MATLAB: I can’t find solution with solve fuction

solve

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

Best Answer

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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MATLAB: Error encountered using ‘fzero’

First of all, it looks like P is maybe supposed to be restricted to be a positive number, and when it's not, your function returns a complex number. However, fzero doesn't respect bounds on the search variable (P in your case): it looks for any value of P that zeros the function, regardless of whether P is postiive or negative. If it encounters a complex function value at some point, however (e.g., in your case if it evaluates F(P) for P<0), fzero doesn't know how to proceed, so it stops and reports an error. This is what you're seeing I believe.

There are various ways you can fix this problem, but the simplest to implement in your case is probably just to do a variable transformation like logP = log(P), P = exp(logP). For any real value of logP, P will be positive here, so you can use fzero to search among values of logP instead of directly for P. Here's how you might implement this:

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. 
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I think this should do what you want.

A couple of other comments/pointers:

Do you really need to do this with symbolic variables? Couldn't you just write a regular MATLAB function called F.m that contains everything up to just before you start the fzero loop, but where logP is the argument passed into the function, and excluding the syms and the call to matlabFunction? Symbolic math is slow, so if you can avoid it you should.
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What happens if you try

sym r
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