Zheng Zhang an Assistant Professor of Electrical and Computer Engineering, University of California at Santa Barbara (UCSB). He received his Ph.D degree in Electrical Engineering and Computer Science from the Massachusetts Institute of Technology (MIT), Cambridge, MA, in 2015, M.Phil degree from the University of Hong Kong in 2010, and B. Eng degree from Huazhong University of Science and Technology in 2008. His industrial experiences include Coventor Inc., Cambridge, MA, and Maxim-IC, Colorado Springs, CO, USA Supervisors: Luca Daniel
Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impac... more Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners. This paper propose a rigorous and efficient solution to address the challenge of non-Gaussian correlation. We first extend generalized polynomial chaos, and propose a class of smooth basis functions to efficiently handle non-Gaussian correlations. Then, we consider high-dimensional parameters , and develop a scalable tensor method to compute the proposed basis functions. Finally, we develop a sparse solver with adaptive sample selections to solve high-dimensional uncertainty quantification problems. We validate our theory and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. The results show that our approach outperforms Monte Carlo by 2500× to 3000× in terms of efficiency. Moreover, our method can accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which is hard to handle by existing methods. Based on the results in this paper, many novel uncertainty quantification algorithms can be developed and can be further applied to a broad range of engineering domains.
—Fabrication process variations are a major source of yield degradation in the nano-scale design ... more —Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique to quantify the uncertainties caused by process variations. Despite their superior efficiency over Monte Carlo for many design cases, these algorithms suffer from the curse of dimensionality; i.e., their computational cost grows very fast as the number of random parameters increases. In order to solve this challenging problem, this paper presents a high-dimensional uncertainty quantification algorithm from a big-data perspective. Specifically, we show that the huge number of (e.g., 1.5 × 10 27) simulation samples in standard stochastic collocation can be reduced to a very small one (e.g., 500) by exploiting some hidden structures of a high-dimensional data array. This idea is formulated as a tensor recovery problem with sparse and low-rank constraints; and it is solved with an alternating minimization approach. Numerical results show that our approach can simulate efficiently some ICs, as well as MEMS and photonic problems with over 50 independent random parameters, whereas the traditional algorithm can only handle several random parameters.
—Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling c... more —Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents " tensor computation " as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano... more Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters. However, their computational cost significantly increases as the number of random parameters increases. This paper presents a big-data approach to solve high-dimensional uncertainty quantifi-cation problems. Specifically, we simulate integrated circuits and MEMS at only a small number of quadrature samples; then, a huge number of (e.g., 1.5 × $10^{27}$) solution samples are estimated from the available small-size (e.g., 500) solution samples via a low-rank and tensor-recovery method. Numerical results show that our algorithm can easily extend the applicability of tensor-product stochastic collocation to IC and MEMS problems with over 50 random parameters, whereas the traditional algorithm can only handle several random parameters.
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our appr... more This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result can also speed up other essential routines in power systems (e.g., stochastic planning, operations and controls).
Instead of simulating a power flow equation at all quadrature points, our approach only simulates an extremely small subset of samples. We suggest a model to exploit the underlying low-rank and sparse structure of high-dimensional simulation data arrays, making our technique applicable to power systems with many random parameters. We also present a numerical method to solve the resulting nonlinear optimization problem.
Our algorithm is implemented in MATLAB and is verified by several benchmarks in MATPOWER $5.1$. Accurate results are obtained for power systems with up to $50$ independent random parameters, with a speedup factor up to $9\times 10^{20}$.
IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems
Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit s... more Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVAbased stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.
IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, Oct 2013
Uncertainties have become a major concern in integrated circuit design. In order to avoid the hug... more Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the non-intrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method. Compared with the popular intrusive stochastic Galerkin (SG) method, the coupled deterministic equations resulting from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST requires fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems.
Process variations can significantly degrade device performance and chip yield in silicon photoni... more Process variations can significantly degrade device performance and chip yield in silicon photonics. In order to reduce the design and production costs, it is highly desirable to predict the statistical behavior of a device before the final fabrication. Monte Carlo is the mainstream computational technique used to estimate the uncertainties caused by process variations. However, it is very often too expensive due to its slow convergence rate. Recently, stochastic spectral methods based on polynomial chaos expansions have emerged as a promising alternative, and they have shown significant speedup over Monte Carlo in many engineering problems. The existing literature mostly assumes that the random parameters are mutually independent. However, in practical applications such assumption may not be necessarily accurate. In this paper, we develop an efficient numerical technique based on stochastic collocation to simulate silicon photonics with correlated and non-Gaussian random parameters. The effectiveness of our proposed technique is demonstrated by the simulation results of a silicon-on-insulator based directional coupler example. Since the mathematic formulation in this paper is very generic, our proposed algorithm can be applied to a large class of photonic design cases as well as to many other engineering problems.
International Conference on Computer-Aided Design, Nov 2013
Due to significant manufacturing process variations, the performance of integrated circuits (ICs)... more Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the application of conventional stochastic Galerkin and stochastic collocation schemes to nonlinear circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.
Process variations are a major concern in today’s chip design since they can significantly degrad... more Process variations are a major concern in today’s chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit’s
performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulator.
In circuit simulation, when a large RLC network is connected with delay elements, such as transmi... more In circuit simulation, when a large RLC network is connected with delay elements, such as transmission lines, the resulting system is a time-delay system (TDS). This paper presents a new model order reduction (MOR) scheme for TDSs with state time delays. It is the first time to reduce a TDS using balanced truncation. The Lyapunov-type equations for TDSs are derived, and an analysis of their computational complexity is presented. To reduce the computational cost, we approximate the controllability and observability Gramians in ...
In this paper a half-size singularity test matrix for fast and reliable passivity assessment of r... more In this paper a half-size singularity test matrix for fast and reliable passivity assessment of rational models are discussed. The discussers would like to remark that the half-size singularity matrix test, in fact, applies only to symmetric systems, unlike the Hamiltonian matrix passivity test that is applicable to state-space systems without regard to symmetry considerations. The discussers have come up with a more elegant derivation of the singularity test matrix and new results concerning the stronger nature of the passivity ...
IEEE Trans. Circuits and Systems I: Regular Papers, Jun 2015
Brain-inspired arrays of parallel processing oscillators represent an intriguing alternative to t... more Brain-inspired arrays of parallel processing oscillators represent an intriguing alternative to traditional computational methods for data analysis and recognition. This alternative is now becoming more concrete thanks to the advent of emerging oscillators fabrication technologies providing high density packaging and low power consumption. One challenging issue related to oscillator arrays is the large number of system parameters and the lack of efficient computational techniques for array simulation and performance verification. This paper provides a realistic phase-domain modeling and simulation methodology of oscillator arrays which is able to account for the relevant device nonidealities. The model is employed to investigate the associative memory performance of arrays composed of resonant LC oscillators.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Jan 2015
An array of weakly coupled oscillators can generate multiphase signals, i.e., multiple sinusoidal... more An array of weakly coupled oscillators can generate multiphase signals, i.e., multiple sinusoidal signals with specific phase separations. Multiphase oscillators are attractive solutions in many electronic applications such as the synchronization of multiple processing units in digital electronics and the frequency synthesis in mixed-signal radio frequency circuits. Due to the complexity of multiphase oscillators and the large number of design parameters, novel simulation techniques are highly desired to efficiently handle such large-scale problems. In this paper, an efficient phase-domain simulation technique is proposed to calculate the phase response of inductance capacitance oscillator array. By some practical examples, it is shown how the proposed method can be exploited to identify the array topologies and parameter settings that guarantee stable phase separations. It is also shown how the proposed technique can be used to evaluate phase-noise performance.
Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impac... more Since the invention of generalized polynomial chaos in 2002, uncertainty quantification has impacted many engineering fields, including variation-aware design automation of integrated circuits and integrated photonics. Due to the fast convergence rate, the generalized polynomial chaos expansion has achieved orders-of-magnitude speedup than Monte Carlo in many applications. However, almost all existing generalized polynomial chaos methods have a strong assumption: the uncertain parameters are mutually independent or Gaussian correlated. This assumption rarely holds in many realistic applications, and it has been a long-standing challenge for both theorists and practitioners. This paper propose a rigorous and efficient solution to address the challenge of non-Gaussian correlation. We first extend generalized polynomial chaos, and propose a class of smooth basis functions to efficiently handle non-Gaussian correlations. Then, we consider high-dimensional parameters , and develop a scalable tensor method to compute the proposed basis functions. Finally, we develop a sparse solver with adaptive sample selections to solve high-dimensional uncertainty quantification problems. We validate our theory and algorithm by electronic and photonic ICs with 19 to 57 non-Gaussian correlated variation parameters. The results show that our approach outperforms Monte Carlo by 2500× to 3000× in terms of efficiency. Moreover, our method can accurately predict the output density functions with multiple peaks caused by non-Gaussian correlations, which is hard to handle by existing methods. Based on the results in this paper, many novel uncertainty quantification algorithms can be developed and can be further applied to a broad range of engineering domains.
—Fabrication process variations are a major source of yield degradation in the nano-scale design ... more —Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique to quantify the uncertainties caused by process variations. Despite their superior efficiency over Monte Carlo for many design cases, these algorithms suffer from the curse of dimensionality; i.e., their computational cost grows very fast as the number of random parameters increases. In order to solve this challenging problem, this paper presents a high-dimensional uncertainty quantification algorithm from a big-data perspective. Specifically, we show that the huge number of (e.g., 1.5 × 10 27) simulation samples in standard stochastic collocation can be reduced to a very small one (e.g., 500) by exploiting some hidden structures of a high-dimensional data array. This idea is formulated as a tensor recovery problem with sparse and low-rank constraints; and it is solved with an alternating minimization approach. Numerical results show that our approach can simulate efficiently some ICs, as well as MEMS and photonic problems with over 50 independent random parameters, whereas the traditional algorithm can only handle several random parameters.
—Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling c... more —Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents " tensor computation " as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.
Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano... more Stochastic spectral methods have become a popular technique to quantify the uncertainties of nano-scale devices and circuits. They are much more efficient than Monte Carlo for certain design cases with a small number of random parameters. However, their computational cost significantly increases as the number of random parameters increases. This paper presents a big-data approach to solve high-dimensional uncertainty quantifi-cation problems. Specifically, we simulate integrated circuits and MEMS at only a small number of quadrature samples; then, a huge number of (e.g., 1.5 × $10^{27}$) solution samples are estimated from the available small-size (e.g., 500) solution samples via a low-rank and tensor-recovery method. Numerical results show that our algorithm can easily extend the applicability of tensor-product stochastic collocation to IC and MEMS problems with over 50 random parameters, whereas the traditional algorithm can only handle several random parameters.
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our appr... more This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result can also speed up other essential routines in power systems (e.g., stochastic planning, operations and controls).
Instead of simulating a power flow equation at all quadrature points, our approach only simulates an extremely small subset of samples. We suggest a model to exploit the underlying low-rank and sparse structure of high-dimensional simulation data arrays, making our technique applicable to power systems with many random parameters. We also present a numerical method to solve the resulting nonlinear optimization problem.
Our algorithm is implemented in MATLAB and is verified by several benchmarks in MATPOWER $5.1$. Accurate results are obtained for power systems with up to $50$ independent random parameters, with a speedup factor up to $9\times 10^{20}$.
IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems
Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit s... more Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient ANOVAbased stochastic circuit/MEMS simulator to extract efficiently the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is simulated efficiently by our simulator at the cost of only 10 minutes in MATLAB on a regular personal computer.
IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, Oct 2013
Uncertainties have become a major concern in integrated circuit design. In order to avoid the hug... more Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the non-intrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method. Compared with the popular intrusive stochastic Galerkin (SG) method, the coupled deterministic equations resulting from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST requires fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems.
Process variations can significantly degrade device performance and chip yield in silicon photoni... more Process variations can significantly degrade device performance and chip yield in silicon photonics. In order to reduce the design and production costs, it is highly desirable to predict the statistical behavior of a device before the final fabrication. Monte Carlo is the mainstream computational technique used to estimate the uncertainties caused by process variations. However, it is very often too expensive due to its slow convergence rate. Recently, stochastic spectral methods based on polynomial chaos expansions have emerged as a promising alternative, and they have shown significant speedup over Monte Carlo in many engineering problems. The existing literature mostly assumes that the random parameters are mutually independent. However, in practical applications such assumption may not be necessarily accurate. In this paper, we develop an efficient numerical technique based on stochastic collocation to simulate silicon photonics with correlated and non-Gaussian random parameters. The effectiveness of our proposed technique is demonstrated by the simulation results of a silicon-on-insulator based directional coupler example. Since the mathematic formulation in this paper is very generic, our proposed algorithm can be applied to a large class of photonic design cases as well as to many other engineering problems.
International Conference on Computer-Aided Design, Nov 2013
Due to significant manufacturing process variations, the performance of integrated circuits (ICs)... more Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper discusses the recent advances of stochastic spectral circuit simulators based on generalized polynomial chaos (gPC). Such techniques can handle both Gaussian and non-Gaussian random parameters, showing remarkable speedup over Monte Carlo for circuits with a small or medium number of parameters. We focus on the recently developed stochastic testing and the application of conventional stochastic Galerkin and stochastic collocation schemes to nonlinear circuit problems. The uncertainty quantification algorithms for static, transient and periodic steady-state simulations are presented along with some practical simulation results. Some open problems in this field are discussed.
Process variations are a major concern in today’s chip design since they can significantly degrad... more Process variations are a major concern in today’s chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit’s
performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulator.
In circuit simulation, when a large RLC network is connected with delay elements, such as transmi... more In circuit simulation, when a large RLC network is connected with delay elements, such as transmission lines, the resulting system is a time-delay system (TDS). This paper presents a new model order reduction (MOR) scheme for TDSs with state time delays. It is the first time to reduce a TDS using balanced truncation. The Lyapunov-type equations for TDSs are derived, and an analysis of their computational complexity is presented. To reduce the computational cost, we approximate the controllability and observability Gramians in ...
In this paper a half-size singularity test matrix for fast and reliable passivity assessment of r... more In this paper a half-size singularity test matrix for fast and reliable passivity assessment of rational models are discussed. The discussers would like to remark that the half-size singularity matrix test, in fact, applies only to symmetric systems, unlike the Hamiltonian matrix passivity test that is applicable to state-space systems without regard to symmetry considerations. The discussers have come up with a more elegant derivation of the singularity test matrix and new results concerning the stronger nature of the passivity ...
IEEE Trans. Circuits and Systems I: Regular Papers, Jun 2015
Brain-inspired arrays of parallel processing oscillators represent an intriguing alternative to t... more Brain-inspired arrays of parallel processing oscillators represent an intriguing alternative to traditional computational methods for data analysis and recognition. This alternative is now becoming more concrete thanks to the advent of emerging oscillators fabrication technologies providing high density packaging and low power consumption. One challenging issue related to oscillator arrays is the large number of system parameters and the lack of efficient computational techniques for array simulation and performance verification. This paper provides a realistic phase-domain modeling and simulation methodology of oscillator arrays which is able to account for the relevant device nonidealities. The model is employed to investigate the associative memory performance of arrays composed of resonant LC oscillators.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Jan 2015
An array of weakly coupled oscillators can generate multiphase signals, i.e., multiple sinusoidal... more An array of weakly coupled oscillators can generate multiphase signals, i.e., multiple sinusoidal signals with specific phase separations. Multiphase oscillators are attractive solutions in many electronic applications such as the synchronization of multiple processing units in digital electronics and the frequency synthesis in mixed-signal radio frequency circuits. Due to the complexity of multiphase oscillators and the large number of design parameters, novel simulation techniques are highly desired to efficiently handle such large-scale problems. In this paper, an efficient phase-domain simulation technique is proposed to calculate the phase response of inductance capacitance oscillator array. By some practical examples, it is shown how the proposed method can be exploited to identify the array topologies and parameter settings that guarantee stable phase separations. It is also shown how the proposed technique can be used to evaluate phase-noise performance.
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Papers by Zheng Zhang
Instead of simulating a power flow equation at all quadrature points, our approach only simulates an extremely small subset of samples. We suggest a model to exploit the underlying low-rank and sparse structure of high-dimensional simulation data arrays, making our technique applicable to power systems with many random parameters. We also present a numerical method to solve the resulting nonlinear optimization problem.
Our algorithm is implemented in MATLAB and is verified by several benchmarks in MATPOWER $5.1$. Accurate results are obtained for power systems with up to $50$ independent random parameters, with a speedup factor up to $9\times 10^{20}$.
performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulator.
Instead of simulating a power flow equation at all quadrature points, our approach only simulates an extremely small subset of samples. We suggest a model to exploit the underlying low-rank and sparse structure of high-dimensional simulation data arrays, making our technique applicable to power systems with many random parameters. We also present a numerical method to solve the resulting nonlinear optimization problem.
Our algorithm is implemented in MATLAB and is verified by several benchmarks in MATPOWER $5.1$. Accurate results are obtained for power systems with up to $50$ independent random parameters, with a speedup factor up to $9\times 10^{20}$.
performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulator.