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  • 1. Stability and Power-Gain Invariants of Linear Twoports

    Publication Year: 1962, Page(s):29 - 32
    Cited by:  Papers (190)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (528 KB)

    It is shown that the stability of a linear twoport is invariant under arbitrary lossless terminations, under interchange of input and output, and under "immittance substitution," a transformation group involving the arbitrary interchanging of impedance and admittance formulations at both ports. The quantity k = frac {2 \Re (\gamma _{11}) \Re (\gamma _{22}) - \...
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  • 2. On the Design of Filters by Synthesis

    Publication Year: 1958, Page(s):284 - 327
    Cited by:  Papers (17)  |  Patents (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (4344 KB)

    Following an introduction to the methods and significance of filter design, this paper deals with definitions and filter synthesis according to prescribed attenuation requirements. It shows how the characteristic function for cases of practical importance can be calculated, particularly for the special cases 1) where this function is a power term in the frequency variable (maximally flat), 2) wher... View full abstract»

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  • 3. Theoretical Limitations on the Broad-Band Matching of Arbitrary Impedances

    Publication Year: 1961, Page(s): 165
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (120 KB)

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  • 4. A practical method of designing RC active filters

    Publication Year: 1955, Page(s):74 - 85
    Cited by:  Papers (135)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    IN THE FREQUENCY range below about 30 cps, the dissipation factors of available inductors are generally too large to permit the practical design of inductance-capacitance (LC) or resistance-inductance-capacitance (RLC) filter networks. The circuits described in the following pages were developed and collected to provide an alternative method of realizing sharp cut-off filters at very low frequenci... View full abstract»

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  • 5. On the Stability of Time-Varying Linear Systems

    Publication Year: 1962, Page(s):420 - 422
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (424 KB)

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  • 6. On Nonuniform Sampling of Bandwidth-Limited Signals

    Publication Year: 1956, Page(s):251 - 257
    Cited by:  Papers (279)  |  Patents (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 KB)

    The purpose of this investigation is to examine four special nonuniform sampling processes in detail, and to deduce some interesting properties of bandwidth-limited signals. The main results are contained in four generalized sampling theorems. These theorems not only contain the nature of determination (unique-specification, over-specification, and underspecification) of signals but also include e... View full abstract»

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  • 7. The Scattering Matrix in Network Theory

    Publication Year: 1956, Page(s):88 - 97
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1192 KB)

    This paper gives an introductory treatment of the concept and uses of scattering methods in network problems. The scattering parameter description for linear networks is defined and the utility of this formalism for problems involving power flow in terminated networks is discussed. Examples of scattering computations for transformer 4-ports, transformerless impedance matching networks and transduc... View full abstract»

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  • 8. Synthesis of a Class of Strip-Line Filters

    Publication Year: 1958, Page(s):104 - 109
    Cited by:  Papers (76)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (624 KB)

    This paper describes a design theory for a class of strip-line filters on an insertion loss basis. The important part of the paper is the equivalent transformations showing the close correspondence between lumped and coupled-line distributed parameter circuits. An introduction is provided for clarification. Line type, low-pass ladder, high-pass ladder, and band-pass ladder type filters are realize... View full abstract»

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  • 9. Negative-Impedance Converters

    Publication Year: 1957, Page(s):124 - 131
    Cited by:  Papers (39)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (856 KB)

    The conditions under which an active device exhibits an input impedance at one terminal pair which is exactly the negative of the load impedance connected to the other terminal pair are discussed. There are an infinite number of ways by which such a device, which is called a negative-impedance converter (NIC), can be made. One of the limits of this set is represented by a transistor circuit which ... View full abstract»

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  • 10. Noise in Negative-Resistance Amplifiers

    Publication Year: 1960, Page(s):166 - 170
    Cited by:  Papers (33)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (512 KB)

    Negative-resistance amplifiers that consist of a noisy negative resistance imbedded in a lossless three-terminal-pair linear network to make a two-port amplifier are analyzed. It is shown that Haus and Adler's noise measure M_{e} , is not constrained to lie between two eigenvalues of a noise matrix, as is the case for bona fide two-port amplifiers. Instead, ... View full abstract»

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  • 11. Some Extensions of Liapunov's Second Method

    Publication Year: 1960, Page(s):520 - 527
    Cited by:  Papers (312)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1064 KB)

    >In the study of the stability of a system, it is never completely satisfactory to know only that an equilibrium state is asymptotically stable. As a practical matter, it is necessary to have some idea of the size of the perturbations the system can undergo and still return to the equilibrium state. It is never possible to do this by examining only the linear approximation. The effect of the no... View full abstract»

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  • 12. Bounded Real Scattering Matrices and the Foundations of Linear Passive Network Theory

    Publication Year: 1959, Page(s):102 - 124
    Cited by:  Papers (101)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2312 KB)

    In this paper the most general linear, passive, time-invariantn-port (e.g., networks which may be both distributed and non-reciprocal) is studied from an axiomatic point of view, and a completely rigorous theory is constructed by the systematic use of theorems of Bochner and Wiener. Ann-portPhiis defined to be an operator inH_n, the space of all... View full abstract»

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  • 13. A Study of Rough Amplitude Quantization by Means of Nyquist Sampling Theory

    Publication Year: 1956, Page(s):266 - 276
    Cited by:  Papers (133)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1288 KB)

    Quantization is an operation that takes place when a physical quantity is represented numerically. It is the assignment of an integral value to a physical quantity corresponding to the nearest number of units contained in it. Quantization is like "sampling-in-amplitude," which should be distinguished from the usual "sampling-in-time." The probability density distribution of the signal is sampled i... View full abstract»

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  • 14. A Survey of Network Realization Techniques

    Publication Year: 1955, Page(s):291 - 297
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    This paper is a brief survey of network realization techniques, from a general point of view. By realization techniques is meant methods of finding explicit networks (configurations and element values) from prescribed characteristics (such as impedance functions) which can be realized exactly. The statement of conditions under which prescribed characteristics are realizable is included in the defi... View full abstract»

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  • 15. Q Factors of a Transmission Line Cavity

    Publication Year: 1957, Page(s):3 - 5
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (288 KB)

    On investigating the properties of a transmission line cavity, new expressions for the Q factor and logarithmic decrement \delta were derived, and were compared with the expressions for a single shunt or series LCR circuit. It was expected that the expressions for Q and View full abstract»

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  • 16. Topics in the Design of Insertion Loss Filters

    Publication Year: 1955, Page(s):337 - 346
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1152 KB)

    This paper combines the theory of scattering matrices and the design of filters on an insertion loss basis. It is not intended to add substantially new results. Its purposes are to simplify the presentation of the insertion-loss theory, with the help of the scattering parameters, and to study a number of particular cases serving as a guide in practical design and as a starting point of approximate... View full abstract»

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  • 17. The A Matrix, New Network Description

    Publication Year: 1957, Page(s):117 - 119
    Cited by:  Papers (67)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (344 KB)

    Both the loop and node methods of network analysis produce a system of second-order differential equations. A method of analysis is proposed which produces a set of first-order differential equations. With this method, the network equations obtained can be expressed in the form F + dy/dt = Ay , where F and View full abstract»

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  • 18. Kirchhoff's 'Third and Fourth Laws'

    Publication Year: 1958, Page(s):8 - 30
    Cited by:  Papers (12)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (2816 KB)

    The epoch-marking publication of Kirchhoff in 1847 is considered in this paper. The rule given by Kirchhoff deserves to be understood by almost all engineers, for it shows how to determine in a simple and straightforward way the system functions of any passive network that contains no transformers. Preliminary to the consideration of the rule and its dual, the basic concepts of combinatorial topol... View full abstract»

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  • 19. The Fourier Integral-A Basic Introduction

    Publication Year: 1955, Page(s):227 - 230
    Cited by:  Papers (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    The object of this introduction is to give the reader an idea of the various kinds of problems in which the Fourier series or integral is useful, and to discuss not only the essential properties which make it useful, but also to point out the limitations and restrictions imposed by these properties. Collaterally it is significant to recognize the flexibility that is inherent in the Fourier represe... View full abstract»

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  • 20. Survey of Some Properties of Linear Networks

    Publication Year: 1957, Page(s):70 - 78
    Cited by:  Papers (7)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (888 KB)

    An attempt is made to give a brief exposé of some modern works on linear network properties. The concepts treated are the following: passivity, stability, efficiency, and nonreciprocity; n -terminal-pair networks and two-terminal-pair networks in particular are studied at a fixed frequency. View full abstract»

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  • 21. Computation of Elliptic Functions of Rational Fractions of a Quarterperiod

    Publication Year: 1958, Page(s):352 - 355
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (496 KB)

    The evaluation of Jacobian elliptic functions with arguments which are rational fractions of a quarterperiod is often necessary in network design. Conventional methods, using theta functions, are quite satisfactory for this purpose, but, in the more interesting range of the modulus k near unity, they do not represent the best that can be done. A slight modific... View full abstract»

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  • 22. A Synthesis Procedure for Transmission Line Networks

    Publication Year: 1958, Page(s):172 - 181
    Cited by:  Papers (18)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (944 KB)

    Richards has shown that by a suitable frequency transformation, networks composed of transmission lines all of a fixed length and resistors behave over a range of frequencies zero to f_0 as lumped constant networks behave over the frequency range zero to infinity. In this paper the synthesis procedure of a general class of lossless filters using transmission ... View full abstract»

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  • 23. Elementary Applications of the Scattering Formalism in Network Design

    Publication Year: 1956, Page(s):97 - 104
    Cited by:  Papers (32)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (832 KB)

    The purpose of this paper is to show the considerable simplification introduced by the scattering formalism in the derivation of many theorems of elementary network theory, and to illustrate how often this concept discloses new aspects of known results, or new connections between apparently unrelated properties. The examples chosen are somewhat unrelated, but they have been selected to emphasize t... View full abstract»

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  • 24. Design Principles for Single Loop Transistor Feedback Amplifiers

    Publication Year: 1957, Page(s):145 - 156
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1888 KB)

    The design of single loop transistor feedback amplifiers is considered. A criterion of stability is introduced which is useful for either calculating or measuring the stability margins of transistor amplifiers, and in particular, single loop feedback amplifiers. Expressions are derived for relating sensitivity and impedance to feedback. Practical design techniques are discussed and are illustrated... View full abstract»

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  • 25. About Such Things as Unistors, Flow Graphs, Probability, Partial Factoring, and Matrices

    Publication Year: 1957, Page(s):90 - 97
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1000 KB)

    The purpose here is to point out three things. 1) Topological circuit analysis, in which we look for trees, and topological flow-graph analysis, in which we look for loops, are intimately related, since both have to do with simultaneous linear algebraic equations. The intimate relationship becomes an indentity when we deal with Markoff probability diagrams, for which the circuit model of the probl... View full abstract»

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  • 26. Normalized Design of 90° Phase-Difference Networks

    Publication Year: 1960, Page(s):128 - 136
    Cited by:  Papers (40)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (776 KB)

    The theoretical background exists for the design of 90° phase-difference networks. Continued interest in the design of such wide-band networks for single-sideband and other applications indicates the need for methods to ease the computational difficulties inherent in network design involving elliptic functions. Concise design data are given in the form of equations, curves and tables which si... View full abstract»

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  • 27. RC Active Networks Using Current Inversion Type Negative Impedance Converters

    Publication Year: 1957, Page(s):140 - 144
    Cited by:  Papers (55)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (416 KB)

    The RC active filter, which has been established by J. G. Linvill, has a circuit configuration of a negative impedance converter sandwiched between two RC networks. This paper deals with a new circuit also using two RC networks and a converter, but its configuration is based on the parallel or series connection and the converter must be a current-inversion type. The main results obtained here are ... View full abstract»

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  • 28. Two Extensions of the Darlington Synthesis Procedure

    Publication Year: 1961, Page(s):284 - 288
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (456 KB)

    Two methods are presented which make it possible to synthesize a driving-point impedance function by a Darlington-type synthesis without surplus factors. One method relies on the use of nonreciprocal devices (gyrators) in the synthesized network. The additional constraints due to presence of gyrators are discussed. It is shown that the residue condition for physical realizability now becomes View full abstract»

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  • 29. Flow-Graph Solutions of Linear Algebraic Equations

    Publication Year: 1959, Page(s):170 - 187
    Cited by:  Papers (35)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1864 KB)

    A weighted, oriented topological structure, denoted by G and called a flow graph, is associated with a set of m equations in n variables, denoted by KX = 0 , such that K is a connection matrix and View full abstract»

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  • 30. Some Properties of Time Varying Networks

    Publication Year: 1960, Page(s):69 - 78
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (784 KB)

    In this paper, the general theory of reactance amplifiers is exemplified, with attention centered on three aspects. 1. Why may gain be obtained from a nonlinear reactance and not from a nonlinear resistance? 2. Where there is gain and feedback, the possibility of oscillation exists. But the situation is more complex than it is with vacuum tube amplifiers because the feedback path is through the mo... View full abstract»

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  • 31. Design of Unsymmetrical Band-Pass Filters

    Publication Year: 1957, Page(s):33 - 40
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (904 KB)

    The paper presents a new approach to the synthesis of band-pass filters, in particular of filters with electrical characteristics which are not symmetrical with respect to their center frequency when plotted on an arithmetic frequency scale. The synthesis proceeds in three steps: approximation, representation by means of fictitious network elements in the low-pass domain, and subsequent low-pass, ... View full abstract»

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  • 32. Application of Scattering Matrices to the Synthesis of n Ports

    Publication Year: 1956, Page(s):111 - 120
    Cited by:  Papers (10)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (976 KB)

    Scattering matrices are applied to the synthesis of finite passive n -ports ( n -terminal pair networks) with frequency dependence. A realizability theorem for scattering matrices is shown and an n -port is synthesized as a nondissipative network terminated in resistances. By considering ... View full abstract»

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  • 33. A Note on Stable, Physically Realizable, Linear, Time Invariant Systems

    Publication Year: 1962, Page(s):405 - 408
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (464 KB)

    A time invariant system is said to be physically realizable if its unit impulse response h(t) is zero for t < 0 . It is often assumed, in treatments of physical realizability, that the Fourier transform of h(t) is square integrable (L_2(-\infty ...
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  • 34. Theoretical Aspects of Nonlinear Oscillations

    Publication Year: 1960, Page(s):368 - 381
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1800 KB)

    This review gives an outline of the modern theory of nonlinear oscillations. This field, originated about four decades ago by the late Prof. B. van der Pol, acquired a considerable momentum in recent years with a gradually increasing number of ramifications, some of which are still in a state of development. For this reason the selection of topics for this review is narrowed down to matters which ... View full abstract»

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  • 35. Physical Realizability Criteria

    Publication Year: 1960, Page(s):50 - 68
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1520 KB)

    The main objective of this paper is to present a brief survey of the theory of linear, passive, time-invariant n-ports both from an axiomatic standpoint and a synthesis point of view. hthe first approach the n-port is defined in terms of its behaviour in real-time and its steady-state behaviour is deduced as a logical consequence. In the second approach the network is restricted, apriori, to be of... View full abstract»

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  • 36. Nonlinear control systems with random inputs

    Publication Year: 1954, Page(s):9 - 18
    Cited by:  Papers (20)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (643 KB)

    The describing-function method for the analysis of nonlinear systems with sinusoidal inputs is interpreted as a mean-square quasi-linearization technique and is generalized to apply to random signals. An amplitude-sensitive (or zero-memory) nonlinearity is interpreted as being approximately equivalent to a linear frequency-insensitive device, and a formula is derived for its equivalent gain. A sim... View full abstract»

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  • 37. Evaluation of Fourier Transforms

    Publication Year: 1955, Page(s):243 - 250
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (936 KB)

    This paper deals with numerical methods as well as with the use of digital and analog computer methods for the evaluation of Fourier integrals. Graphical methods of integration are described which enable one to obtain arbitrarily good accuracy with a minimum amount of computational effort through the use of the Fourier integral property that permits a representation in terms of an appropriate high... View full abstract»

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  • 38. Frequency Entrainment in a Self-Oscillatory System with Ex-ternal Force

    Publication Year: 1960, Page(s):413 - 422
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (864 KB)

    This paper deals with forced oscillations in a self-oscillatory system of the negative-resistance type. When no external force is applied, the system produces a self-excited oscillation. Under the impression of a periodic force, the frequency of the self-excited oscillation falls in synchronism with the driving frequency within a certain band of frequencies. This phenomenon of frequency entrainmen... View full abstract»

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  • 39. On Matrices of Residues of the Impedance or Admittance Matrices of n Ports

    Publication Year: 1957, Page(s):20 - 21
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (216 KB)

    In the paper some properties of matrices of residues for the open-circuit impedance or the short-circuit admittance representation of n -ports are discussed. It is shown that at a simple pole, located wherever in the complex plane, the matrix of residues of the impedance or admittance matrix is, in general, highly degenerate. The rank of the matrix of residues ... View full abstract»

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  • 40. Application of the Fourier Integral in Circuit Theory and Circuit Problems

    Publication Year: 1955, Page(s):237 - 243
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 KB)

    The straightforward application of the Fourier integral to determine the response of a linear invariable circuit to an arbitrary impressed force is reviewed. When a Fourier integral representation of the impressed force exists and the system starts from rest, the problem is routine. Extensions to cases such as impulses, step functions, and ramp functions, for which the Fourier integral along the r... View full abstract»

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  • 41. Wave Representation of Amplifier Noise

    Publication Year: 1962, Page(s):84 - 86
    Cited by:  Papers (40)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (416 KB)

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  • 42. Synthesis of Resistive N-Port Networks with N + 1 Nodes

    Publication Year: 1962, Page(s):69 - 73
    Cited by:  Papers (8)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (520 KB)

    In this paper a systematic procedure is proposed to obtain the n -port structure appropriate to the Y matrix of a resistive network containing exactly n + 1 nodes. The method presents: A set of necessary conditions which may eliminate quickly a large class of matrices from further con... View full abstract»

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  • 43. Application of Mellin and Hankel Transforms to Networks with Time-Varying Parameters

    Publication Year: 1959, Page(s):197 - 208
    Cited by:  Papers (14)  |  Patents (1)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (848 KB)

    Integral transform techniques for solving linear integro-differential equations can provide insight and flexibility in solving physical problems, especially network problems. The type of differential equation which describes the physical system will dictate the transform that should be applied to simplify the solution and this paper deals with two transforms, namely, the Mellin transform and the H... View full abstract»

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  • 44. High-Frequency High-Power Operation of Tunnel Diodes

    Publication Year: 1961, Page(s):416 - 425
    Cited by:  Papers (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1136 KB)

    The operation of oscillators using high-current tunnel diodes above their self-resonant frequency is presented. General stability conditions of the tunnel diode, including external circuits (lumped and distributed), are discussed. Based on a nonlinear analysis of a tunnel-diode oscillator, the power generated by the diode, the power dissipated within the diode and the power delivered to an externa... View full abstract»

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  • 45. Minimum-Loss Two-Conductor Transmission Lines

    Publication Year: 1958, Page(s):214 - 216
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (312 KB)

    Of all two-conductor transmission lines in which the harmonic mean of the perimeters of the two conductors is fixed, the one having the lowest loss is a conventional round coaxial line. It is conjectured that the same is true of the class having fixed cross section area. View full abstract»

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  • 46. Some Simplification for Analysis of Linear Circuits

    Publication Year: 1957, Page(s):120 - 124
    Cited by:  Papers (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (544 KB)

    Any linear, passive, or active two-terminal pair network is describable in terms of six, interrelated "characteristic polynomials." A method for finding them is presented which requires less labor than is usually involved in finding a set of the conventional circuit parameters. Examples are given. Having found the characteristic polynomials, all of the conventional parameters, such as the open-cir... View full abstract»

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  • 47. The Explicit Form of Bashkow's A Matrix

    Publication Year: 1962, Page(s):303 - 306
    Cited by:  Papers (79)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (256 KB)

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  • 48. Equivalent Distributed RC Networks of Transmission Lines

    Publication Year: 1962, Page(s):247 - 251
    Cited by:  Papers (21)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (480 KB)

    There are any number of pairs of resistance and capacitance density functions, i.e., r(x) and c(x) , which can provide the same electrical performance as a given distributed RC laddernetwork. In general these equivalent networks will have different lengths. A criterion for equivalence of density functions is expressed i... View full abstract»

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  • 49. On the Analysis and Synthesis of Single-Element-Kind Net-works

    Publication Year: 1960, Page(s):303 - 312
    Cited by:  Papers (42)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1080 KB)

    This paper presents a method for the realization of a given nth order node conductance (or capacitance or reciprocal inductance) matrix as an (n + 1) -node network with all positive elements and no ideal transformers. The first part establishes simple relations between branch conductances and elements in the given matrix which are assumed to be based upon a ... View full abstract»

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  • 50. Comment on the paper “A mathematical analysis of a series circuit containing periodically varying resistance” by L. A. Pipes

    Publication Year: 1955, Page(s):72 - 73
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (276 KB)

    AT FIRST sight, the application of W.K.B. approximation to a time-dependent circuit seems perfectly straightforward. Unfortunately, there are two different and equally plausible ways to apply it to the circuit treated by Pipes, and the two results will generally not agree. The W.K.B. solution of the homogeneous equation (43) contains two arbitrary constants. These can be chosen so that at some par... View full abstract»

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