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Multiconductor transmission lines wideband modeling: A delay-rational Green’s-function-based method
Luleå University of Technology, Department of Computer Science, Electrical and Space Engineering, Embedded Internet Systems Lab.ORCID iD: 0000-0003-0015-0431
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The performance of variable-frequency drives (VFDs) commonly used in energy production plants can be severely affected by electromagnetic (EM) noise in the form of conducted disturbances.

A VFD is composed of an inverter, a motor, and a connecting power cable. The insulated-gate bipolar transistor (IGBT) technology and the pulse-width modulation (PWM) technique, used in the inverter, amplified the role of the power cable, which experiences the so-called “high-frequency” or “transmission line” effects, such as reflections, crosstalk, and distortion. Therefore, a complete EM assessment of a VFD requires an accurate and computationally efficient mathematical model of the cable, which can be studied as a multiconductor transmission line (MTL). Accordingly, we developed the “delay-rational Green’s-function-based” (DeRaG) model that should overcome the main limitations of the existing methods in the literature. In the DeRaG model, the impedance (or admittance) matrix is the sum of a rational series and a so-called hyperbolic part realized by hyperbolic functions. The rational series consists of poles and residues and can be truncated to a suitable size by a delay extraction technique. The hyperbolic part retains the primary information of the high-frequency behaviors, such as attenuation and propagation delays, of a line; thus, the DeRaG model is a wideband model. The DeRaG model is independent of the terminations and sources of the line and enables a delayed state-space representation; it can also account for EM interference. Nevertheless, an EM assessment of a complex system can be performed only using a calculator and proper software. Most of the advanced models for MTLs have been adapted for SPICE-like transient solvers. However, power electronics applications are commonly simulated by using software packages such as Simulink that are optimized for system-level simulations. We thus proposed the implementation of the DeRaG model both in SPICE and in Simulink to embrace a larger group of users and applications. The Simulink implementation was notably proven to be extremely simple and easy to describe. In addition, we focused on the hyperbolic part to qualitatively assess the behavior of an MTL. Our investigation resulted in an outstanding outcome; namely, we provided the distortionless condition for MTLs, whereas the distortionless condition was previously defined only for single-conductor transmission lines as the well-known Heaviside condition. In conclusion, the DeRaG model is a wideband model for the EM analysis of generic transmission lines that is suitable for system-level simulations required in power electronics applications and offers new insights into the physics of the system.

 

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2018.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
National Category
Engineering and Technology Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
URN: urn:nbn:se:ltu:diva-71021ISBN: 978-91-7790-214-0 (print)ISBN: 978-91-7790-215-7 (electronic)OAI: oai:DiVA.org:ltu-71021DiVA, id: diva2:1251839
Public defence
2018-11-27, A1547, Luleå tekniska universitet, Luleå, 10:00 (English)
Opponent
Supervisors
Available from: 2018-09-28 Created: 2018-09-28 Last updated: 2018-11-21Bibliographically approved
List of papers
1. Delayed Impedance Models of Two-Conductor Transmission Lines
Open this publication in new window or tab >>Delayed Impedance Models of Two-Conductor Transmission Lines
2014 (English)In: 2014 International Symposium on Electromagnetic Compatibility - EMC Europe 2014: Swedish Exhibition and Congress Centre, Gothenburg, Sweden : 1 - 4 September, Piscataway, NJ: IEEE Communications Society, 2014, p. 670-675, article id 6930989Conference paper, Published paper (Refereed)
Abstract [en]

This paper presents a new delayed model of two-conductortransmission lines with frequency-independent per-unit-length parameters. In particular, the line delay extractionproblem is considered. By use of a dyadic Green’s functionmacromodel method, the rational form of the open-endimpedance matrix allows an easy identification of poles andresidues, and a new technique for the extraction of the linedelay in an analytical way is gained, without any impact onthe complexity of the line macromodel itself. By use of Laplaceand Fourier transforms, the transfer function is expressed interms of the Dirac comb. The delay is then easily identified anddirectly incorporated into the system impulse response. Giving acurrent-controlled representation, the port voltages are evaluated.Thanks to the formulation of the transfer function by use ofthe Dirac comb, the convolution product is avoided, gainingaccuracy and time-saving from a computational point of view.Numerical results confirm the validity of the proposed delay-extractiontechnique. The basic ideas for the extension of theproposed technique to the lossy case are outlined.

Place, publisher, year, edition, pages
Piscataway, NJ: IEEE Communications Society, 2014
Series
IEEE International Symposium on Electromagnetic Compatibility, ISSN 2158-110X
Keywords
Technology - Electrical engineering, electronics and photonics, Teknikvetenskap - Elektroteknik, elektronik och fotonik
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-28191 (URN)10.1109/EMCEurope.2014.6930989 (DOI)2-s2.0-84908681004 (Scopus ID)1e70ae86-de86-4aa4-957d-96940861b0fb (Local ID)9781479932252 (ISBN)1e70ae86-de86-4aa4-957d-96940861b0fb (Archive number)1e70ae86-de86-4aa4-957d-96940861b0fb (OAI)
Conference
IEEE International Symposium on Electromagnetic Compatibility : 01/09/2014 - 04/09/2014
Projects
Frekvensomriktares funktion i beredskapskritiska system
Note

Validerad; 2016; Nivå 1; 20140303 (mardel)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-09-28Bibliographically approved
2. A Delay-Rational Model of Lossy Multiconductor Transmission Lines with Frequency Independent Per-Unit-Length Parameters
Open this publication in new window or tab >>A Delay-Rational Model of Lossy Multiconductor Transmission Lines with Frequency Independent Per-Unit-Length Parameters
2015 (English)In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, Vol. 57, no 5, p. 1235-1245Article in journal (Refereed) Published
Abstract [en]

Cables, printed circuit boards, and VLSI interconnects are commonly modelled as multiconductor transmission lines. Models of electrically long transmission lines are memory and time consuming. In this paper, a robust and efficient algorithmfor the generation of a delay-based model is presented. The impedance representation via the open-end matrix Z is analyzed. In particular, the rational formulation of Z in terms of poles and residues is exploited for both lossless and lossy cases. The delaysof the lines are identified, and explicitly incorporated into the model. A model order reduction of the system is automatically performed, since only a limited number of poles and residues are included in the rational part of the model, whereas the highfrequency behaviour is captured by means of closed expressions that accounts for the delays. The proposed method is applied to two relevant examples and validated through the comparison with reference methods. The time domain solver is found to be more accurate and significantly faster than the one obtained froma pure-rational model.

National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-16264 (URN)10.1109/TEMC.2015.2423327 (DOI)000363189200037 ()2-s2.0-85027953789 (Scopus ID)fe34757e-04d4-4224-9a37-f093e4560e91 (Local ID)fe34757e-04d4-4224-9a37-f093e4560e91 (Archive number)fe34757e-04d4-4224-9a37-f093e4560e91 (OAI)
Projects
Frekvensomriktares funktion i beredskapskritiska system
Note

Validerad; 2015; Nivå 2; 20150401 (jekman)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-09-28Bibliographically approved
3. Enhanced Delay-Rational Green's Method for Cable Time Domain Analysis
Open this publication in new window or tab >>Enhanced Delay-Rational Green's Method for Cable Time Domain Analysis
2015 (English)In: 2015 International Conference on Electromagnetics in Advanced Applications (ICEAA): Turin, 7-11 Sept. 2015, Piscataway, NJ: IEEE Communications Society, 2015, p. 1228-1231Conference paper, Published paper (Refereed)
Abstract [en]

State-space models of multiconductor transmissionlines can be generated by means of the Green’s function basedmethod which allows to write the open-end impedance in arational form as an infinite sum of “modal impedances”. Itcan be then embedded in a circuit simulation environment forefficient time domain analysis. The previous rational approachhas been improved through a proper mathematical formulation,that makes use of explicit delay extraction and pole/residueasymptotic behavior. Nevertheless, the computation of the polesbecomes computationally expensive when the number of conductorsincreases, since the zeros of high order polynomials haveto be evaluated. A rational fitting over the “modal impedances”is proposed, which allows a fast identification of the poles that,together with the delays, model the high frequency behavior ofthe cable in terms of standard hyperbolic functions. The lowfrequencybehavior is captured by a reduced size state-spacemodel, via rational fitting. Numerical results confirm the accuracyof the proposed modeling approach for electrically long cables,with a large number of conductors.

Place, publisher, year, edition, pages
Piscataway, NJ: IEEE Communications Society, 2015
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-34794 (URN)10.1109/ICEAA.2015.7297314 (DOI)2-s2.0-84955472717 (Scopus ID)916affa3-6bd1-41a5-83cf-97797b2dc9e5 (Local ID)916affa3-6bd1-41a5-83cf-97797b2dc9e5 (Archive number)916affa3-6bd1-41a5-83cf-97797b2dc9e5 (OAI)
Conference
International Conference on Electromagnetics in Advanced Applications : 07/09/2015 - 11/09/2015
Projects
Frekvensomriktares funktion i beredskapskritiska system
Note

Validerad; 2016; Nivå 1; 20150409 (jekman)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2018-09-28Bibliographically approved
4. Delay-Rational Model of Lossy and Dispersive Multiconductor Transmission Lines
Open this publication in new window or tab >>Delay-Rational Model of Lossy and Dispersive Multiconductor Transmission Lines
2015 (English)In: IEEE International Symposium on Electromagnetic Compatibility (EMC), 2015 [joint conference with] EMC Europe: Dresden, 16-22 Aug. 2015, Piscataway,NJ: IEEE Communications Society, 2015, p. 969-974, article id 7256297Conference paper, Published paper (Refereed)
Abstract [en]

In this paper, the transient analysis of lossy anddispersive multiconductor transmission lines is considered. Theexisting Green’s function-based method is extended to explicitlyinclude delays extraction, thus leading to a significant compressedtime-domain state-space model. The proposed method is mainlybased on poles and residues asymptotic analysis and losslessdelays extraction. The resulting hybrid state-space model incorporatesDirac-combs in the input and results into a reducednumber of state variables. A test case has been considered inorder to clearly demonstrate the effectiveness of the proposedmethodology. The results are compared with the original rationalGreen’s function method, and with the standard inverse fastFourier transform technique.

Place, publisher, year, edition, pages
Piscataway,NJ: IEEE Communications Society, 2015
Series
IEEE International Symposium on Electromagnetic Compatibility, ISSN 2158-110X
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-40322 (URN)10.1109/ISEMC.2015.7256297 (DOI)2-s2.0-84953850209 (Scopus ID)f68bf0ca-e403-4339-99c8-b0e6ca6c9fed (Local ID)978-1-4799-6615-8 (ISBN)f68bf0ca-e403-4339-99c8-b0e6ca6c9fed (Archive number)f68bf0ca-e403-4339-99c8-b0e6ca6c9fed (OAI)
Conference
Joint IEEE International Symposium on Electromagnetic Compatibility and EMC Europe : 16/08/2015 - 22/08/2015
Projects
Frekvensomriktares funktion i beredskapskritiska system
Note

Validerad; 2016; Nivå 1; 20150401 (jekman)

Available from: 2016-10-03 Created: 2016-10-03 Last updated: 2018-09-28Bibliographically approved
5. A SPICE Realization of the Delay-Rational Green's-Function-based Method for Multiconductor Transmission Lines
Open this publication in new window or tab >>A SPICE Realization of the Delay-Rational Green's-Function-based Method for Multiconductor Transmission Lines
2016 (English)In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, Vol. 58, no 4, p. 1158-1168Article in journal (Refereed) Published
Abstract [en]

Virtual prototyping has become an unavoidable step in the design of electrical and electronic systems.In this context, time-domain models have to be efficiently embedded in circuit simulator environments, such as SPICE-like transient simulators.Recently, the authors focused on the interconnections, modeled using the multiconductor transmission lines theory, and a Delay-Rational method has been developed, based on Green's functions and line-delay extraction.This work presents a SPICE synthesis of the Delay-Rational method previously developed by the authors.The solution was tested for three transmission lines with frequency-independent per-unit-length parameters.We compared the SPICE results of the Delay-Rational method with those of two standard techniques: one based on a pure rational model and one based on the inverse fast Fourier transform.The time-domain simulations in SPICE of the Delay-Rational method show both accuracy and a remarkable reduction in the number of components used with respect to a purely rational approach, by virtue of the delay extraction.

Keywords
Transmission lines, interconnections, SPICE, Technology - Electrical engineering, electronics and photonics, Teknikvetenskap - Elektroteknik, elektronik och fotonik
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-7309 (URN)10.1109/TEMC.2016.2546552 (DOI)000381435700026 ()2-s2.0-84981765159 (Scopus ID)5a7bbb0a-150d-4d5a-b071-e36775096c8b (Local ID)5a7bbb0a-150d-4d5a-b071-e36775096c8b (Archive number)5a7bbb0a-150d-4d5a-b071-e36775096c8b (OAI)
Note

Validerad; 2016; Nivå 2; 20160129 (mardel)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-09-28Bibliographically approved
6. Delayed-rational Green's-function-based method of transmission lines and the Heaviside condition
Open this publication in new window or tab >>Delayed-rational Green's-function-based method of transmission lines and the Heaviside condition
2016 (English)In: 2016 IEEE Electrical Design of Advanced Packaging and Systems Symposium, EDAPS 2016, Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 143--145, article id 7893147Conference paper, Published paper (Refereed)
Abstract [en]

In electronics as well as in communications, it ishighly desirable to be able to transmit a signal that is preservedfrom any distortions that is due to the lossy nature of themedium in which the signal travels, normally a transmission line.In this paper, we exploit the connections between the delayedGreen’s-function-based method from the authors and the wellknowndistortionless Heaviside condition. It is found that, inthe method, an important results was already present but itsimportance not yet understood. In particular, we prove that weare able to identify the distortionless transmission line associatedto a generic transmission line. We consider only 1-conductortransmission lines, with frequency-independent per-unit-lengthparameters. The multiconductor transmission-line case will beaddressed in future works.

Place, publisher, year, edition, pages
Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2016
Keywords
Heaviside condition, transmission lines, interconnections.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-59665 (URN)10.1109/EDAPS.2016.7893147 (DOI)000408917200034 ()2-s2.0-85018459154 (Scopus ID)9781509061846 (ISBN)
Conference
IEEE Electrical Design of Advanced Packaging and Systems (EDAPS) Symposium 2016,Dec 14-16 2016, Honolulu, HI USA
Projects
SvK
Available from: 2016-10-11 Created: 2016-10-11 Last updated: 2018-09-28Bibliographically approved
7. A delay‐rational model of electromagnetic interference on multiconductor transmission lines
Open this publication in new window or tab >>A delay‐rational model of electromagnetic interference on multiconductor transmission lines
2018 (English)In: International journal of numerical modelling, ISSN 0894-3370, E-ISSN 1099-1204, Vol. 31, no 4, article id 2342Article in journal (Refereed) Published
Abstract [en]

Multiconductor transmission lines have found a wide range of applications, as power lines, as high‐speed interconnects, and as on‐chip interconnects. Electromagnetic interference (EMI) can be described in terms of plane waves that couple to these lines, leading to unwanted disturbance. This paper presents a delayed spectral formulation for the analysis of plane‐wave coupling to multiconductor transmission lines in both the frequency and time domains, called the DeRaG‐EMI model (short for “delay‐rational model based on Green's functions for electromagnetic interference”). The model is based on Green's functions and is described in terms of delayed differential equations in the time domain. The model is suitable for studying the EMI on multiconductor transmission lines in the case of incident fields. The coupling of a plane wave to a line is described in terms of equivalent sources that account for both the delay of the line and the delays of the incoming plane wave. The delay is explicitly extracted and incorporated into the model with hyperbolic functions. The DeRaG‐EMI model does not require any segmentation of the line. Numerical results confirm its accuracy and its improved performance compared with the previous spectral model and with the inverse fast Fourier transform technique.

Place, publisher, year, edition, pages
John Wiley & Sons, 2018
National Category
Engineering and Technology Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-67878 (URN)10.1002/jnm.2342 (DOI)000435938900007 ()
Note

Validerad;2018;Nivå 2;2018-06-25 (svasva)

Available from: 2018-03-07 Created: 2018-03-07 Last updated: 2018-09-28Bibliographically approved
8. On the Distortionless Propagation in Multiconductor Transmission Lines
Open this publication in new window or tab >>On the Distortionless Propagation in Multiconductor Transmission Lines
2018 (English)In: IEEE Transactions on Components, Packaging, and Manufacturing Technology, ISSN 2156-3950, E-ISSN 2156-3985, Vol. 8, no 4, p. 538-545Article in journal (Refereed) Published
Abstract [en]

In this paper, we investigate the distortionless conditions for multiconductor transmission lines (MTLs) with frequency-independent per-unit-length (p.u.l.) parameters. In fact, the well-known distortionless Heaviside condition is valid only for single-conductor transmission lines. The MTL is modeled using the delayed Green's-function-based method recently proposed by the authors. In this method, the impedance matrix is described in terms of a rational part, which accounts for the low-frequency behavior, and a hyperbolic part, which determines the high-frequency response of the MTL. We find that the hyperbolic part is already distortionless at high frequency and that this property can be used to identify the p.u.l. parameters of the distortionless lossy MTL associated with the original line. To serve this purpose, the line is decoupled using a frequency-independent modal decomposition. The Heaviside condition can be enforced in the modal domain on each of the single-conductor decoupled lines. The features of the distortionless lines in the modal domain are preserved in the physical domain as a consequence of the real-valued similarity transform. The numerical results demonstrate that the new line completely characterizes the distortionless propagation of a generic MTL with frequency-independent p.u.l. parameters. The proposed formulation could be used in the optimization design process by enforcing the distortionless condition along with other design constraints.

Place, publisher, year, edition, pages
IEEE, 2018
National Category
Engineering and Technology Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-67397 (URN)10.1109/TCPMT.2017.2780097 (DOI)000429960300005 ()
Note

2018-04-18 (rokbeg);konferensartikel i tidskrift

Available from: 2018-01-25 Created: 2018-01-25 Last updated: 2018-09-28Bibliographically approved
9. A Simulink implementation of the Delay-Rational Green's-Function-based Method for Multiconductor Transmission Lines
Open this publication in new window or tab >>A Simulink implementation of the Delay-Rational Green's-Function-based Method for Multiconductor Transmission Lines
2018 (English)In: EMC Europe 2018, Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 817-822, article id 8485071Conference paper, Published paper (Refereed)
Abstract [en]

The electromagnetic compatibility (EMC) performances of a product can seriously be affected by interconnects. Interconnects can be studied by using the multiconductor transmission lines (MTLs) theory. Mathematical models of MTLs are normally validated with the aid of well-known software, such as MATLAB or PSpice. Simulink is part of the MATLAB suite but is not frequently used, and it is often underestimated both in academia and in the university education. In this paper, we briefly review the mathematical model for MTLs called DeRaG, which is a rational model based on delay extraction. Then, we propose the corresponding Simulink implementation for a 3-conductor transmission line. The Simulink has high readability, is accurate and the simulation time is remarkably faster than the corresponding model obtained in PSpice.

Place, publisher, year, edition, pages
Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2018
Series
IEEE International Symposium on Electromagnetic Compatibility, ISSN 2158-110X
Keywords
Transmission lines, MATLAB/Simulink, SPICE, transient simulations
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Industrial Electronics
Identifiers
urn:nbn:se:ltu:diva-69302 (URN)10.1109/EMCEurope.2018.8485071 (DOI)000454901100150 ()2-s2.0-85056136450 (Scopus ID)978-1-4673-9698-1 (ISBN)
Conference
International Symposium and Exhibition on Electromagnetic Compatibility, Amsterdam, August 27-30, 2018
Available from: 2018-08-20 Created: 2018-08-20 Last updated: 2019-01-28Bibliographically approved

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