# AEGPWB: An open source electromagnetic power balance toolbox and solver

The Applied Electromagnetics Group (AEG) power balance (PWB) toolbox and solver for MATLAB and GNU Octave is an Open Source set of tools for undertaking PWB analysis of electrically large enclosed spaces. It was developed in the Department of Electronic Engineering at the University of York for research in electromagnetic compatibility (EMC).

## The power balance method

The origins of the Power Balance (PWB) approach are in the work of Hill et al in a paper that showed how to divide the power loss in a cavity into four component parts (Hill1994):

1. Power lost through apertures;
2. Power absorbed by receiving antennas in the cavity;
3. Power absorbed in lossy objects;
4. Power absorbed in the cavity walls.

Further theoretical work was carried out at NIST and the method was developed into a systematic simulation technique overlaid on the Electromagnetic Topology (EMT) methodology by Parmantier and Junqua at ONERA (Junqua2005, Parmantier2007). A very similar approach has recently being reported by (Tait2011). PWB treats the problem space as a topological model of shielded cavities, coupled with wires, apertures, antennas etc. Each of these is assigned a model for its coupling cross section, and the power transferred and the resulting power density in each cavity is calculated over a broadband from a set of linear equations derived from the overall power balance in each cavity.

The set of linear equations can also be represented as a equivalent circuit in which cavities are nodes of the circuit and power absorption and transmission processes are admittances on the edges connecting the nodes. The power densities in the cavities are the across variables ("voltages") and the powers absorbed or coupled through the admittances are the through variables ("currents"). For a power absorption process, the average power absorbed is the product of the average power density in the cavity and the average absorption cross-section (ACS). For a process that transfers energy between two cavities the net power transmitted from one side to the other is the product of the difference in the average power densities in the two cavities and the average transmission cross-section (TCS) of the process.

The power balance relationship for the equilibrium state of each cavity in the system requires the total power transmitted into the cavity to be equal to the total power absorption within the cavity; this leads to a linear equation relating the power densities with the ACSs and TCSs as coefficients, analogous to Kirchhoff's Current Law. The ACSs and TCSs can be referred to collectively as coupling cross-section (CCSs). If a system contains `N` cavities then `N` such linear equations can be formed from the power balance in each cavity and then solved for the power densities of the cavities.

The AEG PWB toolbox provides functions for the determination of average CCSs and associated utilities and the solver implements the equivalent circuit approach to constructing the EMT and solving the problem.

## Code features

The toolbox and solver include:

• Models for the absorption in cavity walls;

• Determination of polarisabilities and average transmission cross-sections of apertures;

• Models for absorption in metal, dielectric and arbitrary laminated surfaces;

• Models for absorption in homogeneous and layered spheres;

• Models for transmission and absorption in semi-transparent walls;

• Support for user supplied CCS, for example, from experiments;

• Probabilities distributions for electromagnetic quantities in cavities and received electrical parameters in antenna and transmission lines;

## Requirements

The code is written in a portable subset of GNU Octave and MATLAB. Additional requirements are:

1. (Optional) To view the EMT of a model the graphviz package must be installed on the system.

2. (Optional) A Mie series code needs to be installed in order for the absorption in spherical bodies to be calculated. See Install.md for the supported codes.

3. (Optional) To help with development or as an alternative way to download the source a client for the Mercurial Version Control System is required.

The code has been primarily developed using GNU Octave on Linux platforms, but should run under both GNU Octave and MATLAB on Linux and Windows systems.

## Documentation

Installation instructions are contained in the file Install.md in the source distribution.

The best place to start after installing the software is with the detailed tutorial example for the PWB solver in the tutorial directory of the software package.

There are also user manuals for the toolbox in doc/ToolboxUserManual.md and the solver in doc/SolverUserManual.md.

## Bugs and support

The code is still under development and no doubt will contain many bugs. Known significant bugs are listed in the file doc/Bugs.md in the source code.

Please report bugs using the bitbucket issue tracker at https://bitbucket.org/uoyaeg/aegpwb/issues or by email to ian.flintoft@googlemail.com.

For general guidance on how to write a good bug report see, for example:

Some of the tips in http://www.catb.org/esr/faqs/smart-questions.html are also relevant to reporting bugs.

There is a Wiki on the bitbucket project page.

## How to contribute

We welcome any contributions to the development of the code, including:

• Fixing bugs.

• Interesting examples that can be used for test-cases.

• Improving the user documentation.

• Items in the to-do list in the file doc/ToDo.md.

## Publications using AEG PWB

(Flintoft2018) I. D. Flintoft, S. J. Bale, A. C. Marvin, M. Ye, J. F. Dawson, S. L. Parker, C. Wan, M. Zhang and M. P. Robinson, “Representative contents design for shielding enclosure qualification from 2 to 20 GHz”, IEEE Transactions on Electromagnetic Compatibility, vol. 60, no. 1, pp. 173-181, 2018.

(Flintoft2017b) I. D. Flintoft, A. C. Marvin, F. I. Funn, L. Dawson, X. Zhang, M. P. Robinson and J. F. Dawson, “Evaluation of the diffusion equation for modelling reverberant electromagnetic fields”, IEEE Transactions on Electromagnetic Compatibility, vol. 59, no. 3, pp. 760-769, 2017.

(Flintoft2017a) I. D. Flintoft and J. F. Dawson, “3D electromagnetic diffusion models for reverberant environments”, 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA2017), Verona, Italy, pp. 511-514, 11-15 Sep. 2017.

(Marvin2016) A. C. Marvin, I. D. Flintoft, M. Ye, J. F. Dawson, M. P. Robinson, S. J. Bale, S. L. Parker, M. Ye, C. Wan and M. Zhang, “Enclosure shielding assessment using surrogate contents fabricated from radio absorbing material”, 7th Asia-Pacific International Symposium on Electromagnetic Compatibility & Signal Integrity and Technical Exhibition (APEMC 2016), Shenzhen, China, pp. 994-996, 18-21 May, 2016.

## References

(Hill1994) D. A. Hill, M. T. Ma, A. R. Ondrejka, B. F. Riddle, M. L. Crawford and R. T. Johnk, "Aperture excitation of electrically large, lossy cavities", IEEE Transactions on Electromagnetic Compatibility, vol. 36, no. 3, pp. 169-178, Aug 1994.

(Hill1998) D. A. Hill, "Plane wave integral representation for fields in reverberation chambers," IEEE Transactions on Electromagnetic Compatibility, vol. 40, no. 3, pp. 209-217, Aug. 1998.

(Junqua2005) I. Junqua, J.-P. Parmantier and F. Issac, "A Network Formulation of the Power Balance Method for High-Frequency Coupling", Electromagnetics, vol. 25 , no. 7-8, pp. 603-622, 2005.

(Parmantier2007) J.-P. Parmantier and I. Junqua, "EM Topology: From theory to application", Ultra-Wideband, Short-Pulse Electromagnetics 7, Springer, New York, pp. 3-12, 2007.

(Tait2011) G. B. Tait, R. E. Richardson, M. B. Slocum, M. O. Hatfield and M. J. Rodriguez, "Reverberant microwave propagation in coupled complex cavities", IEEE Transactions on Electromagnetic Compatibility, vol. 53, no. 1, pp. 229-232, Feb. 2011.