**Research topics** (in chronological order)

- hydrogen-oxygen fuel cells
- frequency control of induction motors
- electromagnetic field theory
- analytical and numerical methods for the analysis and synthesis of electromagnetic and electromechanical apparatus
- modelling and analysis of switched networks
- high-frequency modelling of wound components
- electrical characterization of alternative energy sources (fuel cells, photovoltaic modules and thin film solar cells)
- electromagnetic compatibility (EMC): electromagnetic shielding, conducted disturbances in ac motors supplied by inverters, compact environments for EMC testing, radiated emissions from cables and printed circuit boards, analysis of electromagnetic interference (EMI) source mechanisms, conducted and radiated disturbances from switching converters , modelling of electrical properties of dispersive materials for shielding effectiveness prediction, electromagnetic coupling inside metallic enclosures, electromagnetic interferences of rolling stock power systems and railway traction systems
- wireless power transfer via resonant magnetic coupling (inductive power transfer: IPT)

**Current research topics**

**Electromagnetic compatibility**

*Modelling of electrical properties of dispersive materials
for shielding effectiveness prediction*

This research activity concerns the modelling of the electrical properties of dispersive materials for predicting their shielding effectiveness against electromagnetic waves. The activity is mainly addressed to the development of methods for the extraction of the complex permittivity as a function of frequency of dispersive materials. The complex permittivity is reconstructed indirectly from the knowledge of a measurable quantity, whose analytical expression as a function of the complex permittivity is known. Deterministic or stochastic methods can be used to solve this inverse problem. For this purpose, algorithms based both on the method of least squares of the type of Marquardt-Levenberg and on stochastic methods of the type of the Particle Swarm Optimization (PSO) algorithm are developed. The inverse problem can be solved by different procedures, extracting directly the complex permittivity for each individual frequency of the range of interest (i.e. point-by-point), or in the whole frequency range assuming a dielectric relaxation model (Debye, Deby series, Cole-Cole, Havriliak-Negami), and extracting its parameters. The procedure has a general validity as it can be applied to different measurement techniques and materials.

*Electromagnetic coupling inside metallic enclosures*

This research deals with the development of a method to predict the electromagnetic coupling inside a metallic enclosure. The method is based on an analogy between a mono-modal rectangular waveguide and a transmission line, i.e. between the transmitted power in a mode of propagation in the waveguide and the transmitted power in the equivalent transmission line. The fundamental radiators (sources and victims) considered inside the enclosure are straight wires and loops modelled as electric monopoles/dipoles and magnetic dipoles, respectively. The electromagnetic coupling is represented in terms of equivalent circuits for the elementary dipoles and of transmission lines for the multi-modal propagation path. The coupling between an elementary dipole inside the metallic enclosure, considered as a rectangular waveguides short-circuited at both ends, and each waveguide mode occurs through mutual capacitances and/or a mutual inductances and can be represented through dependent sources. The section of the transmission line between the source and the victim is represented for each propagation mode by a two-port network. The equivalent circuit obtained can be solved by the node analysis.

The method can be extended to treat the electromagnetic coupling between electric monopoles and conducting planes inside a metallic enclosure. The conducting planes are represented with an equivalent impedance through a transmission line analogy. In this case the problem gets more complex when the analysis does not consider only the dominant mode but takes higher-order modes into account as the conducting plane acts as a source of mode coupling.

The results obtained with this method are compared to experimental measurements and transmission-line modeling method (TLM) numerical simulations.

The goal of this research activity is the development of a computer code to predict the electromagnetic coupling among printed circuit boards and other radiators, for example interconnecting cables inside metallic enclosures.

*Electromagnetic interferences of rolling stock power
systems*

The research activity concerns the modelling of phenomena and dominant coupling paths of the electromagnetic disturbances of the rolling stock power systems. The main contribution to the on-board radiated emissions is given by the internal elements that act as unintentional antennas (e.g., interconnecting cables of the various electric and electronic apparatus, heatsinks of the power electronic devices) because of the conducted emissions present in these elements. For the victim circuits internal to the rolling stock and the relevant infrastructure conductors, current driven and voltage driven mechanisms of electromagnetic coupling can be identified and represented by equivalent circuits containing current and voltage controlled sources. In particular, one can determine the currents injected into the conductors of the infrastructure, which represent the new sources for the inductive and capacitive couplings with close infrastructures, telecommunication and signalling lines. These couplings can be studied by means of the multiconductor transmission-line theory.

*Prediction of near field electromagnetic interference in
power converters via the induced EMF method*

The research activity concerns an approach to predict the
electromagnetic interference (EMI) generated by a switched-mode
power supply (SMPS) on a victim circuit. The electromagnetic field
coupling between the main sources (currents and voltages) of
electromagnetic interference of the SMPS and the victim is
represented by two-port networks characterized in terms of their
mutual impedances or admittances, which are calculated via the
induced EMF method, a classical method for the calculation of self-
and mutual impedances of radiating structures (or their elements).
Once the spectra of the source currents and voltages are known in
the time domain, the noise voltage on circular magnetic field
probes used in near-field measurements is then predicted.
Measurements on some flyback converters with different layouts are
carried out to assess the approach. The proposed method can be
applied also to predict the intra-system coupling, i.e., with
source and victim circuits internal to the SMPS. The knowledge of
the spectra of the two-port parameters (open-circuit impedances and
short-circuit admittances) allows one to rapidly assess the
behaviour of the EMI noise for different source current and voltage
spectra, without having to repeat the analysis of the
system.

**Electrical characterization of alternative energy sources:
fuel cells, photovoltaic modules and thin film solar cell**

In this research activity a nonlinear circuit model of a polymer electrolyte membrane (PEM) fuel cell is studied. The model allows the simulation of both steady-state and dynamic behavior of the cell 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 purpose of this research is to model a commercial PEM fuel cell stack 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.

Another topic in this research field concerns a numerical procedure for the extraction of the double-diode model parameters of photovoltaic (PV) modules. A particle swarm optimization algorithm can be used to fit the calculated current-voltage characteristic of a PV module to the experimental one. As no recurrent solution is found in the large number of simulations carried out, mainly because the stochastic nature of the optimization algorithm, statistics in combination with cluster analysis can be employed to give an insight into PV module parameters. The aim is to obtain a set of parameters which is reasonable and representative of the physical system.

Recently, the research is also focused on the modeling and
electrical characterization of CIGS thin film solar cells. A simple
analytical model for the photocurrent density of a CIGS thin film
solar cell with band gap graded linearly is studied, showing
that the photocurrent density of this cell is greater than that of
a cell with constant band gap. A four-diode equivalent circuit of a
CIGS solar cell to take account of phenomena such as the "trap
states" and "grain boundaries" is proposed. A new profile of band
gap which exploits the widening of both the valence
and conduction bands is studied by simulations.

**Inductive power transfer (IPT)**

The research activity deals with the 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 (resistance, self- and mutual inductances) are determined with analytical formulas taken from the literature and validated by comparison with numerical simulations through 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. Once the lumped-circuit parameters are known with good accuracy, the assessment of the power transfer system can be carried out by evaluating the current and voltage gains and the efficiency as a function of frequency for different system geometries and load conditions.

The research also includes the development of procedures for the
electrical characterization (self- and mutual inductances and
parasitic capacitance) of flat spiral inductors (straight or with
zig-zag arms) which are used as intermediate resonators or as a
metamaterial to improve the wireless transmission efficiency with
nonradiative technique.

Finally, a theoretical and experimental analysis of the wireless
power transfer through a coplanar resonator array is considered. In
particular, six identical spiral resonators are used to form an
array and to transfer power between an emitter and a receiver. All
the spiral resonators resonate at about 20 MHz and the emitter and
receiver coils are designed with formulas taken from literature.
The resonant system is modeled using mutual inductances, being
retardation not significant.