As electronic devices become smaller and more ubiquitous, the printed circuit boards and components that drive them face increasing power densities and evermore complexity. To ensure product reliability and performance, accurate and detailed analysis methodologies are necessary. In a three-part series, Mike Bak and I will discuss modeling approaches for the thermo-mechanical analysis of printed circuit boards and their components. In part one of this series, I will cover modeling approaches for the PCB itself.

A typical PCB will have multiple layers, each one having its own distribution of FR-4 and copper traces and vias. Take the board layout shown in Figure 1 as an example, which has over 16,000 traces and vias across 7 layers. The complex board geometry leads to spatially varying material properties (i.e. modulus of elasticity, density, thermal conductivity, etc.) that must be accurately specified by the analyst for any type of simulation.

So, what are some ways that we can model this type of geometry? I've outlined below some common approaches:

### Method 1: Lumped material properties

The most basic approach to dealing with the complex geometry of a PCB is to assume "lumped" material properties. In this method, a percentage copper coverage of each layer of the board is assumed and effective orthotropic material properties can be calculated. The extent to which material properties are lumped can be decided by the analyst - properties can be lumped across all layers or on a layer-by-layer basis.

Using the board thermal conductivity as an example, if properties are averaged on a layer-by-layer basis, then the effective thermal conductivity of each layer can be computed as:

where *β*_{i }is the fraction of layer *i *covered by copper. To take things a step further and compute an effective thermal conductivity for the entire board, we must account for the difference

This simple approach affords the analyst a reliable first order estimate of board properties, but can be expected to lead to local errors due to the “smearing out” of spatial property variations.

### Method 2: Detailed geometry

Using a method that lies to the opposite extreme of the simplicity of Method 1, the analyst can choose instead to model the entire board explicitly by extracting the full 3-dimensional geometry of the PCB layup. In this approach, no assumptions are made as to the distribution of the materials within the board as each trace and via is modeled in detail. As mentioned previously, a typical board such as the one shown in Figure 1 may have 10’s of thousands of traces and vias across multiple layers. The consequence of this geometric complexity is mesh and model sizes that can become computationally intractable. Therefore, this approach is typically only used in local submodels or models in which joule heating occurs where the geometric details are significant and worth the computational expense.

### Method 3: Mapped material properties

In the past few years, a new analysis methodology that lies in between the simplicity of Method 1 and the computational expense of Method 2 has been developed to handle the complex geometry of PCB’s. In this approach, a rectangular background grid is constructed on each layer of the board. Each cell of the background grid computes effective orthotropic material properties based on the local concentration of copper and dielectric. This effectively forms a map of the material properties across each layer of the PCB. The local properties are computed in a manner similar to Method 1, however only a finite section of the board is considered in each cell, allowing the material map to capture local changes in properties. An example of this material map constructed in ANSYS Mechanical is shown in Figure 2 below.

The mesh in your FEA or CFD model can then reference this underlying material map in determining local material properties of the PCB. This method allows for a more accurate representation of the PCB material distribution than the lumped material approach in Method 1 at a more reasonable computational expense than the detail approach in Method 2. The fidelity of this modeling approach is demonstrated in the plot of equivalent elastic strain in Figure 3 below.

In the next section of this blog series we will discuss approaches for modeling component properties – stay tuned!

For more information on the modeling methodology in Method 3, please check out this this presentation: