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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.
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   

3.
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   

4.
A new set of realizability conditions for the driving point impedance of a passive-lumped-terminated cascade of lossless two-ports separated by noncommensurate transmission lines is presented. The proposed set of realizability conditions eliminates the multivariable positive-reality requirement in favour of some simpler explicit conditions. Formulae for the chain matrices of the lumped lossless two-ports and the terminating impedance function are also given. Examples are provided to illustrate the main results.  相似文献   

5.
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   

6.
In this paper, the characterization of a two-variable reactance polynomial φ(λ,μ) is given in terms of the residue matrices of a single variable reactance matrix, Y(λ). Specificially, if Y(λ) is expressed in terms of its partial fraction as Y(λ)=λH∞+ΣHi+jβiλ+jωi+G where the residue matrices in general are p.s.d. Hermitian, then the ranks of these residue matrices are fixed in relation to the construction of φ(λ,μ) as the determinant of the two-variable reactance matrix μ1+Y(λ). Three theorems concerning these ranks—one each corresponding to the finite poles, poles at ∞ and the behaviour at λ=0 of Y(λ) are stated and proved. Several properties following from these theorems are studied. Also, implications of these theorems from a network theoretic point of view, like the minimum number of gyrators required to synthesize Y(λ) to yield the specific type of φ(λ,μ) etc., are studied. In the sequel, the concept of “generalized compact pole conditions” is introduced. Finally, these results are applied for the generation of two-variable reactance functions and matrices.  相似文献   

7.
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   

8.
New necessary and sufficient conditions, which are also algorithmic in nature, are obtained for the decomposition of a multivariable reactance function or a multivariable positive real function into a sum of several single variable reactance functions or several single variable positive real functions, respectively.  相似文献   

9.
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   

10.
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   

11.
A simple theory is presented for decoupling a pair of lossless coupled nonuniform transmission lines (CNUTL), with a common return and supporting TEM waves, into two lossless nonuniform transmission lines (NUTL). This theory is independent of the port terminations, symmetry conditions, etc. The method directly relates the line parameters of the lossless CNUTL's to those of the decoupled lines and vice versa; further, the matrix parameters of the CNUTL's as a four-port are explicitly expressed in terms of those of the decoupled lines as two-ports. This theory is then utilized to study the applications of CNUTL's as directional couplers.It is shown that for CNUTL's to behave as a codirectional coupler, each of the decoupled lines should be a proportional line, while for contradirectional coupler action, the two decoupled lines have to be duals of each other. The coupling response of the codirectional coupler is found to be periodic, while the phase shift between coupled and transmitted signals varies linearly with frequency. The coupling response of various contradirectional couplers with smooth transition at one of the ends, for which the decoupled lines are “basic NUTL's with hyperbolic solutions”, are studied in detail. It is shown that all these couplers have a high-pass response and that the CNUTL's with “hyperbolic cosine squared lines” as decoupled lines have the best response of all the CNUTL's considered.  相似文献   

12.
This paper discusses a multivariable array whose elements are multivariable homogeneous polynomials which may have missing terms in any of the variables. This array permits one to obtain conditions for the realizability of a driving-point function or a transfer function as a resistively terminated low-pass ladder network. By reac- tance transformations, other forms of ladder structures can be obtained. The case of cascade-separable ladder networks is discussed in detail.  相似文献   

13.
The classical problem of broadband matching was first studied by Bode (1) and developed later by Fano (2); however, Fano's solution, although very elegant, has a practical limitation. The key idea is to replace the load Z2(S) by its Darlington equivalent ending in 1 ohm, but the optimum design is, in general, not very simple. Youla (3) proposed an alternative method where it is relatively easy to find the optimum network even for the more complex impedance load. The paper shows that maximization of the gainbandwidth product, in the presence of load or source variations, depends on the choice of the reflection coefficient zeros, either in the left half-plane or in the right half-plane.  相似文献   

14.
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   

15.
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   

16.
A basic theorem describing the convexity of the energy domain for the general family of linear time-invariant (active or passive, reciprocal or non-reciprocal, lumped or distributed, single variable or multivariable) physical system {T} is proved.Theorem: Let F = P + jQ represent the complex energy associated with any linear physical system T (n-port). For any specified excitation of frequency s and the family of constant energy content input signals {i:∥i∥= constant}, the point F describes a convex domain in the {P;Q} plane.Part I contains a mathematical and a network theoretic proof of the foregoing theorem. In Part II the geometric nature of the energy loci for the two-ports is examined. It is shown that for all two-ports with double eigenvalves the energy domain is circular. For two-ports with distinct eigenvalves, the convex energy domain is an ellipse. The geometric characterization of this elliptic domain is examined and examples verified by computer.The concept of convexity is frequently exploited in optimization of energy in electric power system and quadratic cost functions in control theory. In this respect the central theorem of this paper, its proof and geometric ramifications should prove to be of basic interest for all linear systems.  相似文献   

17.
It is shown that Youla's theory of broadband matching between a passive load and a resistive generator with a preassigned transducer power gain characteristic is completely equivalent to Wohlers' solution to the problem of compatible impedences, which transforms a given passive impedance by a lossless coupling network into another specified one.  相似文献   

18.
In this paper, necessary and sufficient conditions are derived for the existence of temporally periodic “dissipative structure” solutions in cases of weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion equations ?ci/?t = Di?2ci+Qi(c), where the enumerator index i runs 1 to n, ci = ci(x, t) denotes the concentration or density of the ith participating molecular or biological species, Di is the diffusivity constant for the ith species and Qi(c), an algebraic function of the n-tuple c = (c1,\3., cn), expresses the local rate of production of the ith species due to chemical reactions or biological interactions.  相似文献   

19.
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   

20.
Applying a state-space technique and the reactance extraction principle in the realization of multiport network functions by means of grounded active RC networks containing grounded voltage-controlled voltage sources (VCVSs) and using a minimum number of grounded capacitors, a new theorem concerning the least upper bound on the number of grounded VCVSs sufficient for the realization is proved. The obtained expression for the least upper bound allows one to generate the least upper bound on the number of VCVSs sufficient to realize each of all possible different types of multiport network functions.The proof of the theorem is based upon the use of results concerning the number of VCVSs sufficient and, in general, necessary to realize an arbitrary real multiport network function by means of grounded active resistive multiport networks embedding grounded VCVSs, and on the results concerning the possibility of choosing a convenient equivalent minimal system realization.  相似文献   

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