ACElec1: Plane capacitor
This is an example of the plane capacitor simulation, performed with QuickField software.
Problem Type:
A plane-parallel problem of AC conduction.
Geometry:
Due to symmetry only a small part of 1 mm heigh is used. The length of capacitor in z direction is L = 10 mm.
Given:
Relative permittivity of substrate ε = 10.
Conductivity of substrate g = 10-8 S/m;
Voltage U = 5 V,
Frequency f = 50 Hz.
Problem:
Find current and dissipation factor tg(δ) of the plane capacitor with nonideal dielectric inside.
Solution:
Capacitor with nonideal dielectric can be replaced by electric circuit with ideal capacitor C and resistivity R connected in parallel. The capacitance of the plane capacitor is calculated by the equation
C = εε0S/d, where S is the plate area S = h·l.
Resistance of the substrate is calculated by the equation R = ρ·d/S.
Current I has two components: active IA and reactive IR. For parallel scheme IA = U / R, IR = U / XC.
tg(δ) = |PA / PR| = |U·IA / U·IR| = |XC|/R = 1/ωC·R, tg(δ) = 1 / 2πf·C·R
Results:
|
QuickField |
Theoretical result |
IA, μA |
0.05000 |
0.05000 |
IR, μA |
0.13908j |
0.13902j |
tg(δ) |
0.3595 |
0.3596 |
|
