电磁场数值分析

1、电磁场数值分析（作业）2016年学院：学号：姓名：联系方式：任课教师：2016年6月6日一个二维正方形（边长a=10mm）的静电场区域，电位边界条件如图所示（单位：V）,求区域内的电位分布。要求用超松弛迭代法求解差分方程组进行计算。代码：hx=11;hy=11;v1=zeros(hy,hx);v1(hy,:)=ones(1,hx)*100;v1(1,:)=ones(1,hx)*50;fori=1:hy;v1(i,1)=0;v1(i,hx)=100;endw=2/(1+sin(pi/(hx-1);maxt=1;t=0;v2=v1;n=0;while(maxt>1e-6)n=n+1;maxt

2、=0;fori=2:hy-1;forj=2:hx-1;v2(i,j)=(1-w)*v1(i,j)+w*(v1(i+1,j)+v1(i,j+1)+v2(i-1,j)+v2(i,j-1)/4;t=abs(v2(i,j)-v1(i,j);if(t>maxt)maxt=t;endendendv1=v2;endsubplot(1,2,1)mesh(v2)axis(0,11,0,11,0,100)subplot(1,2,2)contour(v2,20)结果：Figure1文中n闻加Fl百司喷IffiA(l)IPKT)明明Dsaw谎期E3i|3'"场*"/1Son24631

3、0Mur模拟真空中二维TM电磁波的传播，边界设置为一阶吸收边界，观察电磁波的传播过程。波源为正弦函数：L.，、.，CC、Ez=sin(-t)=sin(2ntLt)25,150波源代码：xmesh=150;ymesh=150;mu0=4*pi*(1.0e-7);eps0=8.85e-12;c=3.0e-8;dx=1.0;dt=0.7*dx/c;timestep=200;ez(1:xmesh+1,1:ymesh+1)=0.0;hx(1:xmesh+1,1:ymesh)=0.0;hy(1:xmesh,1:ymesh+1)=0.0;coef1=dt/(mu0*dx);coef2=dt/(eps0*dx

4、);coef3=(c*dt-dx)/(c*dt+dx);ezold=ez;fornow=1:timestep;hx=hx-coef1*(ez(:,2:ymesh+1)-ez(:,1:ymesh);hy=hy+coef1*(ez(2:xmesh+1,:)-ez(1:xmesh,:);ez(2:xmesh,2:ymesh)=ez(2:xmesh,2:ymesh)-coef2*(hx(2:xmesh,2:ymesh)-hx(2:xmesh,1:ymesh-1)-coef2*(hy(2:xmesh,2:ymesh)-hy(1:xmesh-1,2:ymesh);ez(1,:)=ezold(2,:)+co

5、ef3*(ez(2,:)-ezold(1,:);ez(xmesh+1,:)=ezold(xmesh,:)+coef3*(ez(xmesh,:)-ezold(xmesh+1,:);ez(:,1)=ezold(:,2)+coef3*(ez(:,2)-ezold(:,1);ez(:,ymesh+1)=ezold(:,ymesh)+coef3*(ez(:,ymesh)-ezold(:,ymesh+1);ez(xmesh/2+1,ymesh/2+1)=sin(now*dt*2*pi*c/25.0);mesh(ez)pause(0.01)ezold=ez;end结果：0.00001基于Pocklingto

6、n方程用MoM分析半波对称振子天线观察天线线径和分段数目分别取不同值对天线阻抗和辐射特性的影响（半径分别取0.001入，0.0001人，入，分段数取11,21,31）代码：%n始化参数c=3e-8;r=1;f=c/r;w=2*pi*f;e0=8.85e-12;u0=4*pi*1e-7;a=0.0001*r;L=0.5*r;k=2*pi/r;N=31;dl=L/(N+1);l=L/2-dl/2;lz=-l:dl:1;lzs=lz(1:N);lzm=lz(1:N)+dl/2;lze=lz(2:N+1);%fl抗矩阵元素求解fi=log(dl/a)/(2*pi*dl)-k/(4*pi)*1j;fi_

7、1=exp(-k*dl*1j)/(4*pi*dl);fi_2=exp(-k*2*dl*1j)/(8*pi*dl);z=ones(N,N);form=1:Nforn=1:Nifm=nfi1=fi;fi2=fi_1;fi3=fi_2;z(m,n)=(kA2*dlA2-2)*fi1+fi2+fi3);elseifabs(m-n)=1fi1=fi_1;fi2=fi;fi3=fi_2;z(m,n)=(kA2*dlA2-2)*fi+fi2+fi3);elsefi1=exp(-k*abs(m-n)*dl*1j)/(4*pi*abs(m-n)*dl);fi2=exp(-k*abs(m+1-n)*dl*1j)/

8、(4*pi*abs(m+1-n)*dl);fi3=exp(-k*abs(n+1-m)*dl*1j)/(4*pi*abs(n+1-m)*dl);z(m,n)=(kA2*dlA2-2)*fi+fi2+fi3);endendend%嚏压矩阵求解V=zeros(N,1);V(N+1)/2)=-1*(1j*w*e0);I=zV;Z_in=1/I(N+1)/2);disp('输入阻抗=',num2str(Z_in)I_amp=abs(I);Max=max(I_amp);Iunit2=0;I_amp/Max(1);0;figure(1)h=0:dl/r:L/r;Ithe=sin(pi*h*r

9、/L);plot(h,Iunit2,'b',h,Ithe,'r','linewidth',2)legend('pocklinton','解析值')gridonxlabel('电长度')ylabel('归一化电流)%吩向图theta=0:0,01:2*pi;abs_f=zeros(1,length(theta);forn=1:1:Nabs_f=abs_f+I(n)*exp(k*(n*dl-L/2)*cos(theta)*1j);endabs_f=abs(sin(theta)*dl.*abs_f

10、);Max_f=abs(sum(I)*dl);Far_patten2=abs_f/Max_f(1);theta_2=0:0.1:2*pi;Far_theory=abs(cos(k*(L/2)*cos(theta_2)-cos(k*L/2)./sin(theta_2);figure(2)polar(theta,Far_patten2,'-b')holdonpolar(theta_2,Far_theory,'or')holdofflegend('pocklinton','解析值')title('半波阵子天线E面方向图)figu

11、re(3)polar(theta,ones(1,length(theta),'-b')title('半波阵子天线H面方向图)%8波阵子增益I_in=I(N+1)/2);A=(w*u0)A2/(4*pi*sqrt(u0/e0)*real(Z_in)*(abs(I_in)A2);G_theta=A*abs_f.A2;Max_gain=max(G_theta);Max_gain_dB=10*log10(Max_gain);disp('半波阵子增益=',sprintf('%.4fdB',Max_gain_dB)结果：*Figure1X文件旧圜查看

12、M届人色工具桌面窗口也帮助(H)Di3difeWC相小口目*Figure3X文件0一闺查看凹庙入印工具桌面BQ(W)帮助(H)?(Ji4+.&痘/豆目挈浓阵子天线H面方向图基于电场积分方程用MoM分析对称振子天线：计算振子总长度分别为0.25入，0.54X,1.5耐，振子的输入阻抗和E面方向图。代码：lamda=1;a=0.0001;me=8.85e-12;mu=4*pi*(1e-7);arg=2*pi*(3e-8)/lamda;L=0.2*lamda;k=2*pi/lamda;N=21;dL=L/(N+1);l=L/2-dL/2;lz=-l:dL:1;lzs=lz(1:N);lzm=

13、lz(1:N)+dL/2;lze=lz(2:N+1);form=1:Nforn=1:Nifn=mFmnmm=(1/(2*pi*dL)*log(dL/a)-1j*k/(4*pi);Fmnee=(1/(2*pi*dL)*log(dL/a)-1j*k/(4*pi);Fmnss=(1/(2*pi*dL)*log(dL/a)-1j*k/(4*pi);Fmnse=exp(-1j*k*dL)/(4*pi*dL);Fmnes=exp(-1j*k*dL)/(4*pi*dL);elseifabs(n-m)=1Fmnmm=exp(-1j*k*dL)/(4*pi*dL);Fmnee=exp(-1j*k*dL)/(4*

14、pi*dL);Fmnss=exp(-1j*k*dL)/(4*pi*dL);ifn>mFmnse=exp(-1j*k*2*dL)/(4*pi*2*dL);Fmnes=exp(1/(2*pi*dL)*log(dL/a)-1j*k/(4*pi);elseFmnes=exp(-1j*k*2*dL)/(4*pi*2*dL);Fmnse=exp(1/(2*pi*dL)*log(dL/a)-1j*k/(4*pi);endelsenum=abs(n-m);Fmnmm=exp(-1j*k*num*dL)/(4*pi*num*dL);Fmnee=exp(-1j*k*num*dL)/(4*pi*num*dL)

15、;Fmnss=exp(-1j*k*num*dL)/(4*pi*num*dL);ifn>mFmnse=exp(-1j*k*(num+1)*dL)/(4*pi*(num+1)*dL);Fmnes=exp(-1j*k*(num-1)*dL)/(4*pi*(num-1)*dL);elseFmnes=exp(-1j*k*(num+1)*dL)/(4*pi*(num+1)*dL);Fmnse=exp(-1j*k*(num-1)*dL)/(4*pi*(num-1)*dL);endendz(m,n)=1j*arg*mu*dL*dL*Fmnmm+(1/(1j*arg*me)*(Fmnee-Fmnes-Fmnse-Fmnss);endendV=zeros(N,1);fedp=(N+1)/2;V(fedp)=1;I=linsolve(z,V);Z=V(fedp)/I(fedp);theta=0:pi/100:2*pi;ftheta=0;form=1:length(theta)F(m)=0;forn=1: