Reply: Electro-thermal device and circuit simulation with thermal nonlinearity due to temperature dependent diffusivity

Batty, W.; David, S.; Snowden, C.M.

doi:10.1049/el:20010992

Cited by 9 publications

(9 citation statements)

References 2 publications

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Section: Thermal Non Linearitymentioning

confidence: 99%

“…Approximating the Laplacian by its conventional rectangular Cartesian form, the time-dependent heat diffusion equation becomes finally (5) The fully linearized equation, (5), can now be solved exactly with general linear boundary conditions, and this approximate linearization should be good for the moderate temperature dependences occurring in semiconductor systems [51], [52]. (Stronger non linearities can be treated, less compactly, within the fully analytical thermal resistance matrix approach by the equivalent linearization, [52].) To illustrate the significance of the time variable transformation, (4), for electrothermal response [50], an analytical thermal impedance matrix is constructed to describe the response to step power input of 0.4 W, over a central square , at the surface of a cubic GaAs die, side m. Such a configuration is illustrative of, for example, a multifinger power FET.…”

Section: Thermal Non Linearitymentioning

confidence: 99%

“…Generation of such solutions requires treatment of thermal non linearity inherent in temperature dependent material parameters. An original treatment of this non linearity, for device and circuit level electrothermal CAD, is presented first [50]- [52]. This is followed by derivation of thermal impedance matrix solutions for a homogeneous MMIC, and for an -level rectangular multilayer.…”

Section: Introductionmentioning

confidence: 99%

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Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems

Batty

Christoffersen

Panks

et al. 2001

IEEE Trans. Comp. Packag. Technol.

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An original, fully analytical, spectral domain decomposition approach is presented for the time-dependent thermal modeling of complex non linear three-dimensional (3-D) electronic systems, from metallized power FETs and MMICs, through MCMs, up to circuit board level. This solution method offers a powerful alternative to conventional numerical thermal simulation techniques, and is constructed to be compatible with explicitly coupled electrothermal device and circuit simulation on CAD timescales. In contrast to semianalytical, frequency space, Fourier solutions involving DFT-FFT, the method presented here is based on explicit, fully analytical, double Fourier series expressions for thermal subsystem solutions in Laplace transform-space (complex frequency space). It is presented in the form of analytically exact thermal impedance matrix expressions for thermal subsystems. These include double Fourier series solutions for rectangular multilayers, which are an order of magnitude faster to evaluate than existing semi-analytical Fourier solutions based on DFT-FFT. They also include double Fourier series solutions for the case of arbitrarily distributed volume heat sources and sinks, constructed without the use of Green's function techniques, and for rectangular volumes with prescribed fluxes on all faces, removing the adiabatic sidewall boundary condition. This combination allows treatment of arbitrarily inhomogeneous complex geometries, and provides a description of thermal material non linearities as well as inclusion of position varying and non linear surface fluxes. It provides a fully physical, and near exact, generalized multiport network parameter description of non linear, distributed thermal subsystems, in both the time and frequency domains. In contrast to existing circuit level approaches, it requires no explicit lumped element, RC-network approximation or nodal reduction, for fully coupled, electrothermal CAD. This thermal impedance matrix approach immediately gives rise to

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Section: Thermal Non Linearitymentioning

confidence: 99%

Section: Thermal Non Linearitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems

Batty

Christoffersen

Panks

et al. 2001

IEEE Trans. Comp. Packag. Technol.

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“…This compact model is obtained through fully analytic solution of the heat diffusion equation in complex structures, based on domain decomposition into regular subvolumes. The nonlinear heat diffusion equation is converted into a fully linear equation by appropriate transformations of variable [15]- [17]. Analytic series solutions for thermal subsystems are accelerated for rapid precomputation prior to coupled electrothermal co-simulation [18].…”

Section: Thermal Impedance Matrix Modelmentioning

confidence: 99%

“…Under successive Kirchhoff transformation of temperature, T → θ, and transformation of time, t → τ [15]- [17], the nonlinear, 3-dimensional heat diffusion equation,…”

Section: Thermal Impedance Matrix Modelmentioning

confidence: 99%

Global coupled EM-electrical-thermal simulation and experimental validation for a spatial power combining MMIC array

Batty

Christoffersen

Yakovlev

et al.

2002 IEEE MTT-S International Microwave Symposium Digest (Cat. No.02CH37278)

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A unique electromagnetic-electro-thermal global simulation tool based on a universal error concept is presented. The advantages of this electro-thermal model are illustrated by comparison with a commercial electro-thermal circuit simulator. The first description of a fully physical, electro-thermal, microwave circuit simulation, based on coupling of the Leeds Physical Model of MESFETs and HEMTs, to a microwave circuit simulator, fREEDA T M (NCSU), is presented. The modeling effort is supported by parallel developments in electrooptic and thermal measurement. The first fully coupled EM-electro-thermal global simulation of a large microwave subsystem, here a whole spatial power combining MMIC array, is described. The simulation is partially validated by measurements of MMIC array temperature rise, and temperature dependent S-parameters. Electrothermal issues for spatial power combiner operation and modeling are discussed. The CAD tools and experimental characterization described, provide a unique capability for the design of quasi-optical systems and for the exploration of the fundamental physics of spatial power combining devices.

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Notes on using temperature-dependent thermal diffusivity—forgotten rules

Gróf

2018

J Therm Anal Calorim

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Reply: Electro-thermal device and circuit simulation with thermal nonlinearity due to temperature dependent diffusivity

Cited by 9 publications

References 2 publications

Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems

Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems

Global coupled EM-electrical-thermal simulation and experimental validation for a spatial power combining MMIC array

Notes on using temperature-dependent thermal diffusivity—forgotten rules

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