3.4 总体设计规划

经过前面的概述，已经具备了设计本次五单元八木天线的所有信息，现在将设计天线的总体参数列出如下：

有源振子长度：La=0.46λ 有缘振子半径：a=0.0026λ 反相器长度：L=0.8λ 引向器长度：Lr=0.506λ 各振子间间距：d=0.2λ

四、MATLAB仿真

4.1 MATLAB仿真源程序

设波长λ=1m，其MATLAB仿真程序如下： clear

lambda=1; %波长

k=2*pi/lambda; %自由空间相移常数 u=4*pi*10^(-7); %自由空间导磁率 e=8.854*10^(-12); %自由空间介电常数 a=0.0026*lambda; %有缘振子半径 LR=0.8*lambda; %反相器长度 L=0.46*lambda; %有源振子长度 LD=0.506*lambda; %引向器长度 SR=0.2*lambda; %各振子间间距 SD=0.2*lambda; w=k/sqrt(u*e); y=120*pi; n=6;

N=5; %振子数目

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dlr=LR/(N+1); dl=L/(N+1); dld=LD/(N+1);

point=zeros(n*(2*N+1),4); mid=zeros(n*N,3); for ii=1:2*N+1

point(ii,1:3)=[-SR LR/2-ii*LR/(2*(N+1)) dlr]; if rem(ii+point(ii,4),2)==0

mid((ii+point(ii,4))/2,:)=point(ii,1:3); end end

for ii=2*N+1+1:2*(2*N+1)

point(ii,2:4)=[L/2-(ii-(2*N+1))*L/(2*(N+1)) dl 1]; if rem(ii+point(ii,4),2)==0

mid((ii-point(ii,4))/2,2:3)=point(ii,2:3); end end

for ii=2*(2*N+1)+1:3*(2*N+1)

point(ii,:)=[SD LD/2-(ii-2*(2*N+1))*LD/(2*(N+1)) dld 2]; if rem(ii+point(ii,4),2)==0

mid((ii-point(ii,4))/2,:)=point(ii,1:3); end end

for ii=3*(2*N+1)+1:4*(2*N+1)

point(ii,:)=[2*SD LD/2-(ii-3*(2*N+1))*LD/(2*(N+1)) dld 3]; if rem(ii+point(ii,4),2)==0

mid((ii-point(ii,4))/2,:)=point(ii,1:3); end end

for ii=4*(2*N+1)+1:5*(2*N+1)

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point(ii,:)=[3*SD LD/2-(ii-4*(2*N+1))*LD/(2*(N+1)) dld 4]; if rem(ii+point(ii,4),2)==0

mid((ii-point(ii,4))/2,:)=point(ii,1:3); end end

for ii=5*(2*N+1)+1:6*(2*N+1)

point(ii,:)=[4*SD LD/2-(ii-5*(2*N+1))*LD/(2*(N+1)) dld 5]; if rem(ii+point(ii,4),2)==0

mid((ii-point(ii,4))/2,:)=point(ii,1:3); end end

V=zeros(n*N,1); V(N+(N+1)/2)=1; U=ones(n*N,1); psi=zeros(n*(2*N+1)); for jj=1:n*(2*N+1) for kk=1:n*(2*N+1) if jj==kk

psi(jj,kk)=log(point(jj,3)/a)/(2*pi*point(jj,3))-(j*k)/(4*pi); else

psi(jj,kk)=exp(-j*k*sqrt((point(kk,1)-point(jj,1))^2+(point(kk,2)-point(jj,2))^2))/(4*pi*sqrt((point(kk,1)-point(jj,1))^2+(point(kk,2)-point(jj,2))^2));

end end end

Z=zeros(n*N); for pp=1:n*N

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for qq=1:n*N

Z(pp,qq)=j*w*u*point(pp,3)*point(qq,3)*psi(2*pp+point(pp,4),2*qq+point(qq,4))+(psi(2*pp+point(pp,4)+1,2*qq+point(qq,4)+1)-psi(2*pp+point(pp,4)+1,2*qq+point(qq,4)-1)-psi(2*pp+point(pp,4)-1,2*qq+point(qq,4)+1)+psi(2*pp+point(pp,4)-1,2*qq+point(qq,4)-1))/(j*w*e); end end

si=Z\\V; %In t=1:n*N; figure(1);

plot(t,abs(si)),ylabel('I'),title('电流分布') in=U'*(Z\\V); i=V'*si; Zin=1/i

theta=(-pi:pi/100:pi)+eps; for m=1:length(theta)

E1=-j*w*u*exp(-j*k).*exp(j*k.*sqrt(mid(:,1).^2+mid(:,2).^2).*cos(abs(atan(mid(:,1)./(mid(:,2)+eps))-theta(m)))).*mid(:,3).*sin(theta(m))/(4*pi); Etheta(m)=E1'*si; end

Etheta=Etheta./max(Etheta); figure(2);

polar(theta,abs(Etheta)/max(abs(Etheta))),title('E平面方向图 (\\Phi = 0)');

Lo=find((abs(Etheta-1/sqrt(2))<0.05)==1);

G=abs(4*pi.*Etheta.*conj(Etheta)/(y*real(Zin).*si((N+1)/2).*conj(si((N+1)/2)))); Gmax=max(G)

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