# Find the exact eigen value graph of dipole antenna using characteristic mode theory

#### shaswatee23

Joined Mar 12, 2013
1
I am doing M.Tech project and my topic is Antenna design using characteristic mode theory. For this project I have taken the impedance matrix of the antenna which is depend on only the shape and size of the antenna not the excitation level.

So for finding the impedance matrix the halfwave dipole antenna has chossen having length 0.5lamda, 0.001lamda diameter.

The eigen value and the eigen vector can be find out by using the formula i.e. [J,D]=eig(X,R). Here the J is eigen current and D is the eigen value of the impedace matrix where X and R are imaginary and real parts of the impedance matrix.
The characteristic current curve i.e. eigen vector curve has come properly but in the curve of eigen value has some problem.

The value of eigen vector are coming correctly as previously found. but the eigen values are coming very small value and the resonat frequency of corresponding eigen value is not matched.For first eigenvalue its coming high frequency and for forth eigen value its coming lower frequency.
For the above problem the code I used posted here.

Rich (BB code):
pi=3.14159265;
beta=2.0*pi;
eta=120*pi;
%mu=(4*pi)*(10^-7);
%******************************************************
%***  INPUT DATA
%******************************************************
nm=(input('NUMBER OF SUBDIVISIONS <ODD NUMBER> ='));
tl1=(input('TOTAL DIPOLE LENGTH <WAVELENGTHS> ='));
%*********************************************************
%***  EXITATION OPTION # : 1 ---> MAGNETIC-FRILL
%                          2 ---> DELTA-GAP
%**********************************************************
disp('EXCITATION :');
disp('        OPTION (1):MAGNETIC-FRILL');
disp('        OPTION (2): DELTA-GAP');
iex=input('OPTION NUMBER :');
na=1;
for f=100:100:1000
c=3*(10^8);
lamda=c / (f * (10^6) );
%beta=(2*pi)/lamda;
tl=tl1*lamda;
ra=ra1*lamda;
hl=tl/2;
nmh=0.5*(nm+1);
dz=2*hl/nm;
zm=hl-0.5*dz;
b=0.5*dz;
a=-0.5*dz;
n=79;
hd=(b-a)/(n+1);
rb=2.3*ra;
tlab=2.0*log(2.3);
for N=1:nm
zm=hl-(N-0.5)*dz;
for I = 1: nm
zn=hl-(I-0.5)*dz;
za1=zn-zm+a;
%******************************************************************
%     FAST ALGORITHM FORM OF THE SIMPSON'S INTEGRAL ROUTINE
%******************************************************************
recgp=sqrt(ra*ra+za1*za1);
cgp1=exp(-j*beta*recgp)*((1.0+j*beta*recgp)*(2.0*recgp*recgp-3.0*ra*ra)+(beta*ra*recgp)^2)/(4.0*pi*beta^2*recgp^5);
zb1=zn-zm+b;
roc=sqrt(ra*ra+zb1*zb1);
cgp2=exp(-j*beta*roc)*((1.0+j*beta*roc)*(2.0*roc*roc-3.0*ra*ra)+(beta*ra*roc)^2)/(4.0*pi*beta^2*roc^5);
crt=cgp1+cgp2;
for k = 1: n
xk=a+k*hd;
zx1=zn-zm+xk;
r=sqrt(ra*ra+zx1*zx1);
cgp3=exp(-j*beta*r)*((1.0+j*beta*r)*(2.0*r*r-3.0*ra*ra)+(beta*ra*r)^2)/(4.0*pi*beta^2*r^5);
if mod(k,2)~=0
crt=crt+4*cgp3;
else
crt=crt+2*cgp3;
end
end
crt=crt*hd*.333333;
zmn1(N,I)=crt;
end
end
zmn1;
X=imag(zmn1);
R=real(zmn1);
%[J,D]=eig(X,R);
[J,D]=eig(imag(zmn1),real(zmn1));
J;
%i=[1:nm];
%xi=i;
%yi=J(i,1);
%li=J(i,2);
%ki=J(i,3);
%di=J(i,4);
%wi=J(i,8);
%plot(xi,yi,'k',xi,li,'r',xi,ki,'g',xi,di,'y')
%grid on;
%xlabel('segmentation')
%ylabel('EigenVector')
%title('CHARACTERISTIC CURRENT DISTRIBUTION ALONG THE DIPOLE')
%legend('J1','J2','J3','J4')
l1(na,1)=D(1,1);
l1(na,2)=D(2,2);
l1(na,3)=D(3,3);
l1(na,4)=D(4,4);
ms1(na,1)=abs(1 / (1 + (j*l1(na,1)) ) );  %modal significans of the first eigen value
na=na+1;
f;
end
t=length(l1);
k=1:t;
xi=[100:100:1000];
yi1=l1(k,1);
yi2=l1(k,2);
yi3=l1(k,3);
yi4=l1(k,4);
plot(xi,yi1,xi,yi2,xi,yi3,xi,yi4)
legend('D1','D2','D3','D4')
xlabel('Freq in MHz')
ylabel('EigenValue')
title('find the resonant frequency')
figure;
zi1=ms1(k,1);
plot(xi,zi1)

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