Modeling Resonant Coupled Wireless Power Transfer System谐振耦合式无线电力传输系统建模This example shows how to create and analyze resonant coupling type wireless power transfer(WPT) system with emphasis on concepts such as resonant mode, coupling effect, and magnetic field pattern. The analysis is based on a 2-element system of spiral resonators.这个例子显示了如何创建和分析谐振耦合式无线电力传输系统（WPT）的概念如谐振模式，强调耦合效应和磁场模式。
此分析是基于两螺旋谐振器系统。
This example requires the following product:这个例子需要以下产品：Partial Differential Equation Toolbox™Design Frequency and System Parameters设计频率和系统参数Choose the design frequency to be 30MHz. This is a popular frequency for compact WPT system design. Also specify the frequency for broadband analysis, and the points in space to plot near fields.选择的设计频率为30MHz。
这是便携式WPT系统设计的一个流行的频率。
还指定了宽带分析的频率，和在附近的空间中的点。
fc=30e6;fcmin = 28e6;fcmax = 31e6;fband1 = 27e6:1e6:fcmin;fband2 = fcmin:0.25e6:fcmax;fband3 = fcmax:1e6:32e6;freq = unique([fband1 fband2 fband3]);pt=linspace(-0.3,0.3,61);[X,Y,Z]=meshgrid(pt,0,pt);field_p=[X(:)';Y(:)';Z(:)'];The Spiral Resonator螺旋谐振器The spiral is a very popular geometry in resonant coupling type wireless power transfer system for its compact size and highly confined magnetic field. We will use such a spiral as the fundamental element in this example.螺旋是一种非常流行的几何形状在谐振耦合型无线功率传输系统，其紧凑的尺寸和高度密闭的磁场。
我们会使用这样一个螺旋的基本元素在这个例子中。
Create Spiral Geometry The spiral is defined by its inner and outer radius, and number of turns. Express the geometry by its boundary points, then import its boundary points into pdetool. The mesh is generated in pdetool and exported. The mesh is described by points and triangles.创建螺旋几何形状的螺旋是由它的部和外部半径定义，和数量的圈数。
由边界点的几何表达，那么进口边界点为有效。
网格产生有效和出口。
网格是由点和三角形描述的。
Rin=0.05;Rout=0.15;N=6.25;[p,t]=createSpiral(Rin,Rout,N);Create custom antenna Use customAntennaMesh to import the mesh. The feed is created at the inner circle of the spiral mesh. This structure is now ready for analysis.创建自定义的天线，使用customAntennaMesh 输入网格。
反馈是在螺旋网格的圆上创建的。
这种结构现在已经准备好进行分析。
spiralobj=customAntennaMesh(p,t);spiralobj.Tilt=90;spiralobj.TiltAxis='Y';createFeed(spiralobj,[0.0525 0.0025],[0.0675 0.0025]);Resonance Frequency and Mode谐振频率和模式It is important to find the resonant frequency of the designed spiral geometry. A good way to find the resonant frequency is to study the impedance of the spiral resonantor. Since the spiral is a magnetic resonator, a lorentz shaped reactance is expected and observed in the calculated impedance result.重要的是要找到所设计的螺旋几何的谐振频率。
找到谐振频率的好方法是研究螺旋谐振器的阻抗。
由于螺旋是一个磁电磁谐振腔，洛伦兹形电抗预计和计算的阻抗结果观察。
figure;impedance(spiralobj,freq);Since the spiral is a magnetic resonator, the dominant field component of this resonance is the magnetic field. A strongly localized magnetic field is observed when the near field is plotted.由于螺旋是一个磁谐振器，这种共振的占主导地位的磁场分量是磁场。
绘制近场时，观察到一个强局部磁场。
figure;EHfields(spiralobj,fc,field_p,'ViewField','H','ScaleFields',[0 5]);Create Spiral to Spiral Power Transfer System创建螺旋到螺旋动力传输系统The complete wireless power transfer system is composed of two parts: the transmitter(Tx) and receiver(Rx). Choose identical resonators for both transmitter and receiver to maximizethe transfer efficiency. Here, the wirelesspower transfer system is modeled as a linear array.完整的无线电力传输系统是由两部分组成：发射机（Tx）和接收机（RX）。
选择发射器和接收器的最大传输效率相同的谐振器效率。
这里的无线电能传输系统建模为一个线性阵列。
wptsys=linearArray('Element',[spiralobj spiralobj]);wptsys.ElementSpacing=Rout*2;figure;show(wptsys);Variation of System Efficiency with Transfer Distance系统效率随传输距离的变化One way to evaluate the efficiency of the system is by studying the S21 parameter. As presented in [1], the system efficiency changes rapidly with operating frequency and the coupling strength between the transmitter and receiver resonator. Peak efficiency occurs when the system is operating at its resonant frequency, and the two resonators are strongly coupled. The results for s-parameter analysis has been precomputed and stored in a MAT-file.评估系统的效率的一个方法是研究的S21参数。
在[ 1 ]中，系统的效率迅速变化与工作频率和耦合强度之间发射机和接收机谐振器。
峰值效率发生时，该系统是在其谐振频率工作，和两个谐振器的强耦合。
参数分析结果已预先计算并存储在一个mat文件。
load arraysparamfigure;rfplot(sparam,2,1,'abs');Critical Coupled Point临界耦合点The coupling between two spirals increases with decreasing distance between two resonators. This trend is approximately proportional to . Therefore, the system efficiency increases with shortertransfer distance till it reaches the critical coupled regime [1]. When the two spirals are over coupled, exceeding the critical coupled threshold, system efficiency remains at its peak, as shown in Fig.3 in[1]. We observe this critical coupling point and over coupling effect during modeling the system. Perform a parameteric study of the system s-parameters as a function of the transfer distance.双螺旋线的增加与减少之间的距离两谐振器之间的耦合。