Dynamic Compact Thermal Models Research Articles

Dynamic compact thermal models for skin temperature prediction of portable electronic devices based on convolution and fitting methods

In most portable electronic devices, besides the temperature of multiple heat sources, i.e. junction temperature, the temperature of the enclosure, i.e. skin temperature, should also be controlled to protect the user experience. Thus, generating the device-level compact thermal model for predicting the skin temperature will not only improve the efficiency of early-stage thermal design but also help to develop the model-based temperature control strategy. However, most of the existing modeling methods mainly focus on predicting the junction temperature. In this paper, the dynamic compact thermal models of two portable electronic devices, including a smartphone and laptop, are first generated based on the convolution method. Under the assumption of linear time-invariant (LTI) systems, the skin temperature of the two test devices could be fast calculated once the step response of each heat source is obtained. The results show that compared to the computational fluid dynamics (CFD) model generated in ANSYS Icepak, the transient deviation of the convolution-based model is within 5%. Then, a linear fitting model is proposed to real-time predict the skin temperature of laptops. Both the experimental and simulation results demonstrate that once the scale factors are trained, the linear fitting model could accurately real-time predict the skin temperature after 60s. The maximum transient deviation in the experiment and simulation are 4% and 7% respectively. The results indicate that the proposed modeling method has tremendous potential for both thermal design and control optimization.

Thermal resistance-capacitance network model for fast simulation on the desiccant coated devices used for effective electronic cooling

Numerous novel devices have already utilized desiccant coating to implement various functions, such as atmospheric water harvesting, energy storage, and thermal/humidity management. The mathematical models employed in former literature, for instance the finite-element or finite-volume models usually suffer significant drawbacks such as extreme complexity and time-consuming. To solve this problem, this paper outlines a general strategy to develop dynamic compact thermal models of the quasi-one-dimensional sorption-based systems in the virtue of the thermal resistance-capacitance network. To be specific, the mass transfer process induced by the adsorption/desorption process is equivalent to a heat/cooling source, therefore the coupled heat and mass transfer kinetics in the corresponding device can be evaluated simultaneously. Two comprehensive experimental prototypes in our previous literature are employed to validate the effectiveness of the proposed model. The results show that our model can forecast the transient thermal behavior of the devices accurately within a few seconds. The dynamic deviation of the system output, for instance the material temperature and outlet air humidity, between simulation and experiment is within 7%. Furthermore, a parametric study is conducted based on the proposed model to analyze the influence of key parameters on system performance, showing great potential for guiding the system design and optimization.

Thermo-Fluidic Characterizations of Multi-Port Compact Thermal Model of Ball-Grid-Array Electronic Package

The concept of a single-input/multi-output thermal network was proposed by the Development of Libraries of Physical models for an Integrated design environment (DELPHI) consortium more than twenty years ago. The present work highlights the recent improvements made to efficiently derive a low-computing-effort model from a fully detailed numerical model and to characterize its performances. The temperature predictions of a deduced ball-grid-array (BGA) dynamic compact thermal model are compared to those of a realistic three-dimensional representation, including the large set of internal copper traces, as well as its board structure, which has been validated by experiment. The current study discloses a method for creating an amalgam reduced-order modal model (AROMM) for that electronic component family that allows the preservation of the geometry integrity and shortening scenarios computation. Typically, the AROMM method reduces by a factor of 600 the computation time needed to obtain the solution while keeping the error on the maximum temperature below 2%. Then, a meta-heuristic optimization is run to derive a more practical low-order resistor capacitor model that enables a thermo-fluidic analysis at the board level. Based on the calibrated numerical model, a novel AROMM method was investigated in order to address the chip behavior submitted to multiple heat sources. The first results highlight the capability to enforce a non-uniform power distribution on the upper surface of the silicon chip. Thus, the chip design layout can be analyzed and optimized to prevent thermal and reliability issues.

A Priori Error Bound for Moment Matching Approximants of Thermal Models

This article focuses on the moment matching methodology for deriving dynamic compact thermal models (DCTMs) of electronic components. For the first time, an a priori error bound is theoretically established both in the time and frequency domains, which is suited to accurately estimate the approximation error introduced by DCTMs in practical electronics applications. By exploiting this result, it is also shown that the near-optimal choice of matching points previously proposed by one of the authors minimizes the error bound here derived, among all the possible choices of matching points. The introduced error bound is verified by applying the moment matching algorithm to a state-of-the-art packaged InGaP/GaAs heterojunction bipolar transistor (HBT) used in output stages of power amplifiers for handset applications.

Extraction of Boundary Condition Independent Dynamic Compact Thermal Models of LEDs—A Delphi4LED Methodology

Multi-domain electro-thermal-optical models of LEDs are required so that their thermal and optical behavior may be predicted during a luminaire design process. Today, no standardized approach exists for the extraction of such models. Therefore, models are not readily provided by LED suppliers to end-users. This results in designers of LED-based luminaires wasting time on LED characterization and ad hoc model extraction themselves. The Delphi4LED project aims to address these deficiencies by identifying standardizable methodologies to extract both electro-optical and thermal compact models of LEDs that together can be used in a multi-domain simulation context. This article describes a methodology to extract compact thermal models of LEDs that are dynamic, in that they accommodate transient thermal effects, and are boundary condition-independent, in that their accuracy is independent of their thermal operating environment. Such models are achieved by first proposing an equivalent thermal nodal network topology. The thermal resistances and capacitances of that network are identified by means of optimization so that the transient thermal response of the network matches that of either an equivalent calibrated 3D thermal model or a transient thermal measurement of a physical sample. The accuracy of the thermal network is then verified by comparing the thermal compact model with a 3D detailed model, which predicts thermal responses within a 3D system-level model.

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.

Thermal model of the IGBT module

In the paper the dynamic compact thermal model of the IGBT module is proposed. This model makes it possible to calculate internal temperatures of diodes and transistors included in the considered IGBT module with selfheating in each device and mutual thermal couplings between them taken into account. The form of this model and the method of estimation of its selected parameters are described. Some results of measurements and calculations illustrating the usefulness of this model are shown and discussed.

Partition-based approach to parametric dynamic compact thermal modeling

This paper presents three procedures for the extraction of parametric Dynamic Compact Thermal Models (DCTMs) with controlled and user-chosen accuracy, namely, (i) a DCTM with dense matrices obtained by a direct conventional method, (ii) a partition-based approach leading to a sparse DCTM suited for heat conduction problems suffering from a massive number of independent heat sources and/or parameters, for which extracting conventional dense DCTMs may be too resource-demanding or even unviable, and (iii) a novel algorithm that quickly translates a sparse DCTM into a dense one, which allows reducing the simulation time. The proposed methodologies are validated through the application to two state-of-the-art electronics systems.

3-D thermal models calibration by parametric dynamic compact thermal models

Detailed 3-D thermal models of electronic systems require the calibration of unknown parameters to accurately describe the experimental data, which is usually obtained by a least square optimization of the measured transient thermal response to a given set of power inputs. This paper presents an extremely efficient technique to perform the identification of boundary conditions, material thermal properties, and geometrical sizes, which is based on the adoption of the trust region algorithm in combination with parametric dynamic compact thermal models. The calibration of parameters of a Package-on-Package system is performed by a simulated experiment procedure to validate the applicability and accuracy of the proposed approach. It is shown that using parametric compact models allows for a significant reduction in computational effort in comparison to conventional brute-force optimization. The calibration robustness with respect to input degradation is examined by observing the variation in the extracted parameters at different levels of noise.

On-Line Junction Temperature Monitoring of Switching Devices with Dynamic Compact Thermal Models Extracted with Model Order Reduction

Residual lifetime estimation has gained a key point among the techniques that improve the reliability and the efficiency of power converters. The main cause of failures are the junction temperature cycles exhibited by switching devices during their normal operation; therefore, reliable power converter lifetime estimation requires the knowledge of the junction temperature time profile. Since on-line dynamic temperature measurements are extremely difficult, in this work an innovative real-time monitoring strategy is proposed, which is capable of estimating the junction temperature profile from the measurement of the dissipated powers through an accurate and compact thermal model of the whole power module. The equations of this model can be easily implemented inside a FPGA, exploiting the control architecture already present in modern power converters. Experimental results on an IGBT power module demonstrate the reliability of the proposed method.

Fast Nonlinear Dynamic Compact Thermal Modeling With Multiple Heat Sources in Ultra-Thin Chip Stacking Technology

This paper presents a model-order reduction technique to extract nonlinear dynamic compact thermal models (DCTMs) with multiple (>1) heat sources. The approach leads to nonlinear DCTMs of small state-space dimensions that allow accurately reconstructing the whole temperature and heat flux fields induced by arbitrary power waveforms in complex structures composed of many materials with thermal conductivities showing different values and temperature dependences. The DCTM extraction requires a small fraction of the CPU time needed for the simulation of a power step response using the finite element method (FEM), while ensuring a very high level of precision. Therefore, the adoption of the proposed strategy is a viable alternative to FEM for performing efficient and accurate nonlinear transient analyses: The advantage of using a DCTM is magnified if many power input waveforms have to be considered for the same structure since any further simulation of the extracted DCTM is nearly instantaneous. As a case study, the proposed technique is used to investigate the impact of two cooling solutions on the thermal behavior of a three-die module in ultra-thin chip stacking technology.

Structure-preserving approach to multi-port dynamic compact models of nonlinear heat conduction

A novel approach for constructing multi-port dynamic compact thermal models of nonlinear heat diffusion in electronic components is presented, extending a technique previously conceived for the one-port case. The approach allows achieving high levels of accuracy even for small state–space dimensions of the model. It is also very efficient since it requires the solutions to a few linear heat diffusion problems in the frequency domain. The multi-port compact models exhibit structure similar to the one-port counterparts and can be used to accurately approximate not only the junction temperatures, but also the whole space–time temperature distribution within the electronic components.

Thermal Characteristics Analysis of Die Attach Layer Based on Time-Constant Spectrum for High-Power LED

The performance and reliability of the high-power light-emitting diodes (HP LEDs) are closely related to the quality of the die attach adhesive (DAA) layer, because voids or delaminations in the layer may cause higher junction temperature, and even result in the break of the chip. In this paper, a dynamic compact thermal model is constructed for an independent HP LED without being attached on a cold plate. The time-constant spectrum method based on the thermal model is applied to characterize the transient thermal behavior of the DAA layer and other layers along the heat flow path. Thermal transient experiments are carried on HP LED samples with different DAA dosages. The theoretical and experimental results demonstrate that the time-constant spectrum for LEDs tested without cold plate can reflect the thermal characteristics of the DAA layer as well as that with cold plate. Differences in the HP LED samples with different DAA layers can be obviously distinguished in the time-constant spectrums as well. Compared with the traditional testing method with cold plate, direct test in air for HP LEDs has the advantages of easy operation, time saving, and no pollution to samples.

Dynamic compact thermal model of high power light emitting diode

Dynamic compact thermal model plays important roles in predicting the junction temperature and characterizing the transient thermal behavior of an electronic device. In this paper, analytical dynamic compact thermal model for high power LEDs is established based on the three-directional heat flow paths under junction-to-ambient definition. Comparative results with finite element method model indicate that the presented model is accurate and efficient. It is further reduced by analyzing the influence of different components of the LED package. Good agreement with experimental results confirms that the reduced analytical model can predict the junction temperature and characterize the thermal behavior effectively.

Nonlinear dynamic compact thermal models by structure-preserving projection

A novel projection-based approach is proposed for constructing compact models of nonlinear heat diffusion problems for electronic components. The method is robust since it preserves the non-linear structure of the heat diffusion equations. It is efficient, since it is constructed by determining few moments of Volterra׳s series expansions of the solution. It leads to compact models of small state-space dimensions which can be numerically solved at negligible computational cost and to accurate approximations of the whole space-time distribution of temperature rises for all significant waveforms of the injected powers.

A dynamic compact thermal model for data center analysis and control using the zonal method and artificial neural networks

Full-scale data center thermal modeling and optimization using computational fluid dynamics (CFD) is generally an extremely time-consuming process. This paper presents the development of a velocity propagation method (VPM) based dynamic compact zonal model to efficiently describe the airflow and temperature patterns in a data center with a contained cold aisle. Results from the zonal model are compared to those from full CFD simulations of the same configuration. A primary objective of developing the compact model is real-time predictive capability for control and optimization of operating conditions for energy utilization. A scheme is proposed that integrates zonal model results for temperature and air flow rates with a proportional–integral–derivative (PID) controller to predict and control rack inlet temperature more precisely. The approach also uses an Artificial Neural Network (ANN) in combination with a Genetic Algorithm (GA) optimization procedure. The results show that the combined approach, built on the VPM based zonal model, can yield an effective real-time design and control tool for energy efficient thermal management in data centers.

Innovative methodology to extract dynamic compact thermal models: Application to power devices

This paper presents a new and innovative methodology for power components manufacturers to generate accurate boundary condition independent dynamic Compact Thermal Models (“BCI” DCTMs). The originality of this methodology is summarized by taking into account the thermal behavior of electronic components containing several cooling surfaces, and representing the non-linear properties of materials, while keeping a simple and recurring structure of generated models. Moreover, the proposed method makes it possible to obtain DCTMs with a limited number of measurements or 3D thermal simulations. The methodology to construct the DCTM is based on the construction of an equivalent thermal RC network. The precision of the RC thermal network is improved using variable resistances and capacitances related to the heat fluxes so that the compact model can adapt automatically with boundary conditions.

Creation and verification of dynamic compact thermal model of a BGA package

PurposeThe purpose of this paper is to develop a dynamic compact thermal model (DCTM) of electronic packages. This model is a necessary tool for rapid thermal analysis of the systems which we exposed to boundary condition variation and/or power switching mode such as mobile systems and battery powered systems.Design/methodology/approachThe methodology of compact model generation used was based on generating the transient dynamic detailed finite element thermal model of a package, designing a resistor/capacitor network topology representative of the dynamic detailed model, calculating the resistors'/capacitors' value by optimization method and validation efforts. The method is demonstrated for a ball grid array (BGA) package, a commonly used modern electronic package.FindingsBased on the obtained results, it can be concluded that the dynamic thermal behavior of a BGA package can be accurately described by a generated dynamic compact model in terms of predicted junction temperature response and heat flux of the desired locations of the package.Originality/valueThis model is capable of calculating the temperatures and heat fluxes at desired locations which can help the designer to perform the thermal analysis much faster and easier with the required accuracy.

A methodology to extract dynamic compact thermal models under time-varying boundary conditions: application to a thermopile based IR sensor

This paper presents the extraction of a boundary independent dynamic compact thermal model (DCTM). The paper specifically focuses on time-varying Dirichlet boundary conditions influence and the methodology proposed to obtain the DCTM is applied to a thermopile based infrared (IR) sensor. These type of sensors are quite sensitive to environment changes because a variation in the sensor bulk silicon temperature usually generates a different temperature influence in the hot and cold areas that can produce incorrect transient measurements of the incident IR radiation. A DCTM can be used to estimate the influence of the environmental temperature evolution in the sensor output and with the help of a temperature sensor correct the measurement of the IR incident radiation in the real device. The methodology to construct the DCTM is based in the construction of an equivalent thermal RC network, the topology of which, as well as its component values, are obtained from the analysis of the dynamic power-temperature relationship on the points of interest.