PCB Parasitic RLC Extraction 

This validation case demonstrates the accuracy of SimScale’s AC Magnetic and Electrostatics analyses for extracting parasitic RLC parameters from a printed circuit board (PCB) structure. Simulation results are compared against analytical data from a published reference and an independent electromagnetic simulation.

Simulation Overview

Parameter	Value
Application	PCB parasitic RLC extraction
Analysis types	Magnetostatics (DC); Time-Harmonic Magnetics (AC); Electrostatics
Reference	Qian, J. (2003). RF Models for Active IPEMs. MS Thesis, Virginia Polytechnic Institute and State University [1]

Geometry

The PCB structure consists of two parallel copper traces routed on a square FR4 substrate, with a continuous copper ground plane on the opposite face. The geometry reproduces the test board described in Qian (2003), used in the original study to characterize parasitic resistance, inductance, and capacitance at frequencies from DC to \(1 \, \text{MHz}\).

Material Properties

Material	Property	Value
Copper	Electrical conductivity \(\sigma\)	\(5.8 \times 10^7 \, \text{S/m}\)
FR4 substrate	Relative electric permittivity \(\varepsilon_r\)	\(4.4\)
Air	Relative electric permittivity \(\varepsilon_r\)	\(1.006\)
Ground plane	Thickness	\(5 \, \text{mils}\)

Simulation Setup

Three analyses target the same PCB geometry, each extracting a different subset of parasitic parameters:

• Magnetostatics (DC): extracts DC resistance \(R_{DC}\) and loop inductance \(L_{DC}\) by driving each copper trace with a \(10 \, \text{A}\) solid coil excitation and computing the resulting magnetic field and resistive losses.
• Time-Harmonic Magnetics (AC): sweeps frequency from \(1 \, \text{kHz}\) to \(1 \, \text{MHz}\) and extracts AC resistance \(R_{AC}(f)\) and loop inductance \(L(f)\) at each frequency point using Resistance Sets result controls.
• Electrostatics: extracts the capacitance matrix between the copper conductors by applying unit potentials to each trace and solving for the charge distribution.

Results

DC Resistance

The DC resistance follows directly from the trace geometry:

$$R_{DC} = \frac{\rho \, L}{A}$$

where \(\rho\) is the resistivity of copper, \(L\) is the trace length, and \(A\) is the cross-sectional area. The table below compares the SimScale Magnetostatics result against the reference.

Parameter	Reference [1]	SimScale	Deviation
DC Resistance \(R_{DC}\)	\(5.4304 \, \text{m}\Omega\)	\(5.4304 \, \text{m}\Omega\)	\(< 0.01\%\)
DC Loop Inductance \(L_{DC}\)	\(50.742 \, \text{nH}\)	\(51.333 \, \text{nH}\)	\(+1.16\%\)

AC Resistance and Inductance

The AC Magnetic analysis sweeps frequency from \(1 \, \text{kHz}\) to \(1 \, \text{MHz}\). As frequency increases, the skin effect concentrates current in a thin layer near the conductor surface, increasing \(R_{AC}\) and reducing the effective loop inductance \(L(f)\). Both quantities are extracted from the Resistance Sets result control.

The skin depth \(\delta\) at angular frequency \(\omega\) is given by:

$$\delta = \sqrt{\frac{2}{\omega \, \mu_0 \, \sigma}}$$

Capacitance

The electrostatic analysis extracts the capacitance matrix between the copper conductors. Three values are reported: each trace to the ground plane, and the mutual capacitance between the two traces. Negative off-diagonal entries in the Maxwell capacitance matrix indicate coupling between conductor pairs.

Parameter	Reference [1]	SimScale	Deviation
Left trace to ground plane	\(-4.3047 \, \text{pF}\)	\(-4.4143 \, \text{pF}\)	\(+2.55\%\)
Right trace to ground plane	\(-4.3046 \, \text{pF}\)	\(-4.4143 \, \text{pF}\)	\(+2.55\%\)
Between the two traces (coupling)	\(-0.1673 \, \text{pF}\)	\(-0.1589 \, \text{pF}\)	\(-5.0\%\)

Last updated: August 4th, 2026