Microstrip self impedance Z0 - QuickField simulation example
This is an example of the microstrip line simulation, performed with QuickField software.
How to find microstrip characteristic impedance trace?
Engineering answer Typical applications Geometry
Given
Task
Solution
Inductance is calculated in the AC magnetic problem. AC current In the conductor flows in one direction. The return current flows in the ground plane. QuickField calculates the total stored magnetic field energy.
Result
Voltage distribution in the microstrip line.
Current density distribution in the microstrip line.
Engineering question
Set up a plane-parallel QuickField Electrostatics problem for a microstrip trace and evaluate characteristic impedance from computed field results.
controlled impedance PCB traces, microwave PCB lines, transmission line structures
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Simulation problem
Problem Type
Plane-parallel problem of electrostatics and AC magnetics.
Relative permittivity of air ε = 1;
Relative permittivity of dielectric ε = 4.3.
Frequency f = 500 MHz.
Line length Lz = 5 inches
Determine the self impedance of the microstrip transmission line.
To calculate the impedance we should find the capacitance C0 and the inductance L0.
Capacitance is calculated in the electric problem. Positive potential is assigned to the conductor, zero potential is assigned to the ground plane. QuickField calculates the total stored electric field energy.
C0 = 2*Energy / ( Potential difference ) ²
L0 = 2*Energy / |Current| ²
C0 = 2*1.553e-11 / 2² = 7.8 pF (per 5" of line length)
L0 = 2*3.35e-20 / (1e-6)² = 67 nH (per 5" of line length)
Impedance Z0 = √L0/C0 = 92.7 Ohm.
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