基于开关电容的双积分环SC振荡器

介绍了开关电容电路及由此构成的SC积分器和SC振荡器。     

A parallel time integrator for solving the linearized shallow water equations on the rotating sphere

With the stagnation of processor core performance, further reductions in the time to solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel‐in‐time exposes and exploits additional parallelism in the time dimension, which is inherently sequential in traditional methods. The rational approximation of exponential integrators (REXI) method allows taking arbitrarily long time steps based on a sum over a number of decoupled complex PDEs that can be solved independently massively parallel. Hence, REXI is assumed to be well suited for modern massively parallel super computers, which are currently trending. To date, the study and development of the REXI approach have been limited to linearized problems on the periodic two‐dimensional plane. This work extends the REXI time stepping method to the linear shallow‐water equations on the rotating sphere, thus moving the method one step closer to solving fully nonlinear fluid problems of geophysical interest on the sphere. The rotating sphere poses particular challenges for finding an efficient solver due to the zonal dependence of the Coriolis term. Here, we present an efficient REXI solver based on spherical harmonics, showing the results of a geostrophic balance test, a comparison with alternative time stepping methods, an analysis of dispersion relations indicating superior properties of REXI, and finally, a performance comparison on the Cheyenne supercomputer. Our results indicate that REXI not only can take larger time steps but also can be used to gain higher accuracy and significantly reduced time to solution compared with currently existing time stepping methods.     

Numerical integrators based on modified differential equations

Inspired by the theory of modified equations (backward error analysis), a new approach to high-order, structure-preserving numerical integrators for ordinary differential equations is developed. This approach is illustrated with the implicit midpoint rule applied to the full dynamics of the free rigid body. Special attention is paid to methods represented as B-series, for which explicit formulae for the modified differential equation are given. A new composition law on B-series, called substitution law, is presented.

     

基于平衡运放的电压模多相位正弦振荡器

为了获得高精度、高稳定性、易集成的电压模式多相位正弦振荡器,以平衡运放及其同相和反相积分器为基础,给出多相位正弦振荡器.该电路能输出2组N(N为奇,亦可为偶)个等幅度、等相位分布的正弦输出,无源灵敏度低;振荡幅度与振荡频率可独立调节;所有电容接地,适宜集成.计算机仿真结果与理论分析一致.     

Solving Hamiltonian systems arising from ODE eigenproblems

This paper presents an algorithm for solving a linear Hamiltonian system arising in the study of certain ODE eigenproblems. The method follows the phase angles of an associated unitary matrix, which are essential for correct indexing of the eigenvalues of the ODE. Compared to the netlib code SL11F [11] the new method has the property that on many important problems – in particular, on matrix–vector Schrödinger equations – the cost of the integration is bounded independently of the eigenparameter λ. This allows large eigenvalues to be found much more efficiently. Numerical results show that our implementation of the new algorithm is substantially faster than the netlib code SL11F.     

测量软X射线脉冲信号的门控积分器

 研制了满足ICF诊断中软X射线能量测量精度要求的具有限定时间积分功能的门控积分器。测试结果表明, 门控积分器的门有效导通时间约为7.8ns; 用信号源做被积信号, 门控积分器与示波器同时测量, 积分非线性小于3%; 门控积分器与示波器测量对比, 最大误差小于门控积分器满量程的5%。     

宽频带无源积分器的设计和实验

 为获得宽频带的无源积分器,建立了考虑杂散参数的等效电路并进行了电路仿真。结果表明无源积分器的频响上限由杂散参数决定。对于相同结构的积分器,增大RC积分常数,会使杂散参数的影响加剧,导致积分器的高频响应变差。使用同轴结构可以减小电容的杂散电感,提高积分器的带宽。对制作的RC常数为10 μs的同轴式积分器进行了频响实验。实验结果表明：在偏差小于5％的范围内,同轴式积分器带宽为50 kHz～80 MHz。在D-dot电压探头线下标定实验和初级试验平台(PTS)单路样机激光触发开关输出电压测量中,使用该同轴积分器获取的测量波形没有波形畸变和高频干扰。     

An efficient pseudo‐spectral Legendre–Galerkin method for solving a nonlinear partial integro‐differential equation arising in population dynamics

The pseudo‐spectral Legendre–Galerkin method (PS‐LGM) is applied to solve a nonlinear partial integro‐differential equation arising in population dynamics. This equation is a competition model in which similar individuals are competing for the same resources. It is a kind of reaction–diffusion equation with integral term corresponding to nonlocal consumption of resources. The proposed method is based on the Legendre–Galerkin formulation for the linear terms and interpolation operator at the Chebyshev–Gauss–Lobatto (CGL) points for the nonlinear terms. Also, the integral term, which is a kind of convolution, is directly computed by a fast and accurate method based on CGL interpolation operator, and thus, the use of any quadrature formula in its computation is avoided. The main difference of the PS‐LGM presented in the current paper with the classic LGM is in treating the nonlinear terms and imposing boundary conditions. Indeed, in the PS‐LGM, the nonlinear terms are efficiently handled using the CGL points, and also the boundary conditions are imposed strongly as collocation methods. Combination of the PS‐LGM with a semi‐implicit time integration method such as second‐order backward differentiation formula and Adams‐Bashforth method leads to reducing the complexity of computations and obtaining a linear algebraic system of equations with banded coefficient matrix. The desired equation is considered on one and two‐dimensional spatial domains. Efficiency, accuracy, and convergence of the proposed method are demonstrated numerically in both cases. Copyright © 2012 John Wiley & Sons, Ltd.     

高重复频率脉冲激光能量测量（英文）

设计了一种用于高重复频率脉冲激光能量测量的峰值保持电路。电路由电荷积分器、2阶低通滤波器、时间延迟触发器和峰值保持器组成,通过将光电流脉冲转换成电压脉冲,电压脉冲的峰值与对应电流脉冲所包含的能量成正比。实验测量结果表明：该电路可以测量脉宽〈10 ns,重复频率≥2 kHz的重频窄脉冲激光的脉冲能量,且工作稳定,其线性动态范围≥140倍。该电路可应用于光电阵列探测系统中,能实现较高的空间分辨力。