Derivation of Craig's formula for Gaussian probability function

A recent work provides two proofs for Craig's formula, which is an integral formula for the Gaussian probability density function. It also highlights the fact that the original proof of the Craig formula is somewhat unclear. The authors of the work provide two proofs, one based on the Stieltjes transform of a Gaussian pulse and another based on the moment generation function (MGF) of a unit Gaussian random variable (GRV). Another integral formula for Q(x) based on the characteristic function (CHF) of a unit GRV is also provided. This formula can be applied to the analysis of coherent predetection equal-gain combining diversity receivers     

Calculation of leakage inductance in transformer windings

A formula is presented to calculate mutual impedance between transformer windings on ferromagnetic cores. The formula is based on the solution of Maxwell's equations for coils on ferromagnetic cores and as such offers the ultimate in accuracy. The formula is frequency dependent, taking into account the effect of eddy currents in the core on the flux distribution as well as representing the eddy current core loss as an equivalent resistance. Experimental results are presented for leakage inductance and an illustrative example is presented showing how leakage inductance affects the operation of a typical switching mode power supply. Approximations for the formula are also presented to simplify the calculations under certain operating conditions     

开关电源全波整流输出电压公式的实验验证

采用半桥式变换电路进行功率输出。对半桥驱动型开关电源的输出电压估算公式Uout=1n1/2n1 ton/ton toff Uin进行验证。得到实际结果值与公式值有差别．均比公式值大1．86～7．27倍。输出电压Uout除与公式中的几项因素有关外，还与负载电阻和滤波电容有关．当负载电阻较小时比较接近公式值。     

弹簧消隙小模数齿轮传动链回差计算分析及工程应用

通过分析影响齿轮传动链误差的因素,结合弹簧消隙的特点,推导出一种可供设计参考的计算方法,并通过工程实例验证其准确性和可使用性。     

Accurate determination of antenna directivity

The derivation of a formula for accurate estimation of the total radiated power from a transmitting antenna for which the radiated power density is known in a finite number of points on the far-field sphere is presented. The main application of the formula is determination of directivity from power-pattern measurements. The derivation is based on the theory of spherical wave expansion of electromagnetic fields, which also establishes a simple criterion for the required number of samples of the power density. An array antenna consisting of Hertzian dipoles is used to test the accuracy and rate of convergence of the derived formula. Its performance is compared to that of numerical integration using Simpson's formula     

多层膜周期厚度的精确计算

布拉格修正公式可以用于计算基底是平面的软X射线多层膜周期厚度,但对于基底是曲面的多层膜,小角X射线衍射峰角度常常发生漂移,用该公式计算的周期厚度就与实际周期厚度不一致。分析了衍射峰角度位置漂移现象,对以布拉格公式为基础的多层膜周期厚度计算公式进行了修正,实验结果显示,利用修正公式获得的多层膜周期厚度比较接近多层膜实际周期厚度。     

Attenuation of cutoff modes and leaky modes of dielectric slab structures

A simple formula is developed for the attenuation constant of higher order cutoff modes of a dielectric slab guide and of the modes of leaky guides. The formula is based on a perturbation analysis that reduces the problem to that of the transmission characteristic of a Fabry-Perot resonator. Under certain approximations, the formula for leaky guides reduces to that of Hall and Yeh, but the formula has a wider range of applicability.     

无透镜激光电线测径仪的测量计算原理及仿真

讨论无透镜系统测量原理的测径方法，建立了测量系统的几何光学模型，得到线径计算公式。通过实验计算程序，分析了线芯直径和位置偏差对测径公式误差的影响，并给出了相应的修正公式。     

三阶电荷泵锁相环锁定时间的研究

对三阶电荷泵锁相环 ( CPPLL)的锁定时间与环路参数之间的关系进行了深入研究 ,提出了一种计算电荷泵锁相环锁定时间的新方法 ,并给出了锁定时间的计算公式。通过行为级模型验证 ,说明该公式可以快速准确地得到三阶电荷泵锁相环的锁定时间 ,并且很直观地反映出锁定时间与环路参数之间的关系。非常适合于电荷泵锁相环 ( CPPLL)的系统级设计和前期验证。     

An empirical formula for the prediction of rain attenuation infrequency range 0.6 - 100 GHz

An empirical formula for calculating the extinction cross section (ECS) by raindrops over a broad frequency range is first derived based on extensive calculations made on a widely varying in mean radius of modified Pruppacher and Pitter (MPP) raindrop models ranging from 0.25 to 3.5 mm. The expansion coefficients in the empirical formula are determined by least-squares curve fitting of numerical data obtained by the volume integral equation formulation (VIEF). The formula satisfies the frequency and raindrop size dependence. Numerical results obtained from the empirical formula for calculating the ECS are generally in good agreement with those calculated by the VIEF for raindrops with mean radius varying from 0.25 to 3.5 mm in the frequency range from 0.6 to 100 GHz. The average error in the ECS is less than 10%. The formula thus provides a simple and inexpensive method for calculating the ECS of raindrops, which otherwise requires complicated and expensive methods of calculation. By implementing this empirical formula of ECS into the rain attenuation equation, a new numerically empirical formula for calculating the specific rain attenuation is also proposed. The validity of the empirical formula for calculating the specific rain attenuation is also checked by comparing the obtained results of specific rain attenuation with those obtained from Li et al.'s (1995) solution, Yeo et al.'s (1993) measurement, and Olsen et al.'s (1978) power-law equation     

用夫朗和费衍射法测定微粒直径的准确度

本文认为文献 [1]的结论是错误的。作者从标量衍射理论的瑞利 - -索末菲公式出发 ,导出了描述通过照明波发散中心并与衍射屏平行的观察面所接受到的衍射花样的夫朗和费衍射公式及其成立条件。并将上述公式应用到二维随机分布的微粒系统 ,从而导出了描述此系统相应的夫朗和费衍射花样的光强公式及粒径测量公式。指出当用夫朗和费衍射法测量微粒直径时 ,只要应用文中导出的在大衍射角情形下亦成立的测量公式 ,便能得到正确的结果 ,并不存在文献 [1]所提出的随衍射角增大而增加的系统误差。相反 ,对于偶然误差而言 ,当衍射距离不变时 ,随着衍射角的增加 ,偶然误差反而减小 ,测量的准确度增加     

计算二维图像欧拉数的新公式

欧拉数是拓扑学的重要特征参数,在二维数字图像中,由局部性质计算图像欧拉数的公式,对于四连通和八连通是不同的.文章在定义图段和相邻数概念的基础上,提出了由局部性质计算二值图像欧拉数的一种新公式,并进行了证明.该算法基于逐行扫描,分图段计算,每段所对应的相邻上一行的段数不同,会引起图像欧拉数的变化,累加求和即可得到整个二值图像的欧拉数.新算法最重要的特点是将四连通和八连通统一在一个公式之中,这是以往局部算法所没有的.     

Exact Expression for the Coherence Bandwidth of Rayleigh Fading Channels

Coherence bandwidth is an important characteristic of multipath fading channels, serving as a useful tool for wireless systems design. Regardless of its importance, the determination of the coherence bandwidth, so far, has relied on an empirical formula. In this correspondence, we derive an exact coherence-bandwidth formula for Rayleigh fading channels. The use of the new formula is illustrated by numerical results.     

估算晶圆有效芯片数的椭圆公式

IC生产线开发新品和核算成本时,需要估算晶圆上有效芯片数。靠经验公式估算通常有较大误差。作者曾提出一个精确的计算晶圆上有效芯片数的椭圆公式[1],适合于大规格晶圆和高成品率的生产线上应用。本文给出了椭圆公式的推导过程。     

Simple formula for current on a cylindrical receiving antenna

An approximate formula is presented for the induced current on a loaded (or unloaded) thin cylindrical receiving antenna which is illuminated by an incident plane wave from an arbitrary direction. This formula involves only elementary functions and therefore can be calculated easily. Its derivation is based on the multiple reflection approach originated by Weinstein, Shen, and others. Currents calculated by the present formula are found to be in good agreement with experimental data.     

合成孔径雷达图像辐射分辨率工程估算公式的校正

该文分析了合成孔径雷达图像辐射分辨率的本质,指出了目前工程应用的合成孔径雷达图像辐 射分辨率估算值存在着较大的误差,只适合于定性分析。在利用信号检测错误概率的基础上推导出了适合于定量分析的合成孔径雷达图像辐射分辨率工程估算公式。     

Geometric MMSE for one-sided and two-sided vector linear predictors: From the finite-length case to the infinite-length case

In the present paper we derive a formula for the geometric minimum mean square error (GMMSE) for one-sided and two-sided finite-length vector linear predictors. This formula is written only in terms of the autocorrelation matrix of the vector process being predicted. We also obtain a formula for the GMMSE for one-sided and two-sided infinite-length vector linear predictors of any wide sense stationary (WSS) vector process. This GMMSE expression for the infinite-length case is derived from the GMMSE expression obtained for the finite-length case.     

脉冲位置键控系统误比特性能分析

梳理基于等待门限判决的脉冲位置键控系统相关文献资料,发现文献给出的误比特率(BER)理论公式不能准确描述系统误比特率,尤其是在低信噪比情况下一些理论公式计算的误比特率已经高于0.5,超过了通信系统误比特率上限,不符合通信理论。分析了各文献资料误比特率理论公式推导过程中的问题所在,推导得到了一个新的误比特率理论公式。进行了数值仿真,结果表明,新的误比特率理论公式与仿真吻合良好,能够准确描述系统误比特率,并且在低噪比下计算的误比特率不高于0.5,符合通信理论。在新的误比特率理论公式基础上,分析了基于等待门限判决的脉冲位置键控系统能量效率,并与二进制相移键控(BPSK)系统进行了比较,表明基于等待门限判决的脉冲位置键控系统是一种具有较高能量效率的系统,在一定条件下甚至优于BPSK系统。     

Simple formula for error probability of RAKE demodulator for noncoherent binary orthogonal signals and Rayleigh fading

A simple alternative formula for the error probability of a RAKE demodulator for noncoherent, square-law detected, binary orthogonal signals and Rayleigh fading is presented. The formula is more compact and considerably easier to evaluate than the classical formula while providing identical numerical results. The derivation of the alternative formula is shown to be much simpler than the derivation of the classical formula.     

Transmission-Line Properties of a Round Wire in a Polygon Shield

A family of transmission lines is based on a round wire in a cylindrical shield of polygon cross-section. There is presented a simple formula which gives a smooth transition between the extremes of a small wire and a wire near contact. The same formula is adapted for different shapes by entry of different constants depending on the number of shield planes and the degree of symmetry. The formula is reversible for synthesis or analysis by explicit expression of either shape ratio or wave resistance in terms of the other. For comparison in the transition region, there is computed for each shape a close approximation by the method of images.