### Lecturer

### Timing and Structure

Weeks 6-8 Lent term. 6 lectures, 2 lectures/week

## Aims

The aims of the course are to:

- To understand what a transmission line is, and how by analysing an equivalent circuit for a short length of the line allows us to understand wave propagaion along the line.
- To understand the Maxwell Equations of Electric and Magnetic Fields which allow us to understand the propagation of electromagnetic waves through free space and how such waves interact with other conducting and insulating materials.
- To appreciate how we can engineer the propagation of waves in free space and along transmission lines with a focus on communications applications.

## Objectives

As specific objectives, by the end of the course students should be able to:

- To be able to create and solve a wave equation for an ideal transmission line from an equivalent circuit and appreciate how this differs in a lossy transmission line.
- To understand the characteristic impedance of a transmission line, and be able to use this to solve problems involving reflection and transmission of waves along transmission lines.
- To understand the physical significance of the Maxwell Equations and how the differential (vector calculus) form can be produced from the integral form.
- To use the Maxwell Equations to produce a wave equation for the free-space propagation of electromagnetic waves and deduce their behaviour (e.g. direction of propagation relative to the E and H field, the Poynting vector).
- To understand the basic operation of antennas and their figures of merit.
- To use the intrinsic impedance to understand how electromagnetic waves are reflected and transmitted at interfaces with dielectics
- To understand how electromagnetic waves interact with conductors.

## Content

#### Transmission Lines

- What is a transmission line?
- Ideal transmission line equivalent circuit
- The Telegrapher's Equations
- The wave equation solution to the Telegrapher's Equations
- Expressions for current and voltage waves
- Description of how waves propagate along transmission lines.
- Importance of the wavelength in considering whether wave effects on a line need to be considered
- The 'lossy' transmission line equivalent circuit and how this affects wave propagation
- Characteristic impedance
- Reflections from a load impedance
- Input impedance of a terminated line
- Ringing

#### The Maxwell Equations in Integral and Differential (Vector Calculus) Form

- The Gauss Law of Electric Fields
- The Gauss Law of Magnetic Fields
- The Faraday Law of Magnetic Fields
- The Ampère-Maxwell Law

#### Electromagnetic Waves in Dielectrics

- Derivation of wave equation for electric and magnetic fields from the Maxwell Equations
- Expressions for the electric and magnetic fields in plane electromagnetic waves
- Intrinsic impedance
- The power in an electromagnetic wave and the Poynting Vector

#### Antennas

- What is an antenna and a description of how they work
- Figures of merit for antennas including the Antenna Gain, Radiation Resistance and Effective Area

#### Electromagnetic Waves at Interfaces

- Boundary conditions: the conservation of E, D, H and B at interfaces
- Polarised plane electromagnetic waves
- Reflection and refraction of plane waves
- Polarisation by reflection and the Brewster Angle
- Anti-reflection coatings

#### Electromagnetic Waves in Conducting Media

- Derivation of wave equation for electric and magnetic fields from the Maxwell Equations
- Expressions for the electric and magnetic fields in plane electromagnetic waves
- The Skin Effect
- Intrinsic impedance of a conducting medium
- Waves at conducting interfaces

### Booklists

Please see the Booklist for Part IB Courses for references for this module.

### Examination Guidelines

Please refer to Form & conduct of the examinations.

### UK-SPEC

The UK Standard for Professional Engineering Competence (UK-SPEC) describes the requirements that have to be met in order to become a Chartered Engineer, and gives examples of ways of doing this.

UK-SPEC is published by the Engineering Council on behalf of the UK engineering profession. The standard has been developed, and is regularly updated, by panels representing professional engineering institutions, employers and engineering educators. Of particular relevance here is the 'Accreditation of Higher Education Programmes' (AHEP) document which sets out the standard for degree accreditation.

The Output Standards Matrices indicate where each of the Output Criteria as specified in the AHEP 3rd edition document is addressed within the Engineering and Manufacturing Engineering Triposes.

Last modified: 21/05/2018 13:24