# [MATLAB] complex permittivity for earth ionosphere syntax

1. Oct 10, 2013

### s_hy

1. The problem statement, all variables and given/known data

I have these equations:

ga = exp(-$σ^{R}$Δt/$ε_{0}$*$ε^{R}_{r}$)

2. Relevant equations

$σ^{R}$=($ε_{0}$*$ω^{2}_{p}$*v)/($ω^{2}$+$v^{2}$)

3. The attempt at a solution

Code (Text):

%ionospheric profile for earth-ionosphere waveguide as coefficients
e = 1.602e-19;          % electron charge
ms = 9.109e-31;         % electron mass

for h = 10:150^3;
v = 1.816*10^11*exp(-0.15*h);
end

A = N(1,:);                   % electron density, N
omegap = A*e.^2/ms*eps;
epsr   = 1-(omegap.^2/omega.^2+v.^2);
sigmar = (eps*omegap.^2*v)/(omega.^2+v.^2);

%property coefficient
for i=1:k
for j=1:k;
ga(i,j)=exp(-(sigmar*dt)/(eps*epsr));
gb(i,j)=(1-ga(i,j))/sigmar;
end;
end;

the problem is, i have problem with matrix dimension.

Warning: Rank deficient, rank = 0, tol = NaN.
> In propagation2d at 60
Error using /
Matrix dimensions must agree.

Error in propagation2d (line 61)
gb(i,j)=(1-ga(i,j))/sigmar;

i declare ga(i,j) in 2d because ga value is depend on height and distance as well but sigmar is in 1d (the value of sigma is depends on v where v depends on h-height only)..

anyone have idea what i should do in order to use the value of sigmar in gb(i,j)..i use matlab for this coding.

thank you.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution