Transient eddy currents in a two-wire line - QuickField simulation example
This is an example of the two-wire line simulation, performed with QuickField software.
How to find transient currents in two wire transmission line?
Engineering answer Typical applications Geometry
Transmission line consists of two copper conductors with equal but opposite currents. All dimensions are in millimeters.
Given
Task
Solution
The inductance of the transmission line can be calculated as L = μ0·l/π · (ln(D/r) + 0.25), where The transient current for equivalent electric circuit with lumped parameters (R and L in series) is described by the formula
Results
Transmission line inductance (analytical value) is L = 4π·10-7·1/π · (ln(0.02/0.0001) + 0.25) = 2.219 μH
Engineering question
Set up a plane-parallel QuickField Transient Magnetics problem for a two-wire transmission line and evaluate transient currents from computed field results.
two-wire transmission lines, parallel conductors, switching transient paths
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Simulation problem
Problem Type
Plane-parallel problem of transient magnetics.
Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper g = 56 MS/m;
Voltage applied U = 0.001 V;
Calculate the transient currents within the conductors.
The resistance of one conductor can be calculated as Rcond = l / (g · S),
where
S = πr² - cross-section area of conductor,
R - radius of conductor,
L - length of the line.
D - distance between conductors.
I(t) = U/R · (1 - e-t/T), where T=L/R - characteristic time of the circuit.
Conductor resistance (analytical value) is Rcond = 1 / (56·106 · (π·0.0001²)) = 0.5684 Ohm.
The resistance of both conductors in transmission line is R = 2·Rcond = 2·0.5684 = 1.1368 Ohm
Eddy current density distribution in the wire.
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