PCB line attenuation constant - QuickField simulation example
The shielded transmission line is considered. The line consists of 2 copper strip-like conductors that are rested on the polyethylene substrate. The whole structure, that includes partly an air, is protected by a screen of the complicated geometry.
How to find microstrip line attenuation constant?
Engineering answer Typical applications Geometry
Given
Task
Solution
C1,2 is determined by applying a voltage V on the electrode #2 and a zero voltage on the shield. Then the total charge Q on the electrode #1 is measured, and C1,2 = Q / V [F/m].
One has to repeat the previous 2 runs with the only change: a substitution of the dielectric by air (electric permittivity should be assign a value of 1). Thus L1,2 and L1,0 are obtained.
Results
Electric potential distribution in transmission line:
Microstrip transmission line magnetic field:
Engineering question
Set up a plane-parallel QuickField AC Magnetics problem for a PCB microstrip line and evaluate attenuation constant from computed field results.
PCB transmission lines, RF PCB traces, high-frequency routing structures
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Simulation problem
Problem Type
A plane-parallel problems of AC magnetics and electrostatics.
Copper electric conductivity 56 MS/m
Dielectric relative electric permittivity ε = 4
Frequency f = 100 MHz
Current I = 1 A
Find the attenuation constant of the transmission line.
Attenuation constant of the shielded microstrip-like transmission line is obtained on the basis of the electrostatics and time-frequency analysis.
Method of calculation of the characteristic impedance Z0 is based on the calculation of the mutual capacitance C1,2 between two electrodes and mutual capacitance C1,0 between an electrode and a shield.
Similarly, C1,0 is determined, but in this case both electrodes are placed under voltage V and the shield has a zero voltage.
Characteristic impedance Z0 = 2·Z1,2·Z1,0 / (Z1,2 + 2·Z1,0), where
differential impedance Z1,2 = √L1,2 / C1,2
self impedance Z1,0 = √L1,0 / C1,0
Characteristic impedance Z0 = 104 Ohm.
Resistance of the line R = 1.026 [Ohm/m].
Attenuation of the line α = 869·0.5·R/Z0 [dB/100m].
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