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?

When there is no analytical solution to a problem in a complicated system, a multiphysics simulation can give you a full numerical solution that describes the behavior of multiple aspects of your system. The right 3D 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 modelling behavior in complex systems that is not amenable to SPICE-based simulations.

## What is Multiphysics Anyways?

A multiphysics simulation involves modelling the interaction between different physical aspects of a system in a single simulation. Many systems are complicated, especially electronics systems, and different physical quantities (e.g., electrical current and temperature) are related in complicated ways. In addition to individual physics simulations, engineers need to consider the interaction between different aspects of physics, which requires a multiphysics simulation approach. This provides a more complete view of the behavior of your system.

The challenge in any multiphysics model for simulating a PCB is to accurately model the behavior of sourcing 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 with the goal of minimizing power fluctuations, crosstalk, and susceptibility to EMI. Evaluating thermal reliability requires thermal simulations in order 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 temperature, 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 the 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 a number of 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 fracture 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. Allegro PCB Designer includes the features you need to layout advanced circuit boards, 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.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.

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