Master's degree in
Electronic Engineering (MEE)
Why study this master?


The master's degree in Electronic Engineering provides graduates with a broad profile that includes skills and expertise in power, analogue and RF electronics, instrumentation and sensors, digital systems, micro and nanotechnologies, and microelectronics. After the compulsory subject area, students can choose from a wide variety of subjects in order to acquire a general profile, specialise in a field or engage in research and pursue a doctoral degree. As a result, this master’s degree caters for the needs of two types of students: those who wish to focus on a professional career and those looking to pursue a doctoral degree in Electronic Engineering.

The aim is for the graduates to enter modern industry as benchmark professionals in a new multidisciplinary work and production scenario. To increase their employability, students can take both the master’s thesis and some of the ECTS credits for optional subjects in a company or laboratory.

MEE has a strong international character. It is taught entirely in English and attracts a large number of students from other countries.


The master's degree in Electronic Engineering is associated to content with a high labor demand.

Given the cross-disciplinary nature of electronics, graduates of this degree may pursue careers in a broad range of sectors related to electronic technology.

Medical and consumer electronics systems.

Robotics and automation systems.

Electromagnetic compatibility and microelectronic design.

Smart sensors and data acquisition systems.


The master program comprises 45 ECTS of core subjects, 45 ECTS of elective subjects and a master thesis of 30 ECTS. Students may choose to take one of the academic pathways with intensification in one of the following topics: Energy Management, Micro and NanoTechnologies, Integrated Systems and Biomedical Engineering and Sensors.


Compulsory Subjects


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Optional Subjects


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Master's Thesis


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Duration and start date

Two academic years, 120 ECTS credits.

Starting September and February

Fees and Grants

Approximate fees for the master’s degree, excluding degree certificate fee, 7.904 € (11.856 € for non-EU residents).

More information about fees and payment options.

More information about grants and scholarships for the degree.

Timetable and delivery

Afternoons. Face-to-face and blended learning.

Language of instruction



Barcelona School of Telecommunications Engineering (ETSETB)

Student Profile

Holders of a degree, or students in the last year of studies of a degree, can apply for admission to the master in Electronic Engineering. An official degree certificate is necessary the day of registration, in September. Please check the general academic requirements for master's degrees at UPC-Barcelona Tech.

Holders of a degree in:

  • Bachelor’s degree in Telecommunications Engineering, Electronic Engineering, Electrical Engineering, Computer Engineering or Applied Physics. Students may be admitted to different semesters of the master's programme on the basis of the subject of their degree and their academic CV.
  • Bachelor's degree in Telecommunications or Electronic Engineering may be admitted to the core semester.
  • Students admitted to the official postgraduate programme for the doctoral degree in Electronic Engineering who are required to take bridging courses may be admitted to the specialisation semester. Students from the pre-EHEA second cycle degree in Electronic Engineering who have completed all core and compulsory subjects may also be admitted to the specialisation semester.



Further information can be found on Barcelona School of Telecommunications Engineering (ETSETB)

Academic Calendar

The Academic year consists in 2 semesters, for a more detailed information check the following link


Depending on the subjects chosen they can be on mornings or afternoons. For a more detailed information check the following link

Master Degree Timetables

Contact Us

Academic coordination: Isidro Martín García

Contact mail:

The master in Electronic Engineering is offered at the
Escola Tècnica Superior d'enginyeria de Telecomunicació de Barcelona (ETSETB),
member of Universitat Politècnica de Catalunya - BarcelonaTech (UPC).


  1. Critical phenomena
    • Mean Field
    • Scaling and renormalization group
    • Kinetic Ising models
    • Continuum models
    • Growth Models
    • Percolation
  2. Dynamical Systems
    • Flows and maps
    • Normal Forms
    • Stability; Bifurcations
    • Intermittency; Chaos
    • Pattern formation
  3. Stochastic Processes
    • Markov processes
    • Master equations
    • Stochastic differential equations
    • Fokker-Planck equations
    • Relaxation and First-passage times
  4. Introduction to complex networks
    • Small-world networks
    • Scale-free networks
    • Characterization of networks


  1. Approximate methods in Quantum Mechanics.
    • Description of the problem. Mathematical formulation.
    • Solution of the problem using variational methods. Time-independent perturbation theory approach.
  2. Introduction to Scattering theory in Quantum Mechanics.
    • Formulation of the problem, differential cross section and Lipmann-Schwinger equation. T-matrix, Born approximation and partial wave expansions. Low-energy scattering.
  3. The many-body problem in Quantum Mechanics.
    • Bose and Fermi statistics, wave functions and simmetries.
    • Second quantization: creation and anihilation operators. Operators and observables in second quantization.
    • Hartree-Fock approximation, Gross-Pitaevskii equation and the Bogoliubov approximation.
  4. Magnetic systems
    • Polarized and unpolarized free Systems.
    • Ferromagnetic states. Single-particle excitations and particle-hole pairs. Magnons. Superconductivity and Cooper pairs. Introduction to BCS theory.
  5. Lattice systems: Bose- and Fermi-Hubbapop-contentrd models.


  1. Physical Chemistry of surfaces
    • Introduction to surfaces
    • Structure of surfaces
    • Solid-liquid and solid-gas interphases
    • Characterization techniques
    • Applications in sensors and catalysis
    • Functionalization of nano- and microreactors
  2. Mechanics and Fluid mechanics at micron scale
    • Introduction to micromechanic and microfluidic behavior.
    • Biosensor structure
    • Design and simulation of the biosensor fluidic behavior
    • Design and simulation of the biosensor mechanic behavior
    • Case studies in bioengineering and comunications.
  3. MEMS microdevices applied to communication circuits
    • Introduction to MEMS micro-devices. Materials and structures.
    • Ohmic- and capacitive-contact micro-switches.
    • MEMS micro-switch electromagnetic simulation
    • Application of MEMS micro-switches to reconfigurable communication circuits.
    • Circuit simulation.
    • Experimental characterization of MEMS micro-switches.


  1. Sources of Synchrotron and neutron radiation.
    • Continuous and pulsed sources.
  2. Safety in large facilities.
  3. Design of main devices in Sinchrotron and neutron sources:
    • focusing of photons and neutrons
    • dispersion and detection
  4. Design and use of special sample environments:
    • High pressure
    • high and low temperature
    • magnetic fields.
  5. Experimenal techniques available in large facilities.
    • Complementarity between experimental techniques
  6. Generation, storage and analysis of large facilities:
    • Experimental data


  1. Project planning.
  2. Planning methods based on critical path.
  3. Precedence analysis, PERT and GANTT chart.
  4. Time and cost estimation.
  5. Risk identification and mitigation plans.
  6. Stakeholders communication management.
  7. Project execution management: earned value.
  8. Project closure: success criteria and lessons learned.


  1. Basics of condensed matter
    • Microscopic constituents and effective interactions; condensed phases: normal and supercritical fluids, crystals, glasses, mesophases; classification and examples of transitions (first order, continuous, glassy); van der Waals theory and isomorphic states; miscibility and binary systems
    • Molecular disorder and dynamics; linear response theory, dielectric and mechanical spectroscopy, other experimental methods (thermodynamic and optical probes, scattering)
  2. Single-component systems
    • Small-molecule condensed phases; crystallization kinetics & polymorphism; structural glasses, ultrastable & aged glasses; orientationally disordered solids & plastic crystals; primary & secondary relaxations; charge conduction in molecular solids and liquids
    • Amorphous & semicrystalline linear homopolymers; ideal chain statistics and entanglement effects, entropic forces, Rouse modes and reptation; viscoelasticity, glass transition, and crystallization of linear polymers; branched polymers, gelation and rubber elasticity, affine network model for elastomers; conjugated and conductive polymers
    • Thermotropic liquid crystals (nematic, smectic, columnar) and liquid crystal polymers; optical properties and applications
  3. Multicomponent and aqueous systems
    • Polymer solutions: non-ideal chains, theta-solutions, hydrogels, swelling phenomena; superhydrophobic/hydrophilic, superolephobic, superamphiphilic, and self-healing polymer coatings; biopolymers, helix-coil and coil-globule transitions
    • Self-assembly in condensed matter: specific and non-specific interactions; block copolymers; colloidal systems (glasses, crystals, gels), surfactant-water systems, biomembranes, lyotropic liquid crystals, emulsions; semiflexible polymers & cytoskeleton


  1. Introduction: the hydrogen atom
  2. Interaction between atoms and external fields (static and oscillatory)
  3. Fine and hyperfine structure. Selection rules
  4. Symmetries of the wave function
  5. Many-electron atoms. Thomas-Fermi model, and Hartree-Fock method
  6. Understanding the periodic table of elements
  7. Molecular structure and degrees of freedom
  8. Advanced spectroscopic techniques: infra-red, Raman, and nuclear magnetic resonance
  9. Laser cooling, manipulation and detection of ultracold dilute quantum gases


  1. Mechanical properties of materials
    • Elasticity and related properties
    • Non-linear mechanical properties
    • Thermal expansion and isothermal compressibility
  2. Dielectric and optical properties of materials
    • Polarization and polarization mechanisms
    • Ferroelectricity
    • Pyroelectricity
    • Piezoelectricity
    • Dielectric response to variable frequency electric fields
    • Optical response of materials
  3. Magnetic properties of materials
    • Diamagnetism
    • Paramagnetism
    • Ferromagnetism
    • Other types of magnetism: ferrimagnetism, antiferromagnetism and non-collinear ferromagnetism
  4. Ferroic and multiferroic materials
    • Ferroic transitions
    • Multiferroic coupling: Magnetoelasticity and magnetoelectricity
    • Applications


  1. Biological networks
    • Examples in systems biology (metabolic networks, interactome, regulatory and signalling networks)
    • Biological neural networks
    • Networks in ecology and epidemiology
  2. Complex spatio-temporal dynamics in biology
    • Oscillations, excitability, bistability
    • Synchronization in biological systems: neural networks
    • Spatio-temporal chaos: cardiac fibrillation
  3. Complex biosignal analysis
    • Deterministic and stochastic signals
    • Statistical properties
    • Nonlinear time series analysis
  4. Self-organization in biological systems
    • Morphogenesis
    • Self-assembly (protein folding, membrane formation)
    • Growth processes (chemotaxis, tumour growth)
  5. Collective motion and active matter
    • Flocking, swarming and herd behaviour
    • Cell migration


  1. Introduction to Machine Learning
    • Fundamental problem of Machine Learning
    • Description of the inherent complexity of the problem
    • General approximations to the solution.
  2. Classical models of Neural Networks
    • Hopfield model
    • Recurrent Boltzmann Machines (BM) and Restricted Boltzmann Machines (RBM)
    • Learning with BM and RBM: gradient descent, Contrastive Divergence and variations
    • Single-layer Perceptrons (SLP): lineal regression, logistic regression, Rosenblat perceptron
    • Multi-layer Perceptrons (MLP)
    • Learning with MLP: Back-propagation
    • Convolutional Neural Networks (CNN): model, link with MLP and learning
  3. Deep Learning: link with classical models and modern learning techniques


  1. Introducción. Métodos de discretización del continuo: diferencias finitas, elementos y volúmenes finitos, métodos espectrales y métodos sin malla o de partículas
  2. Formulaciones débiles, variacionales, de Galerkin, de Petrov-Galerkin, de colocación, etc. de diferentes problemas de la Física (Termodinámica, Elasticidad, Mecánica de Fluidos, Electromagnetismo, Mecánica Cuántica, etc.)
  3. El método de los elementos finitos. Aproximación lagrangiana a trozos. Tipología de elementos finitos. Elementos nodales y modales. Elementos isoparamétricos. Errores de interpolación y convergencias h, p i hp
  4. Implementación del método de elementos finitos. Mallado de dominios. Ensamblaje de matrices. Fórmulas de cuadratura. Estimación del error de las soluciones. Ejemplos de aplicación en Matlab/Octave o Python
  5. Complementos de álgebra lineal numérica. Almacenamiento matricial. Técnicas para sistemas lineales y problemas de valores propios para problemas de dimensión elevada.
  6. Librerías de elementos finitos. Introducción a FeniCS-Python
  7. Integración temporal. Métodos de semi-discretización, de líneas, de splitting, etc. Dificutades en problemas de tipo advección-diffusión
  8. Introducción a los métodos de volúmenes finitos y de Galerkin discontinuos. Aplicaciones
  9. Métodos de orden alto. Elementos espectrales. Integración temporal de orden alto.


  1. Monte Carlo integration: distribution functions and their sampling. Crude Monte Carlo and rejection methods. Improving efficiency: variance reduction methods. Multidimensional integrals and Metropolis sampling.
  2. Monte Carlo methods for the study of many-particle systems: discrete systems (Ising), continuous systems in different statistical collectivities. Finite-size scaling. Advanced Monte Carlo methods.
  3. Stochastic optimization: simulated annealing and genetic algorithms.
  4. Dynamic Monte Carlo: randowm walks and the diffusion equation. Fokker-Planck and Langevin methods. Brownian dynamics.
  5. Application of Monte Carlo methods to quantum systems. Wave functions for bosons and fermions. Variational Monte Carlo. Diffusion Monte Carlo. Path integral Monte Carlo for the study at finite temperature.


  1. Finite difference methods applied to stellar evolution
    • Finite difference approximations
    • Von Neumann stability criterion
    • Initial values and boundary conditions
    • Explicit vs. Implicit methods
    • Lagrangian and Eulerian formalisms
    • Nuclear reaction networks. Adaptive networks
    • Relativistic hydrodynamics
  2. Smoothed-Particle Hydrodynamics
    • Fluid dynamics interpolation schemes
    • Eulerian SPH equations
    • Variable resolution in space and time
    • Lagrangian SPH equations
    • Applications of the Eulerian equations
    • Heat conduction and mass diffusion
    • Viscosity
    • Application to shocks and rarefaction problems
    • Astrophysical applications
    • Other applications
    • SPH in special and general relativity
    • Future developments
  3. Astrophysical applications of Monte Carlo and classification methods
    • Overview of basic concepts
    • Simple applications of the Monte Carlo methods
    • Classification methods: data analysis
    • Examples of classification