Some Fundamental Properties of Transmission Systems
01 Mar 1952-Vol. 40, Iss: 3, pp 271-283
TL;DR: In this article, the minimum loss in relation to the singing point is investigated for generalized transmission systems that must be stable for any combination of passive terminating impedances, and it is concluded that the loss may approach zero db only in those cases where the image impedances seen at the ends of the system are purely resistive.
Abstract: The problem of the minimum loss in relation to the singing point is investigated for generalized transmission systems that must be stable for any combination of passive terminating impedances. It is concluded that the loss may approach zero db only in those cases where the image impedances seen at the ends of the system are purely resistive. Moreover, in such cases, the method of overcoming the transmission loss, whether by conventional repeaters or by series and shunt negative impedance loading, or otherwise, is quite immaterial to the external behavior of the system as long as the image impedances are not changed. The use of impedance-correcting networks provides one means of insuring that phase of the image impedance of the over-all system approaches zero. General relations are derived which connect the image impedance and the image gain of an active system with its over-all performance properties.
Citations
More filters
19 Oct 1999
TL;DR: By decoupling the haptic display control problem from the design of virtual environments, the use of a virtual coupling network frees the developer of haptic-enabled virtual reality models from issues of mechanical stability.
Abstract: This paper addresses fundamental stability and performance issues associated with haptic interaction. It generalizes and extends the concept of a virtual coupling network, an artificial link between the haptic display and a virtual world, to include both the impedance and admittance models of haptic interaction. A benchmark example exposes an important duality between these two cases. Linear circuit theory is used to develop necessary and sufficient conditions for the stability of a haptic simulation, assuming the human operator and virtual environment are passive. These equations lead to an explicit design procedure for virtual coupling networks which give maximum performance while guaranteeing stability. By decoupling the haptic display control problem from the design of virtual environments, the use of a virtual coupling network frees the developer of haptic-enabled virtual reality models from issues of mechanical stability.
703 citations
Cites background from "Some Fundamental Properties of Tran..."
...For linear two-ports, Llewellyn’s stability criteria provide both necessary and sufficient conditions for unconditional stability [22]...
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TL;DR: In this paper, it was shown that the stability of a linear two-port 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.
Abstract: 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}) - Re(\gamma_{12} \gamma_{21})} {|\gamme_{12} \gamma_{21}|} (where the \gamma may be any of the conventional immittance z, y, or hybrid h, g matrix parameters) is the simplest invariant under these transformations, and describes uniquely the degree of stability, provided Re(\gamma_{11}), Re(\gamma_{22}) \geq 0; the larger k is, the greater the stability, and in particular k = 1 defines the boundary between unconditional and conditional stability. The quantity k is thus the basic invariant stability factor. Its definition is also extended to include the effect of terminating immittances, which may be padding resistances or source and load immittances, or both. Certain power-gain functions, including the maximum available power gain, are shown to be invariant under immittance substitution, and k is identified as a function of ratios between them, where they exist. This provides a fundamental way of determining k, apart from calculating it from matrix parameters, and indicates that it is a measure of an inherent physical property.
378 citations
18 Jun 1969
TL;DR: The realisation of negative-impedance convertors and invertors using the bridge-type circuit using the nullor to infinite-gain controlled sources is briefly surveyed and a relevant theorem concerning passivity is proved.
Abstract: The realisation of negative-impedance convertors (n.i.c.s) and invertors (n.i.i.s) using the bridge-type circuit is briefly surveyed. An equivalence relating the nullor to infinite-gain controlled sources is first proved, and is then used for the derivation of nullator-norator equivalent circuits for n.i.c.s and n.i.i.s. Some properties of networks containing singular elements, which are used in the realisation of gyrators, are investigated. Nullator-norator equivalent circuits for gyrators are derived by using the n.i.c.s and n.i.i.s. They are converted into physical networks by using the proved equivalence. Gyrator circuits are obtained by replacing nullors by operational amplifiers. A stability analysis of the gyrator circuits is produced and a relevant theorem concerning passivity is proved. The feasible Qfactors and the accuracy of the gyrator circuits are indicated by some experimental results. A generalised-impedance convertor (g.i.c.) is defined by generalising the n.i.c. theory, and it is shown that the gyrator circuits described can be used as g.i.c.s. The application of the gyrator and g.i.c. circuits in the synthesis of RC-active networks is considered. Finally, a highpass filter using gyrators and a bandpass filter using g.i.c.s are designed, and the experimental results are given.
252 citations
TL;DR: A bilateral teleoperation experiment with Engineering Test Satellite 7 (ETS-VII) was conducted on November 22, 1999 as mentioned in this paper, where several experiments, such as slope-tracing task and peg-in-hole task, were carried out.
Abstract: A bilateral teleoperation experiment with Engineering Test Satellite 7 (ETS-VII) was conducted on November 22, 1999. Round-trip time for communication between the National Space Development Agency of Japan ground station and the ETS-VII was approximately seven seconds. We constructed a bilateral teleoperator that is stable, even under such a long time delay. Several experiments, such as slope-tracing task and peg-in-hole task, were carried out. Task performance was compared between the bilateral mode and the unilateral mode with force telemetry data visually displayed on a screen. All tasks were possible by bilateral control without any visual information. Experimental results showed that kinesthetic force feedback to the operator is helpful even under such a long time delay, and improves the performance of the task.
203 citations
TL;DR: A control design approach which stabilizes a haptic interface when coupled to a broad class of human operators and virtual environments is outlined, including structural flexibility and noncollocation of sensors and actuators.
Abstract: The goal of control law design for haptic displays is to provide a safe and stable user interface while maximizing the operator's sense of kinesthetic immersion in a virtual environment. This paper outlines a control design approach which stabilizes a haptic interface when coupled to a broad class of human operators and virtual environments. Two-port absolute stability criteria are used to develop explicit control law design bounds for two different haptic display implementations: the impedance display and admittance display. The strengths and weaknesses of each approach are illustrated through numerical and experimental results for a three degree-of-freedom device. The example highlights the ability of the proposed design procedure to handle some of the more difficult problems in control law synthesis for haptics, including structural flexibility and noncollocation of sensors and actuators.
183 citations
Cites background from "Some Fundamental Properties of Tran..."
...Llewellyn’s stability criteria provide both necessary and sufficient conditions for absolute stability of linear two-ports [14],[15], • P s ( ) has no poles in the right half s - plane, only simple poles on the imaginary axis,...
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References
More filters
01 Jul 1939
TL;DR: In this paper, the maximum uniform amplification that can be secured over a wide frequency band by means of a single vacuum tube is much greater than that of the usual simple circuits, which can be achieved by either of two arrangements, one using an individual filter coupling each tube to the next, and the other using degenerative feedback in each stage to make the stage behave as a section of a confluent filter.
Abstract: The maximum uniform amplification that can be secured over a wide frequency band by means of a single vacuum tube is much greater than that of the usual simple circuits. It can be secured by either of two arrangements, one using an individual filter coupling each tube to the next, and the other using degenerative feedback in each stage to make the stage behave as a section of a confluent filter. In either case, the shunt capacitance on each side of each tube is included in an individual full-shunt arm of a band-pass or low-pass filter. One end of each interstage filter, or of each filter including one or more feedback stages, is extended to a dead-end termination with resistance approximately matching the image impedance. The other end is terminated at one of the tubes in a full-shunt arm, where the filter presents the maximum uniform impedance that can be built up across the tube capacitance. These concepts in terms of wave filters lead to practical wide-band circuits adapted to meet any given requirements. The following general formula is shown to express the maximum uniform amplification that can be secured in one tube: gm A= 7rfwVCgCp in which A is the voltage ratio between input and output circuits of equal impedance, g m is the transconductance of the tube, C g , and C p , are the grid and plate capacitance of the tube, and f w is the width of the frequencv band.
50 citations
TL;DR: In this paper, the theoretical response curves of finite chains of the feedback networks described by Wheeler are studied and a generalization of a standard formula for passive filters is obtained and applied to the problem.
Abstract: The theoretical response curves of finite chains of the feedback networks described by Wheeler are studied. A generalization of a standard formula for passive filters is obtained and applied to the problem. The paper presents computed reflection coefficients for various simple terminations and computed response curves for feedback chains of three, four, and five stages, using these terminations. Many of the response curves are unsatisfactory. These occur with the simpler types of terminations such as normally occur in practice. It is shown how matching at both ends of the amplifier can greatly improve the response curves with a loss of gain. Curves are also given that show the advantage of using a constant-k; half-section as a termination.
1 citations