Laminated busbars - QuickField simulation example
Capacitance, inductance, and AC resistance of laminated bus bars, illustrating their low-inductance behavior and comparison with published reference values.
How to calculate the capacitance, inductance, and AC resistance of laminated busbars?
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
Use electrostatics for capacitance and AC magnetics for complex impedance, then separate the impedance into resistance and inductance.
laminated power busbars, high-current distribution bars, inverter busbar assemblies
Download
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
Related examples