The University of Southampton
Courses

# ELEC2214 Circuits and Systems

## Module Overview

The module aims to provide a detailed understanding of the representation and analysis of dynamic systems, and their solution. It goes on to apply this to simple circuit problems as well as to mechanical systems. Vibration problems in mechanical systems are further studied using frequency response and energy approximation methods, and modelling and analysis is then extended to continuous mechanical systems, including beams and shafts. Application to circuit theory is used to develop a good understanding of the fundamental theory of three phase circuits.

### Aims and Objectives

#### Module Aims

The module aims to provide a detailed understanding of the representation and analysis of dynamic systems, and their solution, and apply such analysis tools to electrical circuits and mechanical systems.

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• State-space method applied to circuit problems and mechanical systems
• Power in AC circuits, and conservation of power
• The causes and effects of vibration within various mechanical systems
• Methods of analysis, measurement and control of vibration
• Balanced and unbalanced three phase circuit theory
##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Undertake laboratory experiment as part of a small team
• Record and report laboratory work
##### Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Perform range of electrical measurements on three-phase circuits
• Undertake measurements to estimate dynamic parameters of mechanical beams
##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Analyse and solve simple electrical circuit and mechanical system problems
• Calculate electrical power in single and three-phase circuits
• Translate a physical problem in mechanical vibration to an appropriate dynamic model
• Make engineering judgement on the problem or reducing vibration when required
• Apply circuit theorems for the solution of unbalanced three-phase circuits

### Syllabus

Mechanical Systems: - One Degree of Freedom Systems Application of Laplace transform and state space methods to mechanical systems. Analysis of dynamic response and role of Damping (Viscous and Coulomb) Base Excitation, Displacement Transmissibility Vibration Isolation. - Two Degree of Freedom Systems Modelling of two degree of freedom systems in state space form. Physical interpretation of solutions. Free Vibration and Normal Modes, Co-ordinate Coupling and Principal Co-ordinates, Forced Vibration, Damping, Impedance Matrix, Vibration Absorber. Decoupling using Modal Matrix. - Multi Degree of Freedom Systems Orthogonality, Modal Space Matrix Methods, Approximate Frequency Analysis, e.g. Rayleigh’s, Dunkerley’s Methods Lagrange’s Equations - Continuous Systems Vibration of Strings, Rods, Beams and derivation of equations of motion. - Application of Rayleigh’s method to approximate natural frequencies. Vibration and Instrumentation, Transmissibility. Three-phase: - Unbalanced mesh and four-wire star circuits; unbalanced three-wire star circuits; solution by Millman's theorem, star-delta transform and graphical methods; symmetrical components and use in solving unbalanced systems; positive, negative and zero sequence networks; use of two-wattmeter method on balanced and unbalanced systems for kW and kVAr measurement. State Space: - Application of circuit and mechanical analogies. - Need for state space method; definition of terms: state-variable, state-matrices, etc.; consideration of the elements that store energy; formation of equations, in particular the formation of matrix equation in the form of X = A.X + B.E, nature of these terms. - Solution of state space equations by Laplace transform methods; solution of simple circuit network problems. - Solution of state equations in the time domain (linear-time invariant case): solution of the state differential equation (exponential of a matrix, its computation, forced- and free response in the state-space setting). Laboratory Coursework: - 3-phase Star and Mesh circuit relationships; Cantilever vibration experiment

### Learning and Teaching

TypeHours
Tutorial12
Revision10
Follow-up work12
Lecture24
Preparation for scheduled sessions12
Total study time150

William J. Palm III (2007). Mechanical Vibration.

Van Valkenburg M E (1974). Network Analysis.

Thomas R E and Rosa A J (2000). The Analysis and Design of Linear Circuits.

Morrison J L M & Crossland B. Introduction to the Mechanics of Machines.

Tse, Morse & Hinkle. Mechanical Vibrations.

Rao. Mechanical Vibrations.

Dorf and Svoboda (2006). Electric Circuits.

Thomson W T. Theory of Vibration with Applications.

Rogers (1965). Topology and Matrices in Solution of Networks.

### Assessment

#### Summative

MethodPercentage contribution
Exam  (2 hours) 90%
Laboratory 10%

#### Referral

MethodPercentage contribution
Exam 100%

#### Repeat Information

Repeat type: Internal & External