1、第 14 題雙位法求解八木天線Consider a three-element Yagi-Uda dipole antennaThe length of reflector is 0.500l , the length of diver is 0.460l , and the1.0.419l .length of director is2.The spacing between reflector and driver is equal to the spacing between driver and director, both are equal to 0.2l .The charact

2、eristic impedance of transmission line feeding the antenna isequal to Zc = 50W .3.The objective is to calculate the following parameters:The input impedance. ( Zin = 33 - j7.5W )1.um power gain. ( G = 7.6dBi )2.3.4.TheThe front-to-back ratio. ( FBR = 18.6dB ) The standing wave ratio. ( SWR = 1.57 )G

3、= Zin - Zcand SWR =Zin + Zc（1）示意圖圖 11+ G 1- G 圖 2（2）電流分布圖圖 3（3）E 面方向圖圖 4(4)H 面方向圖圖 5（5）三維圖圖 6（6）運(yùn)行結(jié)果Zin=36.515 -5.1745i W G=7.9953dB FBR=18.62dBSWR=1.4(7) 程序clear; clc;clf;global k lr l ld a N m n LR L LD S lambda=1;c=3*108; f=c/lambda; w=2*pi*f;ep=(10(-9)/(36*pi);k=2*pi/lambda;mu=4*pi*10(-7); LR=0.

4、5*lambda; L=0.46*lambda; LD=0.419*lambda; S=0.2*lambda; N=51;a=0.002; lr=LR/(N-1);l=L/(N-1);ld=LD/(N-1); v0=1; Zc=50;z=zeros(N-2)*3,(N-2)*3);%N 為奇數(shù)ll1=ones(1,(N-2)*lr,ones(1,(N-2)*l,ones(1,(N-2)*ld;for m=1:(N-2)*3for n=1:(N-2)*3z(m,n)=j*w*mu*ll1(m)*ll1(n)*psi1(m,n)+(psi1(m+0.5,n+0.5)-psi1(m+0.5,n-0.

5、5)-psi1(m-0.5,n+0. 5)+psi1(m-0.5,n-0.5)/(j*w*ep);endendv=zeros(N-2)*3,1);v(N-2)*3+1)/2,1)=v0;i=inv(z)*v; i1=zeros(1,N); for n=1:(N-2)i1(1,n+1)=i(n,1);end i2=zeros(1,N);for n=(N-1):2*(N-2) i2(1,n+2-(N-1)=i(n,1);end i3=zeros(1,N);for n=2*(N-2)+1:3*(N-2)i3(1,n+2-(2*(N-2)+1)=i(n,1);endfigure(1)z1=-LR/2:

6、LR/(N-1):LR/2;plot(z1,abs(i1),'b'); hold on;z2=-L/2:L/(N-1):L/2;plot(z2,abs(i2),'g'); hold on;z3=-LD/2:LD/(N-1):LD/2;plot(z3,abs(i3),'r'); xlabel('分段的坐標(biāo)'); ylabel('Magnitude/A'); title('電流分布');legend('反射器','有源陣子','引向器')Zin=v0/i(

7、N-2)*3+1)/2);%輸入阻抗figure(2) ll2=ones(1,N)*lr,ones(1,N)*l,ones(1,N)*ld; y1=zeros(1,N);y2=S*ones(1,N); y3=2*S*ones(1,N); y=y1 y2 y3; z=z1 z2 z3; i4=i1 i2 i3; phi=pi/2; thita=0:0.01:2*pi;for m=1:length(thita)u=i4*sin(thita(1,m).*exp(j*k*(y*sin(thita(1,m)*sin(phi)+z*cos(thita(1,m).*ll2; f(m)=sum(u);endp

8、olar(thita,abs(f)./max(abs(f); title('E 面方向圖');G=10*log10(30*k2*max(abs(f)2/(real(Zin)*abs(i(N-2)*3+1)/2)2);%功率增益FBR=20*log10(max(abs(f)/abs(f(fix(3*pi/(0.01*2)+1);%前后功率比gamma=(Zin-Zc)/(Zin+Zc);SWR=(1+abs(gamma)/(1-abs(gamma);%駐波比f(wàn)igure(3) thita=pi/2; phi=0:0.01:2*pi; for m=1:length(phi)u=i4

9、*sin(thita).*exp(j*k*(y*sin(thita)*sin(phi(1,m)+z*cos(thita).*ll2; g(m)=sum(u);endpolar(phi,abs(g)./max(abs(g); title('H 面方向圖');figure(4)syms thita phi F=abs(sum(i1*sin(thita).*exp(j*k*(y1*sin(thita)*sin(phi)+z1*cos(thita)*lr+sum(i2*sin(thita).*exp(j*k*(y2*sin(thita)*sin(phi)+z2*cos(thita)*l+sum(i3*sin(thita).*exp(j*k*(y3*sin(thita)*sin (phi)+z3*cos(thita)*ld