Microstrip differential impedance - QuickField simulation example
This is an example of the microstrip line simulation, performed with QuickField software.
How to find microstrip differential pair impedance?
Answer Typical applications Geometry
Given
Task
Solution
Inductance is calculated in the AC magnetic problem. In the left trace AC current flows in one direction. The return current flows in the right trace. Total current in ground plane is zero. 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 differential pair and evaluate differential impedance from computed field results.
differential PCB traces, high-speed signal pairs, controlled impedance differential lines
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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 differential impedance of the microstrip transmission line.
To calculate the differential impedance we should find the differential capacitance Cdiff and the differential inductance Ldiff.
Capacitance is calculated in the electric problem. Positive potential is assigned to the left trace, negative potential is assigned to the right trace, zero potential is assigned to the ground plane. QuickField calculates the total stored electric field energy.
Cdiff = 2*Energy / ( Potential difference )²
Ldiff = 2*Energy / |Current|²
Cdiff = 2*1.19e-11 / 2² = 6.0 pF (per 5" of line length)
Ldiff = 2*4.15e-20 / (1e-6)² = 83 nH (per 5" of line length)
Impedance Zdiff = √Ldiff/Cdiff = 118 Ohm.
Video
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