I can't find solution with solve fuction

Question

sohyeon jung 2018-12-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/435081-i-can-t-find-solution-with-solve-fuction

评论： madhan ravi 2018-12-11

采纳的回答： madhan ravi

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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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Walter Roberson 2018-12-11

you define S21_dB but you use S21dB

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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Answer 1

madhan ravi 2018-12-11

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https://ww2.mathworks.cn/matlabcentral/answers/435081-i-can-t-find-solution-with-solve-fuction#answer_351625

编辑：madhan ravi 2018-12-11

在 MATLAB Online 中打开

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 2018-12-11

在 MATLAB Online 中打开

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

sohyeon jung 2018-12-11

编辑：madhan ravi 2018-12-11

在 MATLAB Online 中打开

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