共查询到20条相似文献，搜索用时 15 毫秒
1.
In this paper necessary and sufficient conditions are derived for a two-variable positive real function to be the driving-point impedance of certain classes of doubly-terminated lossless ladder networks. Specifically, two classes of networks are studied: (a) the class of networks in which the lossless structure is a cascade of p1- and p2-variable two-ports, each two-port having its transmission zeros at the origin and/or at infinity; (b) the class of networks in which the lossless structure is a lowpass or highpass ladder network with series arms having p1- and p2-type elements in series and shunt arms having the p1- and p2-type elements in parallel. It is indicated that via suitable transformations of the variables, conditions for many other types of ladder structures can be derived. 相似文献
2.
A linearly variable element is any passive two-terminal network element in which the immittance varies linearly with respect to an independent (of frequency) real variable, x. A definite set of fundamental passive two terminal network elements (F- elements) consisting of fixed passive elements and linearly variable elements is presented. It is shown that any network consisting of only F-elements has a driving point immittance, D(s,x), that is positive real for s complex, x real and positive real for x complex, s real. Conditions on the variable coefficients, degree and location of zeros and poles of D(s,x) are established. A method of testing whether D(s,x) is positive real for one complex and one real variable is developed. This testing is accomplished by extending the Hurwitz and Sturm test to one complex and one real variable. 相似文献
3.
T.N. Lee 《Journal of The Franklin Institute》1982,313(1):41-60
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
4.
A well-known discrete stability test is used to derive from the denominator D(z) of a given stable high-order transfer function G(z), the denominator of a low-order approximant of G(z). The proposed method, based on the truncation and inversion of a continued fraction formed with the coefficients of D(z), yields a reduced denominator d(z) of degree, say m, which is always stable. Furthermore, depending on the neglected parts of the continued fraction, d(z) approximates m1 and m2 = m−m1 zeros of D(z), located very near the points z=1 and z=-1, respectively. In the special case m1=m, d(z) is identical to the polynomial obtained by applying to D(z) the indirect technique, which combines the bilinear transformation with the Routh or the Schwarz approximation method. 相似文献
5.
M.O. Ahmad C.H. Reddy V. Ramachandran M.N.S. Swamy 《Journal of The Franklin Institute》1979,307(2):71-81
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
6.
M.O. Ahmad C.H. Reddy V. Ramachandran M.N.S. Swamy 《Journal of The Franklin Institute》1979,307(6):315-329
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
7.
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
8.
F.M. Reza 《Journal of The Franklin Institute》1983,316(3):279-290
A new theorem expands the domain of the scalar immittance functions Z(p) to the operator Z(T) where T(s) is an invertible linear passive n-port system. Elements R, L, C of Z(p) are replaced by operators RI, LT, and [CT] - 1. All frequency transformations may be considered contained in this theorem when T is a scalar. 相似文献
9.
In this paper, we use Leggett-Williams multiple fixed point theorem to obtain different sufficient conditions for the existence of at least three nonnegative periodic solutions of the first order functional differential equation of the form
y′(t)=-a(t)y(t)+λf(t,y(h(t))). 相似文献
10.
H.C. Reddy C.P. Reddy M.N.S. Swamy V. Ramachandran 《Journal of The Franklin Institute》1982,313(4):197-206
In this paper a method for the realization of RC transfer immittance functions with an unsymmetrical lattice is presented. The method yields minimal capacitor realizations for Z12(s) with no pole at s = 0 and ?y12(s) having no pole at s = ∞. The number of resistors needed are only two more than the minimum needed. 相似文献
11.
When designing lossless networks, one is faced with the problem of choosing a zero configuration for the reflection coefficient ?(s). Bode showed that if parasitic capacitances are present as well as for power transfer optimization, the best zero configuration is to locate all of them in the left half-plane. Recently, Bode's result was generalized to include parasitic immitances at both ends (source and load) of the quadripole.This work adds a new result to the theory by looking at the overall transfer function poles. It is shown that (a) if the source resistance varies, one should select left half-plane zeros for ?(s); and (b) if the load impedance varies, one should select right half-plane zeros.The pole sensitivity criterion used is the distance between the actual transfer function poles and the poles of the ideal transfer function. 相似文献
12.
Jay I. Frankel Majid Keyhani Rao V. Arimilli 《Journal of The Franklin Institute》2010,347(9):1681-1688
This paper derives a new integral relationship between heat flux and temperature in a transient, three-dimensional heat conducting Cartesian half space (x>0, y∈(−∞,∞), z∈(−∞,∞)). A unified mathematical treatment has been developed based on operational and transform methods; and singular integral equation regularization. Regularization is accomplished based on a series of observations involving the diffusive nature of the operator. This newly developed relationship provides the local heat flux perpendicular to the front surface at any location within the half space. This expression suggests that an embedded plane of temperature sensors parallel to the surface can be used to acquire the local, in-depth heat flux in the x-direction. The relationship does not require a priori knowledge of the surface boundary condition which has analytically been removed in the process. The ill-posed nature of diffusion is highlighted owing to the appearance of the heating/cooling rate (°C/s) in the integrand of the new relationship. Integral relationships of this type are highly useful for experimental investigations since the in-depth heat flux can be extracted from well-established temperature transducers. 相似文献
13.
This paper proposes a new scheme for ensuring data consistency in unstructured p2p networks where peers can subscribe to multiple content types (identified by labels) and are rapidly informed of content updates. The idea is based on using a static tree structure, the Cluster-K+ tree, that maintains most of the structural information about peers and labels. A label denotes a set of replicated or co-related data in the network. The Cluster-K+ tree provides efficient retrieval, addition, deletion and consistent updates of labels. Our proposed structure guarantees a short response search time of O(H + K), where H denotes the height of the tree and K the degree of an internal tree node. We present theoretical analytic bounds for the worst-case performance. To verify the bounds, we also present experimental results obtained from a network simulation. The results demonstrate that the actual performance of our system is significantly better than the theoretical bounds. 相似文献
14.
15.
M. Sobral 《Journal of The Franklin Institute》1975,300(3):209-212
Given the linear system = Ax - bu, y = cTx, it is shown that, for a certain non-quadratic cost functional, the optimal control is given by uopt(x) = h(cTx), where the function h(y) must satisfy the conditions ky2?h(y)y>0 for y≠0, h(0) = 0 and existence of h-1 everywhere. The linear system considered must satisfy the Popov condition 1/k + (1 +?ωβ) G(?ω)>0 for all ω, G(s) being the y(s)/u(s) transfer function. 相似文献
16.
Huaqing Li Hao Zhang Zheng Wang Yifan Zhu Qi Han 《Journal of The Franklin Institute》2019,356(6):3733-3761
This paper considers solving a class of optimization problems over a network of agents, in which the cost function is expressed as the sum of individual objectives of the agents. The underlying communication graph is assumed to be undirected and connected. A distributed algorithm in which agents employ time-varying and heterogeneous step-sizes is proposed by combining consensus of multi-agent systems with gradient tracking technique. The algorithm not only drives the agents’ iterates to a global and consensual minimizer but also finds the optimal value of the cost function. When the individual objectives are convex and smooth, we prove that the algorithm converges at a rate of if the homogeneous step-size does not exceed some upper bound, and it accelerates to O(1/t) if the homogeneous step-size is sufficiently small. When at least one of the individual objectives is strongly convex and all are smooth, we prove that the algorithm converges at a linear rate of O(λt) with 0?<?λ?<?1 even though the step-sizes are time-varying and heterogeneous. Two numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate the theoretical findings. 相似文献
17.
Mathematical results are derived, which enable one to find a vector of parameters k0 such that (P1(s,k0)?H)∩(P2(k0)=0), where P1(s,k) is a polynomial in s and in the components of k,P2(k) is a polynomial in the components of k, and H is the set of Hurwitz polynomials. The algorithm is based on an extension of the root locus technique to the multiparameter case. The design problem of coupling networks between a resistive generator and a passive load, under prescribed power gain characteristics, is translated into the above formulation. A numerical example is provided. 相似文献
18.
By means of Mawhin's continuation theorem, we study a third-order p-Laplacian differential equation
(?p(u″(t)))′+f(t,u′(t),u″(t))+g(t,u(t-τ(t)))=e(t). 相似文献
19.
V.K. Bhargava 《Journal of The Franklin Institute》1977,303(6):543-548
The binary matrices A which are circulant with one or more of the following properties: (1) A is symmetric, i.e. A = AT, (2) A is orthogonal, i.e. AAT = I (mod 2), (3) A has low multiplicative order, i.e. Am = I, occur often in communication, control and network theory problems. In this paper we construct a number of such matrices. The results are based on the theory of power-residues modulo an odd prime p, and the fact that the algebra of all p × p circulant matrices is isomorphic to the algebra of polynomials modulo (xp?1). 相似文献
20.
Reza Hashemian 《Journal of The Franklin Institute》1973,295(5):383-394
A class of matrices with 1, -1 and 0 entries, called the H-matrices, is introduced and properties of such matrices are investigated. It is shown that for an H-matrix K the matrix G = KDKT, where D is a diagonal matrix with nonnegative diagonal entries, has certain properties applicable to topological synthesis of networks. A technique for decomposing a particular symmetrical matrix G, called the Q-matrix, into KDKT, where K is an H-matrix and D is a diagonal matrix with positive diagonal entries, is also developed. 相似文献