lsqcurvefit - Parameter Optimization (Levenberg-Marquardt algorithm)

I am currently doing an lsqcurvefit - Parameter Optimization project using the Levenberg-Marquardt algorithm for parameter optimisation for values asd1,asd2,asd3,etc, which are found in the following equation obtained using the spice model of a component.

This is an expression for a capacitance, however it’s expressed as Q (charge) in terms of V(source, drain) (source- drain Voltage).

Q=CV

Hence I considered V(source-drain) as X and integrated the whole expression in order to obtain an expression for C (capacitance) in terms of X which is V(source, drain). I did this simply because my ydata values are measured Capacitance values for varying V(source, drain) voltage values (xdata). I did this integration using Matlab so I doubt there are any errors there, however, I would like to know whether integration is the right thing to do if we want an expression for C from a Q expression.

This is the code that I used (Corrected by @Star Strider) :

xdata2=[0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 27.5 30 32.5 35 37.5 40 42.5 45 47.5 50 52.5 55 57.5 60 62.5 65 67.5 70 72.5 75 77.5 80];

ydata2=[2458.8e-12 2448e-12 2418.8e-12 2400.1e-12 2355.5e-12 2261.1e-12 2102.4e-12 1874.4e-12 1551.5e-12 1356.8e-12 1246.8e-12 1196e-12 1160.6e-12 1137.2e-12 1125.7e-12 1105.8e-12 1093.7e-12 1073.9e-12 1058e-12 1046.3e-12 1038.6e-12 1022.6e-12 1006.5e-12 994.7e-12 978.8e-12 970.9e-12 950.9e-12 947e-12 931e-12 923.2e-12 915.3e-12 899.2e-12 895.5e-12];

asd1=6.7066e-10; asd2=1.3833e-09; asd3=-0.38247; asd4=47.537; asd5=1.1034e-09; asd6=-17.887; asd7=2.4197;

pinit2=[0.25;0.25;0.25;0.25;0.25;0.25;0.25];

psol = lsqcurvefit(@(param2,x)f2eq(param2,x,xdata2),pinit2,xdata2,ydata2);

disp(psol)

subplot(1,2,1)

p2 = plot(xdata2,ydata2,'ko');

p2.LineWidth=3;

subplot(1,2,2)

p2 = plot(xdata2,f2(xdata2,psol(1),psol(2),psol(3),psol(4),psol(5),psol(6),psol(7)),'b-');

p2.LineWidth=3;

function err2=f2eq(param2,x,y)

asd1=param2(1);

asd2=param2(2);

asd3=param2(3);

asd4=param2(4);

asd5=param2(5);

asd6=param2(6);

asd7=param2(7);

err2=x-f2(y,asd1,asd2,asd3,asd4,asd5,asd6,asd7);

end

function y2=f2(x2, asd1, asd2, asd3, asd4, asd5, asd6, asd7)

y2 = -asd2*asd4*polylog(2, -(exp(-asd3)*exp(x2))/asd4) - asd5*asd7*polylog(2, -(exp(-asd6)*exp(x2))/asd7)+asd1;

end

Hence, in the end, I must obtain values that are very similar to the asd1,asd2,asd3…. values given initially as the results contain negligible errors.

asd1=6.7066e-10; asd2=1.3833e-09; asd3=-0.38247; asd4=47.537; asd5=1.1034e-09; asd6=-17.887; asd7=2.4197;

However, the results I obtain are :

asd1=-47.5158

asd2=0.0004

asd3=0.1029

asd4= 0.5431

asd5= 17.8671

asd6=-116.5874

asd7= 0.0004

Could someone kindly help me identify what I have done wrong, because I must get equal or very similar values for asd1, asd2, asd3… just as given in the code as outputs.