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.
How to find laminated busbar inductance capacitance and ac resistance?
Answer Typical applications Geometry
Given
Task
Solution
Results
Mutual capacitance is 2*1.42nJ / 2² = 0.710 nF per 200 mm of busbars length.
Reference
Engineering question
Set up a plane-parallel QuickField AC Magnetics problem for laminated busbars and evaluate inductance capacitance and AC resistance from computed field results.
laminated power busbars, high-current distribution bars, inverter busbar assemblies
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Simulation problem
Problem Type
Plane-parallel problem of AC Magnetics, Electrostatics.
Busbars length is 200 mm.
Copper electric conductivity 58.5 MS/m;
AC current frequency f = 1 kHz.
Insulation relative dielectric permittivity ε = 4.
Calculate the capacitance between copper conductors, inductance and AC resistance and compare with the reference values*.
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
Inductance of the laminated busbars is 6.5 nH per per 200 mm of busbars length, AC resistance is 29.2 μΩ.
Online calculator for laminated bus-bar yields capacitance 0.704 nF.
https://www.wdint.com/SupportCalculate.html
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