Learning outcomes of the course unit
By the end of the course, students should be able to understand:
• how to process measurement data, use curve fitting and evaluate the goodness of fit;
• how to estimate measurement uncertainty, using design stage and multiple measurement analysis; the propagation of individual uncertainties to final measurement results;
• operational principles of digital data acquisition and spectral analysis of data;
• basic signal conditioning circuits, evaluating more relevant non-idealities;
• basic electronics instruments behaviour.
Moreover, students should be able to do the followings:
• correctly apply basic instrumentation;
• design, conduct, and analyze laboratory experiments;
• properly report the results, with advance proficiency in professional communications and interactions.
It is expected that students will know: complex numbers, probability and signal theory, electrical and electronic (OpAmps) circuits
Course contents summary
To introduce students with the fundamentals of modern metrology, with particular reference to the electronic measurements.
1) An introduction to metrology (measuring system modeling, International System of measurement units, electrical standards), and to evaluation of measurement uncertainty.
2) Analysis of some blocks of measurement systems: non-idealities of resistors, capacitors, and inductors; static non-idealities and noise of op-amps; their measurement effects, with reference to simple circuits; metrological characteristics and architectures of Analog-to-Digital converters; metrological characteristics of Digital-to-Analog converters, example of R-2R architecture.
3) Description and use of some basic instruments: multimeter, digital scope, spectrum analyser, frequency meter and time interval counter. Techniques, precautions for each measurement type, and required instrumentation configurations are stressed.
1) Metrology theory: (14 hours)
1.1) Measurements for monitoring physical phenomena. Errors and uncertainty. Physical quantity, measurement units and standards. The International System of measurement units.
1.2) Modelling the measurement process: identifying sources of error, understanding and quantifying errors, codifying error effects on a specific reported value in a statement of uncertainty. Uncertainty propagation, type A and type B evaluations, composite and extended uncertainty, degrees of freedom. Measurement compatibility.
1.3) Least squares curve fitting of experimental data. Chauvenet's criterion of data rejection.
2) Components of electronic measurement systems: (14 hours)
2.1) Non-idealities in resistors, capacitors, and inductors.
2.2) Op-amp static non-idealities (offset, bias) and noise (input referred sources). Effects on some elementary measurement circuit.
2.3) Analog-to-Digital conversion. Sampling and quantisation. Non-idealities in real A/D converters. Dithering. Effective number of bits.
2.4) A/D converter's architectures:
2.4.1) Integrating converters (dual-slope, multi-slope, voltage-to-frequency);
2.4.2) A/D converters for time-varying signals (flash or parallel converter, interleaving, SAR-ADC).
3) Basic measurement instruments: (10 hours)
3.1) Digital multimeter architecture (DC and AC voltage and current, resistance).
3.2) Digital scope: architecture, trigger, memory, real-time and equivalent-time sampling, interpolation (linear versus sinc), processing. Passive and active probes. Specifications.
3.3) Spectrum of a sampled signal (folding, noise level, leakage and windowing).
3.4) Superetherodyne spectrum analyser: architecture and behaviour.
3.5) Interval time, period, and frequency measurements: conventional and reciprocal electronic counter. Analogue and digital interpolation techniques for measuring time-intervals with picosecond resolution. Measurement uncertainty.
4.1) design and characterisation of a Schmitt trigger and of an astable multivibrator
4.2) design and characterisation of a RMS-to-DC converter with implicit RMS computation
4.3) design and characterisation of a charge balancing V/f converter
4.4) design and characterisation of a function generator / VCO
4.5) design and characterisation of a PLL
J.R. Taylor, Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, University Science Books; 2nd edition (August 1, 1996)
As an alternative:
P. Bevington, D. K. Robinson, Data Reduction and Error Analysis for Physical Sciences, McGraw-Hill; 3rd edition (July 23, 2002)
The course is divided roughly in 19 lectures (2 hours each) and 5 labs.
A detailed schedule of lectures, material to read, labs, and homework is available on the course website.
Assessment methods and criteria
No midterm exam.
The examination consists of three steps:
- an exercise with some simple computation,
- oral analysis of two theoretical argument,
Online material is available on Elly at the course beginning, and will be finally updated at the end