# Single-Layered Braided Shield Models

A summary is given of the single-layered braided shield models available in CADFEKO and EDITFEKO.

Many cables used today in the industry and at home, has a flexible woven braid to shield the cable from EMI as well as to provide mechanical strength. The braid consists of conducting filaments or wires, with the weave providing a series of periodic apertures along the cable length and around its circumference.

At high frequencies, the shielding properties are dominated by the braid coverage and at lower frequencies, it is the number of wires, weave angle and the shield material conductivity.
Common to all the models are the diffusion impedance ( ${Z}_{d}$ ) due to the current induced in the shield:
${Z}_{d}=\frac{{R}_{0}\gamma d}{\mathrm{sinh}\left(\gamma d\right)}$
where:
• ${R}_{0}$ is the resistance per unit length of the shield
• $\gamma =\frac{1+j}{\delta }$ is the skin depth in the wire
• d is the filament diameter

## Vance

This model takes into account hole inductance caused by fields penetrating the apertures in the braided cable.

The transfer impedance expression consists of two terms:

${Z}_{t}\approx Z{}_{d}+j\omega {L}_{h}$

where:

${L}_{h}$ represents penetration of magnetic fields through diamond shaped holes.

## Tyni

This model takes into account braid inductance caused by magnetic coupling between the inner and outer braid layers.

The transfer impedance expression consists of three terms:

${Z}_{t}\approx {Z}_{d}+j\omega {L}_{h}±j\omega {L}_{b}$
where:

${L}_{b}$ represents a porpoising term given by the mutual inductance between inner and outer carrier layers at the crossovers

## Demoulin

This model takes into account that ${Z}_{t}$ is not linearly increasing with frequency and that the phase variance is not between \ $±\frac{\pi }{2}$ as theory predicts for the diffraction model.

The transfer impedance expression is given by:

${Z}_{t}\approx {Z}_{d}+j\omega {L}_{h}+{k}^{\text{'}}\sqrt{\omega }{e}^{\frac{j\pi }{4}}±j\omega {L}_{b}$

## Kley

This model relies on tuning models using measurement data. The transfer impedance expression is given by:
${Z}_{t}\approx {Z}_{d}+j\omega {L}_{t}+\left(1+j\right)\omega {L}_{s}$
where:
• ${L}_{t}={M}_{L}+{M}_{G}$ is the penetration inductance
• ${M}_{L}$ is a hole inductance, also correcting for shield curvature
• ${M}_{G}$ is a mutual braid inductance between the carriers in the braid
• $\left(1+j\right)\omega {L}_{s}$ is due to the magnetic field inducing two types of eddy currents

## References

• E.F. Vance, “Shielding Effectiveness of Braided-Wire Shields,” IEEE Transactions on Electromagnetic Compatibility, vol. EMC-17, no. 2, pp. 71-77, May 1975.
• F.M. Tesche, M.V. Ianoz, and T. Karlsson, “EMC Analysis Methods and Computational Models,” Wiley Interscience, Chapter 9, 1997.
• T. Kley, “Optimized Single-Braided Cable Shields,” IEEE Transactions on Electromagnetic Compatibility, vol. EMC-35, no. 1, Feb. 1993.
• M. Schoeman, E.A.Attardo, J.S Castany, "Recent Advances to the Feko Integrated Cable Harness Modeling Tool", 2019 International Symposium on Electromagnetic Compatibility - EMC EUROPE, September 2019.