Prerequisites

This course requires the material covered in the IA Physics and IA Maths for Natural Scientists courses, and exploits the ideas of Fourier theory that are more fully developed in the Mathematics options that run in parallel with this course in the Michaelmas term. Ideas of Fourier decomposition will be introduced, along with Fourier series, but they are covered more fully in the Mathematics course.

Learning Outcomes and Assessment

Physics is an empirical subject based on measuring physical phenomena. This course introduces techniques for constructing experiments and analysing their results. In experimental physics there is generally a signal chain from the physical phenomenon under investigation up to a polished measurement. This can involve many sequential and complex components such as transducers, amplifiers, filters and detectors. In many cases an experimental rig will have elements of feedback as a form of control.

The course explores this process – sometimes with  reference to some of the experiments undertaken in the practical classes. It aims to introduces some of the essential material that a physicist needs to know to design effective experiments (including computational ones), to analyse data, and to evaluate other people’s results.

Synopsis

Syllabus

Basic data handling: taking and recording data. Sampling, aliasing, Nyquist’s criterion. Digitization errors, Fourier and Laplace Transforms, correlation functions and power spectra.

Systems: Impedance and measurement. Operational amplifiers and filters. Positive and negative feedback with ideal and non-ideal amplifiers.

Control: elements of control, leading to PID with examples in electronics.

Random and Systematic errors: examples, propagation, reduction with repeated sampling. Systematic errors: examples, designs to reduce them (e.g. nulling), selection effects.

Exclusion of unwanted influences: filtering, phase-sensitive detection and lock-in amplifiers.

Probability distributions: binomial, Poisson and Gaussian; central limit theorem; shot noise and Johnson noise.

Parameter estimation: likelihood, inference and Bayes’ theorem, chi-squared, least-squares, hypothesis testing, non-parametric tests.

Getting the message across: writing a scientific report and presenting results.

References

BOOKS

There are no books which cover the complete course syllabus, and so each lecture handout will be augmented with a set of supplementary notes. Reading these notes prior to the lectures will be helpful. The following books may be useful to refer to on certain aspects of the course:

The Art of Electronics, Horowitz P & Hill W (3rd edn CUP 2015)

An Introduction to Experimental Physics, Cooke C (CRC Press 1996)

Practical Physics, Squires G L (4th edn CUP 2001)

Control Theory for Physicists, Bechhoefer J (CUP 2021)