Arrays have incompatible sizes for this operation.

clear;
% Frequency range from 1 MHz to 100 GHz
v = logspace(6, 11, 1000); % Using logspace for a smoother frequency range
w = 2*pi*v ;
T = 15 ;   % temperature of seawater in degree celcius
e = 8.854*(10^-12);   % permittivity of free space
% Salinity range from 20 to 40 PSU (Practical Salinity Units)
S = linspace(20,40,100);
mu = 4*pi*10^-7;      % permeability of sea water
d = 100;    % distance in meters

a0 = 5.72;
a1 = 2.24*(10^-2);
a2 = -7.12*(10^-4);
a3 = 5.05 ;
a4 = -7.03*(10^-2);
a5 = 6.006*(10^-4);
a6 = 3.6;
a7 = 2.9*(10^-2);
a8 = 1.4*(10^-1);
a9 = 1.5*(10^-3);
a10 = 2.4*(10^-4);
b0 = -3.56*(10^-3);
b1 = 4.75*(10^-6);
b2 = 1.16*(10^-5);
b3 = 2.4*(10^-3);
b4 = -3.14*(10^-5);
b5 = 2.52*(10^-7);
b6 = -6.3*(10^-3);
b7 = 1.76*(10^-4);
b8 = -9.22*(10^-5);
b9 = -1.99*(10^-2);
b10 = 1.812*(10^-4);
b11 = -2.05*(10^-3);
b12 = 1.58*(10^-4);
c1 = (3.709*10^4-8.22*10*T)/(4.22*10^2+T);
c2 = a0+a1*T+a2*(T^2);
e_1 = c2*(exp(b6.*S+b7*(S.^2)+b8*T.*S));
e_s = exp(b0.*S+b1*S.^2+b2.*S*T);
e_inf = (a6+a7*T)*(1+S*(b11+b12*T));     % dielectric constant at high frequencies
e_0 = c1*e_s;   % static dielectric constant at low frequencies
v_01 = (45+T)/(a3+a4*T+a5*(T^2));
v1 = v_01.*(1+S*(b3+b4*T+b5*(T^2)));
v_02 = (45+T)/(a8+a9*T+a10*(T^2));
v2 = v_02*(1+S*(b9+b10*T));
R1 = (37.5109-5.45216*S+1.4409*(10^(-2))*(S.^2))/( 1004.75+182.283*S+(S.^2));
s = T-15;
A1 = (6.9431+3.2841*s-9.9486*(10^(-2))*(s^2))/( 84.850+69.024*s+(s^2)) ;
A2 = 49.843+0.2276*S+0.198*(10^(-2))*(S.^2)+T;
R2 = 1+(A1./A2);
temp_2 = R1.*R2;
sigma_0 = S*( 2.903602+8.607*(10^(-2))*T+4.738817*(10^(-4))*(T^2)-2.991*(10^(-6))*(T^3)+4.3047*(10^(-9))*(T^4));
sigma = sigma_0.*temp_2;
temp = (e_0 - e_1)./(1+1i*v./v1);

Arrays have incompatible sizes for this operation.

temp_0 = (e_1 - e_inf)./(1+1i*v./v2);
temp_1 = sigma./(w*e);
e_sw = e_inf + temp +temp_0 - 1i*temp_1;
epsilon = e_sw.*e ;

temp_inner = (w.*epsilon).^2;
temp_inner1 = sqrt(1 + (sigma./temp_inner)) - 1;  % Inner square root
alpha = w.*sqrt((mu*epsilon./2).*temp_inner1);  % Attenuation constant 
z = 2*alpha*d;
A = abs(10*log10(exp(-z)));   % Attenuation loss in dB


figure;
plot(v,A);

% Add labels and a colorbar
xlabel('Frequency (Hz)');
ylabel('Attenuation (dB)');
title('Frequency vs. Salinity vs. Permittivity of Seawater');
colorbar;
grid on;

Answer 1

[Star Strider]

The problem is:

v = logspace(6, 11, 1000); % Using logspace for a smoother frequency range

since everything else has a length of 100. Change that to:

v = logspace(6, 11, 100); % Using logspace for a smoother frequency range

and it works —

clear;
% Frequency range from 1 MHz to 100 GHz
v = logspace(6, 11, 100); % Using logspace for a smoother frequency range
w = 2*pi*v ;
T = 15 ;   % temperature of seawater in degree celcius
e = 8.854*(10^-12);   % permittivity of free space
% Salinity range from 20 to 40 PSU (Practical Salinity Units)
S = linspace(20,40,100);
mu = 4*pi*10^-7;      % permeability of sea water
d = 100;    % distance in meters

a0 = 5.72;
a1 = 2.24*(10^-2);
a2 = -7.12*(10^-4);
a3 = 5.05 ;
a4 = -7.03*(10^-2);
a5 = 6.006*(10^-4);
a6 = 3.6;
a7 = 2.9*(10^-2);
a8 = 1.4*(10^-1);
a9 = 1.5*(10^-3);
a10 = 2.4*(10^-4);
b0 = -3.56*(10^-3);
b1 = 4.75*(10^-6);
b2 = 1.16*(10^-5);
b3 = 2.4*(10^-3);
b4 = -3.14*(10^-5);
b5 = 2.52*(10^-7);
b6 = -6.3*(10^-3);
b7 = 1.76*(10^-4);
b8 = -9.22*(10^-5);
b9 = -1.99*(10^-2);
b10 = 1.812*(10^-4);
b11 = -2.05*(10^-3);
b12 = 1.58*(10^-4);
c1 = (3.709*10^4-8.22*10*T)/(4.22*10^2+T);
c2 = a0+a1*T+a2*(T^2);
e_1 = c2*(exp(b6.*S+b7*(S.^2)+b8*T.*S));
e_s = exp(b0.*S+b1*S.^2+b2.*S*T);
e_inf = (a6+a7*T)*(1+S*(b11+b12*T));     % dielectric constant at high frequencies
e_0 = c1*e_s;   % static dielectric constant at low frequencies
v_01 = (45+T)/(a3+a4*T+a5*(T^2));
v1 = v_01.*(1+S*(b3+b4*T+b5*(T^2)));
v_02 = (45+T)/(a8+a9*T+a10*(T^2));
v2 = v_02*(1+S*(b9+b10*T));
R1 = (37.5109-5.45216*S+1.4409*(10^(-2))*(S.^2))/( 1004.75+182.283*S+(S.^2));
s = T-15;
A1 = (6.9431+3.2841*s-9.9486*(10^(-2))*(s^2))/( 84.850+69.024*s+(s^2)) ;
A2 = 49.843+0.2276*S+0.198*(10^(-2))*(S.^2)+T;
R2 = 1+(A1./A2);
temp_2 = R1.*R2;
sigma_0 = S*( 2.903602+8.607*(10^(-2))*T+4.738817*(10^(-4))*(T^2)-2.991*(10^(-6))*(T^3)+4.3047*(10^(-9))*(T^4));
sigma = sigma_0.*temp_2;
temp = (e_0 - e_1)./(1+1i*v./v1);
temp_0 = (e_1 - e_inf)./(1+1i*v./v2);
temp_1 = sigma./(w*e);
e_sw = e_inf + temp +temp_0 - 1i*temp_1;
epsilon = e_sw.*e ;

temp_inner = (w.*epsilon).^2;
temp_inner1 = sqrt(1 + (sigma./temp_inner)) - 1;  % Inner square root
alpha = w.*sqrt((mu*epsilon./2).*temp_inner1);  % Attenuation constant 
z = 2*alpha*d;
A = abs(10*log10(exp(-z)));   % Attenuation loss in dB


figure;
plot(v,A);

% Add labels and a colorbar
xlabel('Frequency (Hz)');
ylabel('Attenuation (dB)');
title('Frequency vs. Salinity vs. Permittivity of Seawater');
colorbar;
grid on;

.

[Staley Arya]

Thanks

[Star Strider]

As always, my pleasure!