify any nonminimum phase system behavior, pinpoint unstable frequencies, and serve as an element of a piecewise transfer function in the development of an overall transfer function matrix covering all system inputs and outputs of interest. Further loop shaping techniques and state space representation can be applied to this matrix in a multivariate control algorithm.

Icetools: A full Stokes finite element model for glaciers

Detailed studies of glacier flow and deformation of ice require high-resolution numerical modeling. The model presented in this paper, icetools, solves the Stokes equation including all components of the stress tensor, termed full Stokes, with the finite element method to enable such detailed studies. Icetools is capable of running in parallel on computational clusters providing the computing power for large-scale simulations. Two different numerical tests were performed to demonstrate the capability of the model; (1) a comparison with the analytical solution for gravity driven plane flow down an inclined plane, and (2) flow over a Gaussian-shaped bed disturbance in comparison with the analytical transfer functions for this case. The second test involves time evolution of the surface geometry from an initially uniformly sloping surface. A linear rheology medium with a viscosity of 8 × 10 13 Pa s and a non-linear medium with Glen rheology exponent n = 3 and rate factor of A = 23 × 10 - 16 s - 1 kPa - 3 were studied. Both correlate well with the analytical solution and reach steady state, defined as when the maximum vertical movement drops below 5 × 10 - 5 times the mean ice thickness per year, after 282 years for the linear case and 135 years for the non-linear case, respectively.

Application of Euler–Maclaurin sum formula to obtain an approximate closed-form Green's function for a two-dimensional acoustical space

The Green's function solution for the acoustic wave equation in a two-dimensional rectangular space is expressed as an infinite series of terms based on the cross modes of the duct. An approximate closed-form solution is obtained by applying the Euler–Maclaurin sum formula. The procedure provides a closed-form expression in both the space–time and Laplace domains along with an upper bound for a remainder. Plane wave and higher-order waves components are identified. A numerical example for an exponential input gives comparisons of the transient response for the approximate closed form and series Green's function solutions. The time response and analytical transfer function frequency spectrum of the series and Euler–Maclaurin closed-form Green's function are computed. Lastly, the approximate closed-form Green's transfer function expression is used in model-based designed feedforward and feedback control schemes to reduce peaks in the frequency response and provide system damping.

Use of numerical modelling to identify the transfer function and application to the geostatistical procedure in the solution of inverse problems in groundwater

The restoring of the pollutant release history makes use of transfer functions (TFs) usually known by analytical formulation. In many cases the computation of an analytical TF is not possible; this fact limits the application of the inverse procedures to very simple conditions or it forces to drastic simplifications of complicated problems. In this paper a new procedure, useful to compute the numerical transfer functions in transport problems with no analytical solution, is outlined. This method, analogous to the computation of the Instantaneous Unit Hydrograph (IUH) in surface hydrology, makes use of mathematical modelling

Optical transmission properties of light propagation through Fibonacci-class ring-resonators

An interesting topology with easy integration capability (from mask designing aspect) for optical filters using Fibonacci-class (FC(J,n)) ring-resonators is introduced. For some special cases, analytical transfer function (Transmission Coefficient Hm(n)) is obtained and corresponding simulated result is illustrated. In this work, optical multi-band filter design and analysis using Fibonacci-class ring resonators is considered. With suitable selection of system parameters and FC(J,n), we report multi-band characteristic for this structure. Also, dominant factors effects on multi-band operation are shown. We show that the coupling coefficients, effectively affects (e.g. generation or annihilation of additional band) the multi-band properties obtained in proposed structure. Also, the bandwidth and position of additional band can be controlled using Fibonacci-class basic elements (A, B) parameters such as rings diameters. Also, proposed system is easier than general multistage rings coupled to main waveguide from implementation point of view.

Performance Evaluation of Linear Turbo Receivers Using Analytical Extrinsic Information Transfer Functions

Turbo receivers reduce the effect of the interference-limited propagation channels through the iterative exchange of information between the front-end receiver and the channel decoder. Such an iterative (turbo) process is diffcult to describe in a closed form so the performance evaluation is often done by means of extensive numerical simulations. Analytical methods for performance evaluation have also been proposed in the literature, based on Gaussian approximation of the output of the linear signal combiner. In this paper, we propose to use mutual information to parameterize the logarithmic-likelihood ratios (LLRs) at the input/output of the decoder, casting our approach into the framework of extrinsic information transfer (EXIT) analysis. We find the EXIT functions of the front-end (FE) receiver analytically, that is, using solely the information about the channel state. This is done, decomposing the FE receiver into elementary blocks described independently. Our method gives an insight into the principle of functioning of the linear turbo receivers, allows for an accurate calculation of the expected bit error rate in each iteration, and is more flexible than the one previously used in the literature, allowing us to analyze the performance for various FE structures. We compare the proposed analytical method with the results of simulated data transmission in case of multiple antennas transceivers.

Two-Dimensional Pipe Model for Laminar Flow

The one-dimensional Zielke model of the energy loss in laminar pipe flow is exact but gives no information about the velocity profile. Here a two-dimensional pipe model is presented which gives the two-dimensional velocity profile in the time domain for an unstationary pipe flow of a compressible fluid that follows an equation of state. The continuity and the motion equations are projected over two sets of functions accounting for the radial and the axial dependence. A set of ordinary differential equations for the time-dependent coefficients is obtained, which is numerically integrated according to the boundary conditions at the pipe ends needed in practical applications. The model reproduces the experimental results of a water hammer and the analytical transfer functions over a wide range of frequencies.

EMPIRICAL EVALUATION OF SITE EFFECTS BY MEANS OF H/V SPECTRAL RATIOS AT THE LOCATIONS OF STRONG MOTION ACCELEROMETERS IN ISRAEL

Acceleration data from local and regional earthquakes is of prime importance in evaluating the seismic hazard. Consequently, strong motion accelerometers are currently installed at more than 60 locations in Israel. We have explored the possibility of site amplification effects at 10 sites where local earthquakes triggered strong motion accelerometers by integrating empirical and analytical estimations. Implementing H/V spectral ratio techniques using 15 accelerograms from nine earthquakes, 105 seismograms shear-wave records of 35 local and regional earthquakes and seismograms of microtremors were used in the empirical evaluations. The subsurface models were constructed by integrating available geological and geophysical information at the analysed site with empirically evaluated site response functions. Amplification effects of factor 3-6 are observed at various frequencies in the 0.8-6.0 Hz band. Through the analysis process it became evident that the instant availability of many useful time windows of microtremors provides systematic estimations of the fundamental resonance frequency of each site and their associated amplification levels, which are similar to those obtained from H/V spectral ratios of seismograms and accelerograms and to those inferred from the subsurface geology. Analytical transfer functions should be reviewed with respect to empirical site response evaluations. Estimations that are based on only one approach may be totally misleading.

Transverse magnetization transfer under planar mixing conditions in spin systems consisting of three coupled spins 1/2

Polarization transfer under planar mixing conditions is a widely used tool in modern NMR-experiments. In the case of two coupled spins 1/2 or a chain of three or more spins 1/2 with only nearest neighbor couplings, it is only possible to transfer a single magnetization component (longitudinal magnetization in the principle axis system of the planar coupling tensors). However, if all couplings in a three-spin system are non-zero, it turns out that all magnetization components can be efficiently transferred even under strictly planar mixing conditions. In this article a detailed theoretical analysis is presented based on analytical transverse coherence transfer functions and on the underlying commutator algebra. In addition, transverse magnetization transfer is demonstrated experimentally. The results show that in highly coupled spin systems, as for example in the case of partially aligned samples with many residual dipolar couplings, special care has to be taken to avoid phase distortions if planar mixing steps are used.

Experimental Study of Motorcycle Transfer Functions for Evaluating Handling

Summary The transfer functions of a motorcycle, especially that between roll angle and steering torque, qualify input-output characteristics - that is, motion produced as a function of steering torque - and are closely related to ease of use and handling. This paper describes the measurement of the transfer functions of a typical sports motorcycle, resulting from data collected in slalom tests. These functions are then compared to analytical transfer functions derived from known models in the literature. The comparison shows fair to good agreement. Lastly, the formation of steering torque is analysed and the observed transfer functions are interpreted in this framework. It is shown that gyroscopic effects are mostly responsible for the lag between steering torque and roll angle, and that there is a velocity for which the various terms that combine to form steering torque cancel each other out, yielding a ‘maximum gain condition’ for torque to roll transfer function which drivers rated ‘good handling’.