The research activity of Leonardo Sandrolini is mainly in the
fields of

(b) electromagnetic couplings within metallic enclosures

(c) models to predict electromagnetic interference in switching converters

(d) electromagnetic interferences in railway systems

(b) Study of the electrical properties of adhesive materials for restorative dentistry

(b) wireless transmission of electrical energy with nonradiative techniques

The research activity in this field has been started by Leonardo Sandrolini during the Ph.D. period and concerned the development and setup of an analytical methodology for the calculation of the shielding effectiveness of multilayered shields for low-frequency magnetic fields. This methodology allows one to obtain a good estimate of the shielding effectiveness of multilayered shields and a simple shield model at the same time. In fact, numerical techniques cannot be applied easily to multilayered configurations, especially when the number of layers is large and the layer thickness is much larger than the skin depth. The shield is represented by means of a transmission matrix which expresses relationships between continuous field components at the two layer surfaces and allows the multilayered shield to be represented through multiplying the transmission matrices of all layers of the shield. The analytical method, based on the solution of the diffusion equation for the magnetic field (quasistatic approximation) was validated for frequencies higher than the industrial one. The highest admissible frequency (as a function of the distance between source and field points) for the quasimagnetostatic approximation was found from the comparison between the solutions obtained with this methodology and those from the wave equation. The methodology was then applied to magnetic fields generated by nonsinusoidal currents. The development of an analytical method made it possibile to implement this methodology in an optimization procedure for multilayered shields. The objectives can be either to obtain the minimum shield volume with the constraint of keeping the magnetic induction field below a threshold, or to ensure a minimum shielding effectiveness. Two optimization procedure have been developed, the former based on a heuristic algorithm, the latter on an evolutionary approach that makes use of the particle swarm optimization algorithm. The latter has been found particularly effective as the number of optimization variables for a multilayered shield is not fixed.

More recently, a research activity devoted to the methods and techniques of measurement for the shielding effectiveness has been started. Polymeric conductive materials and conductive woven and nonwoven textiles have been considered.

(b) electromagnetic couplings within metallic enclosures

A research activity was started to develop a methodology to predict electromagnetic coupling inside metallic enclosures. This activity was born from a joint collaboration with the George Green Institute for Electromagnetic Research, University of Nottingham, United Kingdom (directed by Prof. Christopoulos) through a formal Agreement with the aim to develop joint research programmes.

The methodology is based on the analogy between a mono-modal rectangular waveguide and a transmission line. This analogy originates from the equality between the power carried by a propagating mode in the waveguide and that carried by the equivalent transmission line. The basic radiating structures considered are wires and loops, that can be modelled as electric monopoles/dipoles and magnetic dipoles, respectively. The position of the radiators can be totally arbitrary within the metallic enclosure. The complete coupling can be represented in terms of equivalent circuits for the radiating structures and transmission line circuits for the multi-modal waveguide propagation path. Inside a metallic enclosure (modelled as a waveguide short-circuited at both ends) an electric dipole (monopole) will couple via a mutual capacitance with the waveguide modes and a magnetic dipole will couple via a mutual inductance. Dependent current sources effect the mutual coupling of the wire (monopole) to the waveguide via a propagating mode. In the same way, dependent voltage sources effect the mutual coupling of the loop (magnetic dipole) to the waveguide via a propagating mode. The section of the transmission line between source and victim is modelled as a two-port network. The equivalent circuit can be easily extended to include higher order modes than the dominant one, TE10. For each additional mode, an extra analogous transmission line is added to the circuit (with its associated current or voltage sources and impedances). Nodal analysis can then be employed to solve the equivalent circuit. A number of experimental tests has been carried out to validate the methodology and the calculation procedures.

This methodology can be extended to treat coupling between electric monopoles/dipoles and magnetic dipoles inside a metallic enclosure in presence of conducting planes. Conducting planes within the enclosure can be modelled by means of a transmission line analogy. In fact, the way an electric field is scattered by a conducting plane inside an enclosure is similar to the scattering of a voltage wave by a shunt impedance across a transmission line. The ultimate aim of the methodology is to implement a calculation code to predict the electromagnetic coupling between printed circuit boards and other radiating structures, such as interconnecting cables, inside metallic enclosures.

(c) models to predict electromagnetic interference in switching converters

The research activity in this field is focused to develop mathematical models for the calculation of radiated electromagnetic fields. Different methodologies to predict the radiated electromagnetic fields from straight interconnect cables carrying high-frequency currents have been studied. Measurements on an experimental setup have been carried out to verify the accuracy of the analytical models in different configurations where a pair of cables located at various distances from a conducting ground plane, parallel to the plane of the cables, has been examined. Similarly, radiated emissions from PCB lands were studied; the p.u.l. parameters of the PCB lands were preliminarily calculated.

An alternative approach to describe The electromagnetic field coupling at low frequency (9 kHz-30MHz) between electromagnetic interference (EMI) sources of switched-mode power supplies (SMPS) and a victim circuit makes use of two-port networks represented by short-circuit admittance and open-circuit impedance matrices. The currents in the primary and secondary loops of a SMPS (source circuit) create a time-varying magnetic flux which links the victim circuit where a resulting voltage is induced. This coupling is known as inductive or magnetic field coupling. Furthermore, the voltage between a heatsink and the reference ground of the SMPS (source circuit) creates a time-varying electric field which extends through space and thus generates a displacement current, which may terminate in the victim circuit. This coupling is called capacitive or electric field coupling. The key point of this research activity is to calculate the relevant open-circuit impedance and short-circuit admittance parameters. The mutual impedance between source and victim circuit is calculated by the induced EMF method.

(d) electromagnetic interferences in railway systems

Possible electromagnetic interferences in the new High-Speed railway systems of the Italian railways generated by dc conventional railway systems have been studied. The research activity outlined the main interference electromagnetic sources and the provisions to adopt in the design stage of the High-Speed lines in order to limit possible electromagnetic couplings. Recently, Leonardo Sandrolini participated to a PRIN (research Project of Relevant National Interest) project and presented a contribution to the Workshop WS1 "EMC Management and Assurance in Railway" at the 18th Int. Zurich Symp. on Electromagnetic Compatibility, Munich, Germany, Sep. 24-28 2007. In this contribution the main EMI sources in a railway system were classified. Moreover, a study on possibile EMI situations between two different railway signalling systems was carried out.

The research activity in this field, in partial collaboration with foreign industry researchers, concerns the electrical properties of dispersive materials with the aim to predict their shielding effectiveness to electromagnetic waves. Energy loss inside the material is taken into account by means of a complex permittivity, whose real part is an effective permittivity and whose imaginary part is a term that depends on the effective electrical conductivity of the material and is inversely proportional to the frequency. Effective permittivity and effective electrical conductivity can be measured and used to predict the shielding effectiveness of a planar infinite shield by means of the transmission line theory. Nonideal shields can still be studied with numerical simulators and the electrical properties of the materials can be represented by theoretical analytical models. In particular, construction materials were studied, with reference to concrete. Among the models implemented in numerical simulators, the most appropriate one to represent the electric properties of concrete is the extended Debye model, where an additional term is introduced in the imaginary part of the complex permittivity to take explicit account of the energy loss due to the material electrical conductivity. The parameters (effective permittivity and effective conductivity) of the Debye model were obtained by fitting to experimental values with a nonlinear least-squares Marquardt–Levenberg algorithm. The comparison between the shielding effectiveness obtained with a commercial TLM numerical simulator and that obtained analytically with the classical transmission-line theory showed a good agreement for concrete with different moisture content.

(b) electrical properties of adhesive materials for restorative dentistry

The application of an electric field has been shown to positively influence the impregnation of the resin monomers currently used in dentin bonding systems during hybrid layer formation. This study presents an experimental characterization of the electrical properties of these monomers with the aim of both correlating them to their chemical structures and seeking an insight into the mechanisms of the monomer migration under an applied electric field.

This research activity has been carried out mainly within two research projects financed by both the Italian Ministry for the University and the University of Bologna. Leonardo Sandrolini started a research activity focused at the development of a nonlinear equivalent circuit for a 1.2 kW polymer electrolyte membrane (PEM) fuel cell stack available at the Department of Electrical Engineering of the University of Bologna. The model allows the simulation of both steady-state and dynamic behaviour of the stack on condition that the values of some of its parameters are changed in the two operating conditions. The circuit parameters can be obtained by means of simple experimental tests and calculations. The commercial PEM fuel cell stack is modelled as seen from the power conditioning system side, without requiring parameters necessary for complex mathematical models and not easily obtainable by the majority of users. The equivalent circuit can be used in power generation systems to verify their stability in normal and fault operating conditions.

Furthermore, the research concerned the electrical characterization of photovoltaic (PV) modules whose experimental current-voltage characteristic is known. A distributed computing technique has been implemented to extract the parameters of the equivalent circuit, that can be useful during the design stage (to design and improve the devices) as well as to integrate these energy sources in more complex systems. A trial current-voltage characteristic, that represent the output voltage of the PV module equivalent circuit, is fitted to the experimental characteristic by means of an iterative algorithm based on the particle swarm optimization. In the algorithm, interlaced computing is exploited to decrease the computational load, whereas parallel computing is used to collect as many data as possible and save computational time. Statistics applied on the obtained data allows one to control the typical instability of numerical fitting algorithms.

(b) wireless transmission of electrical energy with a nonradiative technique

The research concerns an accurate characterization of a wireless power transfer system consisting of two resonant air-core coils mutually coupled in free space. The lumped-circuit parameters of the equivalent circuit are determined with analytical formulas taken from the literature and validated by comparison with numerical simulations with a finite-element computer code and with experiments. The parameters are determined taking as input only the geometry of the system (coil size and mutual distance, conductor radius, and turn distance) and the frequency.

- Electromagnetic compatibility

(b) electromagnetic couplings within metallic enclosures

(c) models to predict electromagnetic interference in switching converters

(d) electromagnetic interferences in railway systems

- Electromagnetic characterization of materials

(b) Study of the electrical properties of adhesive materials for restorative dentistry

- Electrical aspects of energetics

(b) wireless transmission of electrical energy with nonradiative techniques

- Analysis of electromagnetic fields

- Electromagnetic compatibility

The research activity in this field has been started by Leonardo Sandrolini during the Ph.D. period and concerned the development and setup of an analytical methodology for the calculation of the shielding effectiveness of multilayered shields for low-frequency magnetic fields. This methodology allows one to obtain a good estimate of the shielding effectiveness of multilayered shields and a simple shield model at the same time. In fact, numerical techniques cannot be applied easily to multilayered configurations, especially when the number of layers is large and the layer thickness is much larger than the skin depth. The shield is represented by means of a transmission matrix which expresses relationships between continuous field components at the two layer surfaces and allows the multilayered shield to be represented through multiplying the transmission matrices of all layers of the shield. The analytical method, based on the solution of the diffusion equation for the magnetic field (quasistatic approximation) was validated for frequencies higher than the industrial one. The highest admissible frequency (as a function of the distance between source and field points) for the quasimagnetostatic approximation was found from the comparison between the solutions obtained with this methodology and those from the wave equation. The methodology was then applied to magnetic fields generated by nonsinusoidal currents. The development of an analytical method made it possibile to implement this methodology in an optimization procedure for multilayered shields. The objectives can be either to obtain the minimum shield volume with the constraint of keeping the magnetic induction field below a threshold, or to ensure a minimum shielding effectiveness. Two optimization procedure have been developed, the former based on a heuristic algorithm, the latter on an evolutionary approach that makes use of the particle swarm optimization algorithm. The latter has been found particularly effective as the number of optimization variables for a multilayered shield is not fixed.

More recently, a research activity devoted to the methods and techniques of measurement for the shielding effectiveness has been started. Polymeric conductive materials and conductive woven and nonwoven textiles have been considered.

(b) electromagnetic couplings within metallic enclosures

A research activity was started to develop a methodology to predict electromagnetic coupling inside metallic enclosures. This activity was born from a joint collaboration with the George Green Institute for Electromagnetic Research, University of Nottingham, United Kingdom (directed by Prof. Christopoulos) through a formal Agreement with the aim to develop joint research programmes.

The methodology is based on the analogy between a mono-modal rectangular waveguide and a transmission line. This analogy originates from the equality between the power carried by a propagating mode in the waveguide and that carried by the equivalent transmission line. The basic radiating structures considered are wires and loops, that can be modelled as electric monopoles/dipoles and magnetic dipoles, respectively. The position of the radiators can be totally arbitrary within the metallic enclosure. The complete coupling can be represented in terms of equivalent circuits for the radiating structures and transmission line circuits for the multi-modal waveguide propagation path. Inside a metallic enclosure (modelled as a waveguide short-circuited at both ends) an electric dipole (monopole) will couple via a mutual capacitance with the waveguide modes and a magnetic dipole will couple via a mutual inductance. Dependent current sources effect the mutual coupling of the wire (monopole) to the waveguide via a propagating mode. In the same way, dependent voltage sources effect the mutual coupling of the loop (magnetic dipole) to the waveguide via a propagating mode. The section of the transmission line between source and victim is modelled as a two-port network. The equivalent circuit can be easily extended to include higher order modes than the dominant one, TE10. For each additional mode, an extra analogous transmission line is added to the circuit (with its associated current or voltage sources and impedances). Nodal analysis can then be employed to solve the equivalent circuit. A number of experimental tests has been carried out to validate the methodology and the calculation procedures.

This methodology can be extended to treat coupling between electric monopoles/dipoles and magnetic dipoles inside a metallic enclosure in presence of conducting planes. Conducting planes within the enclosure can be modelled by means of a transmission line analogy. In fact, the way an electric field is scattered by a conducting plane inside an enclosure is similar to the scattering of a voltage wave by a shunt impedance across a transmission line. The ultimate aim of the methodology is to implement a calculation code to predict the electromagnetic coupling between printed circuit boards and other radiating structures, such as interconnecting cables, inside metallic enclosures.

(c) models to predict electromagnetic interference in switching converters

The research activity in this field is focused to develop mathematical models for the calculation of radiated electromagnetic fields. Different methodologies to predict the radiated electromagnetic fields from straight interconnect cables carrying high-frequency currents have been studied. Measurements on an experimental setup have been carried out to verify the accuracy of the analytical models in different configurations where a pair of cables located at various distances from a conducting ground plane, parallel to the plane of the cables, has been examined. Similarly, radiated emissions from PCB lands were studied; the p.u.l. parameters of the PCB lands were preliminarily calculated.

An alternative approach to describe The electromagnetic field coupling at low frequency (9 kHz-30MHz) between electromagnetic interference (EMI) sources of switched-mode power supplies (SMPS) and a victim circuit makes use of two-port networks represented by short-circuit admittance and open-circuit impedance matrices. The currents in the primary and secondary loops of a SMPS (source circuit) create a time-varying magnetic flux which links the victim circuit where a resulting voltage is induced. This coupling is known as inductive or magnetic field coupling. Furthermore, the voltage between a heatsink and the reference ground of the SMPS (source circuit) creates a time-varying electric field which extends through space and thus generates a displacement current, which may terminate in the victim circuit. This coupling is called capacitive or electric field coupling. The key point of this research activity is to calculate the relevant open-circuit impedance and short-circuit admittance parameters. The mutual impedance between source and victim circuit is calculated by the induced EMF method.

(d) electromagnetic interferences in railway systems

Possible electromagnetic interferences in the new High-Speed railway systems of the Italian railways generated by dc conventional railway systems have been studied. The research activity outlined the main interference electromagnetic sources and the provisions to adopt in the design stage of the High-Speed lines in order to limit possible electromagnetic couplings. Recently, Leonardo Sandrolini participated to a PRIN (research Project of Relevant National Interest) project and presented a contribution to the Workshop WS1 "EMC Management and Assurance in Railway" at the 18th Int. Zurich Symp. on Electromagnetic Compatibility, Munich, Germany, Sep. 24-28 2007. In this contribution the main EMI sources in a railway system were classified. Moreover, a study on possibile EMI situations between two different railway signalling systems was carried out.

- Electromagnetic characterization of materials

The research activity in this field, in partial collaboration with foreign industry researchers, concerns the electrical properties of dispersive materials with the aim to predict their shielding effectiveness to electromagnetic waves. Energy loss inside the material is taken into account by means of a complex permittivity, whose real part is an effective permittivity and whose imaginary part is a term that depends on the effective electrical conductivity of the material and is inversely proportional to the frequency. Effective permittivity and effective electrical conductivity can be measured and used to predict the shielding effectiveness of a planar infinite shield by means of the transmission line theory. Nonideal shields can still be studied with numerical simulators and the electrical properties of the materials can be represented by theoretical analytical models. In particular, construction materials were studied, with reference to concrete. Among the models implemented in numerical simulators, the most appropriate one to represent the electric properties of concrete is the extended Debye model, where an additional term is introduced in the imaginary part of the complex permittivity to take explicit account of the energy loss due to the material electrical conductivity. The parameters (effective permittivity and effective conductivity) of the Debye model were obtained by fitting to experimental values with a nonlinear least-squares Marquardt–Levenberg algorithm. The comparison between the shielding effectiveness obtained with a commercial TLM numerical simulator and that obtained analytically with the classical transmission-line theory showed a good agreement for concrete with different moisture content.

(b) electrical properties of adhesive materials for restorative dentistry

The application of an electric field has been shown to positively influence the impregnation of the resin monomers currently used in dentin bonding systems during hybrid layer formation. This study presents an experimental characterization of the electrical properties of these monomers with the aim of both correlating them to their chemical structures and seeking an insight into the mechanisms of the monomer migration under an applied electric field.

- Electrical aspects of energetics

This research activity has been carried out mainly within two research projects financed by both the Italian Ministry for the University and the University of Bologna. Leonardo Sandrolini started a research activity focused at the development of a nonlinear equivalent circuit for a 1.2 kW polymer electrolyte membrane (PEM) fuel cell stack available at the Department of Electrical Engineering of the University of Bologna. The model allows the simulation of both steady-state and dynamic behaviour of the stack on condition that the values of some of its parameters are changed in the two operating conditions. The circuit parameters can be obtained by means of simple experimental tests and calculations. The commercial PEM fuel cell stack is modelled as seen from the power conditioning system side, without requiring parameters necessary for complex mathematical models and not easily obtainable by the majority of users. The equivalent circuit can be used in power generation systems to verify their stability in normal and fault operating conditions.

Furthermore, the research concerned the electrical characterization of photovoltaic (PV) modules whose experimental current-voltage characteristic is known. A distributed computing technique has been implemented to extract the parameters of the equivalent circuit, that can be useful during the design stage (to design and improve the devices) as well as to integrate these energy sources in more complex systems. A trial current-voltage characteristic, that represent the output voltage of the PV module equivalent circuit, is fitted to the experimental characteristic by means of an iterative algorithm based on the particle swarm optimization. In the algorithm, interlaced computing is exploited to decrease the computational load, whereas parallel computing is used to collect as many data as possible and save computational time. Statistics applied on the obtained data allows one to control the typical instability of numerical fitting algorithms.

(b) wireless transmission of electrical energy with a nonradiative technique

The research concerns an accurate characterization of a wireless power transfer system consisting of two resonant air-core coils mutually coupled in free space. The lumped-circuit parameters of the equivalent circuit are determined with analytical formulas taken from the literature and validated by comparison with numerical simulations with a finite-element computer code and with experiments. The parameters are determined taking as input only the geometry of the system (coil size and mutual distance, conductor radius, and turn distance) and the frequency.

- Electromagnetic field analysis

The research concerns the implementation of a procedure which
exploits a sufficient condition for determining X-points in
quasistatic magnetic induction fields characterized by
translational or axisymmetrical geometry.