Single‐step algorithm for the cascade assembly of multiple S‐parameters based multiports networks

Paulis, Francesco de; Scafati, Simone; Olivieri, Carlo; Orlandi, Antonio

doi:10.1002/mmce.23070

Cited by 4 publications

(5 citation statements)

References 25 publications

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“…The procedure is applied to a complex and accurately characterized multipin connector. The comparison of the scattering parameters of the connector obtained by its direct characterization 21,22,24 and by the proposed de-embedding is quantified by specific (AME) and global (RMSE) error parameters that confirm the accuracy of the proposed analytical method. The proposed methodology can be readily applied by implementing a simple matrix expression, and its accuracy does not depend on the frequency.…”

Section: Numerical Validationmentioning

confidence: 61%

“…In (21), I ¼ d is the identity matrix. For sake of compactness, the matrix constant MA is defined according to ( 22)…”

Section: Left Fixture Multiport Deembeddingmentioning

confidence: 99%

“…From Figure 1 by definition

([], \begin{matrix} b_{1} \\ b_{4} \end{matrix}) goodbreak= ([], \begin{matrix} S_{m, 11} & S_{m, 12} \\ S_{m, 21} & S_{m, 22} \end{matrix}) ([], \begin{matrix} a_{1} \\ a_{4} \end{matrix})

and

([], \begin{matrix} b_{1} \\ b_{2} \end{matrix}) goodbreak= ([], \begin{matrix} S_{FL, 11} & S_{FL, 12} \\ S_{FL, 21} & S_{FL, 22} \end{matrix}) ([], \begin{matrix} a_{1} \\ a_{2} \end{matrix})

The boundary (or continuity) conditions between the two networks at their common Ports 2 and 3 as in (3), similarly to the S ‐parameter based procedure developed for the multiport network cascading assembly in references 21,23 can be set according to (3)

b_{2} goodbreak= a_{3}

a_{2} goodbreak= b_{3}

By combining () and () and the boundary conditions in (3), the expressions in (4) are obtained,

b_{1} goodbreak= S_{FL, 11} a_{1} goodbreak+ S_{FL, 12} b_{3}

a_{3} goodbreak= S_{FL, 21} a_{1} goodbreak+ S_{FL, 22} b_{3}

From () the wave a 1 can be obtained according to ().

…”

Section: Single Side Fixture De‐embedding Of 2‐port Dutmentioning

confidence: 99%

“…The present contribution extends the analytical approach presented in reference 18 to the case of the complete de‐embedding of the left fixture (FL) and right fixture (FR) (whose S ‐parameters are known in advance) from the S ‐parameter measurement of a 2‐port FL‐DUT‐FR assembly, avoiding any transformation of S ‐ and T ‐parameters. The single‐step approach for the generalized multiport S‐parameter cascade in reference 21 cannot be applied and inverted for the case of a port number greater than 2. Therefore, the proposed method achieves the de‐embedding objective in two steps.…”

Section: Introductionmentioning

confidence: 99%

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Generalized analytical formulation for de‐embedding of multiport devices based on known fixtures

Scafati

Paulis

Olivieri

et al. 2022

Int J RF Mic Comp-Aid Eng

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The de-embedding is a technique used in radio frequency and signal integrity measurements to extract the scattering (S)-parameters of the device under test (DUT) from the measured data of a global assembly and based on known S-parameters of the left and right test fixtures; thus, it removes the impact of the text fixtures used for the connection of the DUT to the instrumentation. Once the S-parameters are measured, the de-embedding is performed by a multistep approach involving the bidirectional transformation of the S-parameters into the corresponding transfer scattering (T)-parameters. The latter approach is well established for two-and four-port networks and has been recently expanded to the multiport case. This work proposes an alternative analytical formulation to de-embed a multiport device, knowing in advance only the S-parameters of the global multiport assembly and those of the test fixtures. The proposed method does not involve the S-to-T conversion and it requires only the algebraic manipulation of the S-parameter matrix elements; its practical implementation is very well fitted especially for multiport cases, and it is very fast in calculating the de-embedded DUT S-parameters for large port numbers. The results of the proposed formulation, applied to the case of a multipin high-speed connector, are compared with those obtained by measurement and simulations.Their accuracy is shown and discussed to demonstrate the validity of the proposed approach.

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Section: Numerical Validationmentioning

confidence: 61%

“…In (21), I ¼ d is the identity matrix. For sake of compactness, the matrix constant MA is defined according to ( 22)…”

Section: Left Fixture Multiport Deembeddingmentioning

confidence: 99%

“…From Figure 1 by definition

([], \begin{matrix} b_{1} \\ b_{4} \end{matrix}) goodbreak= ([], \begin{matrix} S_{m, 11} & S_{m, 12} \\ S_{m, 21} & S_{m, 22} \end{matrix}) ([], \begin{matrix} a_{1} \\ a_{4} \end{matrix})

and

([], \begin{matrix} b_{1} \\ b_{2} \end{matrix}) goodbreak= ([], \begin{matrix} S_{FL, 11} & S_{FL, 12} \\ S_{FL, 21} & S_{FL, 22} \end{matrix}) ([], \begin{matrix} a_{1} \\ a_{2} \end{matrix})

b_{2} goodbreak= a_{3}

a_{2} goodbreak= b_{3}

By combining () and () and the boundary conditions in (3), the expressions in (4) are obtained,

b_{1} goodbreak= S_{FL, 11} a_{1} goodbreak+ S_{FL, 12} b_{3}

a_{3} goodbreak= S_{FL, 21} a_{1} goodbreak+ S_{FL, 22} b_{3}

From () the wave a 1 can be obtained according to ().

…”

Section: Single Side Fixture De‐embedding Of 2‐port Dutmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized analytical formulation for de‐embedding of multiport devices based on known fixtures

Scafati

Paulis

Olivieri

et al. 2022

Int J RF Mic Comp-Aid Eng

Self Cite

View full text Add to dashboard Cite

show abstract

“…Usually, to obtain the network parameters of a cascade of two multi-port networks, one converts the individual networks' impedance matrices to their ABCD (or T) representation [10]- [12], assembles the cascade, and transforms back to the impedance representation. In principle, the cascade can also be performed directly with scattering parameters using fairly complex mathematical expressions [13]- [17].…”

Section: The Multi-port Network Cascadementioning

confidence: 99%

Deeply Subwavelength Localization with Reverberation-Coded Aperture

2021

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Physics-compliant models of RIS-parametrized channels assign a load-terminated port to each RIS element. For conventional diagonal RIS (D-RIS), each auxiliary port is terminated by its own independent and individually tunable load (i.e., independent of the other auxiliary ports). For beyonddiagonal RIS (BD-RIS), the auxiliary ports are terminated by a tunable load circuit which couples the auxiliary ports to each other. Here, we point out that a physics-compliant model of the load circuit of a BD-RIS takes the same form as a physics-compliant model of a D-RIS-parametrized radio environment: a multi-port network with a subset of ports terminated by individually tunable loads (independent of each other). Consequently, we recognize that a BD-RIS-parametrized radio environment can be understood as a multi-port cascade network (i.e., the cascade of radio environment with load circuit) terminated by individually tunable loads (independent of each other). Hence, the BD-RIS problem can be mapped into the original D-RIS problem by replacing the radio environment with the cascade of radio environment and load circuit. The insight that BD-RIS can be physics-compliantly analyzed with the conventional D-RIS formalism implies that (i) the same optimization protocols as for D-RIS can be used for the BD-RIS case, and (ii) it is unclear if existing comparisons between BD-RIS and D-RIS are fair because for a fixed number of RIS elements, a BD-RIS has usually more tunable lumped elements.

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Overload cascading failure detection algorithm for multi-layer supply chain network considering delay probability factor

Lu,

2024

RAIRO-Oper. Res.

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At present, the supply chain is multi-layered and complicated, and its failure detection is based solely on the characteristic threshold, which does not lack the ability to describe the complex supply chain. An overload cascading failure detection algorithm for multi-layer supply chain network considering delay probability is proposed. Based on the multi-layer supply chain network including raw material suppliers, manufacturers, distributors and retailers, the overload cascading failure model of the multi-layer supply chain network is constructed through networking, and the overload cascading failure process of the multi-layer supply chain network is described through three aspects: initial load, node capacity and overload node load distribution. By monitoring and analyzing the status update messages of each node in the supply chain network, and considering the delay probability factor, the node and path that may lead to cascading failure are identified by predicting the delay probability of the next message through the historical message delay probability, and the overload cascading failure detection of the multi-layer supply chain network is realized. The experimental results show that the algorithm can effectively detect the failure of each overloaded enterprise node in the multi-layer supply chain network, which is helpful to enhance the early warning and response ability of the cascade failure of the supply chain network. The algorithm can realize the failure detection of supply chain network under different attack conditions and initial failure ratio of nodes, and measure the anti-risk ability of supply chain network. Under deliberate attack and when the initial attack node is a supplier network layer node, it has a greater impact on the multi-layer supply chain network.

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Single‐step algorithm for the cascade assembly of multiple S‐parameters based multiports networks

Cited by 4 publications

References 25 publications

Generalized analytical formulation for de‐embedding of multiport devices based on known fixtures

Generalized analytical formulation for de‐embedding of multiport devices based on known fixtures

Deeply Subwavelength Localization with Reverberation-Coded Aperture

Overload cascading failure detection algorithm for multi-layer supply chain network considering delay probability factor

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