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transmission line current distribution, transmission line impedance, transmission line losses

This is an example of the symmetric double line of conductors simulation, performed with QuickField software. Two copper square cross-section conductors with equal but opposite currents are contained inside rectangular ferromagnetic coating.

**Problem Type**

Plane-parallel problem of AC magnetics.

**Geometry**

**Given**

Magnetic permeability of air μ = 1;

Magnetic permeability of copper μ = 1;

Conductivity of copper σ = 56 MS/m;

Magnetic permeability of coating μ = 100;

Conductivity of coating σ = 10 MS/m;

Current in the conductors *I* = 1 A;

Frequency *f* = 100 Hz.

**Task**

Determine current distribution within the conductors and the coating, complex impedance of the line, and power losses in the coating.

**Solution**

We assume that the flux is contained within the coating, so we can put a Dirichlet boundary condition on the outer surface of the coating.

The complex impedance per unit length of the line can be obtained from the equation

*Z* = ΔV / *I*,

where ΔV = *V*_{1} - *V*_{2}

*V*_{1}, *V*_{2} are voltage drops per unit length in each conductor. To obtain a voltage drop, switch to Local Values mode in postprocessing window, and then pick an arbitrary point within a conductor.

To obtain power losses in the coating:

- In the postprocessing mode, choose
**Pick Elements**and pick the coating block to create the contour. - Choose
**Integral Values**and select*Joule heat*from the list of integral quantities and choose**Calculate**.

**Results**

The impedance of the line *Z* = 0.000484 + *i* 0.000736 Ohm/m.

The power losses in the coating of the double line *P* = 0.0000427 W/m.

Current density in symmetric double line of conductors:

- View simulation report in PDF
- Download simulation files (files may be viewed using any QuickField Edition).