Academic Year 2023/2024

  • Teaching Mode: Traditional lectures
  • Campus: Bologna
  • Corso: First cycle degree programme (L) in Electronics and Telecommunications Engineering (cod. 9065)

Learning outcomes

After successfully attending the Course, the student is capable of qualitatively identifying and quantitatively evaluating the effects of the main non-idealities within instruments and circuits for measurement applications, with the aim of selecting and correctly exploiting them for the modern measurement procedures. In particular the student: - knows and understands the operation of modern instrumentation, with particular attention to sampling-based instruments; - is capable of achieving a deep insight of instrument specifications, and thus evaluating their actual performance in the application of interest; - knows the modern standards and methodologies for the evaluation and expression of the uncertainty of measurement.

Course contents

§ Fundamentals of Metrology and Measurement Science

Measurement scales. Coherent and non-coherent systems of units. Coordination equations. The International System of Units (SI): base and derived quantities. Unit standards and traceability. Standard of resistance: quantum Hall effect. Standard of electromotive force: Josephson effect. Unit writing and reporting standard rules. Measurand and measurement process. Resources and activities associated with the process. The model of a measurement process and the influence quantities. Uncertainty of measurement. Methodologies for the evaluation of standard uncertainty: type A and type B evaluation. Uncertainty propagation: combined standard uncertainty. Expanded uncertainty. Expression of the result of a measurement process. Application examples for the law of propagation of uncertainty.

§ Analogue-to-Digital (A/D) and Digital-to-Analogue (D/A) Conversion

Fundamentals of analogue-to-digital conversion. Quantization and quantization step, full-scale value, unipolar and bipolar discretization. Encoding of a discrete quantity by means of the natural binary code, the bipolar offset code, the two's complement code. Main sources of non-ideality in the quasi-static transfer characteristics of an analogue-to-digital converter (ADC). Offset, gain error. Integral non-linearity and its graphical representation. Differential non-linearity. Elements of quantization noise theory. Model of the A/D conversion. Effective bits of an ADC. ADC classification. Flash ADCs: single- and multiple-stage. Counting ADC. Tracking ADC. Successive approximation A/D converter. Integrating ADCs: dual- and multiple-slope. Sources of uncertainty within the different ADC architectures. Digital-to-analogue conversion. Main architectures for digital-to-analogue converters (DACs): binary weighted resistance DAC, R-2R ladder network DAC. Sources of uncertainty in the D/A conversion.

§ AC/DC Converters for Measurement Instrumentation

Parameters for the “overall” characterization of a waveform: peak value, rectified mean value, root mean square (RMS) value. Rectified mean value-AC/DC converters: measurement of voltage and current, sensitivity. Peak value-AC/DC converters: lower and upper cut-off frequencies, sensitivity. True RMS-value AC/DC converters: example of integration.

§ Metrological Characterization of Components and Sub-Systems

- Resistor: equivalent circuit in static operation. Relative uncertainty expression and the old concept of tolerance. Thermal coefficient. Technological/physical factors of influence on the resistivity parameter. Power rating. Thermo-electromotive forces and the Seebeck effect. Thermal noise. Overview on low-frequency noise. Resistor technologies for measurement applications.

- Reference electromotive force generators: quantities of influence and circuital examples. Temperature dispersion compensation of Zener diode-based generators.

- Amplifiers in DC operation: offset, sensitivity, gain, saturation.

- Op Amp-based circuits. Static parameters of Op Amps: offset voltage, CMRR, bias and offset currents. Methodologies for the measurement of Op Amp static parameters.

- General approach to the metrological characterization of electronic components in dynamic operation. Resistor: equivalent circuit. Skin effect. Time constant. Resistor technologies of interest for measurement applications. Capacitor: equivalent circuit. Apparent capacity and resonance angular frequency. Dissipation factor for the estimation of power losses in a capacitor. Capacitor technologies of interest for measurement applications. Inductor: equivalent circuit. Losses due to eddy (Foucault) currents and hysteresis phenomena. Resonance angular frequency, quality factor Q. Inductor technologies of interest for measurement applications.

- Generalization to the dynamic operation of the metrological characterization of amplifiers and Op Amp-based circuits.

§ Digital Multimeter

Instrument fundamentals and general architecture. Input conditioning network, ranges, sensitivity. Display digits. Integration time. Normal mode rejection ratio. Input equivalent circuit. Current and resistance measurement. Evaluation and expression of uncertainty. Use of the digital multimeter for AC measurements. Examples of commercial instruments.

§ Sampling Oscilloscope

Instrument fundamentals, functional block-diagram. Front-end circuits for the input signal conditioning. Analogue-to-digital acquisition channel: input impedance, sample/hold, A/D converter. Trigger circuit and methods. Time base. Sampling strategies. Real-time equally-spaced sampling, Shannon/Nyquist criterion, ideal continuous-time reconstruction of the sampled signal and practical methods based on finite impulse response digital filters. Equivalent-time and random sampling. Architectures for the maximization of the equivalent sampling frequency. Examples of state-of-the-art commercial instruments for RF/microwave applications and high-resolution applications.

§ Analogue Spectrum Analyzer

Instrument fundamentals and measurand definition, basic architecture. Superheterodyne scheme, analysis at the intermediate frequency. Image frequency issue. Multiple conversion architectures. Frequency resolution. Main parameters and features of the instrument. Examples of state-of-the-art commercial instruments.

§ Digital Spectrum Analysis

Fundamentals, architectures. Algorithms for the vector estimate of the spectrum of a sampled signal: DTFT, DFT, FFT. Aliasing, frequency resolution, zero-padding. Observation interval, spectral leakage. Time windows for the reduction of spectral leakage.


Educational documentation (slides, user manuals, component datasheets) provided by the professor and/or downloadable from "Virtuale" platform.

Teaching methods

Class lectures, integrated with laboratory activity.

Assessment methods

Individual oral exam

Office hours

See the website of Pier Andrea Traverso