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  • 1.
    Bengtsson, Mats
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Lilliesköld, Joakim
    KTH, School of Electrical Engineering (EES), Industrial Information and Control Systems.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Skog, Isaac
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Sohlström, Hans
    KTH, School of Electrical Engineering (EES), Micro and Nanosystems.
    Developing and Implementing a Program Interfacing Project Course in Electrical Engineering2012Conference paper (Refereed)
    Abstract [en]

    In this paper, we describe the ideas behind a second-year Design-Build course in Electrical Engineering. Electrical Engineering is a theoretical subject, and in such it is difficult to maintain the theoretical level in project courses introduced too early in the program, especially when core subjects like electromagnetic field theory are involved. This issue is addressed and we also describe our approach for the assessment of the students. We also discuss the different goals that were set up prior to the course from a program perspective; how we reasoned when designing the course, the assessment structure, and the output once the course was implemented

  • 2.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Emadi, Seyed Mohamad Hadi
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Perturbation Approach to Reconstructing Deformations in a Coaxial Cylindrical Waveguide2015In: Mathematical problems in engineering (Print), ISSN 1024-123X, E-ISSN 1563-5147, article id 915497Article in journal (Refereed)
    Abstract [en]

    We study a detection method for continuous mechanical deformations of coaxial cylindrical waveguide boundaries, using perturbation theory. The inner boundary of the waveguide is described as a continuous PEC structure with deformations modeled by suitable continuous functions. In the present approach, the computation complexity is significantly reduced compared to discrete conductor models studied in our previous work. If the mechanically deformed metallic structure is irradiated by the microwave fields of appropriate frequencies, then, by means of measurements of the scattered fields at both ends, we can reconstruct the continuous deformation function. We apply the first-order perturbation method to the inverse problem of reconstruction of boundary deformations, using the dominant TEM-mode of the microwave radiation. Different orders of Tikhonov regularization, using the L-curve criterion, are investigated. Using reflection data, we obtain reconstruction results that indicate an agreement between the reconstructed and true continuous deformations of waveguide boundaries.

  • 3.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Motevasselian, Alireza
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    On using multiple modes to reconstruct conductor locations in a power transformer winding2012In: Progress in Electromagnetics Research Symposium (PIERS 2012), Electromagnetics Academy , 2012, p. 516-523Conference paper (Refereed)
    Abstract [en]

    An initial study of a novel method to diagnose the effects of the various degradation mechanisms on the power transformers, while in operation, is presented. We model a transformer winding surrounded by the transformer-tank wall and the magnetic core as a two-dimensional parallel plate waveguide, where one plate represents the wall of the transformer tank and the other plate represents the iron core that conducts the magnetic flux. In between there is a set of parallel conductors representing the winding segments. The new principle is to insert antennas inside the transformer tank to radiate and measure microwave fields that interact with the metallic structure and the insulation. The responses from the radiated waves are assumed to be sensitive to material properties that reflect any harmful deterioration processes. In particular, we study the mechanical deformations of the transformer winding by determining the locations of the individual conductors, from measurements of the scattered fields at both ends. The propagation problem is solved accurately and efficiently by conventional waveguide theory, including mode- matching and cascading techniques. We employ optimization as a suitable method to solve the inverse problem and obtain a good agreement between the calculated and measured positions of winding segments.

  • 4.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Motevasselian, Alireza
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Online power transformer diagnostics using multiple modes of microwave radiation to reconstruct winding conductor locations2014In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 22, no 1, p. 84-95Article in journal (Refereed)
    Abstract [en]

    A novel approach to diagnostics of transformer winding deformations, caused by mechanical forces from short-circuit currents, is presented. We employ a simple model of a transformer as a two-dimensional parallel plate waveguide. The upper plate represents the transformer tank wall and the lower plate represents the iron core which carries the magnetic flux. Between the two plates, we model the transformer winding by a set of parallel conductors. We utilize commercial simulation software to simulate the generation and measurement of microwave radiation at both ends of the winding structure. The radiation interacts with the metallic structures in the model waveguide. The measured responses from the model waveguide are expected to be sensitive to mechanical deformations of the transformer winding. We use conventional waveguide theory to solve the direct propagation problem, and an optimization method to solve the inverse problem. In particular, we determine the locations of winding segments, and obtain a good agreement between reconstructed and true conductor positions.

  • 5.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Motevasselian, Alireza
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Using multiple modes to reconstruct conductor locations in a cylindrical model of a power transformer winding2013In: International journal of applied electromagnetics and mechanics, ISSN 1383-5416, E-ISSN 1875-8800, Vol. 41, no 3, p. 279-291Article in journal (Refereed)
    Abstract [en]

    A study of a novel method to detect mechanical deformations of windings in a power transformer, while in operation, is presented. We employ an approximate model of a transformer winding surrounded by the transformer-tank wall and the magnetic core. The transformer winding is viewed as a structure consisting of thin conducting cylindrical rings (winding segments or turns) situated within a coaxial cylindrical waveguide, where the inner conducting cylinder represents the iron core that conducts the magnetic flux and the outer conducting cylinder represents the wall of the transformer tank. The basic principle is to insert antennas inside the transformer tank above and below the winding to radiate and measure microwave fields that interact with the metallic structure and the insulation. The responses from the radiated waves are assumed to be sensitive to any mechanical deformations that could be caused by electromagnetic forces due to short-circuit currents and possible manufacturing weaknesses. The goal is to be able to determine the radial locations of the individual winding segments or individual turns from measurements of the scattered fields at both ends. The propagation problem is solved by conventional waveguide theory, including mode-matching and cascading techniques. We utilize optimization as a suitable method to solve the inverse problem and obtain a good agreement between the reconstructed and true positions of the winding segments.

  • 6.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Boundary shape reconstructions in a coaxial waveguide using Bessel functions2016In: 2016 URSI INTERNATIONAL SYMPOSIUM ON ELECTROMAGNETIC THEORY (EMTS), IEEE, 2016, p. 826-829Conference paper (Refereed)
    Abstract [en]

    This paper investigates boundary shape reconstructions in coaxial waveguides using microwave scattering. Electromagnetic field perturbation theory together with inverse problem theory is used to reconstruct two-dimensional small boundary deformations on the inner boundary of a coaxial waveguide. Due to the first-order perturbation theory employed, the scattering parameters of the waveguide have linear dependencies on the continuous deformation function. Thus, the corresponding inverse problem can be linearized, and direct inversion can be employed to obtain the shape parameters. Tikhonov regularization is used to regularize the resulting ill-conditioned linear system. Finally, reconstruction results are presented for a few examples of two-dimensional localized shape deformations of coaxial waveguide boundaries, being in agreement with the actual shapes.

  • 7.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Conductor Locations Reconstruction in a Cylindrical Winding Model2013In: Proceedings of PIERS 2013 in Stockholm, Sweden, August 12-15, 2013, 2013Conference paper (Refereed)
  • 8.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    First-order perturbation approach to elliptic winding deformations2013In: 2013 International Symposium on Electromagnetic Theory, EMTS 2013 - Proceedings, IEEE , 2013, p. 13-16Conference paper (Refereed)
    Abstract [en]

    We apply a novel on-line method to detect elliptic deformations of winding turns in a power transformer. We employ the first-order perturbation theory to a transformer winding surrounded by the transformer tank wall and the magnetic core. The transformer winding is modeled as a structure consisting of thin conducting cylindrical rings (winding segments or turns) situated within a coaxial cylindrical waveguide, where the inner conducting cylinder represents the magnetic core and the outer conducting cylinder represents the wall of the transformer tank. We simulate antennas inside the transformer tank to radiate and measure microwave fields, in order to identify and quantify elliptic deformations of the individual winding segments or individual turns. The propagation problem is solved by conventional waveguide theory, including mode-matching and cascading techniques. We utilize optimization to solve the inverse problem and obtain a good agreement between the reconstructed and true deformations of the winding segments.

  • 9.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    First-order perturbation approach to transformer winding deformations2013In: Progress In Electromagnetics Research Letters, ISSN 1937-6480, Vol. 43, p. 1-14Article in journal (Refereed)
    Abstract [en]

    An on-line method to detect radial mechanical deformations of power transformer winding turns is presented. First-order perturbation theory is applied to a transformer winding surrounded by the transformer tank wall and the iron core. The transformer wind- ing is modeled as thin conducting cylindrical rings (winding segments or turns) situated within a coaxial waveguide, where the outer con- ducting cylinder represents the transformer tank wall while the inner conducting cylinder represents the iron core. Antennas which radi- ate and measure microwave fields are proposed inside the transformer tank in order to identify and quantify the mechanical deformations of winding turns. The direct propagation problem is solved using conventional waveguide theory with mode-matching and cascading techniques. An optimization algorithm is then used to solve the inverse problem whereby a good agreement between the reconstructed and true deformations of the winding segments is obtained.

  • 10.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Inverse scattering of two-dimensional boundary deformations in waveguide structures2015In: 2015 IEEE Radio and Antenna Days of the Indian Ocean, RADIO 2015, IEEE , 2015Conference paper (Refereed)
    Abstract [en]

    This paper presents the principles for an on-line microwave-based monitoring system for power grid components. Such systems would be able to provide diagnostic information about the component in real time. The microwave propagation in complex waveguide structures, here representing the interior of the power grid components, is studied with the aim to detect and quantify shape or material changes with sufficient accuracy. Electromagnetic field analysis in conjunction with inverse problem theory is used to reconstruct the material and shape parameters. In this paper, we present preliminary results for reconstructions of two-dimensional localized deformations of a waveguide boundary, representing the inner structure of a power grid component.

  • 11.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Two-dimensional boundary shape reconstructions in rectangular and coaxial waveguides2016In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 66, p. 10-20Article in journal (Refereed)
    Abstract [en]

    We present a method for shape reconstruction of deformed metallic boundaries in rectangular and coaxial waveguides using microwave scattering. Our developed reconstruction method is a theoretical basis for a future on-line microwave-based monitoring system for power grid components. The bundle of winding conductors in the active part of a typical power grid component is modeled as a continuous metallic surface. Then, electromagnetic field perturbation theory in conjunction with inverse problem theory is used to reconstruct the shape parameters of this surface. We assume small perturbations of the boundaries, such that the scattering parameters of the waveguide in the first-order perturbation have linear dependencies of the continuous deformation function. Thus, the corresponding inverse problem can be linearized and we can employ direct inversion, without the need for optimization which requires a higher computational effort. Tikhonov regularization is used to regularize the arising ill-conditioned linear system. The reconstructions, performed with noisy synthetic measurement data, show a good agreement with the actual shapes of the studied two-dimensional localized shape deformations for both rectangular and coaxial waveguide boundaries.

  • 12.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Asenov, T.
    Doncov, N.
    Gradient index metamaterial with arbitrary loss factors in RHM and LHM media: The case of constant impedance throughout the structure2012In: PIERS 2012 Moscow: Progress In Electromagnetics Research Symposium, Electromagnetics Academy , 2012, p. 1390-1394Conference paper (Refereed)
    Abstract [en]

    The transmission and reflection properties of lossy structures involving left-handed materials with graded permittivity and permeability have been investigated. We present an exact analytical solution to Helmholtz' equation for a lossy case with the graded both real and imaginary parts of permittivity and permeability profile changing according to a hyperbolic tangent function along the direction of propagation. This allows for different loss factors in the two media. The expressions and graphical results for the field intensity along the graded structure are presented. The analytical solution is validated by a dispersive numerical model of lossy metamaterials that uses a transmission line matrix method based on Z-transforms, where a close agreement between the analytic and numerical results is obtained.

  • 13.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Asenov, T.
    Doncov, N.
    Lossy transmision with arbitrary gradient permittivity and permeability and constant impedance throughout the structure2013In: 2013 11th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services, TELSIKS 2013, IEEE , 2013, p. 25-28Conference paper (Refereed)
    Abstract [en]

    We present a remarkably simple exact analytical solution for the electromagnetic field distribution across an infinite metamaterial composite with an arbitrary graded variation of complex effective permittivity and permeability for the case of constant impedance across the structure. Arbitrary temporal dispersion and losses are allowed and the model is generally applicable to different inhomogeneous and anisotropic media simultaneously containing positive and negative refractive index constituents, as long as the effective medium approximation remains valid. The analytical solution is validated by a dispersive numerical model of lossy metamaterials that uses a transmission line matrix method based on Z-transforms, where a close agreement between the analytic and numerical results is obtained.

  • 14.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Asenov, Tatjana
    Doncov, Nebojsa
    Arbitrary Loss Factors In The Wave Propagation Between RHM And LHM Media With Constant Impedance Throughout The Structure2013In: Progress In Electromagnetics Research, ISSN 1070-4698, E-ISSN 1559-8985, Vol. 137, p. 527-538Article in journal (Refereed)
    Abstract [en]

    We investigate the wave propagation properties in lossy structures with graded permittivity and permeability involving left-handed metamaterials. An exact analytic solution to Helmholtz' equation for a lossy case with both real and imaginary parts of permittivity and permeability profile, changing according to a hyperbolic tangent function along the direction of propagation, is obtained. It allows for different loss factors in RHM and LHM media. Thereafter, the corresponding numerical solution for the field intensity along the composite structure is obtained by means of a dispersive numerical model of lossy metamaterials that uses a transmission line matrix method based on Z-transforms. We present the expressions and graphical results for the field intensity along the composite structure and compare the analytic and numerical solutions, showing that there is an excellent agreement between them.

  • 15.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Asenov, Tatjana
    Doncov, Nebojsa
    Jaksic, Zoran
    Exact analytical solution for fields in gradient index metamaterials with different loss factors in negative and positive refractive index segments2013In: Journal of Nanophotonics, ISSN 1934-2608, Vol. 7, p. 073086-Article in journal (Refereed)
    Abstract [en]

    Gradient refractive index metamaterials are of interest for various applications of transformation optics. Wave propagation through gradient index metamaterials using an exact analytical approach is investigated. Composite materials containing constituents with negative real and positive real indexes of refraction are considered. An exact analytical solution for the field distribution is obtained for the sinusoidal spatial variation of complex effective permittivity and permeability along a fixed direction, under the assumption that the wave impedance remains spatially uniform across the structure. Loss factors in the constituent materials can be different from each other corresponding to the realistic situations. Temporal dispersion can be arbitrary subject to the physical limitations imposed by the Kramers-Kronig relations. A numerical model based on the Z-transform is developed to verify the analytical results. The approach can be applied to arbitrary periodic refractive index profiles using the Fourier series method.

  • 16.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Dalarsson, Nils
    KTH.
    Jaksic, Z.
    Analytical approach to lossy wave propagation through a graded interface containing negative index material2011In: Int. Conf. Telecommun. Mod. Satell., Cable Broadcast. Serv., TELSIKS - Proc. Pap., 2011, p. 39-42Conference paper (Refereed)
    Abstract [en]

    The transmission and reflection properties of lossy structures involving left-handed materials with graded permittivity and permeability have been investigated. We present an exact analytical solution to Helmholtz' equation for a lossy case with the graded real parts of permittivity and permeability profile changing according to a hyperbolic tangent function along the direction of propagation. The simple analytical solutions and graphical results for the field intensity along the graded structure are presented. The model straightforwardly allows for arbitrary temporal dispersion. © 2011 IEEE.

  • 17.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Doncov, N.
    Univ Nis, Nish, Serbia.
    Jaksic, Z.
    Univ Belgrade, Belgrade, Serbia.
    Lossy gradient index transmission optics with arbitrary periodic permittivity and permeability and constant impedance throughout the structure2012In: Journal of Optics, ISSN 2040-8978, E-ISSN 2040-8986, Vol. 14, no 6, p. 065102-Article in journal (Refereed)
    Abstract [en]

    A remarkably simple exact analytical solution is obtained for the electromagnetic field distribution across infinite metamaterial-containing composites with any arbitrary periodic variation of complex effective permittivity and permeability for the case of constant impedance across the structure. Arbitrary temporal dispersion and losses are allowed and the model is generally applicable to different inhomogeneous and anisotropic media simultaneously containing positive and negative refractive index constituents, as long as the effective medium approximation remains valid. The analytical solution is validated by a dispersive numerical model of lossy metamaterials that uses a transmission line matrix method based on Z-transforms, where a close agreement between the analytic and numerical results is obtained.

  • 18.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Jaksic, Z.
    Lossy gradient index metamaterial with general periodic permeability and permittivity: The case of constant impedance throughout the structure2012In: Proceedings Of Progress In Electromagnetics Research Symposium (PIERS 2012), Electromagnetics Academy , 2012, p. 190-194Conference paper (Refereed)
    Abstract [en]

    We utilize an exact analytical approach to investigate the electromagnetic wave propagation across an infinite metamaterial composite with general periodic gradient effective permittivity and permeability. A general analytic solution for the field distribution is obtained for an arbitrary periodic variation of complex refractive index across the structure. The calculation is done for the case of constant impedance across the structure. Arbitrary temporal dispersion and losses are allowed and the model is generally applicable to inhomogeneous and anisotropic media simultaneously containing positive and negative refractive index constituents as long as the effective medium approximation is valid.

  • 19.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    Jaksic, Zoran
    Exact Analytical Solution for Fields in a Lossy Cylindrical Structure with Linear Gradient Index Metamaterials2015In: Progress In Electromagnetics Research, ISSN 1070-4698, E-ISSN 1559-8985, Vol. 151, p. 109-117Article in journal (Refereed)
    Abstract [en]

    We investigate the electromagnetic wave propagation across a finite inhomogeneous and anisotropic cylindrical metamaterial composite containing both positive and negative effective refractive index parts with linear spatial gradient. Exact analytical solutions for the electric and magnetic field distributions are obtained for a linear variation of effective refractive index across the structure. The exact analytical results for the electric and magnetic fields are compared to the numerical results obtained using the numerical simulation software HFSS. The model allows for general temporal dispersion and uniform losses within the composite.

  • 20.
    Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Jaksic, Zoran
    Lossy gradient index metamaterial with sinusoidal periodicity of refractive index: case of constant impedance throughout the structure2011In: J NANOPHOTONICS, ISSN 1934-2608, Vol. 5, p. 051804-Article in journal (Refereed)
    Abstract [en]

    We used an exact analytical approach to investigate the electromagnetic wave propagation across an isotropic metamaterial composite with i. a sinusoidally periodic gradient of the real parts of the effective permittivity and permeability, ii. spatially uniform imaginary parts of the effective permittivity and permeability, and iii. spatially uniform impedance. The real part of the effective refractive index can be positive and negative along the direction of nonhomogeneity. A remarkably simple direct solution for the field distribution was obtained.

  • 21.
    Ellgardt, Anders
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    A study of edge effects in triangular grid tapered-slot arrays using coupling coefficients2010In: Radio Science, ISSN 0048-6604, E-ISSN 1944-799X, Vol. 45, p. RS2005-Article in journal (Refereed)
    Abstract [en]

    Edge effects for tapered-slot elements in triangular grid array antennas are studied by using finite difference time domain codes. The S parameters for finite-by-infinite arrays are computed and evaluated for two different edge models and, to evaluate the edge effects, the results are compared with the S parameters for the infinite array. As expected, the largest difference between the results occurs for the elements closest to the edges, because of the missing coupling from nearby elements and the perturbed element currents due to the edge geometry. By using the proposed method it is possible to distinguish between these two edge effects. A method to combine the finite-by-infinite array results and the infinite array results is presented and used to characterize the perturbation caused by the truncation of the infinite array.

  • 22.
    Ellgardt, Anders
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    A Study of Edge Elements in Triangular Grid Tapered-Slot Arrays2010In: International Symposium on Microwaves-2010, 2010Conference paper (Refereed)
  • 23.
    Ellgardt, Anders
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Edge element evaluation of tapered-slot elements in phased arrays2010In: EuCAP 2010 - The 4th European Conference on Antennas and Propagation, 2010Conference paper (Refereed)
    Abstract [en]

    The edge elements in large phased arrays of tapered-slot elements are analyzed and compared with the infinite array. In large phased arrays the elements that are close to the center of the antenna have similar performance. However, the elements close to an edge will have different coupling coefficients and embedded radiation patterns due to the truncated geometry. In this paper the edge effects in a triangular grid tapered-slot array is studied by using finite-by-infinite arrays. The array is infinite in the direction along the edge and finite in the other direction. The S-parameters for three truncations of the tapered slot element are compared with the infinite array solution for the case when the edge is orthogonal to the E-plane.

  • 24.
    Engdahl, Göran
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Blomberg, Lars
    Brunsell, Per
    Edin, Hans
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Rosander, Staffan
    Electrotechnical modelling2011Other (Other academic)
  • 25.
    Frid Dalarsson, Mariana
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Two-dimensional boundary shape reconstructions in rectangular and coaxial waveguidesManuscript (preprint) (Other academic)
  • 26.
    Ghasemifard, Fatemeh
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Johansson, M.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Current reconstruction from magnetic field using spherical harmonic expansion to reduce impact of disturbance fields2016In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, p. 1-15Article in journal (Refereed)
    Abstract [en]

    A current reconstruction method, for determining currents in a set of parallel infinitely long conductors located above the ground from measured magnetic field, is developed. The method is designed to work even if three-dimensional external disturbance fields from external sources are present. The external field is written as an expansion in spherical harmonics. Therefore, the field in the different measurement points is regarded as a linear combination of the expansion coefficients and the currents to be determined. A linear equation system is formed with the currents and the expansion coefficients as the unknowns. The currents are reconstructed by solving the equation system using least squares method and Tikhonov regularization. If the characteristics of the ground below the conductors are known with sufficient precision, the ground effect can also be included into the model. Results of various simulations show that the method works well and noise in the measured magnetic field can be handled.

  • 27.
    Ghasemifard, Fatemeh
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering. KTH.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Contact-free Measurement of Currents inTwo-dimensional Parallel Conductors Using the Green Identity Approach2016In: 2016 URSI International Symposium on Electromagnetic Theory, EMTS 2016, IEEE, 2016, p. 338-340, article id 7571391Conference paper (Refereed)
    Abstract [en]

    The Green identity approach is used to reconstructcurrents in very long parallel conductors above the groundfrom magnetic field data measured at some points under theconductors. By assuming that the conductor positions are known,this method can be used for contact-free measurement of currentsin transmission lines in power system. This method gives thepossibility of measuring high-frequency currents which cannotbe measured with current transformers.

  • 28.
    Ghasemifard, Fatemeh
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Handling the ill-posedness of current retrieval in power lines from magnetic field data using Tikhonov regularization method2015In: 2015 USNC-URSI Radio Science Meeting (Joint with AP-S Symposium), USNC-URSI 2015 - Proceedings, 978-147997817-5: IEEE , 2015, p. 56-56Conference paper (Refereed)
    Abstract [en]

    An inverse source problem of reconstructing the currents in parallel conductor structures from magnetic field data is considered. In this kind of inverse source problems which arise in contact-free measurements of currents in bus bars, power lines, and cables, the magnetic field data collected by a set of sensors in the vicinity of the conductors is used to determine the currents in conductors. The method is based on inversion of the direct map from the currents to the magnetic field data using a proper model of the problem.

  • 29.
    Ghasemifard, Fatemeh
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Sensor Selection via Convex Optimization in Remote Contact-free Measurement of Currents2017In: 2017 International Applied Computational Electromagnetics Society Symposium - Italy, ACES 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, article id 7916351Conference paper (Refereed)
    Abstract [en]

    The sensor positions have substantial effect on the accuracy of remote contact-free reconstruction of currents in power transmission lines from magnetic field data, measured by a set of sensors located under the conductors. By maximizing a performance metric, based on the Fisher information matrix, Nopt sensors are selected from N candidate sensors. The main optimization problem is changed to a convex optimization problem using a relaxation of the integer constraints. The result for optimized sensor positions for a remote current reconstruction in power transmission lines using a planar sensor array is demonstrated.

  • 30.
    Ghasemifard, Fatemeh
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Sensor Selection via Convex Optimization in Remote Contact-free Measurement of Currents2017In: 2017 INTERNATIONAL APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY SYMPOSIUM - ITALY (ACES), IEEE , 2017Conference paper (Refereed)
    Abstract [en]

    The sensor positions have substantial effect on the accuracy of remote contact-free reconstruction of currents in power transmission lines from magnetic field data, measured by a set of sensors located under the conductors. By maximizing a performance metric, based on the Fisher information matrix, Nopt sensors are selected from N candidate sensors. The main optimization problem is changed to a convex optimization problem using a relaxation of the integer constraints. The result for optimized sensor positions for a remote current reconstruction in power transmission lines using a planar sensor array is demonstrated.

  • 31.
    Ghasemifard, Fatemeh
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Quevedo-Teruel, Oscar
    KTH, School of Electrical Engineering and Computer Science (EECS), Electromagnetic Engineering.
    Dispersion Analysis of 2-D Glide-Symmetric Corrugated Metasurfaces Using Mode-Matching Technique2018In: IEEE Microwave and Wireless Components Letters, ISSN 1531-1309, E-ISSN 1558-1764, Vol. 28, no 1, p. 1-3Article in journal (Refereed)
    Abstract [en]

    In this letter, wave propagation in 2-D doubled corrugated metasurfaces, including glide-symmetric corrugated metasurfaces, embedded in a thin parallel plate waveguide have been analyzed using the mode matching method. The general dispersion equation for propagation at different directions is derived and dispersion surfaces have been obtained for three different cases. The results are in good agreement with reference results obtained using CST Microwave Studio. Moreover, the method is accurate and computationally much faster than CST Microwave Studio and similar commercial software.

  • 32.
    Hu, Xin
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    He, Sailing
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Left-Handed Transmission Line with Finger-Shorted Interdigital CapacitorArticle in journal (Other academic)
  • 33.
    Jonsson, B. Lars G.
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Asymptotic wave-splitting in anisotropic linear acoustics2010In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 47, no 5, p. 318-326Article in journal (Refereed)
    Abstract [en]

    In the present paper, we present a simple wave-splitting procedure for instantaneously reacting anisotropic media that includes spatial variation in depth. The method includes both the traditional (approximate) and a 'true amplitude' wave-field decomposition. The results are presented in time-Laplace domain. One of the main advantages of the method presented here is that it gives an explicit asymptotic representation of the linear acoustic-admittance operator to all orders of smoothness for the smooth, positive definite anisotropic material parameters considered here. Once the admittance operator is known we obtain an explicit asymptotic wave-splitting solution. (C) 2009 Elsevier B.V. All rights reserved.

  • 34.
    Jonsson, B. Lars G.
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Venkatesulu, Bandapalle
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Edin, Hans
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Observations on the Resistive Losses and the Electrostatic Field Distribution in anInsulating Nanocomposite2011Conference paper (Refereed)
    Abstract [en]

    It has been reported that adding insulating nanoparticles to an epoxy like polymers increases its dielectric breakdown strength. Thermal runaway can act as one of several precursors to the electrical breakdown process, and resistive losses can be an underlying cause of the temperature increase. In this paper, to examine the influence of nanoparticles on the breakdown strength, the magnitude of the electric field distribution and its corresponding resistive losses around insulating Al2O3-nanoparticles has been determined for linear and non-linear epoxy polymer media w.r.t. filling degree of particles. The dc-E-field distribution has been ascertained using both analytical and numerical methods. It was observed that nanoparticle addition to a polymer creates both "no heating" regions and "significant heating" regions in the close vicinity of the interface.

  • 35. Lundstedt, J.
    et al.
    Norgren, Martin
    KTH, Superseded Departments, Electrical Systems.
    Comparison between frequency domain and time domain methods for parameter reconstruction on nonuniform dispersive transmission lines - Abstract2003In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 17, no 12, p. 1735-1737Article in journal (Refereed)
  • 36.
    Månsson, Daniel
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    On the Assessment of Written Exams and Possible Bias due to Dynamic Rater Effects Emerging from Student Initials and Rater Fatigue2016In: Högre Utbildning, ISSN 2000-7558, E-ISSN 2000-7558, Vol. 6, no 1, p. 21-30Article in journal (Refereed)
    Abstract [en]

    In this paper the possibility of an existing bias, due to the order (here by the initial letters of the family names) in which the results of the students are judged, was studied. This would constitute of a dynamic rater effect of harshness, or leniency, toward the performance of these students due to rater fatigue. A substantial dataset, consisting of 12 years of written exams, for a course, for 2512 examinees, was mined and the results analyzed. The evidence point to the fact that the assessment procedure does not favor, or disfavor, students with family names having initial letters placed late in the alphabet.

  • 37.
    Norgren, Martin
    KTH, Superseded Departments, Electrical Systems.
    A hybrid FDFD-BIE approach to two-dimensional scattering from an inhomogeneous biisotropic cylinder - Abstract2003In: Journal Electromagnetic Waves and Applications, ISSN 0920-5071, E-ISSN 1569-3937, Vol. 17, no 3, p. 489-490Article in journal (Refereed)
  • 38.
    Norgren, Martin
    KTH, Superseded Departments, Electrical Systems.
    A simple approach to quasi-TEM analysis of a planar multiconductor structure embedded in an elliptically stratified environment2003In: Microwave and optical technology letters (Print), ISSN 0895-2477, E-ISSN 1098-2760, Vol. 36, no 1, p. 20-24Article in journal (Refereed)
    Abstract [en]

    The quasi-TEM modes on a planar multiconductor transmission line embedded in an elliptically stratified cross section are considered. Electro- and magneto-static problems are solved using separation of variables in elliptical coordinates. It is shown that asymptotic solutions for the radial dependences of the terms of the series can be used, under certain conditions, on the profiles of stratification. Results about the convergence and the usefulness of the asymptotic solution are presented.

  • 39.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    An alternative integral equation for calculating the surface charge in a parallel disk capacitor2010In: Symposium Digest - 20th URSI International Symposium on Electromagnetic Theory, EMTS 2010, 2010, p. 608-611Conference paper (Refereed)
    Abstract [en]

    The potential from a parallel disk capacitor can be obtained by solving the Love integral equation. Although an expansion of the kernel yields fast convergence of the capacitance, at not too small disk separations, other quantities like the surface charge exhibit a considerably slower convergence. We present an alternative integral equation formulation of the problem that leads to more rapid convergence when computing the surface charge on the disks. The derivation of the kernel is outlined as well as the numerical implementation using a suitable set of expansion functions. Numerical results for the capacitance and the surface charge are presented, for several orders of disk separations.

  • 40.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Chebyshev collocation and Newton-type optimization methods for the inverse problem on nonuniform transmission lines2005In: IEEE transactions on microwave theory and techniques, ISSN 0018-9480, E-ISSN 1557-9670, Vol. 53, no 5, p. 1561-1568Article in journal (Refereed)
    Abstract [en]

    A frequency-domain inverse problem for the nonuniform LCRG transmission line is considered. The parameters of the nonuniform line are interpolated by Chebyshev polynomials, and the Telegraphers equations are solved by a collocation method using the same polynomials. The interpolation coefficients for the unknown parameters are reconstructed by means of Newton-type optimization methods for which the Jacobian matrix has been calculated explicitly. For the reconstruction of one or two parameters, the algorithm is tested on synthetic data, and the necessity to use regularization is discussed. Finally, the algorithm is tested with measured reflection data to reconstruct shunt capacitances with piecewise constant profiles.

  • 41.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Explicit reconstruction of line-currents and their positions in a two-dimensional parallel conductor structure2014In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 22, no 7, p. 1196-1213Article in journal (Refereed)
    Abstract [en]

    The magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic field on a contour surrounding the conductors to be reconstructed. Using a scalar-vector Green identity, an explicit reconstruction algorithm is derived. The numerical implementation of the algorithm is described and simulation results are presented, demonstrating the influences from numerical errors and noise in measurement data. The algorithm can handle an arbitrary number of conductors, but benchmarking against the Cramer-Rao lower bounds indicate that the algorithm is non-optimal and becomes increasingly unstable when increasing the number of conductors. Mathematically, the Green identity approach removes the influence of external disturbances and thus has potential usefulness in current reconstruction for determining optimal sensor positions and how to process measurement data.

  • 42.
    Norgren, Martin
    KTH.
    On the exact solution for the eigenmodes of the tape helix2017In: 2017 32nd General Assembly and Scientific Symposium of the International Union of Radio Science, URSI GASS 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 1-4Conference paper (Refereed)
    Abstract [en]

    The eigenmodes of the tape helix are analysed by expanding the surface current density on the tape, or the tangential electric field in the interspacing gap, into Chebyshev polynomials. Numerical results for the dispersion relation, the surface current and the gap electric field are presented, and the two approaches are cross-verified against each other. The numerical stability as well as similarities and differences with other approaches are discussed.

  • 43.
    Norgren, Martin
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    On the problem with intermodal dispersion when using multiconductor transmission lines as distributed sensors2006In: Progress in Electromagnetics Research-Pier, ISSN 1559-8985, Vol. 56, p. 129-150Article in journal (Refereed)
    Abstract [en]

    The inverse problem of using an unshielded multiconductor transmission line (MTL) as an distributed sensor is considered. The MTL is analyzed by means of the quasi-TEM mode theory and a propagator formalism. In the inverse problem, the focus is on the problem with intermodal dispersion, due to the possibility of more than one propagating mode. Reconstruction results, from both measured and simulated reflection data, are presented for a three conductor MTL that has been used for diagnosing soil and snow. Both the case when one mode propagates, and the case when two modes propagate are considered. For the latter case it is demonstrated that intermodal dispersion deteriorates the resolution in the reconstruction, due to corruption of the high frequency part of the spectrum.

  • 44.
    Norgren, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Avelin, J.
    Sihvola, A.
    Depolarization dyadic for a cubic cavity: Illustrations and interpretation2005In: Electrical engineering (Berlin. Print), ISSN 0948-7921, E-ISSN 1432-0487, Vol. 87, no 5, p. 227-230Article in journal (Refereed)
    Abstract [en]

    The depolarization dyadic of the cubic cavity is examined for off-center positions inside the cavity. It is shown that at an edge two of the diagonal components have ill-defined limiting values and at a corner all three diagonal components are ill defined. Figures illustrating those peculiarities are presented. The explanation is found to be the non-unique limit of the solid angle subtended by an open surface when approaching a point on its rim.

  • 45.
    Norgren, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Dalarsson, Mariana
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Motevasselian, Alireza
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Reconstruction of boundary perturbations in a waveguide2013In: 2013 International Symposium on Electromagnetic Theory, EMTS 2013 - Proceedings, IEEE , 2013, p. 934-937Conference paper (Refereed)
    Abstract [en]

    The inverse problem of reconstructing boundary deformations in a parallel plate waveguide is solved by using a first order perturbation method applied to the dominant TEM-mode. Regularization using the L-curve criterion is applied and investigated. Reconstruction results from using reflection data are presented and influences from higher order propagating and trapped modes are demonstrated.

  • 46.
    Norgren, Martin
    et al.
    KTH, Superseded Departments (pre-2005), Electrical Systems.
    de Saracho, Irene Ortiz
    KTH, School of Electrical Engineering and Computer Science (EECS). KTH Royal Inst Technol, Sch Elect Engn, Stockholm, Sweden..
    Dalarsson, Mariana
    Linnaeus Univ, Fac Technol, Vaxjo, Sweden..
    Perturbation Approach to Shape Reconstruction in a Rectangular Waveguide using Experimental Data2018In: 2018 INTERNATIONAL APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY SYMPOSIUM (ACES), IEEE , 2018Conference paper (Refereed)
    Abstract [en]

    We consider the inverse problem of reconstructing the shape of a deformation in one of the broad walls of a rectangular waveguide. Assuming a small deformation, resulting in weak scattering, the direct problem is solved using a first order perturbation approach. Hence, the inverse problem becomes linear and is formulated as an equation system for a set of expansion coefficients. The illposedness of the inverse problem is handled with regularization, by adding a penalty term which weight is determined by the L-curve method. The theory is tested on experimental reflection data, using the dominant mode of the waveguide. The reconstructed shape is in qualitative agreement with the true shape, but a detailed resolution cannot be obtained due to insufficient quality of the experimental data. Extensions and improvements of the method are discussed.

  • 47.
    Norgren, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Ghasemifard, Fatemeh
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Dalarsson, Mariana
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Scattering of lower order modes in a parallel plate waveguide loaded with a slightly deformed layer of conducting strips2016In: 2016 URSI INTERNATIONAL SYMPOSIUM ON ELECTROMAGNETIC THEORY (EMTS), IEEE, 2016, p. 349-352Conference paper (Refereed)
    Abstract [en]

    The lower order modes are derived for a parallel plate waveguide loaded with a sheet of parallel conducting strips. Using a first order perturbation method, we derive the scattering parameters due to a small deformation of the sheet. Results for scattering within and between the novel slow mode and the ubiquitous TEM-mode are presented. With increasing angle between the strips and the direction of propagation, the interaction between the slow mode and the deformation shifts downwards in frequency, due to the reduced phase velocity.

  • 48.
    Norgren, Martin
    et al.
    KTH, Superseded Departments, Electrical Systems.
    He, Sailing
    KTH, Superseded Departments, Electromagnetic Theory.
    Exact and explicit solution to a class of degaussing problems2000In: IEEE transactions on magnetics, ISSN 0018-9464, E-ISSN 1941-0069, Vol. 36, no 1, p. 308-312Article in journal (Refereed)
    Abstract [en]

    An exact and explicit solution to a class of degaussing problems is given. The solution is shown to be unique. The stability of the solution is also analyzed.

  • 49.
    Norgren, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Jonsson, B. Lars G.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    THE CAPACITANCE OF THE CIRCULAR PARALLEL PLATE CAPACITOR OBTAINED BY SOLVING THE LOVE INTEGRAL EQUATION USING AN ANALYTIC EXPANSION OF THE KERNEL2009Article in journal (Refereed)
    Abstract [en]

    The capacitance of the circular parallel plate capacitor is calculated by expanding the solution to the Love integral equation into a Fourier cosine series. Previously, this kind of expansion has been carried out numerically, resulting in accuracy problems at small plate separations. We show that this bottleneck can be alleviated, by calculating all expansion integrals analytically in terms of the Sine and Cosine integrals. Hence, we can, in the approximation of the kernel, use considerably larger matrices, resulting in improved numerical accuracy for the capacitance. In order to improve the accuracy at the smallest separations, we develop a heuristic extrapolation scheme that takes into account the convergence properties of the algorithm. Our results are compared with other numerical results from the literature and with the Kirchhoff result. Error estimates are presented, from which we conclude that our results is a substantial improvement compared with earlier numerical results.

  • 50.
    Norgren, Martin
    et al.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Takenaka, Takashi
    Full Newton method for inverse transmission line problems, utilising explicit second order derivatives2007In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 15, no 8, p. 827-853Article in journal (Refereed)
    Abstract [en]

    The full Newton's method is considered as,in optimisation approach to the inverse transmission line problem in the frequency-domain. For the sake of accuracy and computational efficiency, the gradient and the Hessian of the cost-functional, with respect to parameter functions in the L-2-space, are derived explicitly by means of the adjoint transmission line problem and the first and second order Frechet differentials of the cost-functional. The numerical implementation, when reducing to a finite dimensional parameter space, and a regularisation technique for the resulting ill-conditioned Hessian matrix are presented. For the reconstruction of one or two parameters, the algorithm is tested oil synthetic reflection data contaminated with gaussian noise. The algorithm is also tested oil measured reflection data to reconstruct a piecewise constant shunt-capacitance. The generalisation to the three-dimensional inverse scattering problem for bianisotropic media is presented.

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