# Coaxial Cable Analysis

### Application

CADFEKO supports the analysis of arbitrary cable bundles and cable paths. This feature provides the user means of dealing with the problem of irradiation of cables excited by an external field, e.g. a plane wave, but also any other sources of radiation modelled in FEKO.  The analysis approach followed within FEKO is based upon relating the current on the cable’s shield (caused by external radiation) to the voltage induced on the inner conductor by means of the cable’s transfer impedance.

### Technology

Cable coupling modelling technology is based on the application of Multiconductor Transmission Line Theory (MTL) to compute the coupled-in voltage at the termination impedances of a cable close to a conducting metallic ground.  The fields around the cable may be computed with the Method of Moments (MoM), Physical Optics (PO), Multilevel Fast Multipole Method (MLFMM) or the Finite Element Method (FEM) and does not take the cable into account when computing the field distribution.  The cable therefore does not affect the field distribution at all.  In this fact lies the reason for the greatly reduced number of unknowns in comparison to a full MoM solution:  The cable itself is not modelled as a geometric entity and therefore not meshed into geometric segments, making it unnecessary to introduce a very fine mesh underneath the cable on the ground plane.

For shielded cables with an arbitrary cable path which does not run close to a conducting surface, the combined MoM/MTL should be used.
 Figure 1: Side view of the simplified cable path scenario

Capabilities

In the current implementation cable modelling can be used to compute the induced voltage (measured over the termination loads) in arbitrary cable bundles and cable paths (over a conducting ground plane) that are exposed to an arbitrary external field.  The cable path is only restricted by the fact that only straight cable path sections are currently supported.  Within this restriction the cable path can follow any path in 3D space and use any number of cable path sections.

 Figure 2:  Examples of allowable cable paths

Cable properties can be selected from a predefined database of commonly used cables or can be specified by the user.  The user specified cable properties should be valid for the frequency of interest in the current simulation.  Predefined cable properties are frequency dependent and are valid for the frequency range 10 kHz to 500 MHz.

Limitations

There are some limitations to the current implementation that the user should take note.  These include:

• The method is based on assumption that exterior (structure and shield) and interior (cable bundle) problems only couple weakly through the transfer impedance.
• Cable junctions are not supported. In practice this means that connecting nodes always have only two cable path sections connected to them, unless this node specifies the end of a cable path in which case terminating impedance replaces one cable path section.
• Crossing cables are not interconnected, even though it is possible for cables to cross each other geometrically.
• Cables must be homogeneous meaning that all cable path sections must have the same electric properties.
• Cables are decoupled from each other and do not radiate energy from the currents on the cable’s shielding.
• Only shielded cables can be handled. This includes insulated single conductors, coaxial lines and shielded bundles with arbitrarily complex cross sections.
• Internal wires must be connected to the shield at the cable endpoint connectors. The cable endpoint connectors should be connected to the metal structure, optionally  through a lumped load or source.

### Example

The example that is presented here was chosen as it enables comparison with results reported in open literature, [1].  It consists of an RG-58 cable loop close to a monopole antenna.  The monopole is fed with a voltage source at its base and the radiated power scaled to 10 W.  The cable is terminated at both ends in 50 Ω impedance, with the cable shield directly connected to the PEC ground plane (implying a shield terminating impedance of 0 Ω).  The maximum segment length is set to 0.5 m for a frequency range 1 MHz to 35 MHz.

 Figure 4: Monopole and RG-58 cable loop geometry setup

A comparison is drawn between the FEKO results and results published in [1] for the same problem.  The agreement between FEKO values and the published data is very good for both magnitude and the position of the sharp resonances in the magnitude.

 Figure 5: Comparison of results from FEKO (blue) with those from [1] (red, light blue and green)

### References

 [1] H.-D. Brüns, H. Singer, “Computation of Interference in Cables Close to Metal Surfaces,”  IEEE Int. Symposium on EMC, Denver, 1998, pp 981-986
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