I can't find solution with solve fuction

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sohyeon jung
sohyeon jung 2018-12-11
评论： madhan ravi 2018-12-11
Literally I can't find the solution with my code, which use 'solve' function to find solution of two equation.
The sol struct is filled with x(which is nowhere in my code) with this error message.
"Unable to convert expression into double array."
The code is below!
Is it because the equation itself is too complex?
How can I do for this?
S21_dB = -3.4964;
S21_deg = 2.1936;
syms er tanL positive;
assume(er, 'real');
assumeAlso(tanL, 'real');
assumeAlso(er<20 );
assumeAlso(tanL < 0.1 );
c = 3*10^8 ;
d = 731 *(10^-6);
f= 75*10^9;
lam = c./f;
w= 2*pi*f;
u_0 = 4*pi*(10^-7);
e_0 = 8.8541*(10^-12);
ec = er.*(1-1i*tanL);
z_0 = sqrt(u_0/(e_0));
z_d = sqrt(u_0/(e_0.*ec));
r = ((2*pi)/lam)*sqrt(ec);
S21_M = ((z_d+z_0).^2 - (z_d-z_0).^2)./((exp(1i.*r.*d).*(z_d+z_0).^2)- (exp(-1i*r*d).*(z_d-z_0).^2));
S21dB_M = real(20*log10(S21_M));
S21deg_M = real(angle(S21_M));
eqn1 = S21_dB- S21dB_M == 0;
eqn2 = S21_deg- S21deg_M == 0;
sol = solve([eqn1 eqn2],[er tanL],'ReturnConditions',true);
eps = double(sol.er);
losst = double(sol.tanL);
sol.er
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sohyeon jung
sohyeon jung 2018-12-11
Thank you for your comment! I edited the code. But there are still some error message. Could you look into this problem again? Thank you so much!!

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madhan ravi
madhan ravi 2018-12-11
编辑：madhan ravi 2018-12-11
You are solving system of non-linear equations so use fsolve()
S21_dB = -3.4964;
S21_deg = 2.1936;
syms er tanL real;
assumeAlso(er<20 );
assumeAlso(tanL < 0.1 );
c = 3*10^8 ;
d = 731 *(10^-6);
f= 75*10^9;
lam = c./f;
w= 2*pi*f;
u_0 = 4*pi*(10^-7);
e_0 = 8.8541*(10^-12);
ec = er.*(1-1i*tanL);
z_0 = sqrt(u_0/(e_0));
z_d = sqrt(u_0/(e_0.*ec));
r = ((2*pi)/lam)*sqrt(ec);
S21_M = ((z_d+z_0).^2 - (z_d-z_0).^2)./((exp(1i.*r.*d).*(z_d+z_0).^2)- (exp(-1i*r*d).*(z_d-z_0).^2));
S21dB_M = real(20*log10(S21_M));
S21deg_M = real(angle(S21_M));
[tanL,er]=fsolve(@rootss,[10,10])
function eqn=rootss(x)
tanL=x(1);
er=x(2);
eqn=[20*real(log((((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) - 6627542629724307/17592186044416)^2 - ((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) + 6627542629724307/17592186044416)^2)/(exp(-(pi*(-er*(- 1 + tanL*1i))^(1/2)*842785619867605125i)/2305843009213693952)*((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) - 6627542629724307/17592186044416)^2 - exp((pi*(-er*(- 1 + tanL*1i))^(1/2)*842785619867605125i)/2305843009213693952)*((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) + 6627542629724307/17592186044416)^2))/log(10));
angle((((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) - 6627542629724307/17592186044416)^2 - ((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) + 6627542629724307/17592186044416)^2)/(exp(-(pi*(-er*(- 1 + tanL*1i))^(1/2)*842785619867605125i)/2305843009213693952)*((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) - 6627542629724307/17592186044416)^2 - exp((pi*(-er*(- 1 + tanL*1i))^(1/2)*842785619867605125i)/2305843009213693952)*((-777820666600722137088/(5480422450918343*er*(- 1 + tanL*1i)))^(1/2) + 6627542629724307/17592186044416)^2))];
end
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sohyeon jung
sohyeon jung 2018-12-11
编辑：madhan ravi 2018-12-11
Hello madhan, sincerely thank you for your guide. I solved the problem by using fsolve function.
The below is my solution.
S21_dB = -3.4964;
S21_deg = 2.1936;
f = 75*10^9;
x0 = [10,0];
x = fsolve(@(x) rootss(x,f,S21_dB,S21_deg),x0)
function eqn=rootss(x, f, S21_dB,S21_deg)
er = x(1);
tanL = x(2);
c = 3*10^8 ;
d = 731 *(10^-6);
lam = c./f;
w= 2*pi*f; %*10^9
u_0 = 4*pi*(10^-7);
e_0 = 8.8541*(10^-12);
ec = er.*(1-1i*tanL);
z_0 = sqrt(u_0/(e_0));
z_d = sqrt(u_0/(e_0.*ec));
r = ((2*pi)/lam)*sqrt(ec);
S21_M = ((z_d+z_0).^2 - (z_d-z_0).^2)./((exp(1i.*r.*d).*(z_d+z_0).^2)- (exp(-1i*r*d).*(z_d-z_0).^2));
S21dB_M = real(20*log10(S21_M));
S21deg_M = real(angle(S21_M));
eqn = [ S21_dB- S21dB_M
S21_deg- S21deg_M];
end

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