# Resources

## Notes and Reports

Electromagnetic Diffusion Model Implementation Notes: Notes on the implementation of the electromagnetic diffusion model in 2D and 3D, used to develop the Electromagnetic Diffusion Model Canonical Test Cases reported in (Flintoft et al., 2017; Flintoft and Dawson, 2017).

Notes on Small Aperture Theory: Some informal notes on the electromagnetic theory of small apertures. The Bethe small aperture theory is widely used in electromagnetic compatibility to estimate the coupling into enclosed spaces.

## Datasets

Human body absorption cross-section datasets: These are the datasets from the paper (Flintoft et al., 2014) as an Excel spreadsheet, containing the average absorption cross-sections of all the subjects. The dataset is in the public domain .

## References

- Flintoft, I.D., Marvin, A.C., Funn, F.I., Dawson, L., Zhang, X., Robinson, M.P. and Dawson, J.F., 2017. Evaluation of the diffusion equation for modelling reverberant electromagnetic fields.
*IEEE Transactions on Electromagnetic Compatibility*, 59(3), pp.760–769.

Determination of the distribution of electromagnetic energy inside electrically large enclosed spaces is important in many electromagnetic compatibility applications, such as certification of aircraft and equipment shielding enclosures. The field inside such enclosed environments contains a dominant diffuse component due to multiple randomizing reflections from the enclosing surfaces. The power balance technique has been widely applied to the analysis of such problems; however, it is unable to account for the inhomogeneities in the field that arise when the absorption in the walls and contents of the enclosure is significant. In this paper we show how a diffusion equation approach can be applied to modeling diffuse electromagnetic fields and evaluate its potential for use in electromagnetic compatibility applications. Two canonical examples were investigated: A loaded cavity and two cavities coupled by a large aperture. The predictions of the diffusion model were compared to measurement data and found to be in good agreement. The diffusion model has a very low computational cost compared to other applicable techniques, such as full-wave simulation and ray-tracing, offering the potential for a radical increase in the efficiency of the solution high frequency electromagnetic shielding problems with complex topologies.

@article{Flintoft2017b, author = {Flintoft, I. D. and Marvin, A. C. and Funn, F. I. and Dawson, L. and Zhang, X. and Robinson, M. P. and Dawson, J. F.}, title = {Evaluation of the diffusion equation for modelling reverberant electromagnetic fields}, journal = {IEEE Transactions on Electromagnetic Compatibility}, year = {2017}, volume = {59}, number = {3}, pages = {760-769}, month = jun, note = {Date of acceptance: 23/10/2016. © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.}, doi = {10.1109/TEMC.2016.2623356}, keywords = {asymptotic techniques, power balance, absorption cross-section, reverberation chamber, shielding}, owner = {idf1}, timestamp = {2016.10.25} }

- Flintoft, I.D. and Dawson, J.F., 2017. 3D electromagnetic diffusion models for reverberant environments. In:
*2017 International Conference on Electromagnetics in Advanced Applications (ICEAA2017)*. Verona, Italy, pp.511–514.

Diffusion equation based modeling has been proposed for mapping the reverberant component of the electromagnetic field in enclosures at high frequencies. Preliminary evaluation of the electromagnetic diffusion model using a dimensional reduction approach showed promising results compared to measurements. Here we develop a full three-dimensional diffusion model of the experimental canonical test cases considered in the preliminary evaluation and obtain finite element method solutions. The results are compared to those of the two-dimensional models. We find that the two and three dimensional models are generally in excellent agreement for the pseudo two-dimensional test-cases considered. Some deviations between the two- and three-dimensional models are observed due to the fact the point source must be effectively represented by a line source in the reduced model. The three-dimensional model is still highly efficient compared to other applicable techniques, offering the prospect of a radical reduction in the resources required for simulating reverberant fields in electrically large structures.

@inproceedings{Flintoft2017c, booktitle = {2017 International Conference on Electromagnetics in Advanced Applications (ICEAA2017)}, month = {11-15 September}, address = {Verona, Italy}, year = {2017}, author = {Flintoft, I. D. and Dawson, J. F.}, title = {3D electromagnetic diffusion models for reverberant environments}, pages = {511-514}, doi = {10.1109/ICEAA.2017.8065293}, keywords = {asymptotic techniques, power balance, absorption cross-section} }

- Flintoft, I.D., Robinson, M.P., Melia, G.C.R., Marvin, A.C. and Dawson, J.F., 2014. Average absorption cross-section of the human body measured at 1-12 GHz in a reverberant chamber: results of a human volunteer study.
*Physics in Medicine and Biology*, 59(13), pp.3297–3317.

The electromagnetic absorption cross-section (ACS) averaged over polarization and angle-of-incidence of 60 ungrounded adult subjects was measured at microwave frequencies of 1–12 GHz in a reverberation chamber. Average ACS is important in non-ionizing dosimetry and exposure studies, and is closely related to the whole-body averaged specific absorption rate (WBSAR). The average ACS was measured with a statistical uncertainty of less than 3% and high frequency resolution for individuals with a range of body shapes and sizes allowing the statistical distribution of WBSAR over a real population with individual internal and external morphologies to be determined. The average ACS of all subjects was found to vary from 0.15 to 0.4 m 2 ; for an individual subject it falls with frequency over 1–6 GHz, and then rises slowly over the 6–12 GHz range in which few other studies have been conducted. Average ACS and WBSAR are then used as a surrogate for worst-case ACS/WBSAR, in order to study their variability across a real population compared to literature results from simulations using numerical phantoms with a limited range of anatomies. Correlations with body morphological parameters such as height, mass and waist circumference have been investigated: the strongest correlation is with body surface area (BSA) at all frequencies above 1 GHz, however direct proportionality to BSA is not established until above 5 GHz. When the average ACS is normalized to the BSA, the resulting absorption efficiency shows a negative correlation with the estimated thickness of subcutaneous body fat. Surrogate models and statistical analysis of the measurement data are presented and compared to similar models from the literature. The overall dispersion of measured average WBSAR of the sample of the UK population studied is consistent with the dispersion of simulated worst-case WBSAR across multiple numerical phantom families. The statistical results obtained allow the calibration of human exposure assessments made with particular phantoms to a population with a range of individual morphologies.

@article{Flintoft2014, author = {Flintoft, I. D. and Robinson, M. P. and Melia, G. C. R. and Marvin, A. C. and Dawson, J. F.}, title = {Average absorption cross-section of the human body measured at 1-12 GHz in a reverberant chamber: results of a human volunteer study}, journal = {Physics in Medicine and Biology}, year = {2014}, volume = {59}, number = {13}, pages = {3297--3317}, month = may, issn = {0031-9155}, note = {Date of acceptance: 06/05/2014. This is an author created, uncopyedited version of an article accepted for publication in IOP Physics in Medicine. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0031-9155/59/13/3297.}, doi = {10.1088/0031-9155/59/13/3297}, owner = {idf1}, timestamp = {2016.10.12} }