PCBs are composed of high thermal conductivity copper and low thermal conductivity dielectric materials stacked alternately, exhibiting significant anisotropy.

Simcenter FLOEDA Bridge simplifies complex layered structures into homogeneous blocks with equivalent thermal conductivity, greatly enhancing the efficiency of system-level thermal analysis. This article will delve into the two core methods used by FLOEDA for calculating the equivalent thermal conductivity of PCBs: Analytical and Empirical, focusing on the key differences between them.

🔬 Fundamental Principles of PCB Thermal Conductivity Modeling

In FLOEDA, a PCB is simplified to a solid model with biaxial thermal conductivity, requiring the calculation of two key values:

1. In-plane Thermal Conductivity (or): The thermal conductivity along the plane of the board.

2. Axial (Through-Board) Thermal Conductivity (or): The thermal conductivity perpendicular to the board direction.

Regardless of the method used, the final equivalent thermal conductivity is calculated based on the inherent properties of the materials and the volume percentage of copper.

1. Analytical Calculation: Theory-Based Analytical Method

The analytical method is based on the theoretical model of composite material heat conduction. It treats the PCB as an ideal composite structure made of copper and dielectric materials, calculating through series or parallel thermal resistance models. Prior to version 17.2 of FLOEFD, the thermal conductivity of all circuit boards was calculated using this method.

🔸 In-plane Thermal Conductivity ()

In in-plane heat conduction, the copper and dielectric layers are viewed as thermally parallel paths. Heat can flow simultaneously through the highly conductive copper and the low-conductivity substrate, thus the calculation formula is based on the volume averages of the materials:

Note: For the entire Compact Board, the final in-plane thermal conductivity is derived from the parallel weighted average of all layers.

🔸 Axial Thermal Conductivity ()

In axial heat conduction, heat must sequentially pass through different material layers, thus it is viewed as thermally series paths. The axial calculation of the analytical method is based on the fundamental Series Calculation model:

Characteristics: The analytical method is quick and based on a clear physical model. However, it assumes a uniform distribution of copper and directly uses the inherent thermal conductivity of the dielectric material in the axial calculation. This may lead to results that are more “optimistic” (higher thermal conductivity) than actual conditions in complex wiring scenarios.

2. Empirical Calculation: Experience-Based Correction Method

The empirical method is the high-precision modeling approach recommended by FLOEFD, which introduces corrections based on experimental data and high-precision model calibration on top of theoretical formulas. The core difference between the empirical and analytical methods lies in the calculation model for axial thermal conductivity.

Key Differences: Replaced by

The axial calculation in the empirical method adopts a Modified Series Calculation approach, replacing the analytical method’s:

• (Minimum Thermal Conductivity): This is an empirically derived function that depends on the percentage of copper in the dielectric layer.

• Physical Significance: In actual PCBs, the presence of copper traces causes thermal flow to experience path contraction in the dielectric material regions, resulting in actual thermal resistance being higher than that of pure dielectric materials. The empirical correction simulates this additional thermal resistance, ensuring that simulation results are closer to physical reality.

Summary of the Empirical Method

1. More Conservative Results: The equivalent thermal conductivity calculated by the empirical method is always lower than the inherent thermal conductivity of the dielectric material, leading to a lower predicted temperature.

2. Higher Accuracy: The empirical method better captures the geometric effects of actual wiring, making it commonly used for final product validation and high-fidelity simulations.

Conclusion and Application Recommendations

Feature	Analytical	Empirical
Base Model	Idealized material volume averages and thermal resistance in series and parallel.	Correction model based on experimental data.
Axial Calculation	Relies on inherent properties (Series Calculation).	Relies on empirical correction values (Modified Series Calculation).
Result Trend	Higher thermal conductivity (optimistic), potentially underestimating device temperature.	Lower thermal conductivity (conservative), predicting temperatures closer to reality.

In summary, it is recommended to choose the Empirical Calculation method for calculating the equivalent thermal conductivity of PCBs. So you might think the author has padded the article.

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