This course has two main objectives. The first is to present a sound theory of uncertainty, according to current accepted international standards and practices, introducing also several advanced tools. The second is to introduce a number of fundamental instruments that are part of a typical electronic laboratory, describing their principle of operation, important specifications, sources of uncertainty and applications.

Knowledge of uncertainty evaluation techniques, and ability to apply in them in basic measurement situations.
Knowledge of the principle of operation of the most common laboratory instruments, and knowledge of the trade-offs required in an instrument design.
Ability to employ the studied laboratory instrumentation in common electronic measurements.

Mathematics: Analysis, basics of theory of probability and stochastic processes.
Electronics: Circuit theory, basic operational amplifier circuits.
Electronic measurements: Basics of propagation of uncertainty. Usage of multimeters and oscilloscopes.

Uncertainty, a probabilistic approach: Introduction to the probabilistic approach, type B evaluation of the uncertainty, type A evaluation of uncertainty, propagation of uncertainty, software tools, type A evaluation with long-memory processes (flicker, random walk) and the Allan variance (1.8 ECTS)
Frequency synthesis and waveform generation: Properties of signal sources, oscillators, direct analogue synthesizers, indirect analogue synthesizers (phase-lock loops), direct digital synthesizers (1.9 ECTS).
Basic frequency counters: Time interval counter, frequency counter, period counter, reciprocal counter. High frequency counters: Prescaler, heterodyne converter, transfer oscillator (0.6 ECTS) .
Integrating analog-to-digital converters (ADCs): Dual-slope ADC, multi-slope ADC, sigma-delta ADC (0.75 ECTS).
AC RMS voltmeters and power measurements: RMS-to-DC analogue converters, thermal converters, sampling methods, diode detector, lock-in amplifier (0.75 ECTS).
Spectrum analysers: Bank-of-filter analyser, swept-spectrum analyser, FFT analyser, hybrid analysers (1.2 ECTS).
Resistance and impedance measurements: Resistance and impedance definitions, IV method, 2-voltmeter method, 3-voltmeter method, bridge methods, vector impedance meter (1 ECTS).

In addition to lectures, the course consists of in-class exercise sessions, laboratory sessions and homework assignments.
Exercise sessions are aimed at analysing practical measurement situations involving different type of instruments.
Laboratory sessions are aimed at developing experimental skills, practicing with the laboratory instrumentation described in the lectures and introduce a number of applications. The laboratory sessions focus on the following topics: uncertainty, frequency measurements, frequency synthesis with phase-lock loops, spectrum analysers.
Homework assignments presenting exam-like problems are aimed at encouraging a gradual study of the subject (optional, with biweekly frequency).

Slide handouts on selected topics, exercises, homework assignments and laboratory manuals are available for download from the course website. There is no single reference textbook, but excerpts from the following additional texts are used as reference for specific topics:

JCGM 100:2008, Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement.
E. Rubiola, Phase Noise and Frequency Stability in Oscillators, Cambridge University Press, 2010.
A. Chenakin, Frequency Synthesizers, Artech House Inc., 2011.
P. Symons, Digital Waveform Generation, Cambridge University Press, 2014.
M. Engelson, Modern Spectrum Analyzer: Theory and Applications, Artech House Inc., 1984
R. A. Witte, Spectrum and Network Measurements, SciTech Publishing Inc., 2014.
L. Callegaro, Electrical Impedance: Principles, Measurement and Applications, CRC Press: Taylor and Francis, 2013.

The exam consists in a written test followed by an oral examination.
The written test is composed of two problems (15 points each) in which students have to analyse or design a measurement set-up, evaluating uncertainties and discussing sources of errors. The written test is open books and students can use a scientific calculator. The minimum pass grade for the written test is 16/30. The oral examination consists of two questions about the operation of devices and instruments described in the course and their uncertainties. The grades of the two parts are averaged to yield the final grade.
Students can deliver an optional, individual, presentation on one of the laboratory sessions of their choice or discuss a research paper: these optional activities can grant up to 4 points to be added to the final grade.