Boundary Condition Independent Research Articles

Boundary Condition Independent Thermal Network Modeling of High-Frequency Power Transformers

With increasing global power demands and the trend of miniaturization of power converters, electronic components are being pushed toward their thermal limits. This has accentuated the need for accurate and low-cost thermal models of electronic components. Lumped Parameter Thermal Network Modeling (LPTNM) is commonly used to evaluate the thermal performance of electronic components, but unlike semiconductors, transformer LPTNM is not standardized in the academic community. Due to this lack of standardization, most proposed transformer thermal models have not been evaluated for Boundary Condition Independence (BCI). This study presents a BCI thermal modeling approach for power transformers based on LPTNM. A thermal network model is developed by discretizing the transformer geometry into smaller volumes and evaluating the thermal resistances by approximating the three-dimensional heat transfer problem as a piecewise one-dimensional model. The network model/geometry discretization is iteratively improved for a set of different boundary conditions, resulting in a BCI model. The modeling approach is experimentally and numerically validated on a PQ40/30 transformer operating in a 3.3 kW switch mode power supply. The BCI transformer thermal model closely matches both numerical and experimental results with a fraction of the computational cost of the numerical model. The proposed BCI modeling approach provides a low-cost alternative to detailed thermal models and can predict transformer thermal performance for varied applications.

Galerkin’s Projection Framework for BCI CTMs—Part I: Extended FANTASTIC Approach

A general Galerkin’s projection framework is proposed for the definition of boundary condition independent (BCI) compact thermal models (CTMs). First, it is shown how the proposals of BCI CTMs, deriving from the works of Bar-Cohen and Sabry, can be straightforwardly reinterpreted within this framework. Then, following such reinterpretation, the approach due to Lasance, nowadays widely adopted for the extraction of BCI CTMs, is generalized into a novel approach, based on the extension of the previous FAst Novel Thermal Analysis Simulation Tool for Integrated Circuits (FANTASTIC) method, from the fixed boundary conditions case to the BCI case. Such an approach allows widely enlarging the set of boundary conditions for which a BCI CTM ensures accuracy and allows overcoming the main limitations of previous approaches, e.g., with multisource problems and dynamic models.

Multi-port dynamic compact thermal models of dual-chip package using model order reduction and metaheuristic optimization

Delphi-like boundary condition independent (BCI) compact thermal models (CTMs) are the standard for modelling single die packages. However their extraction, particularly in the transient case, will be time consuming due to complex numerical simulations for a large number of external conditions. Lately, new approaches to extract a BCI dynamical CTM (DCTM), based on model order reduction (MOR) were developed. Despite the numerous advantages of this recent method, the lack of numerical tools to integrate reduced-order models (ROM) makes it difficult to use at board level. In this study, a novel process flow for extracting Delphi-inspired BCI DCTMs is proposed. Thus a detailed three-dimensional model is replaced by a BCI-ROM model using FANTASTIC matrix reduction code to generate the data used in the creation of a Delphi-style BCI DCTM. That hybrid reduction method has been applied, at first on a single-chip package (QFN16) then on a dual-chip package (DFN12). Their derived CTM and DCTM have been compared in term of accuracy and creation time using, or not, MOR reduction technique. The results show that for a similar accuracy, the integration of MOR technique allows minimizing the time-consuming numerical simulations and consequently reduce the thermal network creation time by 80%.

Versatile MOR-based boundary condition independent compact thermal models with multiple heat sources

This paper shows that the connection of MOR-based boundary condition independent (BCI) dynamic compact thermal models (DCTMs) and detailed models of heat transfer problems is not straightforward and is subject to numerical issues. In order to overcome this drawback, a novel definition of MOR-based BCI DCTMs is provided, which makes this connection feasible. As a result, the proposed BCI DCTMs can be connected without limitations to any detailed model of heat transfer problems and/or to any other MOR-based BCI DCTM.

Boundary-Condition-Independent Reduced-Order Modeling of Complex Electronic Packages by POD-Galerkin Methodology

The objective of the current work is to introduce the concept of boundary-condition-independent (BCI) reduced-order modeling (ROM) for complex electronic packages by employing the proper orthogonal decomposition (POD)-Galerkin methodology. Detailed models of complex electronic packages that consume large computational resources are used within system-level models in computational fluid dynamics (CFD)-based heat transfer analysis. If a package-level model that reduces computational resources (reduced-order model) and provides accurate results in many different flow situations (boundary-condition-independent model) can be deployed, it will accelerate the design and analysis of the end products that make use of these packages. This paper focuses on how the proper orthogonal decomposition-Galerkin methodology can be used with the finite volume method (FVM) to generate reduced-order models that are boundary-condition-independent. This method is successfully used in the present study to generate boundary-condition-independent reduced-order models for 1-D and 2-D objects for isothermal and isoflux boundary conditions. Successful implementation of the method is also shown on 2-D objects made of multiple materials and multiple heat generating sources for isoflux boundary conditions.

Parameterized physical compact thermal modeling

This paper presents a compact thermal modeling (CTM) approach, which is fully parameterized according to design geometries and material physical properties. While most compact modeling approaches facilitate thermal characterization of existing package designs, our method is better suited for preliminary exploration of the design space at both the silicon level and the package level. We show that our modeling method achieves reasonable boundary condition independence (BCI) by comparing a CTM example with a BCI model for a benchmark ball grid array single-chip package under the same standard set of boundary conditions. In essence, the presented CTM method can act as a convenient medium for enhanced interactions and collaborations among designers at the package, circuit and computer architecture levels, leading to efficient early evaluations of different thermally-related design trade-offs at all the above levels of abstraction before the actual detailed design is available. The presented modeling method can be easily extended to model emerging packaging schemes such as stacked chip-scale packaging and three-dimensional integration.

Thermal Transient Modeling and Experimental Validation in the European Project PROFIT

A major objective of the European project PROFIT is to generate boundary condition independent (BCI) dynamic compact thermal models (DCTM) of semiconductor products. Extending the methods for steady BCI-CTM developed in preceding projects DELPHI and SEED to the transient domain, a detailed numerical model of the component is needed, which is validated against four dual cold plate (DCP) experiments extracting heat along the main heat flow paths from a package. The validated detailed model is then used for numerical experiments in many environments represented by external BC. Results are used to optimize resistors and capacitors of a small network forming the DCTM. This work is focused on the first part of developing validated detailed dynamic models by comparison of modeling and measurements. Results of the European project PROFIT on thermal transient measurement and modeling of integrated circuit packages are presented. All together sixteen different packages from the three Semiconductor Manufacturers Infineon, Philips, and ST Microelectronics were measured in four DCP environments as defined in the preceding DELPHI and SEED projects. Solutions to measure TO-type and fine pitch packages in the DCP, especially for the critical DCP-4 boundary condition were demonstrated, as well as reduction of interface resistance and increased reproducibility by using Wood's alloy as an interface material. The measurements were simulated using the commercial software packages ANSYS, FLOTHERM, or MARC. The agreement between simulated and measured thermal impedance is 15% or better from steady state (t=1000 s) to transients with t>0.1, i.e., four orders of magnitude. In a few cases, this level of accuracy was kept even over seven orders of magnitude. Increasing relative inaccuracy with shorter transients corresponds to small absolute errors in temperature. So practical pulse temperature prediction will usually be correct within a few degrees. Extraction of geometrical and material parameters will need further improvement.

Boundary-condition independence of catalysis of proton decay by monopoles

Owing to a remarkable property of the standard model, a derivation of proton-decay catalysis by monopoles can be given which is independent of the structure of the monopole core. The result is valid for one generation of fermions interacting with an eg = (1/2) monopole in the limit of unbroken weak interactions. It is a consequence of the fact that unification-induced and anomaly-induced proton decay are indistinguishable in this limit. An argument is given why this should still be true for broken weak interactions. An example with baryon-number violation due to the anomaly alone is discussed in detail and is compared with the SU(5) case. In the bosonized versions of these models the B-violating process appears in a different way, but leads to the same final states.