Time-Domain Simulation of n Coupled Transmission Lines

In this paper, a general SPICE model for n coupled transmission lines is presented. The model consists of two identical transformation networks and n single-transmission-line models. The transformation networks are realized with linear time-invariant voltage-controlled voltage sources (VCVS's) and current-controlled current sources (CCCS's) only. A simplified model designed to simulate connections on multilayer printed circuit boards is also presented. In this case, the coupling model is adequately described by a capacitance matrix C and an inductance matrix L that are Toeplitz, symmetric, and tridiagonal. The particular structure of C and L makes the computation of the parameters of the transformation network extremely easy and efficient because only simple function evaluations (cosines) are required. Furthermore, the transformation network depends only on the number of coupled lines and not on the parameters of those lines. Therefore, a library of such models needs to be determined only once, and only the characteristic impedances and time delays for the single lines have to be recomputed. The simulation results have been compared against expermental results, and the difference between the two is less than 1 percent.     

Generalized Coupling Coefficient for Filters With Nonresonant Nodes

In this letter, we introduce a generalization of the coupling coefficient definition that applies to filters, including nonresonating nodes. The novel coefficients are evaluated from the synthesized low-pass prototype (suitable formulas are given); they allow an easier prototype de-normalization because no complicated network transformation is requested. Several different solutions with preassigned network parameters can be easily obtained by exploiting the degree of freedom offered by the de-normalized network. Some examples illustrating the use of the new coefficient are given.      

Compact mode expanded lasers using resonant coupling between a1.55-μm InGaAsP tapered active region and an underlying couplingwaveguide

We demonstrate a novel expanded mode laser for enhanced laser-fiber coupling based on resonant coupling between a tapered active waveguide and an underlying coupling waveguide. This device was grown in a single standard epitaxial growth and was processed using conventional fabrication techniques, thus making it attractive for low-cost manufacturing. The total taper length required for mode transformation was 200 μm and the excess transformation loss was 0.6 dB indicating the compact, low-loss mode transformation. Far-field divergence angles (13°×24°) and improved coupling to cleaved single-mode fibers (3.8-dB coupling loss), were achieved     

Effect of Coupling Phase on Mutual Injection Locking Range in Coupled Oscillator Arrays

The performance of a coupled oscillator array depends critically on the coupling network. Determination of the optimal coupling phase depends on the oscillator equivalent circuit and the location of mutual coupling between the oscillators. In this paper, the authors examine the effects of coupling phase on the mutual injection locking range. Three element coupled oscillator arrays (COAs) were mutually coupled at two different locations, with each coupling location presenting a different resonance to the coupling network, and the optimal coupling phase required to generate a linear phase shift in the range of $-90^{circ}$ to 90$^{circ}$ was determined. For each coupling location, when the coupling phase was off by 180$^{circ}$ , the arrays were shown to lock with a limited range and operate in a mode other than the in-phase mode.      

选择性激光相变40Cr钢摩擦磨损性能研究

为了解决40Cr钢零部件表面磨损问题, 结合表面织构理论, 采用激光相变硬化工艺制备分布规则的不同形状(圆形、条状)软硬耦合表面。通过扫描电镜、X射线衍射、摩擦磨损实验和超景深显微镜分别分析相变区微观组织、物相, 评估表面抗磨损性能、磨损表面形貌。结果表明, 圆形相变区截面硬度高于条状, 平均介于(720±3)HV_0.1, 且淬硬层较深; 相变后生成马氏体、Cr₇C₃、Fe₇C₃; 对比40Cr钢未处理表面与软硬耦合表面摩擦系数, 软硬耦合表面摩擦系数均低于0.5且波动小, 具备好的摩擦稳定性; 磨损表面损伤小, 源于磨损过程硬质相能够阻碍磨屑运动、减少表面损伤, 软相区可以缓存能量和碎屑, 软相区以梨削、粘着损伤为主, 硬相区以小点蚀坑为主, 900W圆形软硬耦合表面减磨耐磨效果最好; 塑韧好、表面规律分布、一定比例(50%)硬质相能够有效提升和改善材料工作表面抗磨损性能, 改善对磨副接触表面, 进而能够稳定摩擦系数。该研究可为改善40Cr零部件表面磨损提供参考。     

用谱域导抗法计算铁氧体加载鳍线的传输特性

本文从Maxwell方程出发,经过Fourier变换和坐标旋转,将铁氧体中的非寻常波分解成TE和TM波,并给出它们的波导纳。利用边界条件,忽略TE和TM波间耦合的影响后,将鳍线用一等效网络表示。本文方法与T.Itoh提出的谱域导抗法比较,在等效网络中引入了理想变压器元件。最后对铁氧体加载单侧鳍线的正反向传播常数进行了数值计算,其结果与有关文献中数据吻合得很好。     

Analysis of noise coupling from a power distribution network to signal traces in high-speed multilayer printed circuit boards

As layout density increases in highly integrated multilayer printed circuit boards (PCBs), the noise that exists in the power distribution network (PDN) is increasingly coupled to the signal traces, and precise modeling to describe the coupling phenomenon becomes necessary. This paper presents a model to describe noise coupling between the power/ground planes and signal traces in multilayer systems. An analytical model for the coupling has been successfully derived, and the coupling mechanism was rigorously analyzed and clarified. Wave equations for a signal trace with power/ground noise were solved by imposing boundary conditions. Measurements in both the frequency and time domains have been conducted to confirm the validity of the proposed model.     

Microwave Q Measurements in the Presence of Coupling Losses

In the use of the impedance (Q-circle) method of measuring the cavity Q values, the presence of losses in the coupling network (between the cavity and the available external terminals) is usually neglected. If appreciable losses are present this simplification is not justitied, and its use can lead to significant errors. The losses in any coupling network can be described by means of an equivalent canonical circuit containing a series and a shunt resistor. The losses due to the series element are immediately apparent from the character of the impedance locus when plotted on a Smith Chart and can be corrected for an "apparent" Q value. However, unless the shunt loss can be determined by a separate calibration of the coupling network, the apparent Q value will be ambiguous because the shunt losses occurring in the coupling network are not distinguishable from those in the cavity proper. Methods for using the impedance data for determining the Q values are given on the assumption that the coupling network parameters cm be found. It is also pointed out that due to the presence of coupling losses the loaded and external Q values are no longer uniquely defined, but their meaning depends upon the application of interest. Formulas relating these to the coupling network parameters are given.     

Coupling Holes Between Resonant Cavities or Wave-Guides Evaluated in Terms of Volume Ratios

A hole in a common wall is used to provide coupling between two resonant cavities (k=coefficient of coupling) or between two waveguides (x or b=normalized reactance or susceptance) or between cavity and waveguide (p=loading power factor of cavity). Referring to either side of a thin common wall, the field intensity in the center of a small hole is 1/2 what it would have been at that location on the wall. Between two equal regions, the coupling (k, x or b) by magnetic or electric field is expressed as 1/4 the ratio of the effective volume of the hole over the effective volume of each region, by duality (Booker's principle), the effective volume (related to the polarizability) of an aperture in a thin wall is identified with that of an analogous thin body in a uniform field. For a resonant cavity loaded by coupling to a waveguide, the loading power factor is p=kx; this theorem is proved by reference to an equivalent network. Various cases of coupling by two-dimensional and three-dimensional fields are formulated in terms of area or volume ratios, especially between pillbox resonators (rectangular, circular, or coaxial-circular) and between rectangular waveguides with common side walls or top and bottom walls. The effective area or volume of a small hole in a thin conducting wall is given for various symmetrical shapes, in a magnetic or electric field.     

Unification of generalized hybrid analysis and generalized diakoptics

First, the concept of generalized hybrid basis is introduced and the generalized hybrid analysis for the special linear network having no coupling between its subnetworksN ₁ andN ₂ in Chua and Chen’s paper (1976) is extended to that for the general linear network having coupling betweenN ₁ andN ₂. Second, the concept of generalized diakoptics is introduced and the one-to-one correspondence between it and the generalized hybrid analysis is established. Thus the two analysis methods are unified. Third, the multilevel generalized diakoptics and its algorithm are presented. Fourth, the concepts of the equivalent tree-flower type network and the equivalent interconnected network for fundamental diakoptics are presented.     

实现最大功率传输的阻抗变换方法研究

最大功率传输是信号传输中必须考虑的问题。正弦稳态电路中,在负载阻抗不可调节时,可以通过在电源（或含源线性一端口网络）与固定负载之间级联无源无耗二端口网络来变换负载阻抗,实现负载从正弦稳态电源（或含源线性一端口网络）获得最大功率。本文研究此类无源无耗二端口网络的最简单结构、参数关系及其适用范围。推导可以实现最大功率传输的...     

有互感的介观电感电容耦合电路的量子效应

利用正则变换和幺正变换的方法研究了有互感的介观电感电容耦合电路的量子效应，并把介观电感电容耦合电路和另外几种耦合电路进行了比较。发现在耦合电容存在的有互感的电路中，通过调节互感耦合系数来控制电路的量子涨落和压缩效应是很方便的。电路中电荷和电流的不确定关系与正则变换参数ψ和不确定关系参数ξ有关。当ξ→1或ψ→nπ／2(n=0，1，2，…)时，电荷和电流的不确定关系接近最小值h／2。     

Adaptive processing using a single snapshot for a nonuniformlyspaced array in the presence of mutual coupling and near-fieldscatterers

This paper presents an adaptive technique to extract the signal of interest (SOI) arriving from a known direction in the presence of strong interferers using a single snapshot of data. The antenna elements in this method can be nonuniformly spaced and there can be mutual coupling between them. In addition, near-field scatterers can also be present. First, the voltages induced in the antenna elements of the array due to interferers, mutual coupling between the elements, and near-field scatterers is preprocessed by applying a transformation matrix to these voltages through a rigorous electromagnetic analysis tool. This electromagnetic preprocessing technique transforms the voltages that are induced in a nonuniformly spaced array containing real antenna elements to a set of voltages that will be produced in a uniform linear virtual array (ULVA) containing omnidirectional isotropic point radiators. In the transformation matrix we would like to include various electromagnetic effects like mutual coupling between the antenna elements, presence of near-field scatterers and the platform effects on which the antenna array is mounted. This transformation matrix when applied to the actual measured voltages yields an equivalent set of voltages that will be induced in the ULVA. A direct data domain least squares adaptive algorithm is then applied to the processed voltages to extract the SOI in the presence of interferers. Limited numerical examples are presented to illustrate the novelty of the proposed method     

Analysis of mutual coupling between a finite phased array ofdipoles and its feed network

The mutual coupling effects between a finite phased array of dipoles and its feed network are analyzed. The feed network is typically a corporate feed consisting of split-tee power dividers cascading to form a certain power distribution over the aperture. A simple iterative approach is used to solve the interaction between elements and feed. The radiation of a finite dipole array are first found for a given voltage excitation. These radiation impedances are then used as loads for the feed network, and the n+1 port network problem is analyzed. Due to the interaction between the feed network and dipoles, the antenna parameters such as mismatch, antenna pattern, and gain are all affected. These effects can be determined from the analysis of the network representation. Numerical results for a typical phased array with a corporate feed show that the resultant VSWR of the feed pattern degradation is due to the mutual coupling effects     

Neural Network Approach for Linearization of the Electrostatically Actuated Double-Gimballed Micromirror

In this paper, a hierarchical circuit based approach is used for the development of a reduced-order macro-model for a double-gimballed electrostatic torsional micromirror. The nonlinearity and cross-axis coupling of the micromirror subjected to the differential driving scheme are investigated using the proposed macro-model. The simulation results are used to train a feed-forward neural network which carries out a function approximation of the relation between the desired location and the required driving voltages. The trained neural network is then coded into MAST AHDL. System-level simulation of the micromirror together with the neural network is performed in the SABER simulator. It is found that using a feed-forward neural network, the linearity of the micromirror is greatly improved, the steady state of the cross-axis coupling is reduced to a negligible level and the transient response of the cross-axis coupling is also suppressed. This implies that introducing a feed-forward neural network would be useful to simplify the design of the feedback control system for the double-gimballed electrostatic torsional micromirror.     

A multi-port thermal coupling model for multi-chip power modules suitable for circuit simulators

This paper investigates two compact thermal model representations for multi-chip power modules, namely the thermal impedance matrix model and the thermal admittance matrix model. The latter can shape a multi-port thermal network without controlled temperature sources, and can be readily implemented in circuit simulators. The mutual transformation between the two models and their relationship to parameters in the multi-port network are revealed. In addition, practical tips for thermal model parameter extractions based on temperature measurements and curve-fitting are discussed. The multi-port thermal model is verified by simulations and experimental results. It confirms that more accurate temperature estimation can be achieved compared with the thermal model without the thermal coupling effect.     

Design of Linear Phase Selective Comb-Line Filter

A multiwire approach has been used to develop design equations for linear phase selective comb-line filter. The filter under consideration consists of two rows of inductive resonators separated by a slotted coupling surface. Through the development process a multipath prototype network has been considered. A frequency transformation has been formulated to relate the multipath prototype network and the multiwire comb-line structure. Hence, once the element-values of the prototype network are chosen to meet prescribed requirements, the corresponding comb-line filter element values can be computed through the developed explicit formulas. To illustrate the design procedure a brief design example is presented.     

三维集成电路中TSV-TSV的耦合分析与优化

TSV-TSV耦合会对三维集成电路的性能造成影响,主要的负面效应就是引入了耦合噪声。为了能够在初期设计阶段准确的估计TSV间的耦合强度,本文首先提出了存在于TSV间的基于二端口网络的阻抗级耦合通道模型,然后推导出了TSV间的耦合强度公式用来描述TSV-TSV耦合效应。通过与三维全波仿真结果的对比,公式的准确度得到了验证。另外,本文提出了一种减小TSV间耦合强度的设计方法。通过SPICE仿真,所提出设计方法不仅可以应用在简单TSV-TSV的电路结构中,还可以应用在含有多个TSV的复杂电路结构中,从而体现了所提出设计方法的可行性,并且为设计者提供了改善三维集成电路电学性能的可能性。     

Array thinning by using antennas in a Fabry-Perot cavity for gain enhancement

A Fabry-Perot cavity (FPC) between a ground plane and a partially reflective surface (PRS) is used here to design array antennas with large distance between the radiating elements. This configuration provides some advantages: i) a reduction of the number of array elements to achieve high directivity; ii) large space between contiguous elements that may host a bulky feeding network as required for dual polarization or active antennas; iii) small coupling and easy feeding network designs because of the smaller number of elements with larger inter-element distance. We show that when designing the FPC antenna a frequency shift of the gain maximum may occur, especially in this sparse array configuration. We also show the existence of preferred distances between elements that controls both the directivity and the side lobe level, and how the presence of the FPC and the relaxed requirement of the interelement distance result in a lower interelement coupling. The presented dual polarized antenna comprises two interleaved 2 /spl times/ 2 arrays placed in a 2-layer FPC, and exhibits a 19 dBi gain and 30 dB of isolation between the two ports over an operating bandwidth of approximately 5.7%, i.e., typical for patch antennas.     

强耦合多原子极性晶体中表面磁极化子的性质

本文研究磁场中强耦合多原子极性晶体中表面电子和表面光学声子的相互作用。采用线性组合算符和简单的么正变换,分别导出强、弱耦合情形下表面磁极化子的基态能量。对于弱耦合得到基态能量是不同支声子能量的通常结果,对于强耦合存在一个由于不同支声子之间的交叉项贡献的附加能量。