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Laminated busbars

QuickField simulation example

The inductance of laminated busbars is lower than that of conventional busbars. This results in shorter signal propagation delays. In this example, the inductance, capacitance, and alternating current resistance of a laminated busbar carrying alternating current are calculated.

Problem Type
Plane-parallel problem of AC Magnetics, Electrostatics.

Geometry
Busbars length is 200 mm.
Laminated busbars Laminated busbars feature less inductance and more capacitance comparing to the conventionsl busbars. <> Copper Copper Insulation 100 mm 3 mm 3 mm 1 mm

Given
Copper electric conductivity 58.5 MS/m;
AC current frequency f = 1 kHz.
Insulation relative dielectric permittivity ε = 4.

Task
Calculate the capacitance between copper conductors, inductance and AC resistance and compare with the reference values*.

Solution
The electromagnetic wavelength at a given frequency is much longer than the busbars dimensions. So the capacitance is a pure geometric parameter that does not depend on the voltage magnitude. The electrostatic problem is simulated to calculate the capacitance. The busbars surfaces have potentials +1V and -1V, and the electric field energy is calculated. Capacitance is equal to 2*Electric field energy / (Potential difference)².
There is no materials in the model with properties which depend on the magnetic field strength. So the inductance is a pure geometric factor too. To calculate the inductance the AC magnetic problem is simulated with +1000 A and -1000 A alternating currents specified in the busbars. QuickField calculates the voltage drop in the busbars. The voltage drop is an alternating value too, changing with the same frequency as the current. The ratio of AC voltage drop to the AC current yields the impedance:
Impedance = Voltage drop / Current = Resistance + i*2π*f * Inductance

Results
Inductance of the laminated busbars is 6.5 nH per per 200 mm of busbars length, AC resistance is 29.2 μΩ.
Laminated busbars inductance

Mutual capacitance is 2*1.42nJ / 2² = 0.710 nF per 200 mm of busbars length.
Laminated busbars capacitance

Reference
Online calculator for laminated bus-bar yields capacitance 0.704 nF.
https://www.wdint.com/SupportCalculate.html