Synthesis of Reactance 4‐Poles Which Produce Prescribed Insertion Loss Characteristics: Including Special Applications To Filter Design

Darlington, S.

doi:10.1002/sapm1939181257

Cited by 309 publications

(50 citation statements)

References 13 publications

(54 reference statements)

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“…9.4], [4]. A classical alternative procedure due to Darlington [5] realizes the impedance as a lossless two-port network terminated in a single resistance. The possibility of achieving the synthesis without the use of transformers was first established by Bott and Duffin [3].…”

Section: Classical Network Synthesismentioning

confidence: 99%

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Synthesis of mechanical networks: the inerter

Smith

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

279

532

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Abstract-This paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of this paper is the introduction of a device, which will be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits to be translated over to mechanical ones in a completely analogous way. The inerter need not have large mass. This allows any arbitrary positive-real impedance to be synthesized mechanically using physical components which may be assumed to have small mass compared to other structures to which they may be attached. The possible application of the inerter is considered to a vibration absorption problem, a suspension strut design, and as a simulated mass.

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Section: Classical Network Synthesismentioning

confidence: 99%

“…It is interesting to ask if the admittance (13) may be realized using only one damper. An approach which will achieve this uses the method of Darlington [5], [11,Ch. IX.6].…”

Section: F Realizations Using Darlington Synthesismentioning

confidence: 99%

Synthesis of mechanical networks: the inerter

Smith

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

279

532

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“…A. E. Atia, et al, in [1] and [2] elaborated the synthesis of coupling matrix for general filter functions. Started from the factorization of the two-port filter admittance, the original coupling matrix is obtained from the eigen-matrix and transformation matrix using the standard Darlington procedure [3]. Since transformation matrix is derived from the GramSchmidt Orthonormalization of its first and last rows, all the eigenvalues related to an eigen-matrix can be preserved in the resultant coupling matrix.…”

Section: Introductionmentioning

confidence: 99%

“…Differed from the general synthesis of coupling matrix, Levy's synthesis design [6] is based primarily on constructing an equivalent quadruplet structure and solving its element circuit values, adopting both an approximation method and a much more accurate synthesis also based on standard Darlington procedure [3]. Furthermore, Hong used this quadruplet structure to implement selective band-pass filters on planar microwave structure [8,9].…”

Section: Introductionmentioning

confidence: 99%

Numerical Synthesis Design of Coupled Resonator Filters

Wen¹,

Li²

2009

PIER

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Abstract-This paper proposes a methodology for numerically synthesizing element values of coupled resonator filters. These element values are compatible in retrieving coupling matrix of a cross-coupled quadruplet structure (also known as the folded structure). Differed from direct synthesis by matrix rotation, numerical solution has been adopted here to its equivalent coupling model. For varied specified return loss, numerical solutions of these element values have been derived and their accuracy is verified with their analytical counterparts to be extended for stringent design requirement. In addition, multiple sets of data are tabulated and categorized for efficient filter synthesis design under different specified pass-band return loss. In the end, an example quadruplet filter is designed, fabricated and measured for validation of the presented synthesis design methodology.

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“…T RADITIONAL Darlington synthesis [1] is concerned with the realization of a rational and 'bounded real' transfer function with bound 1 as a partial transfer operator of a 'lossless' transfer matrix , which then has the form (1) and in which the Smith-McMillan degree of is equal to that of (it is equal to the dimension of the state space of a minimal system theoretical realization for ). In addition to the embedding, a cascade realization of , which can always be performed in the rational case, results in an attractive Manuscript received May 1, 1998; revised August 1, 1998.…”

Section: Introductionmentioning

confidence: 99%

Generalized Darlington synthesis

Dewilde

1999

IEEE Trans. Circuits Syst. I

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Abstract-The existence of a "Darlington embedding" has been the topic of vigorous debate since the time of Darlington's original attempts at synthesizing a lossy input impedance through a lossless cascade of sections terminated in a unit resistor. This paper gives a survey of present insights in that existential question. In the first part it considers the multiport, time invariant case, and it gives the necessary and sufficient conditions for the existence of the Darlington embedding, namely that the matrix transfer scattering function considered must satisfy a special property of analyticity known as "pseudomeromorphic continuability" (of course aside from the contractivity condition which ensures lossiness). As a result, it is reasonably easy to construct passive impedances or scattering functions which do not possess a Darlington embedding, but they will not be rational, i.e. they will have infinite dimensional state spaces. The situation changes dramatically when time-varying systems are concerned. In this case also Darlington synthesis is possible and attractive, but the anomalous case where no synthesis is possible already occurs for systems with finite dimensional state spaces. We give precise conditions for the existence of the Darlington synthesis for the time-varying case as well. It turns out that the main workhorse in modern Darlington theory is the geometry of the so called Hankel map of the scattering transfer function to be embedded. This fact makes Darlington theory of considerably larger importance for the understanding of systems and their properties than the original synthesis question would seem to infer. Although the paper is entirely devoted to the theoretical question of existence of the Darlington embedding and its system theoretic implications, it does introduce the main algorithm used for practical Darlington synthesis, namely the 'square root algorithm' for external or inner-outer factorization, and discusses some of its implications in the final section.

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Synthesis of Reactance 4‐Poles Which Produce Prescribed Insertion Loss Characteristics: Including Special Applications To Filter Design

Cited by 309 publications

References 13 publications

Synthesis of mechanical networks: the inerter

Synthesis of mechanical networks: the inerter

Numerical Synthesis Design of Coupled Resonator Filters

Generalized Darlington synthesis

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