Circuit analysis of electromagnetic radiation and field couplingeffects for networks with embedded full-wave modules

With continually increasing operating frequencies, the analysis of electromagnetic interference (EMI)-related effects is becoming an important issue for high-speed designs. An algorithm is presented for fast analysis of radiation and incident field coupling effects in high-speed circuits. The proposed technique provides an efficient means for combining the solutions from full-wave field solvers such as the finite-difference time-domain (FDTD) method with circuit level simulators such as SPICE for calculating radiated/coupled fields in arbitrarily shaped interconnect structures. The technique speeds up the whole simulation process by employing a model-reduction-based approach, and also overcomes the numerical stability problems associated with the FDTD, in the presence of nonlinear terminations. In addition, the proposed algorithm provides a direct access to existing vast device libraries of SPICE in EMI analysis     

Analysis of power delivery network constructed by irregular-shaped power/ground plane including densely populated via-hole

The high speed and low power trend has imposed more and more importance on the design of the power distribution network (PDN) using multilayer printed circuit boards (PCBs) for modern microelectronic packages. This paper presents a fast and efficient analysis methodology in frequency domain for the design of a PDN with a power/ground plane pair, which considers the effect of irregular shape of the power/ground plane and densely populated via-holes. The presented method uses parallel-plate transmission line theory with equivalent circuit model of unit-cell grid considering three-dimensional geometric boundary conditions. Characteristics of PDNs implemented by perforated planes including a densely populated via-hole structure is quantitatively determined based on full-wave analysis using the finite-difference time-domain (FDTD) periodic structure modeling method and full-wave electromagnetic field solver. Using a circuit simulator such as popularly used SPICE and equivalent circuit models for via-hole structure and perforations, the authors have analyzed input-impedance of the power/ground plane pair. Since the presented method gives an accurate and fast solution, it is very useful for an early design of multilayer PCBs.     

Modeling of irregular shaped power distribution planes usingtransmission matrix method

A major problem in power distribution networks is simultaneous switching noise (SSN), which causes several signal integrity issues. To understand the behavior of the power distribution system (PDS) and its contribution to SSN, noise prediction methods are necessary. This paper presents a method for analyzing arbitrary shaped power distribution networks both in the frequency and time domain. Using a two dimensional array of distributed RLCG circuits, the impedance of a power/ground plane pair is computed. For the efficient computation of the power distribution impedances at specific points in the network, a multi-input and multi-output transmission matrix method has been used. To verify the accuracy of this method, the simulation results have been compared with Spice which uses a circuit based approach and an analytical solution based on the cavity modes in the structure. The simulation results have also been compared with measurements for an L-shaped structure. The transmission matrix method has been applied to a split plane and an arbitrary shaped power plane to demonstrate the application of this technique to irregular geometries     

Efficient 2-D Integral Equation Approach for the Analysis of Power Bus Structures With Arbitrary Shape

A 2-D contour integral-equation method for the frequency-domain analysis of arbitrarily shaped power bus structures is presented. The numerically efficient approach allows the rapid and accurate computation of the frequency-dependent transfer parameters between an arbitrary number of ports, as required for embedding the power plane structure into network simulation. A formulation is developed for calculating the voltage distribution between the planes, as well as for determining the resulting radiated fields based on the field-equivalence principle. The method is applied for several test boards including a populated board with a surface-mount decoupling-capacitor network. The suggested approach is well confirmed by an analytical solution for the rectangular structure, by measurement and 3-D full-wave simulation results.      

An Efficient Power-Delivery Method for the Design of the Power Distribution Networks for High-Speed Digital Systems

In this paper, a new power distribution network (PDN) design method from a power delivery viewpoint is proposed. Two new parameters, the power delivery delay and the $Delta V$ time constant, are introduced to characterize the effects of the lead inductors and decoupling capacitors on the timely power delivery respectively for a high-speed PDN. The decoupling time of a PDN is accurately estimated from the power delivery delay introduced by the inductance of the discontinuities, the charge delivery speed, and the charge supply capacity of the decoupling capacitors are accurately characterized by the $Delta V$ time constant. Based on the two parameters, a complete and systematic power-delivery method for the design of a PDN is developed. The proposed design method is verified by SPICE, full-wave simulations, and measurements. For completion, some specific design considerations are also discussed in detail.      

Spice simulation of laser diode modules

For simulating laser diode modules, a subcircuit has been implemented in the SPICE network simulation program. In addition to the properties of the laser chip and electrical package parasitics, incoherent optical reflections from the end of the fibre pigtail are included. Numerical results are compared to measurements on DFB and FP lasers.     

Circuit models for power bus structures on printed circuit boards using a hybrid FEM-SPICE method

Power bus structures consisting of two parallel conducting planes are widely used on high-speed printed circuit boards. In this paper, a full-wave finite-element method (FEM) method is used to analyze power bus structures, and the resulting matrix equations are converted to equivalent circuits that can be analyzed using SPICE programs. Using this method of combining FEM and SPICE, power bus structures of arbitrary shape can be modeled efficiently both in the time-domain and frequency-domain, along with the circuit components connected to the bus. Dielectric loss and losses due to the finite resistance of the power planes can also be modeled. Practical examples are presented to validate this method.     

A coupled efficient and systematic full-wave time-domain macromodeling and circuit Simulation method for signal integrity analysis of high-speed interconnects

This paper presents an accurate and systematic approach for analysis of the signal integrity of the high-speed interconnects, which couples the full-wave finite difference time domain (FDTD) method with scattering (S) parameter based macromodeling by using rational function approximation and the circuit simulator. Firstly, the full-wave FDTD method is applied to characterize the interconnect subsystems, which is dedicated to extract the S parameters of the subnetwork consisting of interconnects with fairly complex geometry. Once the frequency-domain discrete data of the S parameters of the interconnect subnetwork is constructed, the rational function approximation is carried out to establish the macromodel of the interconnect subnetwork by employing the vector fitting method, which provides a more robust and accurate solution for the overall problem. Finally, the analysis of the signal integrity of the hybrid circuit can be fulfilled by using the S parameters based macromodel synthesis and simulation program with integrated circuits emphasis (SPICE) circuit simulator. Numerical experiments demonstrate that the proposed approach is accurate and efficient to address the hybrid electromagnetic (interconnect part) and circuit problems, in which the electromagnetic field effects are fully considered and the strength of SPICE circuit simulator is also exploited.     

基于稀疏迭代协方差矩阵的谐波参数快速估计方法

针对稀疏迭代协方差估计(sparse iterative covariance-based estimation, SPICE)方法功率谱估计精度较低和计算复杂度较高的局限性,提出了一种基于稀疏迭代协方差矩阵的谐波信号功率谱和频率参数的快速估计方法。该方法主要结合渐近最小方差准则和快速傅里叶变换,对功率谱参数进行快速迭代校正估计。首先,使用SPICE算法得到功率谱和频率参数的初估计。然后,通过渐近最小方差准则得到功率谱参数的迭代校正表达式。最后,利用功率谱迭代校正式获得谐波信号的功率谱和频率参数的估计。为提高算法的计算效率,利用观测数据协方差矩阵的Toeplitz结构和导向矢量的指数形式,对协方差矩阵进行(Gohberg-Semencul, G-S)分解,通过快速傅里叶变换对协方差矩阵求逆和矩阵与向量相乘部分进行求解,从而使参数估计的计算时间大大减少。仿真实验表明,验证了所提算法对谐波功率谱和频率参数具有较高的估计精度,并且计算复杂度较低。      

Temperature dependent timing in standard cell designs

This paper proposes a methodology to simulate temperature dependent timing in standard cell designs. Temperature dependent timing characteristics are derived from standard delay format (SDF) files that are created by synthesis tools automatically based on SPICE characterizations. In addition, a fast calculation of temperatures using the equivalent Foster RC network is presented. A case study is also presented in this paper where the temperature dependent frequency variation of a ring oscillator is simulated demonstrating the necessity of temperature dependent timing simulations. An adaptively refineable partitioning method for simulating standard cell designs logi-thermally is proposed as well. This paper also introduces recent enhancements in the CellTherm logi-thermal simulator developed in the Department of Electron Devices, BME, Hungary. Finally, the simulation results are compared and verified with the SPICE compatible ELDO analog simulator from Mentor Graphics.     

Efficient SRAM yield optimization with mixture surrogate modeling

Largely repeated cells such as SRAM cells usually require extremely low failure-rate to ensure a moderate chi yield. Though fast Monte Carlo methods such as importance sampling and its variants can be used for yield estimation, they are still very expensive if one needs to perform optimization based on such estimations. Typically the process of yield calculation requires a lot of SPICE simulation. The circuit SPICE simulation analysis accounted for the largest proportion of time in the process yield calculation. In the paper, a new method is proposed to address this issue. The key idea is to establish an efficient mixture surrogate model. The surrogate model is based on the design variables and process variables. This model construction method is based on the SPICE simulation to get a certain amount of sample points, these points are trained for mixture surrogate model by the lasso algorithm. Experimental results show that the proposed model is able to calculate accurate yield successfully and it brings significant speed ups to the calculation of failure rate. Based on the model, we made a further accelerated algorithm to further enhance the speed of the yield calculation. It is suitable for high-dimensional process variables and multi-performance applications.     

低功耗、高性能多米诺电路电荷自补偿技术

提出了一种电荷自补偿技术来降低多米诺电路的功耗,并提高了电路的性能.采用电荷自补偿技术设计了具有不同下拉网络(PDN)和上拉网络(PUN)的多米诺电路,并分别基于65,45和32nm BSIM4 SPICE模型进行了HSPICE仿真.仿真结果表明,电荷自补偿技术在降低电路功耗的同时,提高了电路的性能.与常规多米诺电路技术相比,采用电路自补偿技术的电路的功耗延迟积(PDP)的改进率可达42.37%.此外,以45nm Zipper CMOS全加器为例重点介绍了功耗分布法,从而优化了自补偿路径,达到了功耗最小化的目的.最后,系统分析了补偿通路中晶体管宽长比,电路输入矢量等多方面因素对补偿通路的影响.     

An efficient crosstalk parameter extraction method for high-speedinterconnection lines

A proposal is presented for an effective extraction method for crosstalk model parameters of high-speed interconnection lines. In the extraction procedure, mutual capacitance and mutual inductance of the coupled interconnection lines are extracted based on S-parameter measurement, time-domain-reflectometry (TDR) measurement and subsequent microwave network analysis. The extraction method is useful for characterizing homogeneous guiding structures, where the propagation of coupled transverse electromagnetic (TEM) modes is supported. In contrast to previous extraction methods, the suggested procedure requires fewer on-wafer probing steps and does not need matched terminations in the test device for high-frequency probing. The extracted models can be readily used with simulation program with integrated circuit emphasis (SPICE) circuit simulation. The procedure can also be used for modeling the crosstalk in packaging structures and multichip modules (MCMs). The proposed procedure has been successfully applied to the crosstalk model extraction of on-chip interconnection lines. Crosstalk model parameters were obtained for different line structures, spaces, and widths. Finally, the validity and reliability of the extracted models were examined by comparing a SPICE circuit simulation using the extracted crosstalk model parameters with high-speed time-domain crosstalk measurement. A close agreement was observed in the amplitude and pulse shape between the simulation and the measurement, showing the accuracy and usefulness of the proposed extraction method     

Efficient Full-Wave Characterization of Discrete High-Density Multiterminal Decoupling Capacitors for High-Speed Digital Systems

This paper presents an efficient surface-based finite-element method for the full-wave characterization of high-density and multiterminal decoupling capacitors (2, 8, 14, and any arbitrary number of terminals). In contrast to traditional finite-element methods that involve 3-D volumetric unknowns, this method reduces the unknowns one needs to solve to those on 2-D surfaces only. In addition, the reduction from the 3-D volume-based matrix to a 2-D surface-based one is achieved efficiently by exploiting the geometrical specialty of the decap structure. The entire numerical procedure is numerically rigorous without making any approximation. Its efficiency and accuracy have been demonstrated by both measurements and numerical experiments. Based on its fast and accurate solution, different design configurations of capacitors were studied to identify the optimal configuration that can maximize the performance of a decoupling capacitor. Furthermore, the full-wave model obtained from the proposed method was employed to assess the accuracy of conventional series lumped RLC capacitor models. In addition, the full-wave model was incorporated into a high-performance microprocessor's power delivery network to investigate system performance.     

Fast modeling of core switching noise on distributed LRC power gridin ULSI circuits

As technology scales, power supply noise caused by core logic switching becomes critical. Shorter signal rise edge, high integration density, and necessity of using on-chip decoupling capacitors require that the on-chip power distribution should be modeled as an LRC transmission line network with millions of switching devices. In this paper, we propose a sophisticated power grid model consisting of distributed LRC elements excited by constant voltage sources and switching capacitors. Based on this, fast equations for core switching noise estimations were formulated. Full-chip noise distribution on the power grid with any topology was efficiently and accurately computed. SPICE simulations confirmed its efficiency and accuracy. Experimental results obtained on our benchmark circuits revealed that the proposed technique speeded up simulations by several orders of magnitude compared with SPICE, whereas typical relative error was between 0±5%. By integrating a packaging model, the new model predicts accurately the upper boundaries of noise level for power bounce, ground bounce, and differential-mode power noise. Meanwhile, locations of hot spots in the power network are precisely identified. The model is suitable for full-chip rapid simulations for on-chip power distribution design in advanced ultra large scale integration (ULSI) circuits, particularly for early stage analysis, in which global and local optimization such as topology selection, power bus sizing, and on-chip decoupling capacitor placement can be easily conducted     

Efficient Distributed On-Chip Decoupling Capacitors for Nanoscale ICs

A distributed on-chip decoupling capacitor network is proposed in this paper. A system of distributed on-chip decoupling capacitors is shown to provide an efficient solution for providing the required on-chip decoupling capacitance under existing technology constraints. In a system of distributed on-chip decoupling capacitors, each capacitor is sized based on the parasitic impedance of the power distribution grid. Various tradeoffs in a system of distributed on-chip decoupling capacitors are also discussed. Related simulation results for typical values of on-chip parasitic resistance are also presented. The worst case error is 0.003% as compared to SPICE.      

Full-Wave Model of Frequency-Dispersive Media With Debye Dispersion Relation by Circuit-Oriented FEM

Dispersive materials play an important role in a wide variety of applications (e.g., waveguides, antenna structures, integrated circuits, bioelectromagnetic applications). In this paper, a full-wave finite-element method (FEM-SPICE) technique for modeling dispersive materials is proposed. A finite-element formulation employing Whitney elements capable of analyzing electromagnetic geometries with dispersive media is described, and a Norton equivalent network is developed for each element. The overall network can be analyzed using a circuit simulator based on SPICE, and is suitable for both frequency- and time-domain analysis. This approach exploits the flexibility of finite-element mesh generation and computational efficiency of modern circuit simulators. Simple test configurations are analyzed to validate the proposed formulation.      

单电子晶体管及其在细胞神经网络中的应用

研究了单电子晶体管的特性及主方程法,建立了基于主方程法的单电子晶体管SPICE模型,实现了对细胞神经网络单元的仿真。仿真结果表明,采用主方程法建立的单电子晶体管模型具有合理的精确度,对细胞神经网络单元的实现具有速度快、低功耗的优点,适合复杂细胞神经网络的进一步构建。     

Circular-pad via model based on cavity field analysis

An equivalent circuit model of a circular-pad grounding via is proposed based on cavity modal analysis. The modes of the via are derived analytically. Each mode is represented by an equivalent circuit taking into account ohmic losses, as well as losses due to spatial and surface wave radiation. It is shown that the degradation of grounding via characteristics at high frequencies is caused by the multimode effects and radiation. The accuracy of the proposed semi-analytical via model is comparable with that of full-wave analysis up to 75 GHz. It is fast and is easily incorporated in high-frequency circuit simulators.