Teaching / electromagnetics
In progressTeaching Assistant
Electromagnetics & Materials Physics - third-year engineering students
Role
- Subject
- Electromagnetics and materials physics
- Audience
- Third-year engineering students
- Institution
- ENSEEIHT, Toulouse INP
- Work
- Support sessions: worked problems, derivations and the questions that come out of them
- Scope
- The course material for the module
Topics taught
01
The material
Electromagnetism in matter: what the field equations become once the medium is not vacuum, and what that costs in energy.
- Maxwell equationsThe four equations in their differential and integral forms, and their form in matter, where the auxiliary fields absorb the response of the medium.
- PolarisationThe dielectric response: how bound charge reorganises under an applied field, and how that becomes a macroscopic polarisation field.
- MagnetisationThe magnetic response: bound currents, magnetisation, and the distinction between the field applied and the field inside the material.
- PermittivityThe constitutive relation for a dielectric, its complex form, and the frequency dependence that makes a material a different material at a different frequency.
- PermeabilityThe corresponding magnetic constitutive relation, and the cases where it cannot be treated as a constant.
- Dielectric mediaBehaviour of dielectrics under a field, and what the constitutive relation does and does not capture.
- Magnetic mediaBehaviour of magnetic media, and the classes of response.
- Interfaces and boundary conditionsWhat is continuous and what jumps at a boundary between two media. This is the part everything else depends on.
- Poynting vectorEnergy flux in the field, the local energy balance, and where the power in a propagating wave actually is.
- Electromagnetic lossesWhere the energy goes: the imaginary part of the permittivity, conduction loss, and the resulting attenuation.
02
The equations the sessions turn on
\[\nabla \cdot \mathbf{D} = \rho_f, \quad \nabla \cdot \mathbf{B} = 0, \quad \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{H} = \mathbf{J}_f + \frac{\partial \mathbf{D}}{\partial t}\]
\[\mathbf{D} = \varepsilon_0 \mathbf{E} + \mathbf{P} = \varepsilon_0 \varepsilon_r \mathbf{E}, \qquad \mathbf{H} = \frac{\mathbf{B}}{\mu_0} - \mathbf{M}\]
\[\mathbf{S} = \mathbf{E} \times \mathbf{H}, \qquad \varepsilon_r = \varepsilon_r' - j\varepsilon_r'', \qquad \tan\delta = \frac{\varepsilon_r''}{\varepsilon_r'}\]
The first line is Maxwell in matter, where the auxiliary fields \(\mathbf{D}\) and \(\mathbf{H}\) exist precisely so that the bound charge and bound current of the medium do not have to be carried explicitly. The second is the constitutive pair that hides the polarisation and the magnetisation inside \(\varepsilon_r\) and \(\mu_r\). The third is what a student needs before they can read a substrate datasheet: the Poynting vector as the energy flux, a complex permittivity whose imaginary part is loss, and the loss tangent that is the number the datasheet actually prints.
03
The same material, as RF engineering
Each topic in the module reappears in RF engineering under another name.
| Topic | The same thing, in RF |
|---|---|
| Boundary conditions | Why a wave reflects at a discontinuity, which is what a reflection coefficient measures and what an impedance mismatch is. |
| Permittivity | The substrate parameter that sets the effective permittivity of a microstrip line, and therefore its width, its guided wavelength and every physical length on the board. |
| Loss tangent | Dielectric loss in a transmission line and in a passive circuit, the term that decides whether a filter or a coupler is worth building on a given laminate. |
| Polarisation and dispersion | Why a high-frequency dielectric is characterised at the frequency it will be used at, and why a datasheet value at 1 MHz says little about behaviour at 18 GHz. |
| Magnetic media | Ferrite behaviour, and the non-reciprocal components built from it. |
| Poynting vector | Radiated power density, which is what an antenna gain and a radiation pattern are made of. |
| Maxwell in matter | Exactly what a full-wave solver discretises. Knowing the continuous problem is what makes a mesh or a boundary setting a decision rather than a default. |
| Wave and material interaction | Antenna substrates, radomes, absorbers and the measurement environment, which is a material problem before it is an instrument problem. |
Where this is used on this siteAntenna and microwave structure characterisationAetherArrayRF and microwave skills
04
How the sessions run
- Derive, do not quoteA constitutive relation that arrives as a formula is forgotten. One that arrives from the bound charge it summarises is usable.
- Boundary conditions firstMost of the problems students get stuck on are boundary-condition problems wearing a different hat.
- Units and orders of magnitudeA wrong answer with the right order of magnitude is a different kind of mistake from a wrong answer without one, and it is worth saying which happened.
- End on the applicationEach topic closed by naming where it appears in a real device.