Some partial derivative properties of the impedance function of a resistively-terminated network which is a cascade of m lossless two-ports of variables p1 to pm dre established. Those cases where some of the lossless two-ports are lowpass or highpass ladder networks with all of their transmission zeros at the origin or at infinity are also examined. Necessary and sufficient conditions involving partial derivatives and under which an m-variable reactance or positive real function can be realized as the impedance function of a pi-variable lowpass or highpass ladder network, with all of its transmission zeros at pi = 0 or pi = ∞, and terminated in a reactance or positive real impedance function in the other variables are derived. 相似文献
Studies of two-element-kind ladder networks are well known in the classical literature, among them, the most celebrated ones are due to Cauer. Driving point immittance function synthesis by using continued fractions to obtain the series and shunt arm L-C element values is a standard and routine work. The idea of introducing a class of more general networks, the inhomogeneous ladder networks, was first developed by Lee and Brown, and subsequently the synthesis techniques of such a network were established.In this paper, new results are found such as: (1) the Iff. conditions of the existence of an inhomogeneous ladder network by a given chain matrix of the network satisfying: (a) determinant of the chain matrix is 1; (b) the zeros of A(s) and z?1B(s) or A(s) and y?1C(s) alternate with respect to [z(s)y(s), k] with an appropriate leading set of zeros of A(s); (c) the poles of A(s) and z?1B(s) or A(s) and y?1C(s) are the poles of z(s)y(s) of multiplicity of n and n?1, where n the number of sections of ladder networks; (2) the Iff. condition for the inhomogeneous ladder network to be optimal is that it be antimetrical, whereas for the extended class of inhomogeneous ladder networks it is symmetrical, where an optimal inhomogeneous ladder network is defined as the corresponding network with the minimum sum of immittance levels in the series and shunt arms; (3) algorithms of synthesis procedures were developed as the by-products of the Theorems. 相似文献
Necessary and sufficient conditions are obtained for the realization of an m-variable positive real function (PRF) as the impedence function of a resistively-terminated ladder network of m lossless two-ports connected in cascade. Each two-port is a single-variable lossless ladder with all of its transmission zeros either at the origin or at finity. Conditions are also obtained when each of the two-ports is a Fujisawa-type lowpass ladder. 相似文献
In this paper, positive-real systems under lossless positive-real transformations are investigated. Let G(s) be the transfer function matrix of a continuous-time positive-real system of order n and F(s) a lossless transfer function of order nF. We prove here that the lossless positive-real transformed system, i.e. G(F(s)), is also positive-real. Furthermore, the stochastic balanced representation of positive-real systems under lossless positive-real transformations is considered. In particular, it is proved that the positive-real characteristic values πj of G(F(s)) are the same of G(s) each with multiplicity nF, independently from the choice of F(s). This property is exploited in the design of reduced order models based on stochastic balancing. Finally, the proposed technique is a passivity preserving model order reduction method, since it is proven that the reduced order model of G(F(s)) is still positive-real. An error bound for truncation related to the invariants πj is also derived. 相似文献
This paper proposes a new wave digital filter derived from doubly terminated LC-ladder networks by replacing each series or shunt arm element of the ladder by its equivalent digital two-port. It is shown that such two-ports may be cascaded without the use of adapters defined by Fettweis (1). A number of realizations of the wave digital two-ports, which are canonic with respect to both multipliers and delays, have been obtained. Also a realization which is canonic with respect to multipliers only is given and an example considered using this realization. The sensitivity of this filter with respect to the multiplier coefficient changes due to finite word length is compared with the conventional cascaded digital filter and also the one proposed by Renner and Gupta. It is found that the proposed filter appears to be a more desirable form of implementation than the conventional cascade form and comparable to that of Renner and Gupta (2). 相似文献
A method is presented for the design of a class of two-dimensional (2-D) stable digital filters satisfying prescribed magnitude and constant group delay specifications. The design method generates a 2-D digital transfer function which is a product of two transfer functions H1(z1,z2) and H2(z1,z2), corresponding to a recursive filter and a nonrecursive filter, respectively, Component H1(z1,z2) ensures a wave-digital realization, that is, the design method guarantees the generation of a corresponding analog function H1A(s1,s2) which is realizable as the transfer function of a doubly-terminated two-variable lossless network. Thus the design technique ensures that not only is a given frequency response achieved, but also the generated transfer function is realizable as a cascade of a wave-digital filter and a nonrecursive digital filter. The class of filters considered here is one in which the doubly-terminated analog network used to realize the wave digital filter is a cascade of s1- and s2-variable lossess two-ports with all their transmission zeros at infinity. 相似文献
Necessary and sufficient conditions for the realization of lossless, lowpass, ladder networks terminated by a resistance are presented, in terms of the poles and zeros of the reflection coefficient. These conditions yield explicit expressions for the element values. They are then extended to highpass networks. These results are next used in solving a bandpass matching problem and the limitations on the performance of matching networks due to constraints imposed by the load are discussed. A suitable example is worked out to illustrate the problem. 相似文献
An n-port gyrator, terminated by s1-type capacitors in m1-ports, by s2-type capacitors in the next m2-ports and by resistors in the remaining (n-m1-m2)-ports is considered. The determinant of the admittance matrix of the network can be made to yield VSHP (a two-variable Hurwitz polynomial without non-essential singularities of the second kind) under certain conditions involving the sub-determinants of the gyrator matrix. With the gyrator constants as variables and the above conditions as constraints, some 2-D stable low-pass filters have been designed using a suitable optimization procedure. The method is illustrated by examples. 相似文献
The multivariable approach to the synthesis of networks composed of a finite number of uniform lossless transmission lines, commensurable or incommensurable, and lumped passive elements is verified by showing that the multivariable rational matrix, W(λ0,λ1, .. ,λn) is bounded real in (n + 1) complex variables if and only if W is bounded real in p after substituting, λ0 = α0p + β0 and λi = tanh (αip + βi) for λi (1?i?n) where all the α's and β's are nonnegative and arbitrary, except for being not simultaneously zero in like indexed pairs. Consequences of this result are discussed. 相似文献
Fixed point properties of the binomial function are developed. It is shown that for any 1 < L < N, TLNhas a unique fixed point p? in (0, 1), and that for large N, the fixed point is L/N. This has application to signal detection schemes commonly used in communication systems. When detecting the presence or absence of a signal with an initial false alarm probability pFAand an initial detection probability pD, then TLN(pFA) < pFAand TLN(pD) > pDif, and only if, pFA < p? < pD. When this condition is satisfied, as N → ∞, TLN(pFA) → 0 and TLN(pD → 1. 相似文献
In this paper, the issue about the stationary distribution for hybrid multi-stochastic-weight coupled networks (HMSWCN) via aperiodically intermittent control is investigated. Specially, when stochastic disturbance gets to zero, the exponential stability in pth moment for hybrid multi-weight coupled networks (HMWCN) is considered. Under the framework of the Lyapunov method, M-matrix and Kirchhoff’s Matrix Tree Theorem in the graph theory, several sufficient conditions are derived to guarantee the existence of a stationary distribution and exponential stability. Different from previous work, the existing area of a stationary distribution is not only related to the topological structure of coupled networks, but also aperiodically intermittent control (the rate of control width and control duration). Subsequently, as an application to theoretical results, a class of hybrid multi-stochastic-weight coupled oscillators is studied. Ultimately, numerical examples are carried out to demonstrate the effectiveness of theoretical results and effects of the control schemes. 相似文献
This article considers the problem of prescribed-time stabilization for a class of uncertain high-order nonlinear systems (i.e., systems in the -normal form) with a pre-specified asymmetric output constraint. A core ingredient, tangent-type barrier function, is proposed first by skillfully excavating and assimilating the inherent properties of system nonlinearities. Based on the barrier function, as well as a serial of nested signum functions, the celebrated technique of adding a power integrator is renovated finely to establish a new design approach by which a continuous state feedback prescribed-time stabilizer, along with a tangent-type asymmetric barrier Lyapunov function, can be constructed in a systematic fashion, thereby guaranteeing the performance of prescribed-time state convergence and ensuring the fulfillment of pre-specified output constraints surely. Benefiting from the composite characteristics of the presented tangent-type barrier Lyapunov function and the signum functions, the proposed approach further offers a unified nature in design enabling us to organize a prescribed-time stabilizer that is simultaneously valid and executable for the system undergone or free from output constraints, without the need of changing the controller structure. The effectiveness and superiority of the developed approach are illustrated by a numerical example. 相似文献
This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l1 performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l1-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results. 相似文献
It is shown that cartesian product and pointwise-sum with a fixed compact set preserve various approximation-theoretic properties. Results for pointwise-sum are proved for F-spaces and so hold for any normed linear space, while the other results hold in general metric spaces. Applications are given to approximation of Lp-functions on the d-dimensional cube, 1?p<∞, by linear combinations of half-space characteristic functions; i.e., by Heaviside perceptron networks. 相似文献
Nanochannels offer a way to align and analyze long biopolymer molecules such as DNA with high precision at potentially single basepair resolution, especially if a means to detect biomolecules in nanochannels electronically can be developed. Integration of nanochannels with electronics will require the development of nanochannel fabrication procedures that will not damage sensitive electronics previously constructed on the device. We present here a near-room-temperature fabrication technology involving parylene-C conformal deposition that is compatible with complementary metal oxide semiconductor electronic devices and present an analysis of the initial impedance measurements of conformally parylene-C coated nanochannels with integrated gold nanoelectrodes.No two cells are exactly alike, either in terms of their genome, the genomic epigenetic modification of the genome, or the expressed proteome.1 The genomic heterogeneity of cells is particularly important from an evolutionary perspective since it represents the stages of evolution of a population of cells under stress.2 Because of the important variances in the genome that occur from cell to cell, it is critical to develop genomic analysis technologies which can do single-cell and single molecule genomic analysis as an electronic “direct read” without intervening amplification steps.3, 4, 5, 6, 7, 8 In this paper, we present a technique which uses conformal coverage of nanochannels containing nanoelectrodes using a room-temperature deposition of parylene-C, a pin-hole-free, excellent electrical insulator with low autofluorescence.9 This procedure should open the door to integration of many kinds of surface electronics with nanochannels. One of the most difficult aspects in introducing electronics into nanochannel technology is the sealing of nanochannel so that the electrodes are not compromised by harsh chemicals or high temperatures. There are various methods to form nanochannels containing nanoelectrodes, including wafer bonding techniques,10 removal of sacrificial materials,11 and nonuniform sputtering deposition.12 Methods employing a sacrificial layer removal show the greater compatibility to electronic integration, but current methods to remove sacrificial materials require either high temperatures11 or harsh chemicals.13, 14The basic device consisted of 12 mm long, 100 nm wide, 100 nm high nanochannels interrogated by 22 pairs of 30 nm wide gold nanoelectrodes. The outline of the fabrication process is shown in Fig. Fig.1.1. The fabrication process was carried out on a standard 4 in. single-side polished p-type ⟨100⟩ silicon wafer with 100 nm of dry thermal oxide on the top as an insulating layer, which also helped the wetting of the nanochannels. The first step involved nanofabrication of the 25 nm thick nanoelectrodes on the SiO2 top of the wafer using electron beam lithography (EBL). External gold connection pads were constructed using standard metal lift-off techniques and photolithography to connect to the nanoelectrodes. A Raith E-Line e-beam writing system (Raith USA, Ronkonkoma, NY) was used to expose polymethyl methacrylate (PMMA) for metal lift-off. Figure Figure1a1a shows a scanning electron microscopy (SEM) image of the nanoelectrodes. The 100 nm sealed nanochannels were constructed using sacrificial removal techniques. We used EBL to expose a 100 nm thick film of PMMA over the gold nanolines in the region around the nanolines, leaving behind lines of unexposed sacrificial layer of PMMA. We next evaporated 25 nm of SiO2 over the nanolines to improve the surface wetting properties of nanochannel and then conformally coated with 4 μm thick of parylene-C [poly(chloro-p-xylylene)] using a Specialty Coating Systems model PDS 2010 parylene coating system (SCS Systems, Indianapolis, IN). Access holes for the gold electrodes and the feeding channels were etched through by oxygen plasma and 1:10 buffered oxide etchant. To avoid autofluorescence induced in parylene by an active plasma15 and ambient UV radiation,16 it is important not to expose the remaining parylene with plasma and to keep the samples in the dark. The sacrificial removal of PMMA in the nanochannels was done in four steps: (1) soaking the chip in 55 °C 1165 MicroChem resist remover (MicroChem, Newton, MA) for 36 h, (2) room-temperature soaking in 1,2-dichloroethane for 12 h, (3) soaking in room-temperature acetone for 12 h, and (4) drying the nanochannels by critical point drying (CPD-030, BAL-TEC AG, Principality of Liechtenstein), which served to prevent the collapse of the nanochannel resulting from surface tension of the acetone.Open in a separate windowFigure 1(a) SEM image of gold nanoelectrodes; scale bar is 200 nm. (b) 100×100 nm2 PMMA nanoline is written over the gold nanoelectrodes by exposure of the surrounding PMMA. (c) Parylene-C conformal coating over the PMMA nanoline. PMMA is dissolved and parylene-C etched by reactive ion etching.Conductance measurements were done using ac techniques. The ac impedance Ztot of an insulating ionic fluid such as water between electrodes is a complex subject.17 The most general model for the complex impedance of an electrode in ionic solution is typically modeled as the Randle circuit, which is shown in Fig. Fig.22.17 There are two major contributions to the imaginary part of the impedance: the capacitance of the double layer (Cdl), which is purely imaginary and has no dc conductance, and the impedance due to charge transfer resulting in electrochemical reactions at the electrode∕electrolyte interface, which can be modeled as a contact resistor (RCT), which is given by the Butler–Volmer equation, which describes the I-V characteristic curve when electrochemical reactions occur at the electrode,18 in series with a complex Warburg impedance (ZW) which represents injected charge transport near the electrode;19 more details can be found in Ref. 20. Since we applied a 10 mV rms ac voltage with no dc offset in our measurements, electrochemical reactions are negligible, which means no electrochemical charge transfer occurred and as a result RCT goes to infinity. We have drawn a gray box around the elements connected to the Warburg impedance branch of the circuit to show that they are negligible in our analysis.Open in a separate windowFigure 2The equivalent circuit of the nanoelectrodes in contact with water lying atop an insulating SiO2 film which covers a silicon substrate. The elements in the gray boxes can be ignored in our measurements since there is no hydrolysis at low voltage, while the elements within the dotted box are coupling reactances to the underlying p-doped silicon wafer.In the case of no direct charge injection, the electrodes are coupled by the purely capacitive dielectric layer impedance Cdl to the solvent and are also coupled capacitively by the dielectric SiO2 film capacitance Cox to the underlying p-doped silicon semiconductor. We model the semiconductor as a purely resistive material with bulk resistivity ρSi. The value of Cdl∕area is on the order of ϵϵoκ, where ϵ is the dielectric constant of water (about 80) and κ is the Debye screening parameter of the counterions in solution: ,20 where is the bulk ion concentration of charge zi. At our salt molarity of 50 mM (1∕2 Tris∕Borate∕EDTA (TBE) buffer), Cdl is approximately 30 μF∕cm2 using 1∕κ∼1 nm.In Fig. Fig.3,3, we show the ac impedance measurements between pairs nanoelectrodes for both dry and TBE buffer wet nanochannels. The electrodes are capacitively coupled to the underlying silicon substrate through an oxide capacitor Cox. We model the doped silicon wafer as pure resistors, so there is an R1 that connects both Cox, and each Cox is connected to the ground with an R2. Curve fitting was done by using the 3SPICE circuit emulation code (VAMP Inc., Los Angeles, CA). We therefore obtained the following parameters for the dry curve: Cox=1.32 nF, R1=17.5 μΩ, and R2=32.8 kΩ. R1 is not sensitive in the fit as long as it is smaller than the impedance of Cox. Given ρSi of the wafer of 1–10 Ω cm, R2 should be on the order of 103 Ω, which is slightly smaller than our fitting results. The same parameters for the wafer coupling parameters were then used for fitting the impedance measurements for wet channels. For TBE buffer solution in the nanochannel, curve fitting yields Cdl=50 pF and Rsol=105 Ω. However, given the dimension of our nanochannels, we should get a transverse resistance R∼109 Ω. One possible explanation for this difference is that the evaporated SiO2 film which was put over the PMMA is porous and allows buffer to penetrate the oxide film,21 but given that the film is only 25 nm thick this would at most increase the cross section by one order of magnitude. However, it is known that there is a high fractional presence of mobile counterions associated with the charged channel walls.22 To calculate exact conductance contribution from the surface charges is a tricky business, but since the surface-to-volume ratios in our nanochannels are much greater than the slits, a larger conductance enhancement can be expected, and more work needs to be done.Open in a separate windowFigure 3ac impedance spectra of TBE buffer solution in a transchannel measurement between adjacent pairs of nanoelectrodes separated by 135 μm. The red circles are data for a dry channel and the solid red line is the fit to the model shown in the upper right hand corner. The green squares and dashed green line are for a nanochannel wet with TBE buffer.We have presented a way to fabricate a nanochannel integrated with electrodes. This technology opens up opportunities for electronic detection of charged polymers. With our techniques to fabricate nanoelectrodes with nanochannels, it should be possible to include integrated electronics with nanofludics, allowing the electronic observation of a single DNA molecule at high spatial resolution. However, the present design has problems. Most of the ac went through the silicon wafer instead of the solution. To enhance the sensitivity, we need either to increase the ratio of current going through the liquid to the current going through the wafer or to have a circuit design that picks up the changes in Cdl and Rsol. 相似文献
The distribution of dopants significantly influences the properties of semiconductors, yet effective modulation and separation of p-type and n-type dopants in homogeneous materials remain challenging, especially for nanostructures. Employing a bond orbital model with supportive atomistic simulations, we show that axial twisting can substantially modulate the radial distribution of dopants in Si nanowires (NWs) such that dopants of smaller sizes than the host atom prefer atomic sites near the NW core, while dopants of larger sizes are prone to staying adjacent to the NW surface. We attribute such distinct behaviors to the twist-induced inhomogeneous shear strain in NW. With this, our investigation on codoping pairs further reveals that with proper choices of codoping pairs, e.g. B and Sb, n-type and p-type dopants can be well separated along the NW radial dimension. Our findings suggest that twisting may lead to realizations of p–n junction configuration and modulation doping in single-crystalline NWs. 相似文献
In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with two deviating arguments of the form
This paper is concerned with the event-triggered H∞ state estimation problem for a class of discrete-time complex networks subject to state saturations, quantization effects as well as randomly occurring distributed delays. A series of Bernoulli distributed random variables is utilized to model the random occurrence of distributed delays. For the energy-saving purpose, an event-triggered mechanism is proposed to decide whether the current quantized measurement should be transmitted to the estimator or not. For the state-saturated complex networks, our aim is to design event-triggered state estimators that guarantee both the exponential mean-square stability of and the H∞ performance constraint on the error dynamics of the state estimation. Stochastic analysis is conducted, in combination with the Lyapunov functional approach, to derive sufficient conditions for the existence of the desired estimators whose gain matrices are obtained by solving a set of matrix inequalities. An illustrative example is exploited to show the usefulness of the estimator design algorithm proposed. 相似文献
Techniques developed in the Sturm—Liouville problem and its Inverse problem are well known in solving the analysis and synthesis problems of non-uniform distributed networks (or NUDN) (1)-(6), (15). However, very few practical results have been obtained from the theory, especially as regards the synthesis part of the problem. In this paper, we show that the chain matrix of an inhomogeneous ladder network (or IHLN) of N sections has undergone exactly the limit process of first-order difference equation approximation of the corresponding differential equation converges to the chain matrix of the corresponding NUDN uniformly on every compact subset of p = z(s)y(s) plane. Therefore an optimal NUDN is proven to be either symmetrical or antimetrical (7). Specifically, a class of optimal NUDN which is optimal on every subinterval of [O,L] has closed-form solutions, and is proven to be both symmetrical and antimetrical. 相似文献
In this paper we present a method for testing the Hurwitz property of a segment of polynomials (1−λ)p0(s)+λp1(s), where λ∈[0,1] and p0(s) and p1(s) are nth-degree polynomials with complex coefficients. The method consists in constructing a parametric Routh-like array with polynomial entries and generating Sturm sequences for checking the absence of zeros of two real λ-polynomials of degrees 2 and 2n in the interval (0,1). The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations because it does not invoke any numerical root-finding procedure. 相似文献
