Transmission-Line Model for Field-to-Wire Coupling in Bundles of Twisted-Wire Pairs Above Ground

Spadacini, Giordano; Grassi, Flavia; Marliani, F.; Pignari, Sergio A.

doi:10.1109/temc.2014.2327195

Cited by 56 publications

(62 citation statements)

References 17 publications

(26 reference statements)

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“…As performed in the previous studies, the p.u.l. inductances can be averaged over one period and

{\overset{true¯}{l}}_{n_{p}, n_{scriptp - 1}, \dots, n_{1}} = \frac{μ_{0}}{2 π} ([], ln ((), \frac{2 h}{r_{w}}) - \sum_{scriptk = 1}^{p} \frac{s_{scriptk}^{2}}{16 h^{2}})

{\overset{true¯}{l}}_{{normalM}_{1}} = \frac{μ_{0}}{2 π} ([], ln ((), \frac{2 h}{s_{1}}) + \sum_{scriptk = 1}^{p} \frac{s_{scriptk}^{2}}{16 h^{2}})

{\overset{true¯}{l}}_{{normalM}_{scriptk}} = \frac{μ_{0}}{4 π} ln ((), 1 + \frac{4 h^{2}}{s_{scriptk}^{2}}), 2 \leq scriptk \leq scriptp

…”

Section: Geometry Of Mtb‐twps and Its Per‐unit‐length Parametersmentioning

confidence: 69%

“…Also, the mode conversion in geometrically unbalanced differential lines and its analogy with crosstalk was investigated in the previous study, where the balanced transmission lines have diagonal characteristic impedance matrix in the modal domain so as to eliminate the CM‐to‐DM conversion. While in the previous study, the TWP bundles are not balanced, due to their asymmetries between them.…”

Section: Introductionmentioning

confidence: 76%

“…The per‐unit‐length (p.u.l.) parameters of MTB‐TWP can be determined by generalizing the method used in the previous studies, with the large separation between the wires assumed, ie, s 1 ≥ 4 r w , and

h \geq 3 s_{p}

, the p.u.l. self and mutual inductances are given by

l_{n_{p}, n_{scriptp - 1}, \dots, n_{1}} = \frac{μ_{0}}{2 π} ([], ln ((), \frac{2 h}{r_{w}}) + ln ((), \frac{{x_{A}}_{n_{scriptp}, n_{p - 1}, \dots, n_{1}}}{h}))

l_{{normalM}_{1}} = \frac{μ_{0}}{4 π} ([], ln ((), \frac{4 h^{2}}{s_{1}^{2}}) + ln ((), 1 + \frac{s_{1}^{2}}{4 h^{2}} {sin}^{2} φ_{n_{p}, n_{scriptp - 1}, \dots, n_{2}} + \frac{2 normalΣ}{h} + \frac{{normalΣ}^{2}}{h^{2}}))

l_{{normalM}_{scriptk}} = \frac{μ_{0}}{4 π} ln ((), \frac{d_{scriptk}^{2} + 4 {x_{A}}_{n_{scriptp}, n_{p - 1}, \dots, 1_{scriptk}, \dots, n_{1}} \times {x_{A}}_{n_{scriptp}, n_{p - 1}, \dots, 2_{scriptk}, \dots, n_{1}}}{d_{k}^{2}})

…”

Section: Geometry Of Mtb‐twps and Its Per‐unit‐length Parametersmentioning

confidence: 99%

“…Thevenin equivalent circuit of the MTB‐TBP. The central block is the chain parameter matrix; V SL and V SR are the column vectors of the induced voltages in the left and right side of the circuit, respectively…”

Section: Mtl Model Of Mtb‐twpmentioning

confidence: 99%

“…and

Z_{{boldc}_{scriptp}} = c_{0} {\overset{true¯}{bold-italicL}}_{p}

is the characteristic impedance matrix and

1_{2^{scriptp}}

is the

2^{p} \times 2^{p}

identity matrix. The induced voltages in Figure are expressed as

V_{SL} = V_{SL}^{(normall)} + V_{SL}^{(normalv)}

V_{SR} = V_{SR}^{(normall)} + V_{SR}^{(normalv)}

where the longitudinal components are given as

V_{SL}^{(normall)} = \int_{0}^{L} \frac{sin ((), k ((), ℓ - scriptL))}{sin ((), k scriptL)} bold-italicE ((), ℓ) normald ℓ

V_{SR}^{(normall)} = \int_{0}^{L} \frac{sin ((), k ℓ)}{sin ((), k scriptL)} bold-italicE ((), ℓ) normald ℓ

while the vertical components are

V_{SL}^{(normalv)} = - ([], \begin{matrix} ⋮ \\ \int_{0}^{x_{n_{p}, n_{scriptp - 1}, \dots, ...}} \end{matrix})

…”

Section: Mtl Model Of Mtb‐twpmentioning

confidence: 99%

See 4 more Smart Citations

Modeling electromagnetic wave coupling and mode conversion effects in multitwisted bundle of twisted‐wire pairs (MTB‐TWP) above ground plane

Gassab

Zhou

Wang

et al. 2018

Int J Numerical Modelling

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A multiconductor transmission line (MTL) model is developed for predicting electromagnetic wave coupling effects with multitwisted bundle of twisted‐wire pairs (MTB‐TWP) running above a ground plane. Such MTB‐TWP is described as a sequential repeated structure, where all its parameters are formulated in terms of sequences. In particular, the parametric equations of all the wires are derived and described by a set of generalized equations, where the unit tangent vector for each wire is also determined analytically. In addition, the averaged per‐unit‐length (p.u.l.) parameters are described by recurrence formulas. Further, the equivalent voltages for describing the field‐to‐wire coupling of MTB‐TWP are obtained and determined analytically. The modal domain decomposition is performed with special loading terminals to split out the common mode (CM) and differential mode (DM) signals, where the CM‐to‐DM conversions are further investigated in order to indicate the balanced property in such MTB‐TWP system. On the other hand, the effect of dielectric coatings of all the wires is also characterized, where the averaged modal p.u.l. capacitance matrix is obtained numerically. A comparison is performed with the other wiring structures to visualize the benefits of our MTB‐TWP model. An extended MTL model is also validated in comparison with the commercial software FEKO.

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“…As performed in the previous studies, the p.u.l. inductances can be averaged over one period and

{\overset{true¯}{l}}_{n_{p}, n_{scriptp - 1}, \dots, n_{1}} = \frac{μ_{0}}{2 π} ([], ln ((), \frac{2 h}{r_{w}}) - \sum_{scriptk = 1}^{p} \frac{s_{scriptk}^{2}}{16 h^{2}})

{\overset{true¯}{l}}_{{normalM}_{1}} = \frac{μ_{0}}{2 π} ([], ln ((), \frac{2 h}{s_{1}}) + \sum_{scriptk = 1}^{p} \frac{s_{scriptk}^{2}}{16 h^{2}})

{\overset{true¯}{l}}_{{normalM}_{scriptk}} = \frac{μ_{0}}{4 π} ln ((), 1 + \frac{4 h^{2}}{s_{scriptk}^{2}}), 2 \leq scriptk \leq scriptp

…”

Section: Geometry Of Mtb‐twps and Its Per‐unit‐length Parametersmentioning

confidence: 69%

Section: Introductionmentioning

confidence: 76%

h \geq 3 s_{p}

, the p.u.l. self and mutual inductances are given by

l_{n_{p}, n_{scriptp - 1}, \dots, n_{1}} = \frac{μ_{0}}{2 π} ([], ln ((), \frac{2 h}{r_{w}}) + ln ((), \frac{{x_{A}}_{n_{scriptp}, n_{p - 1}, \dots, n_{1}}}{h}))

l_{{normalM}_{1}} = \frac{μ_{0}}{4 π} ([], ln ((), \frac{4 h^{2}}{s_{1}^{2}}) + ln ((), 1 + \frac{s_{1}^{2}}{4 h^{2}} {sin}^{2} φ_{n_{p}, n_{scriptp - 1}, \dots, n_{2}} + \frac{2 normalΣ}{h} + \frac{{normalΣ}^{2}}{h^{2}}))

l_{{normalM}_{scriptk}} = \frac{μ_{0}}{4 π} ln ((), \frac{d_{scriptk}^{2} + 4 {x_{A}}_{n_{scriptp}, n_{p - 1}, \dots, 1_{scriptk}, \dots, n_{1}} \times {x_{A}}_{n_{scriptp}, n_{p - 1}, \dots, 2_{scriptk}, \dots, n_{1}}}{d_{k}^{2}})

…”

Section: Geometry Of Mtb‐twps and Its Per‐unit‐length Parametersmentioning

confidence: 99%

Section: Mtl Model Of Mtb‐twpmentioning

confidence: 99%

“…and

Z_{{boldc}_{scriptp}} = c_{0} {\overset{true¯}{bold-italicL}}_{p}

is the characteristic impedance matrix and

1_{2^{scriptp}}

is the

2^{p} \times 2^{p}

identity matrix. The induced voltages in Figure are expressed as

V_{SL} = V_{SL}^{(normall)} + V_{SL}^{(normalv)}

V_{SR} = V_{SR}^{(normall)} + V_{SR}^{(normalv)}

where the longitudinal components are given as

V_{SL}^{(normall)} = \int_{0}^{L} \frac{sin ((), k ((), ℓ - scriptL))}{sin ((), k scriptL)} bold-italicE ((), ℓ) normald ℓ

V_{SR}^{(normall)} = \int_{0}^{L} \frac{sin ((), k ℓ)}{sin ((), k scriptL)} bold-italicE ((), ℓ) normald ℓ

while the vertical components are

V_{SL}^{(normalv)} = - ([], \begin{matrix} ⋮ \\ \int_{0}^{x_{n_{p}, n_{scriptp - 1}, \dots, ...}} \end{matrix})

…”

Section: Mtl Model Of Mtb‐twpmentioning

confidence: 99%

See 3 more Smart Citations

Modeling electromagnetic wave coupling and mode conversion effects in multitwisted bundle of twisted‐wire pairs (MTB‐TWP) above ground plane

Gassab

Zhou

Wang

et al. 2018

Int J Numerical Modelling

View full text Add to dashboard Cite

show abstract

Deterministic and Statistical EMC Models for Field‐to‐Wire Coupling and Crosstalk in Wire Harness

Pignari¹

2018

Handbook of Aerospace Electromagnetic Compatibility

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Crosstalk analysis of twisted bundle of twisted wire pairs (TBTWPs) and star‐quad cables under the effect of inner and outer excitations

Su,

Gassab,

Zhang

et al. 2023

Int J Numerical Modelling

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In this article, deep neural network (DNN) and chain parameter methods are used to analyze the crosstalk coupling of a star‐quad and a twisted bundle of twisted wire pairs (TBTWP) cables for different excitations, respectively. A DNN is used to extract the per‐unit‐length (p.u.l) resistance, inductance, capacitance, and conductance (RLCG) parameters at any position for the star‐quad and TBTWP cables. The induced common mode (CM) and differential mode (DM) currents due to crosstalk are calculated by combining the obtained RLCG parameters with the chain parameter method. The obtained results show good agreement with that of FEKO software. Moreover, it is found that the star‐quad cable can reduce the external coupling more effectively than that of the TBTWP cable. Finally, measurements are performed to further validate the accuracy of our proposed algorithm.

show abstract

Transmission-Line Model for Field-to-Wire Coupling in Bundles of Twisted-Wire Pairs Above Ground

Cited by 56 publications

References 17 publications

Modeling electromagnetic wave coupling and mode conversion effects in multitwisted bundle of twisted‐wire pairs (MTB‐TWP) above ground plane

Modeling electromagnetic wave coupling and mode conversion effects in multitwisted bundle of twisted‐wire pairs (MTB‐TWP) above ground plane

Deterministic and Statistical EMC Models for Field‐to‐Wire Coupling and Crosstalk in Wire Harness

Crosstalk analysis of twisted bundle of twisted wire pairs (TBTWPs) and star‐quad cables under the effect of inner and outer excitations

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