2 YEAR  II semester  6 CFU 
Luciano CANTONE  A.Y. 202324 
(by Engineering Sciences)  
Code: 80300065 SSD: 
2 YEAR  II semester  6 CFU 
Luciano CANTONE  A.Y. 202324 
(by Engineering Sciences)  
Code: 80300065 SSD: 
1 YEAR (Block C)
2 YEAR (Blocks ABDE) 
II semester  9 CFU 
Stefano CORDINER (6/9 cfu) Lorenzo BARTOLUCCI (3/9 cfu) 
A.Y. 202122
Internal Combustion Engines 
Since A.Y. 202223
POWERTRAIN TECHNOLOGIES FOR FUTURE MOBILITY 

Code: 80300079 SSD: ING/IND/08 (by Mechanical Engineering) 
LEARNING OUTCOMES:
The aim of the course is to provide students with indepth scientific training to properly address the design, selection and management of internal combustion engines and their interaction with the environment, as well as to create the conditions for the development of innovative solutions. To this aim, students will develop indepth knowledge of the principles of engine operation and learn simulation procedures for testing and sizing an alternative internal combustion engine and its main components. Special attention is also given to the latest technological development of internal combustion engine technology aimed at exceeding current limits in terms of emissions and efficiency and defining innovative scenarios of sustainable mobility.
KNOWLEDGE AND UNDERSTANDING:
The course aim is to provide the students with tools for the analysis of the performances and the evaluation of proper design solutions for internal combustion engines and their core components. At the end of the course, the student will be able to independently understand the functional link between design variables and the performance of internal combustion engines also in case of innovative design,
APPLYING KNOWLEDGE AND UNDERSTANDING:
The course, through the analysis of specific problems and quantitative data, is aimed at providing the tools for analysis and evaluation of the effects of different design choices. The theme of energy efficiency and pollution reduction are at the heart of the teaching organization. The student will be able to interpret and propose design solutions, even innovative ones, adapted to the specificity of the problems that are presented to him.
MAKING JUDGEMENTS:
By studying theoretical and practical aspects of engine design and critically assessing the influence of different design variables, the student will be able to improve his judgment and proposal in relation to design. and the management of internal combustion engines.
COMMUNICATION SKILLS:
The presentation of the theoretical and application profiles underlying the operation of internal combustion engines will be carried out to allow the knowledge of the technical language of the appropriate specialist terminology; The development of communication skills, both oral and written, will also be stimulated through classroom discussion, participation in seminary activities and through final tests.
LEARNING SKILLS:
The learning capacity, even individual, will be stimulated through numerical exercises, the drafting of papers on specialized topics, the discussion in the classroom, also aimed at verifying the actual understanding of the topics treated. The learning capacity will also be stimulated by integrative educational aids (journal articles and economic newspapers) in order to develop autonomous application capabilities.
SYLLABUS:
General information on internal combustion engines: Characteristics and Classification, thermodynamic and performance analysis. Experimental analysis of the performance of an internal combustion engine Air Supply for 4stroke engines: volumetric efficiency and its evaluation, quasistationary effects; valve sizing; the influence of other engine parameters; Variable Valve Actuation systems; nonstationary phenomena in the intake and exhaust: inertia and wave propagation; variable valve geometry systems, computational models; 2stroke engines: construction schemes; Supercharging; In cylinder charge motion: Turbulence; swirl, squish, tumble, stratified charge engines Traditional and alternative fuels; Fuels general properties: fuel, air stoichiometric; calorific value gaseous fuels: natural gas, hydrogen and mixtures thereof. bioethanol , biodiesel and DME. Features and their use in engines: technical solutions, performance and emissions Fuel metering. Otto engines: carburetor; injection systems; lambda probe. Diesel engines: fuel injectors and injection systems, dimensioning. Experimental tests on a diesel injection system Common Rail Combustion: Fundamentals of analytical study of combustion, thermodynamics of combustion processes, calculation of the chemical composition and temperature in adiabatic equilibrium transport phenomena (notes), chemical kinetics (notes). Combustion in Otto and Diesel engines. Emissions and their control systems: emissions formation mechanisms, effects on health and environment, measurement of emissions; influence of engine parameters, test cycles and legislation; procedures and systems for the reduction of emissions in engines. Experimental tests. Cooling system: Heat flows, heat transfer in the engine cooling systems, liquid and air: structural layouts and sizing; thermal stress of the mechanical parts. Sustainable mobility. Principles of operation of hybrid vehicles: series and parallel solution; engines there and electrical workers, regenerative braking, lithium batteries, performance and prospects. Plugin hybrid vehicles, engines c.i. ” Range extender “. Electric vehicles, characteristics and perspectives For all the topics of the course the numerical simulation tools will be presented
1 YEAR  II semester  6 CFU 
ICT and Internet Engineering  
Marina RUGGIERI (5cfu)
Tommaso ROSSI (1cfu) 
A.Y. 202324 A.Y. 202425 
Code: 8039514 SSD: INGINF/03 
OBJECTIVES
LEARNING OUTCOMES: The course aims at providing to the students the theoretical and practical tools for the development of design capabilities and implementation awareness of Digital Signal Processing (DSP) systems and applications.
KNOWLEDGE AND UNDERSTANDING: Students are envisaged to understand the DSP theoretical, design and algorithm elements and to be able to apply them in design exercises.
APPLYING KNOWLEDGE AND UNDERSTANDING: Students are envisaged to apply broadly and to personalize the design techniques and algorithm approaches taught during the lessons.
MAKING JUDGEMENTS: Students are envisaged to provide a reasoned description of the design and algorithm techniques and tools, with proper integrations and links.
COMMUNICATION SKILLS: Students are envisaged to describe analytically the theoretical elements and to provide a description of the design techniques and the algorithm steps, also providing eventual examples.
LEARNING SKILLS: Students are envisaged to deal with design tools and manuals. The correlation of topics is important, particularly when design tradeoffs are concerned.
BACKGROUND
A good mathematical background (in particular on complex numbers, series, functions of complex variable) is strongly recommended.
PROGRAMME
PART I – Discretetime signals and systems; sampling process; Discretetime Fourier transform (DTFT); Ztransform; Discrete Fourier Series (DFS).
PART II – Processing algorithms: introduction to processing; Discrete Fourier Transform (DFT); finite and long processing; DFTbased Processing; Fast Fourier Transform (FFT); processing with FFT.
PART III – Filter Design: introduction to digital filters: FIR and IIR classification; structures, design and implementation of IIR and FIR filters; analysis of finite word length effects; DSP system design and applications; VLAB and applications (Dr. Tommaso Rossi) with design examples and applications of IIR and FIR filters, Matlabbased lab and exercises (optional).
TEXTBOOKS
[1] “Digital Signal Processing Exercises and Applications”, Marina Ruggieri, Michele Luglio, Marco Pratesi. Aracne Editrice, ISBN: 8879999079.
[2] The River Publishers’ Series in Signal, Image & Speech Processing, “An Introduction to Digital Signal Processing: A Focus on Implementation”, Stanley Henry Mneney. River Publishers, ISBN: 9788792329127.
[3] Slides (exercises are also included therein), published on the teaching website.
1 YEAR  II semester  6 CFU 
Michela GELFUSA  A.Y. 202122
A.Y. 202223 
Code: 80300063 SSD: INGIND/10 (by Engineering Sciences) 
1 YEAR  II semester  6 CFU 
Andrea Micheletti  A.Y. 202122 (9 cfu) 
Andrea Micheletti  A.Y. 202223 (6 cfu) 
Code: 80300064 SSD: ICAR/08 (by Engineering Sciences) 
FORMATIVE OBJECTIVES
LEARNING OUTCOMES: The goal of this course, composed of two Modules, is to provide the student with basic knowledge of the mechanics of linearly elastic structures and of the strength of materials. By completing this class successfully, the student will be able to compute simple structural elements and reasonably complex structures.
KNOWLEDGE AND UNDERSTANDING: At the end of this course, the student will be able to:
– compute constraint reactions and internal actions in rigidbody systems and beams subjected to point/distributed forces and couples
– compute centroid position and central principal secondorder moments of area distributions
– understand the formal structure of the theory of linear elasticity for beams and 3D bodies
– analyze strain and stress states in 3D bodies
– compute the stress state in beams subjected to uniaxial bending, biaxial bending, eccentric axial force
– understand the behaviour of beams subjected to shear with bending and torsion
– understand how to compute displacements/rotations in isostatic beam systems, how to solve statically underdetermined systems, how to apply yield criteria, and how to design beams against buckling
APPLYING KNOWLEDGE AND UNDERSTANDING: The student will apply the knowledge and understanding skills developed during the course to the analysis of practical problems. This includes the analysis of linearly elastic structures and structural members in terms of strength and stiffness.
MAKING JUDGEMENTS: The student will have to demonstrate his awareness of the modeling assumptions useful to describe and calculate structural elements, as well as his critical judgement on the static response of elastic structures under loads, in terms of stresses, strains, and displacements.
COMMUNICATION SKILLS: The student will demonstrate, mostly during the oral test, his capacity of analyzing and computing the static response of linearly elastic structures, as well as his knowledge of the underlying theoretical models.
LEARNING SKILLS: The student will get familiar with the modeling of structures and structural elements in practical problems, mostly during the development of his skills for the written test. This mainly concerns beams and threedimensional bodies.
PREREQUISITES: The student should have already attended the basic courses of calculus, geometry, and physics.
It is required that the student has good skills with regard to differential and integral calculus, linear algebra and matrix calculations.
SYLLABUS:
Together with the other Module of this course, the following topics are covered.
Review of basic notions of vector and tensor algebra and calculus.
Kinematics and statics of rigidbody systems.
Geometry of area distributions.
Strain and stress in 3D continuous bodies and beamlike bodies.
Virtual power and virtual work equation for beams and 3D bodies.
Onedimensional beam models: BernoulliNavier model, Timoshenko model, constitutive equations, governing differential equations.
Constitutive equation for linearly elastic and isotropic bodies, material moduli.
Hypothesis in linear elasticity, equilibrium problem for linearly elastic beams and 3D bodies.
Threedimensional beam model: the SaintVenant problem, uniaxial and biaxial bending, eccentric axial force, shear and bending, torsion.
Elastic energy of beams and 3D bodies, workenergy theorem, Betti’s reciprocal theorem, Castigliano’s theorem.
Yield criteria (maximum normal stress, maximum tangential stress, maximum elastic energy, maximum distortion energy).
Buckling instability, bifurcation diagrams, load and geometry imperfections, Euler buckling load, design against buckling.
Basic notions on the finite element method and structural analysis software.
1 YEAR  II semester  6 CFU + 3 cfu extra 
Rocco Giofre’  A.Y. 202122
A.Y. 202223 
Paolo Colantonio  A.Y. 202324 
Code: 80300060 SSD: INGINF/01 (by Engineering Sciences) 
The students who include Analogue Electronics in their study plan are strongly advised to include it in its 9CFU version, with the last 3 CFUs (out of 9) working as Extra Credits.
LEARNING OUTCOMES:
Learning the basic concept of analogue electronic systems and circuits and developing the competencies to design electronic circuits.
The educational objectives are pursued through lectures and exercises.
KNOWLEDGE AND UNDERSTANDING:
The student acquires the basic conceptual and analytical knowledge, both theoretical and applied, of the main basic electronic components. Subsequently, it acquires knowledge related to the integration of basic electronic components for the development of more complex electronic systems, such as amplifiers, oscillators, rectifiers, etc.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The student will demonstrate to have acquired the methodologies for the analysis and synthesis (design) of simple electronic circuits.
MAKING JUDGEMENTS:
The student must be able to integrate the basic knowledge provided with those deriving from physics, mathematics, and electrical engineering courses, in order to correctly select the most appropriate analytical and circuit synthesis options.
COMMUNICATION SKILLS:
Students must be able to illustrate the basic themes of the course synthetically and analytically, linking together the different concepts that are integrated into more complex electronic systems.
Prerequisite: Knowledge of network analysis in general.
SYLLABUS:
Diode semiconductor devices and circuit applications: clipper, clamper, peak detector, etc. Bipolar Junction and Field Effect Transistors. Biasing techniques for Transistors. Amplifiers classification, analysis, and circuit design. Frequency response of single and cascaded amplifiers. Differential amplifiers and Cascode. Current mirrors. Feedback amplifiers and stability issues. Power amplifiers. Operational amplifiers and related applications. Oscillator circuits. Integrated circuits and voltage waveform generators.
Books for references
“Electronics: a systems approach”, Neil Storey, Prentice Hall
“Elettronica di Millman”, J. Millman, A. Grabel, P. Terreni, McGrawHill
HOW TO ATTEND LESSONS:
Although attendance is optional, given the complexity of the topics covered, it is strongly recommended to follow the lessons.
1 YEAR  II semester  6 CFU 
Antonio Agresti (3cfu) Francesca De Rossi (3cfu) 
A.Y. 202122 
Antonio Agresti (3cfu) Fabio Matteocci (3cfu) 
A.Y. 202223 A.Y. 202324 
Antonio Agresti  A.Y. 202425 
Code: 8039791 SSD: INGINF/01 
(to be updated for A.A. 2425)
LEARNING OBJECTIVES AND EXPECTED LEARNING OUTCOMES:
LEARNING OUTCOMES:
The first part of the Nanotechnology course introduces thin film depositions using both physical and chemical vapour depositions. The main objective is the knowledge of the potential and limits of the different thin film depositions in the nanotechnology field. Particular attention is destinated to the deposition technique used in micro and nanoelectronics based on semiconductors using topdown and bottomup approaches. The interaction of both approaches has been discussed with the student in order to share the importance of multidisciplinary knowledge (physics, chemistry and engineering) where the nanotechnology field is based. The final part of module 1 is destinated to the introduction of the case study of the course about the thin film fabrication of an emergent photovoltaic technology: the perovskite solar cells. In particular, the study of the optoelectronic properties of the materials and the fabrication of several device architectures is important to understand the important role of the manufacturing design in thin film photovoltaic technologies destinated at the industrial level.
KNOWLEDGE AND UNDERSTANDING:
Regarding the first module, at the end of the course, the student will have a clear overview of the main deposition technique studied and applied in nanotechnology for different application fields.
Regarding the second module, at the end of the course, the student will know the main characterization techniques for nanostructured materials and electronic and optoelectronic devices till nanometric size.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The student will be able to recognize the applicability areas for the various characterization and realization techniques at nanometric scales. She/He will also be able to apply the knowledge and understanding developed during the course to study and understand recent literature.
MAKING JUDGEMENTS:
The transversal preparation provided by the course implies
1) the student’s capability to integrate knowledge and manage complexity
2) the student’s ability to deal with new and emerging areas in nanotechnology application to energy and nanoelectronics.
COMMUNICATION SKILLS:
The student will be able to clearly and unequivocally communicate the course content to specialized interlocutors. He will also be able to communicate the main physicochemical characteristics of nanostructured materials and to indicate the most appropriate deposition/processing technique of these materials to technical interlocutors (example: other engineers, physicists, chemists) but not specialists in the field of electronics or devices. The student will also have a sufficient background to undertake a thesis/research work in modern nanotechnology laboratories.
LEARNING SKILLS:
The structure of the course contents, characterized by various topics apparently separated but connected by an interdisciplinary and modular vision, will contribute to developing a systemic learning capacity that will allow the student to approach in a selfdirected or autonomous way to other frontier problems on nanotechnology application to energy and nanoelectronics. Furthermore, the student will be able to read and understand recent scientific literature.
SYLLABUS
First Module: 1 Prof. Antonio Agresti (3 cfu)
1) Quantum Mechanics and pn junction
2 )Solar Cells: main electrical characterization techniques
3) Absorbance and Fluorescence Spectroscopy
4) Electron scanning microscopy (SEM)
5) Electron transmission microscopy (TEM)
6) Scanning tunneling microscopy (STM)
7) Atomic force microscopy (AFM)
8) Kelvin Probe Microscopy (KPFM)
9) Raman spectroscopy
10) BiDimensional Materials
Second module – Prof. Fabio Matteocci (3cfu)
1) Introduction to nanotechnology and thin film properties;
2) Thin Film Deposition: the importance of vacuum and plasma;
3) Thermal Evaporation: Working mechanism, material properties, deposition parameters and applications;
4) DC and RF Sputtering: Working mechanism, material properties, deposition parameters and applications;
5) Pulsed Laser Deposition: Working mechanism, material properties, deposition parameters and applications;
6) Chemical Vapour Deposition: Working mechanism, material properties, deposition parameters and applications;
7) Atomic Layer Deposition: Working mechanism, material properties, deposition parameters and applications;
8) Solution Processing: Spin coating, Screen Printing, Blade Coating, Slot die coating;
9) Patterning Procedures: Photolithography and Laser Ablation;
10) Introduction to Perovskite Solar Cell: Working mechanism, material properties, deposition techniques, upscaling process and applications;
11) Building Integration Photovoltaics;
1 YEAR  II semester  9 CFU 
Luca DI NUNZIO  A.Y. 202122 
Luca DI NUNZIO (5 cfu)
Vittorio MELINI (2 cfu) Sergio SPANO’ (2 cfu) 
since A.Y. 202223 
Code: SSD: INGINF/01 
PREREQUISITES:
It is strictly suggested to take the “Digital Electronics” exam before attending this course. You can contact Prof. Luca DI NUNZIO for any doubts regarding the topic.
LEARNING OUTCOMES:
The VLSI CIRCUIT AND SYSTEM DESIGN course aims to teach the basics of combinational and sequential circuits that represent the basic blocks of any modern digital system. In addition, the course will provide the basic concepts of the VHDL language
KNOWLEDGE AND UNDERSTANDING:
At the end of the course, the student will learn the basic concepts of combinational and sequential circuits that are the basis of any system and the basic concepts of the VHDL language useful for the design of digital systems
APPLYING KNOWLEDGE AND UNDERSTANDING:
Ability to analyze the characteristics of digital circuits with particular emphasis on timing and power consumption.
MAKING JUDGEMENTS:
The student will understand the acquired knowledge independently and critically to be able to connect and integrate the various aspects related to the design of digital systems
COMMUNICATION SKILLS:
The student must be able to communicate their knowledge acquired during the course in clear, correct, and technical language.
LEARNING SKILLS:
Ability to critically approach a digital circuit design problem, know how to manage it, and find implementation solutions using the VHDL language
SYLLABUS:
(L. DI NUNZIO)
Digital electronics basic concepts
Floatingpoint and fixedpoint numeric representation formats
Combinatorial circuits: encoders, decoders, multiplexers
Sequential circuits: flip flops, latch registers, counters, memories
Introduction to VHDL: entity and architecture, levels of abstraction, HDL design flow, combinatorial and sequential processes, objects in VHDL test bench
Practical activities of circuit design in VHDL
(S. SPANO’)
Central unit
ALU
System registers
Address logic
System buses
Scheduler
Branching of instructions
Interrupts
Bus synchronization
RAM memories
ROM memories
Flash memories
CAM memories
1 YEAR  II semester  6 CFU 
Cristiano M. VERRELLI  A.Y. 202122 
A.Y. 202223  
Code: SSD: INGINF/04 
FORMATIVE OBJECTIVES
LEARNING OUTCOMES:
The theory of differential equations is successfully used to gain profound insight into the fundamental mathematical control design techniques for linear and nonlinear dynamical systems.
KNOWLEDGE AND UNDERSTANDING:
Students should be able to deeply understand (and be able to use) the theory of differential equations and of systems theory, along with related mathematical control techniques.
APPLYING KNOWLEDGE AND UNDERSTANDING:
Students should be able to design feedback controllers for linear (and even nonlinear) dynamical systems.
MAKING JUDGEMENTS:
Students should be able to identify the specific design scenario and to apply the most suitable techniques. Students should be able to compare the effectiveness of different controls while analyzing theoretical/experimental advantages and drawbacks.
COMMUNICATION SKILLS: Students are expected to be able to read and capture the main results of a technical paper concerning the topics of the course, as well as to effectively communicate in a precise and clear way the content of the course. Tutorguided individual projects (including Maple and MatlabSimulink computer simulations as well as visits to labs) invite intensive participation and ideas exchange.
LEARNING SKILLS:
Being enough skilled in the specific field to undertake the following studies characterized by a high degree of autonomy.
The matrix exponential; the variation of constants formula.
Computation of the matrix exponential via eigenvalues and eigenvectors and via residual matrices. Necessary and sufficient conditions for exponential stability: RouthHurwitz criterion. Invariant subspaces.
Impulse responses, step responses and steady state responses to sinusoidal inputs. Transient behaviours. Modal analysis: mode excitation by initial conditions and by impulsive inputs; modal observability from output measurements; modes which are both excitable and observable. Popov conditions for modal excitability and observability. Autoregressive moving average (ARMA) models and transfer functions.
Kalman reachability conditions, gramian reachability matrices and the computation of input signals to drive the system between two given states. Kalman observability conditions, gramian observability matrices and the computation of initial conditions given input and output signals. Equivalence between Kalman and Popov conditions.
Kalman decomposition for nonreachable and nonobservable systems.
Eigenvalues assignment by state feedback for reachable systems. Design of asymptotic observers and Kalman filters for state estimation of observable systems. Design of dynamic compensators to stabilize any reachable and observable system. Design of regulators to reject disturbances generated by linear exosystems.
Bode plots. Static gain, system gain and highfrequency gain.
Zeropole cancellation.
A.Y.  Mechatronics students  Other courses Students  Mechatronics average  Other courses average 
2019/2020  10  62  24  23 
2020/2021  19  25  23  24 
2021/2022  13  44  21  22 
2 YEAR  2 semester  9 CFU 
Stefano Bifaretti 
A.Y. 202122 
Stefano Bifaretti (7cfu)
Cristina Terlizzi (2cfu) 
A.Y. 202223 1st Year I semester A.Y. 202324 (NOT HELD) A.Y. 202425 
Code: 8039781 SSD: INGINF/01 
LEARNING OUTCOMES:
The Power Electronics and Electrical Drives course aims to provide a basic understanding of the power semiconductors of the main electronic circuits used for the static conversion of electrical energy as well as the electrical drives. The student will acquire the ability to analyse and perform an initial sizing of power electronic converters operating in either direct or alternating current.
KNOWLEDGE AND UNDERSTANDING:
The student will be gradually guided to the knowledge of the functional characteristics and behavior of the main static power converters used, in particular, in industrial applications, in Distributed Generation Systems and in power trains of electical vehicles. In order to improve the topics understanding, the use of MatlabSimulink specific packages for the simulation of electronic power converters is illustrated.
APPLYING KNOWLEDGE AND UNDERSTANDING:
The knowledge acquired during the course allows the student to select the topology and size of the power converter in relation to the final design.
Different application examples, in particular devoted to distributed energy generation plants, uninterruptible power supplies and electric mobility will allow the student to improve his ability to apply the acquired knowledge.
MAKING JUDGEMENTS:
The student will be able to collect and process specialized technical information on power converters and verify their validity.
COMMUNICATION SKILLS:
The student will be able to relate with power electronics specialists in order to request the technical information necessary for the development of a project activity.
LEARNING SKILLS:
The skills acquired during the course will allow the student to undertake, with a high degree of autonomy, subsequent studies or apply for technical roles in companies working in the field.
SYLLABUS:
POWER SEMICONDUCTORS
Power Semiconductors employed in Power Electronics converters: Diodes, BJT, MOSFET, IGBT, Thyristors, Wide Bandgap Semiconductors).
Static and dynamic behavior. Thermal behavior. Conduction and switching losses.
Technical specifications provided by manufacturers’ datasheets. Driving circuits.
POWER CONVERTER TOPOLOGIES
Behavioral characteristics: unidirectional and bidirectional energy transfer, controlled voltage sources. Analysis method of power converters.
DCDC Converters. Buck, Boost, BuckBoost. Switching losses reduction. Average Model. Modulation techniques (PWM, PFM, PRM). Output voltage openloop control. Closedloop control. Current control.Half and Full Bridge DCDC converters.
DCAC Converters (Inverters). Half and Full Bridge DCAC singlephase converters based on static switches. Threephase converters. Modulation techniques. Selective Harmonic Elimination (SHE). Sinusoidal Pulse Width Modulation (SPWM).
Rectifiers: Singlephase and threephase diode rectifiers. Singlephase and threephase forcecommutated PWM rectifiers: topologies, voltage and current controls. Power Factor Corrector (PFC). Effects on grid side of power converters. Generalized power factor. Compliance with grid codes.
Isolated DCDC converter.
ELECTRICAL DRIVES
Introduction to Electrical Drives. DC, Permanent Magnet Synchronous Motors and Induction Motors. DC motors model.
Power Electronics Applications
Power Converters simulation using MatlabSimulink/Simpowersystem.
Photovoltaic Conversion Systems.
Power trains for electrical vehicles. Battery chargers.