how to make plot for non-trivial solution.

Arjun Kumar

2015 2 10

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problem det(M(n,m)-N(n,m))=0 (-∞<n<∞,1≤m<∞). clc close all clear all c=3*10^8; syms beta step=input('enter the step in odd number'); f=linspace(1.5e9,3e9,step); Lamba=c./f; L=15e-3; r_c=25e-3; r_d=45e-3; T=3e-3; r_w=64e-3; m=input('enter the value of m'); omega=2*pi.*f; k=omega./c; % fs_0=(2.405*c)/(2*pi*r_d); beta_m= m.*3.14./(L-T); % beta=(2*pi)./Lamba; nstep=fix(step/2); n=linspace(-nstep,nstep,step); beta_n=beta+(2.*n.*pi./L); gama_n=sqrt((k).^2-(beta_n).^2); bd=(beta_m).^2-(beta_n).^2; gama_m=sqrt((k).^2-(beta_m).^2); x0=(besselj(0,gama_m.*r_d).*bessely(0,gama_m.*r_w))-(bessely(0,gama_m.*r_d).*besselj(0,gama_m.*r_w)); x0_dash=(besselj(1,gama_m.*r_w).*bessely(0,gama_m.*r_w))-(bessely(1,gama_m.*r_d).*besselj(0,gama_m.*r_w)); z0=(besselj(0,gama_n.*r_d).*bessely(0,gama_n.*r_c))-(besselj(0,gama_n.*r_c).*bessely(0,gama_n.*r_d)); z0_dash=(besselj(1,gama_n.*r_d).*bessely(0,gama_n.*r_c))-(besselj(0,gama_n.*r_c).*bessely(1,gama_n.*r_d)); J1=besselj(1,gama_n.*r_d); md=((-1).^m*exp(-1j.*beta_n.*(L-T))-1)./(bd); M=(2*beta_m)/(L-T) M1=M.*md.*(x0./z0) N=M.*md.*(z0_dash)./(bessely(0,gama_n.*r_c).*gama_n) N1=N.*(gama_m./x0_dash) %we have to solve det(M1-N1)=0 for (-5<n<5,m=0,1) for calculating value of %beta %step and for loop nx=1:step; ny=round(step/2); nz=fix(step/2); for x=0:nz zx=0; for y=ny-x:ny+x zy=M1(y)-N1(y); zx=zx+zy end beta=solve(zx==0) n=x+1; Abeta(n)=beta; end disp('Abeta = ');disp(Abeta);

as we have solve this ,how to solve the value of beta for different value of n and m. please suggest us some process.

i have to plot between frequency and beta. problem is that it is having infinite series which i have truncated for some value of m and n.