I can't find solution with solve fuction

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

[KSSV]

Undefined function or variable 'd'.

Error in Junk (line 19)
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));
 

[Walter Roberson]

you define S21_dB but you use S21dB

[sohyeon jung]

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!!

Answer 1

[madhan ravi]

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

[sohyeon jung]

Sincerely So thank you for your answer!! But, since I have to use for loop, when I change the code like the below. It doesn't work.. Can you help me out to check the reason ?

        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));
         
         eqn1 = S21_dB- S21dB_M; 
         eqn2 = S21_deg- S21deg_M;
        
        x = [tanL, er];
        fun = rootss(x,eqn1, eqn2);
        x0 = [10,0.001];
        [tanL,er] = fsolve(fun,x0);

 function eqn=rootss(x, eqn1, eqn2)
        tanL=x(1);
        er=x(2);
        eqn(1) = eqn1 ;
        eqn(2) = eqn2 ;
 end

[madhan ravi]

Just parameterize your function where only the parameters change and save the outputs using cells , take your time to understand.

[sohyeon jung]

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

[madhan ravi]

Anytime :)