# What Is Multiphysics and How Does it Relate to PCB Design?

### Key Takeaways

• An explanation of multiphysics and its simulation use for PCB design.

• The time-dependency system response and why the frequency domain offers better solutions.

• Some examples of a multiphysics model in action.

Picture the scene: a young grad student is designing a patterned array for a photosensitive material as a new kind of light sensor. When it comes time to examine the response of the system to light that is incident at various angles, what is the young grad student to do? They may consider an analytic solution, but a numerical multiphysics approach may be the best bet. If the reader is mouthing to themself “what is multiphysics?”...worry not! While it may sound like a sci-fi term, multiphysics denotes a model that incorporates various branches of physics to form a more cohesive solution.

Although analytic solutions are helpful and encapsulate some fundamental relationships, they are far from the end-all, be-all. Often, these solutions need to be improved in real-world situations due to their extensive idealization of real-world phenomena. Simulation software instead can rigorously model high-order problems with enough accuracy and better computational speed, making them the clear choice for intricate physical systems. The right software solver allows you to simulate the behavior of your PCB based on the interaction between multiple areas of physics. This type of simulation is extremely useful for modeling behavior in complex systems that are not amenable to SPICE-based simulations.

Let’s jump into discussing what multiphysics is.

## What Is Multiphysics, Anyways?

A multiphysics simulation involves modeling the interaction between different physical aspects of a system in a single simulation. In the real world, multiphysics is simply the state of everyday phenomena overlapping:

• Electromagnetism accounts for the movement of charge, the permanent or temporary magnetization of materials, and the interplay of the associated fields.

• Thermodynamics concerns the generation, radiation, and absorption of heat or heat flux, along with resulting changes in material properties.

• Statics covers a rigid body under the trivial case of Newton’s Second Law, and any forces and deformation therein. Dynamics is used for non-zero accelerations, e.g., vibration or shock encountered during a drop test.

• Other considerations can include chemical (corrosivity, reactivity) and humidity (absorption of ambient water by hygroscopic materials), and more. Active models will tend to focus on the first three points, but these conditions may be pertinent depending on the field usage of a board.

Many systems are complicated, especially electronics systems, and different physical quantities (e.g., electrical current and temperature) are related in obfusticated ways. In addition to individual physics simulations, engineers need to consider the interaction between different aspects of physics, which requires a multiphysics simulation approach. During production and service life, designers and manufacturers must understand how these seemingly disparate mechanisms operate to optimize performance.

Multiphysical systems are a more realistic capture of physical functions and constraints.

The challenge in any multiphysics model for simulating a PCB is to accurately model the behavior of source terms in the system, whether they are mechanical loads, electronic components that dissipate heat, or heat sources and sinks in a system. As multiphysics software may use 3D field solver simulations to solve coupled sets of differential equations in a system, the other challenge involves creating a sufficiently fine mesh of the system in space and time. Fine meshes in space and time are critical for ensuring that the results are accurate, although an overly fine mesh will require longer computation time. Balancing computational accuracy and computational time is a major challenge in multiphysics simulations.

In PCBs, electrical reliability is quantified in terms of power integrity and signal integrity analysis to minimize power fluctuations, crosstalk, and susceptibility to EMI. Evaluating thermal reliability requires thermal simulations to evaluate the temperature of the board and components. This allows you to determine whether the board operates within an appropriate temperature range. Finally, mechanical reliability is related to thermal expansion at high temperatures, and you’ll need to evaluate thermal and mechanical stresses in vias, solder joints, and in the board itself.

## Dynamic/Transient Behavior vs. Steady State Behavior

Multiphysics simulations can be performed in the time domain, although these simulations require a significant amount of computational power, memory, and computation time. A small-scale 3D simulation in the time domain can take days to complete unless you take advantage of parallelization during computation.

Time domain multiphysics simulations can be roughly divided into two types: transient simulations and dynamic simulations. Each type of simulation is similar to its corresponding circuit simulation in a SPICE package. As the state of the system or a source term in the system suddenly changes, e.g., a component turns on or off, the system requires some time to adapt to this change.

Output from a finite element method simulation

One can draw an analogy to a simulation for an RC circuit: if the voltage applied to the capacitor suddenly changes from 0 to some positive voltage, the charge accumulates on the capacitor over time – it does not instantly change to the value Q = CV. This behavior can be examined in multiphysics simulations in the time domain when sourcing terms in the system are discontinuous in time.

The transient behavior shows you have the system transitions into a steady state over time. Once the transient behavior is understood, this gives you a benchmark for the simulation time required to start examining the steady-state behavior of the system. In a PCB, the behavior of the system is constant in time once the system enters the steady state, and you only need to examine the spatial distribution of temperature, mechanical stress, and voltage/current throughout the board.

## Multiphysics Simulations in PCB Design

Multiphysics simulations are used in PCB design to verify design choices, examine electrical behavior, identify possible thermal management problems, and even ensure mechanical reliability. The goal is to identify possible electrical, thermal, or mechanical defects in the design before they create major problems in your board. These could include crosstalk or nonlinear electrical effects in certain circuits, identification of hot spots on a board, or resistance to mechanical shocks.

### An Example: Thermal Cycling

Thermal and mechanical reliability in circuit boards during operation are related in several ways. Active components generate a significant amount of heat in a circuit board, and the low thermal conductivity of FR4 substrates causes heat to accumulate, leading to significant temperature increases. A circuit board will expand as it heats up, creating stress on traces, vias, and other electronic elements throughout the board. This arises due to the mismatch between the volumetric expansion coefficients for different materials throughout the board.

Vias in multilayer boards are susceptible to fractures during thermal cycling. If a board heats up to a high temperature at a slow rate and remains at that temperature, there is less danger of mechanical damage to conductors due to static stress. The danger arises during thermal cycling, where stress can lead to fatigue along a via barrel. Butt joints on in-pad vias are also real failure points, as stress becomes concentrated in these locations.

This type of multiphysics simulation for a PCB under thermal cycling as a board operates allows you to analyze the link between temperature rise in a board and mechanical stress during electrical operation. You’ll be able to view mechanical stress, the electromagnetic field, voltage/current distribution, and temperature throughout the system at various points in time.

You won’t need an infrared camera with a multiphysics simulation

## Going Further: Frequency Domain Simulations

When working with systems that involve purely harmonic sources, it is often quite useful to transform the governing equations in a multiphysics simulation into the frequency domain. While you miss the transient behavior of the system, you gain a complete view of how the system responds to sources with different frequencies.

Working with the right suite of PCB layout and design software allows you to create a design from your idea and simulate its functionality with advanced tools. Designers no longer have to ask, “what is multiphysics,” but instead, “how can a multiphysics model better optimize this build?” Allegro PCB Designer includes the features you need for advanced circuit board layout, and the Clarity 3D Solver includes tools you need for multiphysics simulations. You can also import your board into Cadence’s suite of other analysis tools to simulate and analyze the behavior of your board.

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