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Dielectric losses
Simulation of the dielectric losses in the capacitor with known loss tangent.
Problem Type:
Plane problem of AC conduction.
Geometry:
d=1 mm, h=10 mm.
The length of capacitor in z direction is l = 10 mm.
Given:
Relative permittivity of substrate ε = 2.3.
Loss tangent tgδ = 0.75%.
Voltage U = 220 V,
Frequency f = 100 kHz.
Task:
Calculate dielectric losses in capacitor.
Solution:
Capacitor with nonideal dielectric can be represented by electric circuit with ideal capacitor C and resistivity R connected in parallel, so that R corresponds to the insulation resistance.
For plane capacitor the capacitance can be calculated as C = εε_{0}·S/d, where S=l·h is a plate surface area.
For plane capacitor the resistance can be calculated as R = (1/γ)·d/S
In the AC conduction problems electric conductivity (γ) of materials should be set. We can derivate the electric conductivity value using the formulae:
tg(δ) = X_{C}/R, where
X_{C}  capacitor reactance, X_{C} = 1 / 2πf·C,
R  capacitor resistance.
After substitution we have:
tg(δ) = 1/ 2πfCR = 1 / 2πf·εε_{0}·S/d·(1/γ)·d/S
Electric conductivity is γ = 2πf·εε_{0}·tg(δ)
Results:
Electric conductivity is γ = 2·3.142·100000·8.854e12·2.3·0.0075 = 0.096 uS/m.
Active power dissipated in dielectric is P_{A} = 0.46 mW.
Download simulation files: dielectric_losses.zip
Video.
