Constructing thermal equivalent circuits as a baseline for thermal analysis methods.
A look at some of the math behind thermal transfer and why it endears itself to a computational approach.
How modern computers utilize a divide-and-conquer system for thermal analysis improvements.
PCB thermal analysis tools are a natural outgrowth of the interplay between electromagnetism and thermodynamics
Heat and electricity are closely intertwined. Whether it’s an electric stove or the thermal tab on a TO-220, most designers have some firsthand experience (sometimes painfully unintentional) with this partnership. The shared nature is even more pronounced with the thermoelectric effect: a direct conversion between voltage and temperature is supported via a thermocouple. The link between electric and thermal parameters means proactive board design needs to placate both for long-term functionality. A wealth of PCB thermal analysis tools are available to designers, running the gamut from useful approximations to complex simulations.
Thermal Equivalent Circuits: A Starting Point for PCB Thermal Analysis Tools
The basis of PCB thermal analysis tools are equivalent thermal circuits. To state the obvious, most designers can better utilize their time by running sophisticated modeling software than resorting to pen and paper. In addition, the translation between a thermal system and an electrical is not 1:1. Still, there are merits: an equivalent thermal circuit can provide a quick estimation of the flow of heat in a design. It can strengthen the understanding of how and why particular features contribute to poor or excellent thermal management.
With these, some of the most fundamental electric circuit equations can be adapted to a thermal setting, such as Ohm’s Law. Individual elements, like resistors in parallel and series networks, also operate identically in summation. At the component level, temperature/thermal resistance is broken down into seven values of interest:
- Junction temperature, or the temperature at the transistor. The point of heat generation and therefore the highest temperature of a particular component.
- Resistance from junction to case.
- Case temperature.
- Resistance from the case to the heat sink.
- Heat sink temperature of a heat sink, which facilitates heat flow away from the component through various means (more thermally conductive materials, greater surface area, orientation to airflow/convection, etc.)
- Resistance from the heat sink to ambient.
- Ambient temperature that can loosely be considered a thermal ground in terms of potential difference.
Generalized thermal series resistance and temperature drops for components
Excluding high-speed traces or high-current copper pours, components are likely to be the primary heat generation for a board. However, the path out of the component is only half the battle when it comes to removing heat. It still must be transported away from the source, whether that’s by passive or active cooling methods to dissipate build-up. A proper thermal layout will accommodate this flow with a properly sized landing pad to accommodate a large heat flux. A good rule of thumb if space allows: set thermal pads to maximum dimensions in the bonding plane, use inner layer plane pours to maximize the conductive area for heat to spread, and use thermal vias to facilitate the heat transfer from landing pad to plane pours. The thickness of the copper plating will also play a role in its heat-sinking ability.
A Quick Treatment of Thermal Transfer Modes and Their Mathematics
Alternatively, thermal analysis can rely on computer modeling to provide a more accurate and quicker diagnosis of the thermal performance of a board. It’s imperative to understand that heat has three modes of transfer:
- Conduction, by which heat spreads throughout a body due to the vibration and collision of thermally-excited particles with nearby neighbors. The supporting mechanism can be elastic impacts in fluids, free electron diffusion in conductors, and phonon lattice vibration in insulators.
- Convection, which combines conduction with advection, or the transport of heat through bulk fluid flow. Generally the dominant heat transfer mechanism in fluids.
- Radiation thermally is a subset of electromagnetic radiation (further underscoring their relationship) that occurs when excited particles emit energy to return to a lower, more stable energy state.
Note that conduction alone does not cool a board, it simply distributes heat from higher to lower concentrated areas (assuming passive conduction). Convection and radiation are needed to remove heat from the board. A rough approach for conduction is outlined above in the equivalent thermal circuit section, but it is lacking, as it collapses a three-space problem in one dimension. The heat equation:
The heat equation tracks the independent curvature of temperature diffusivity for n-dimensions multiplied by the constant thermal diffusion for isotropic materials
T is temperature, t is time, α is the thermal diffusivity of the material, and ∇2 is the Laplacian operator, which looks at the temperature diffusion for each dimension in n-space (in this case, three). However, there are two general issues with this equation for real-world applications:
- Results become more meaningful if performed many times over short distances rather than fewer times over longer distances.
- The above equation only holds for isotropic materials or materials that do not exhibit a change in properties with directionality. Anisotropic materials require a more nuanced and generalized form.
Both these conditions mean solving by hand is a fool’s errand. A numerically rich and complex solution relies on finite element analysis (FEA) for both accuracy and completion time. Looking at the other forms of heat transfer, convection is far and away the most complex, as it deals with fluid mechanics, while radiation is computationally the least intensive. However, all three of these heat transfer modes are occurring simultaneously – a truly representative treatment needs to incorporate all three, which FEA can handle with aplomb.
How FEA, CFD, and Parallelization Propel Thermal Solutions
While simulation is the clear-cut answer to thermal analysis of any appreciable rigor, it is not without its drawbacks. Problems this computationally rich can push even cutting-edge systems to their limits. The best implementation utilizes parallel computing, which can be achieved in two manners:
- Subdivision of the calculations across multiple cores for multiprocessing.
- Utilizing multiple discrete computers to effectively function as a multiprocessor.
Allowing for a variety of multiprocessing setups, including cloud-based networking, increases flexibility and reduces technological barriers to rapid thermal analysis tools.
Complex fluid dynamics (CFD) equations are an entirely separate treatment of problems from FEA, but both can synergize to improve a thermal analysis simulation. Software solutions can capture the heat transfer coefficient of convection around the surface of a 3D board model to improve the conduction FEA in two and three dimensions.
Additionally, most thermal analysis tends to evaluate short-term as opposed to long-term, with the reasoning being a board that fails short-term doesn’t have the chance to fail long-term. Heat acts as an aging element for boards, however, and its successive effects built up over many thermal cycles or continuous usage will eventually contribute to material failure. Due to differing coefficients of thermal expansion (CTE) across materials, repeated expansions and contractions will ultimately change the stress-strain matrix of the populated board, leading to failure points of certain mechanical features like vias and solder fillets. Simulating the effects of thermal buildup/cycling over extended periods offers designers a chance to correct egregious mistakes before entering production.
Improve Board Performance and Reliability With Cadence Tools
PCB thermal analysis tools are a necessity for modern board functionality and reliability. Unlike some other forms of analysis, failure to incorporate thermal tools into a design may still result in a producible board that passes testing, but its outlook on reducing the effects of heat falls dramatically. The best thermal management solution is one that minimizes heat production while also optimizing heat away from its source and the board entirely.
Cadence offers thermal modeling tools and many more PCB Design and Analysis Software packages to effortlessly simulate complex problems before manufacturing. Alongside the powerful yet easy-to-use OrCAD PCB Designer, designers can lay out boards with confidence and the backing of industry-leading analysis features.
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