Distributed Parameter Networks Research Articles

Controller design for bush-type 1-d wave networks

In this paper, we introduce a new method for feedback controller design for the complex distributed parameter networks governed by wave equations, which ensures the stability of the closed loop system. This method is based on the uniqueness theory of ordinary differential equations and cutting-edge approach in the graph theory, but it is not a simple extension. As a realization of this idea, we investigate a bush-type wave network. The well-posedness of the closed loop system is obtained via Lax-Milgram's lemma and semigroup theory. The validity of cutting-edge method is proved by spectral analysis approach. In particular, we give a detailed procedure of cutting-edge for the bush-type wave networks. The results show that if we impose feedback controllers, consisting of velocity and position terms, at all the boundary vertices and at most three velocity feedback controllers on the cycle, the system is asymptotically stabilized. Finally, some examples are given.

Low-reflection bandpass filters with a flat group delay

Recently, low-reflection low-pass RLC filters with a linear phase characteristic have been reported. This paper is an extension of this study on bandpass filters, including their realizations with lumped-element and distributed-parameter networks. A topology particularly suitable for microstrip techniques is proposed. It yields a compact design that enables miniaturization and is easy for manufacturing and tuning.

Circuit Theory: Progress and Trends

The paper surveys the important developments in circuit theory during the last twenty- five years. Areas covered are: General network analysis and synthesis methods, network topology, passive networks, active networks, digital filters, distributed-parameter networks, nonlinear networks, computer-aided analysis and synthesis methods and large-scale networks.

Computer-Aided Analysis of Estuarine Dynamics Simulated by a Distributed Parameter Model

A simulation model of water pollution dynamics for computer-aided analysis of water quality along an estuary is developed. The model is based on the analytical solution of the diffusion equation describing the pollution concentration when the vertical and lateral dynamics of the estuary are negligible. The estuary is simulated by a cascade connection of uniform distributed parameter networks which represent estuary segments. Each distributed parameter network is treated as a two-port device whose input-output characteristics in the frequency domain are given by its transmission matrix. An algorithm is given for approximating the two-port parameters to any prescribed accuracy so that the two-port dynamics can be synthesized as an active lumped-parameter electrical network. This network, when used with a computer-aided circuit analysis program, yields the pollution concentration profile along the estuary.

Application of Topological Formulas to Distributed Parameter Networks

Topological formulas for lumped electrical networks are extended to distributed parameter networks, and explicit expressions are obtained for the two-port parameters of a non-uniform transmission line. The results agree with those derived earlier by Protonotarios and Wing following a different procedure.

Bounded input—bounded output stability of systems†

Abstract The bounded input-bounded output stability of nth-order systems is discussed in this work. In essence, one can demonstrate such stability when it is possible to construct a Liapunov function V whose total time derivative under the forcing function can be given by [Vdot] ≤ rV + sV½ where r and s are positive constants. This differential inequality implies a bounded response, and bounded input—bounded output stability is demonstrated via this method for an asymptotically stable constant coefficient system, an asymptotically stable linear periodic system, a forced non-linear system of the Lurie type that satisfies a Popov-type condition,, and a linear time-varying system satisfying a circle criterion. While similar results have been obtained (Kalman and Bertram 1960, Sandberg 1964 a, 1965 a, b. Zames 1965), the approach used in this work following that of Goldwyn et, al. (1966) has been extended to distributed parameter networks and systems (de Figueiredo and Chao 1969) and has been used in the stud...

Remark and Corrections on 'Stability Results for classes of distributed Parameter networks and Systems'

Remark and Corrections on 'Stability Results for classes of distributed Parameter networks and Systems'

Stability Results for Classes of Distributed Parameter Networks and Systems

A number of stability results for general systems of linear and nonlinear partial differential equations that describe distributed parameter networks and systems are obtained by means of Liapunov's direct method. Conditions for the asymptotic stability of the null solution of linear time-invariant distributed parameter systems are given. This result is then extended to a class of distributed parameter systems consisting of a linear system and a zero-memory nonlinear elment described by a set of Lurie-like partial differential equations. Bounded input-bounded output stability for the above two classes of systems is established by extension of a result of Goldwyn, Chao, and Chang for lumped parameter systems. Finally, it is shown how Malkin's theorem on the stability under persistent disturbances can be extended to provide a solution to the dynamic range problem for systems described by a general set of nonlinear partial differential equations.

Sensitivity of Active RC Distributed Networks

Sensitivity limitations in the realization of Yanagisawa active filters with distributed parameter networks of the Heizer single-pole type are discussed. It is demonstrated that such filters cannot be realized in thin-film form with adequately low sensitivity using the available technology.

Analysis of Distributed Parameter Networks — A General Method

A general method is presented f or obtaining approximate analytical solutions for distributed parameter networks where the parameters may be functions of the spatial variable. By means of this technique, an explicit approximate solution for the output of a rather general network is presented. For those cases where exact separable solutions exist the method yields the correct solutions.

Tantalum-film technology

In tantalum film circuitry, capacitors, resistors, and rudimentary interconnections are all produced in a single pattern of tantalum. Important processes are discussed in detail including 1) sputtering, by which tantalum films are produced, 2) pattern generation, and 3) anodization, by which capacitor dielectrics are formed and by which resistors are protected and adjusted to value. Predominantly the discussion is based on developments and practices of Bell Telephone Laboratories. Capacitors withstand stresses of several million volts/cm, have low leakages, a temperature coefficient of +200 to +250 ppm/°C, and a dissipation factor at 1 kc of 1 per cent maximum. Resistors of outstanding quality can be made from tantalum nitride produced by reactive sputtering. These resistors have high electrical stability and low temperature coefficients and can be fabricated to initial tolerances as low as 0.01 per cent. Because of the versatility of tantalum technology, a wide variety of circuit types can be fabricated. Tantalum technology is particularly valuable in the fabrication of thin-film integrated circuits with severe precision requirements as in the precise tuning of thin-film notch filters, and for distributed parameter networks.

The calculus of deviations applied to transistor circuit and network analysis

The Calculus of Deviations is introduced, and its nature and basis are briefly discussed. A deviation is described as “a measure of the lack of complete functional interdependence between two quantities” Rules are given for using the calculus in solving various transistor and network problems, including the analysis of distributed-parameter networks. The complexity of network analysis is verygreatly reduced by the use of this powerful, easy-to-use, mathematical tool

A Distributed-Parameter Approach to the High-Frequency Network Representation of Wide-Band Transformers.

An approach to the high-frequency representation is developed from the point of view of distributed-parameter networks. This viewpoint may be directly employed to compute insertion or transmission functions. Alternatively, it provides a method for determining the element values for lumped-parameter equivalent circuits. This method is most easily applied to transformers having two winding layers with turns ratios which are either very nearly unity or which depart very greatly from unity, and the paper largely confines itself to these cases. Distributed-parameter insertion-voltage ratios for a number of common two-winding transformer connections are presented and compared with experimental results.