Electrical-thermal Co-simulation Research Articles

How Does Ambient Temperature Fluctuation Influence the Short-Term Frequency Stability of OCXO?

Short-term frequency stability (STFS) is one of the most important specification of oven-controlled crystal oscillators (OCXOs). Although numerous studies have investigated factors that influence STFS, research on the impact of ambient temperature fluctuation is rare. This work investigates the relationship between the ambient temperature fluctuation and the STFS by introducing a model of the OCXO's short-term frequency-temperature characteristic (STFTC), which considers the transient thermal response of the quartz resonator, the thermal structure, and the oven control system. According to the model, an electrical-thermal co-simulation is adopted to determine the temperature rejection ratio of the oven control system and estimates the phase noise and Allan deviation (ADEV) that caused by fluctuations in ambient temperature. As a verification, a 10-MHz single-oven oscillator is designed. From the measured results, the estimated phase noise near the carrier agrees well with the measured results, and it can be seen that only when the temperature fluctuation is less than 10 mK at 1-100 s, the oscillator can maintain the characteristics of flicker frequency noise at the offset frequency from 10 mHz to 1 Hz, and the ADEV is possible to reach at the order of E -13 in 100 s. Thus, the model proposed in this study effectively predicts the impact of ambient temperature fluctuation on the STFS of an OCXO.

DC IR-Drop Analysis of Multilayered Power Distribution Network by Discontinuous Galerkin Method With Thermal Effects Incorporated

Due to the temperature-dependent resistivity of power distribution network (PDN) interconnects, a wiser and necessary strategy is to proceed the electrical–thermal cosimulation in order to include the thermal effects caused by Joule heating. As a natural domain decomposition method (DDM), in this article, a discontinuous Galerkin (DG) method is proposed to facilitate the steady-state electrical and thermal coanalysis. With the intention to avoid solving a globally coupled steady-state matrix system equations resulted from the implicit numerical flux in DG, the block Thomas method is deployed to solve the entire domain in a subdomain-by-subdomain scheme. As a direct solver, the block Thomas method is free of convergence problem frequently occurring in iterative methods, such as block Gauss–Seidel method. The capability of the proposed DG method in handling multiscale and complex 3-D PDNs is validated by several representative examples.

Electrical–Thermal Cosimulation of Coaxial TSVs With Temperature-Dependent MOS Effect Using Equivalent Circuit Models

A coupled electrical–thermal cosimulation with consideration of the temperature dependence of the metal-oxide-semiconductor (MOS) effect is performed for coaxial through silicon vias (C-TSVs) by using equivalent electrical and thermal circuit models. In the equivalent electrical circuit (EEC) model, the dependence of the MOS capacitance on bias voltage, operation frequency, oxide charge density, and temperature is studied, and further verified by measurement results from a previous publication. A 3-D equivalent thermal circuit (ETC) model with lump components, including thermal resistance and thermal capacitance analytically calculated from the geometry and material parameters of C-TSVs, is proposed for transient thermal simulation. The accuracy of the EEC and ETC models is verified by comparisons with full-wave simulations. Transient electrical–thermal co-simulation is performed for the C-TSVs with the EEC and ETC models. Results reveal that the temperature dependence of depletion width and corresponding MOS capacitance leads to considerable variations in the S-parameters of C-TSVs.

Accurate and Fast Thermal Analysis of Multistage Depressed Collectors for Traveling-Wave Tubes Using Finite-Element Method

This article presents an accurate and fast thermal analysis method for multistage depressed collectors (MDCs) of traveling-wave tubes using the finite-element method (FEM). In this method, a novel approach named an advanced multigrid nonlinear solver is proposed to significantly reduce the computing cost of thermal analysis of MDCs. Based on this method, a 3-D thermal design tool for MDCs called a thermal simulator (TS) is developed. By modeling the thermal behavior of various MDCs, the TS is validated, and it is found that the TS is much more efficient than the widely used commercial FEM codes, i.e., ANSYS and CST MPS. Moreover, the TS is accurately and seamlessly coupled with our previously developed electron trajectory code. Consequently, by utilizing the TS, the automated electrical–thermal cosimulation of MDCs is realized accurately and efficiently, which would be very useful for the design of high-performance MDCs.

Cadence Launches Celsius Thermal Solver

Company Unveils First Complete Electrical-Thermal Co-Simulation Solution for Use Across Electronic Systems.

Matrix-Free Method for Transient Maxwell-Thermal Cosimulation in Arbitrary Unstructured Meshes

Existing electrical–thermal cosimulation methods require solving a system matrix when handling inhomogeneous materials and irregular geometries discretized into unstructured meshes. In this paper, a matrix-free method is developed for cosimulating full-wave Maxwell’s equations and the thermal diffusion equation in the time domain. The method is free of matrix solutions regardless of the shape of the element used for space discretization. A theoretical stability analysis is also developed for the coupled electrical and thermal analysis, which is nonlinear in nature. Numerical experiments on both unstructured tetrahedral and triangular prism element meshes have validated the accuracy and efficiency of the proposed method.

Electrical-Thermal Co-Simulation for Analysis of High-Power RF/Microwave Components

An electrical-thermal co-simulation based on the finite element method is presented for analysis of high-power RF/microwave circuits. The co-simulation integrates a full-wave electromagnetic analysis and a transient thermal analysis through an iterative scheme, and is devised for the design and analysis of RF/microwave circuits operated at high frequencies and high power levels. To enhance the efficiency in solving large-scale problems, a domain decomposition scheme called the finite element tearing and interconnecting and an adaptive time-stepping scheme based on the algorithm of proportional-integral-derivative control are incorporated into the co-simulation. Temperature stability analysis is performed with the proposed co-simulation for a matching network in high-power RF amplifiers and for a substrate integrated waveguide filter.

Transient Electrical-Thermal Analysis of 3-D Power Distribution Network With FETI-Enabled Parallel Computing

In this paper, the transient electrical-thermal co-simulation is implemented with the finite-element method. The capability of the co-simulation is extended to solve large-scale problems by incorporating a domain decomposition scheme called the finite element tearing and interconnecting (FETI). With the high parallel efficiency of FETI for computing with multiple processors, a significant reduction in computation time is achieved. The transient electrical-thermal behaviors of largescale power distribution networks (PDNs), including on-chip power grids, solder bump arrays, and TSV-based PDN are simulated and analyzed with the proposed method. The impacts on the design of the PDNs from different types of input pulses, power maps, and via pitches are also investigated.

Thermal-Aware High-Frequency Characterization of Large-Scale Through-Silicon-Via Structures

The 3-D integration exacerbates the thermal issues over a single die due to the high-power density and poor thermal conductivity of the adhesive layers in between the stackedup dies. In this paper, an electrical-thermal co-simulation is developed to consider the thermal influence and accurately predict the electrical behaviors of the through-silicon-via (TSV) structures. The co-simulation is implemented with the finite element method (FEM) for its capabilities in modeling complex geometries and materials. A highly efficient domain decomposition scheme is introduced into the co-simulation to deal with large-scale massively coupled TSV structures. The domain decomposition scheme enables simulation with multiple processors in parallel and achieves significant reduction in computation time. Various design parameters in typical TSV structures, such as the TSV array in the silicon interposer and the TSV daisy chains are investigated with the proposed co-simulation.

Electrical–Thermal Cosimulation With Nonconformal Domain Decomposition Method for Multiscale 3-D Integrated Systems

Because of the multiple scales in 3-D integrated systems, numerical simulation methods that are able to handle multiscale problems efficiently are strongly required. In this paper, electrical-thermal cosimulation of multiscale integrated systems using Mortar finite element-based domain decomposition method is proposed. Using the nonconformal domain decomposition approach, integrated systems can be divided into separate subdomains. Individual subdomains can be discretized independently based on its detailed feature size and formulated using the finite element method with associated boundary conditions. The coupling between domains is captured using Lagrange multipliers. For large multiscale 3-D problems, the cascadic multigrid method combined with the subspace confined preconditioned conjugate gradient method is used to accelerate the convergence of the solution with hierarchical meshing grids. Several examples are simulated and the results validate the accuracy and efficiency of the electrical-thermal cosimulation using nonconformal domain decomposition.

Electrical-Thermal Co-Simulation for DC IR-Drop Analysis of Large-Scale Power Delivery

For accurate DC IR-drop analysis of integrated circuits, electrical-thermal co-simulation is necessary to consider the effect of Joule heating. A suitable numerical method for this co-simulation is the finite element method (FEM) because of its capabilities in modeling complex geometries and materials. To deal with large-scale problems, a domain decomposition scheme is applied to the FEM to enable simulation with multiple processors in parallel and achieve significant reduction in computation time.

Electrical-Thermal Co-Simulation of 3D Integrated Systems With Micro-Fluidic Cooling and Joule Heating Effects

In this paper, the electrical-thermal co-simulation of 3D systems with Joule heating, fluidic cooling and air convection effects is proposed. The finite-volume method formulations of voltage distribution equation, heat equations for both fluid flow and solid medium with nonuniform mesh are explained in detail. Based on the proposed iterative co-simulation method, package temperature distribution and voltage drop with Joule heating and fluidic cooling effects can be estimated. Several packaging examples are simulated and the results show that with micro-channel fluidic cooling in high power density 3D integrated packages, the thermal effect on voltage drop is reduced by 10% which is much less than that of using a traditional heat sink.