How do I extract values from fitting my custom equation to a data set with multiple data entries?

Question

Ausamah Hobbi 2018-11-29

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评论： Ausamah Hobbi 2018-12-4

W1umL3um.xlsx

This is for a lab I have to do for class and am sort of stuck at this point. I have a graph with multiple plots. This is at %Plotting Long Channel. I want to fit the equation below to each one of those data sets to extrapolate the mobility term (u) and Threshold Voltage (Vt) for each Vg value. Vt and u are the fitting parameters. At each Vg value I have data sets of Id vs Vd as you can see in my excel spreedsheet. My values for Vg are 0:0.2:1.2. I have the custom fitting toolbox but I am getting no where with it, errors left and right. I want to fit the equation to each of my data sets and find the mobility term that will fit it to the data. Please ignore the Vt already there. I'm trying to get the Vt two seperate ways then compare.

% PLOTTING Id vs Vd
clear all;
clc;
%Long Channel
Vd = xlsread('W1umL3um.xlsx', 'C4:C53');
Id0 = xlsread('W1umL3um.xlsx', 'D56:D5105');
Id2 = xlsread('W1umL3um.xlsx', 'F56:F105');
Id4 = xlsread('W1umL3um.xlsx', 'H56:H105');
Id6 = xlsread('W1umL3um.xlsx', 'J56:J105');
Id8 = xlsread('W1umL3um.xlsx', 'L56:L105');
Id10 = xlsread('W1umL3um.xlsx', 'N56:N105');
Id12 = xlsread('W1umL3um.xlsx', 'P56:P105');
%Short Channel
SVd = xlsread('W1umL60nm.xlsx', 'C4:C53');
SId0 = xlsread('W1umL60nm.xlsx', 'D56:D105');
SId2 = xlsread('W1umL60nm.xlsx', 'F56:F105');
SId4 = xlsread('W1umL60nm.xlsx', 'H56:H105');
SId6 = xlsread('W1umL60nm.xlsx', 'J56:J105');
SId8 = xlsread('W1umL60nm.xlsx', 'L56:L105');
SId10 = xlsread('W1umL60nm.xlsx', 'N56:N105');
SId12 = xlsread('W1umL60nm.xlsx', 'P56:P5105');
%Plotting Long Channel
figure('Name', 'Long Channel IdVd curve');
Lp = plot(Vd, Id0, Vd, Id2, Vd, Id4, Vd, Id6, Vd, Id8, Vd, Id10, Vd, Id12);
title('Drain Voltage vs Drain Current at varying Gate Voltages');
xlabel('Drain Voltage (V)');
ylabel('Drain Current (mA/um)');
legend({'Vg = 0V','Vg = 0.2V','Vg = 0.4V','Vg = 0.6V','Vg = 0.8V','Vg = 1.0V','Vg = 1.2V'},'Location','east')
grid on
%Plotting Short Channel
figure('Name', 'Short Channel IdVd curve');
Sp = plot(SVd, SId0, SVd, SId2, SVd, SId4, SVd, SId6, SVd, SId8, SVd, SId10, SVd, SId12);
title('Drain Voltage vs Drain Current at varying Gate Voltages');
xlabel('Drain Voltage (V)');
ylabel('Drain Current (mA/um)');
legend({'Vg = 0V','Vg = 0.2V','Vg = 0.4V','Vg = 0.6V','Vg = 0.8V','Vg = 1.0V','Vg = 1.2V'},'Location','east');
grid on
%Plotting Id vs Vg for Long Channel @ Vd = 0.2040816
Vg = xlsread('W1umL3um.xlsx','For Vt','D5:D11');
VtId = xlsread('W1umL3um.xlsx','For Vt','E5:E11');
dydx = gradient(VtId,mean(diff(Vg)));                       % Calculate Numerical Derivative At Every Point
[maxslope,idx] = max(dydx);                                 % Find Maximum Slope & Index
x = Vg(idx);
y = VtId(idx);
intcpt = (y - maxslope*x);                                  % Calculate Tangent Line Intercept
tangentline = maxslope*Vg+intcpt;                           % Calculate Tangent Line
Vt = ((-2E-6)-intcpt)/maxslope                              % Minumum X-Axis Intercept
figure('Name','Graph to get Vt');
IdVg = plot(Vg, VtId);
hold on
plot(Vg, tangentline, '--');
hold off
xlabel('Gate Voltage (V)');
ylabel('Drain Current (mA/um)');
legend({'Vd = 0.2040816V', 'Tangent'},'Location','northwest')
ylim([0 max(ylim)])
%Vg for the purpose of finding u
      %Mobility equation from long channel equation
      

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Star Strider 2018-12-1

I am still not getting anything for ‘Id0’. It is an empty matrix. (I am using the file I downloaded previously, since it has the same name.)

I cannot make any sense out of ‘SVd’ and ‘SId0’. They look completely random.

Ausamah Hobbi 2018-12-2

Hey Image Analyst, any progress?

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Answer 1

Ausamah Hobbi 2018-12-3

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/432870-how-do-i-extract-values-from-fitting-my-custom-equation-to-a-data-set-with-multiple-data-entries#answer_350186

编辑：Ausamah Hobbi 2018-12-3

在 MATLAB Online 中打开

To Everyone who might be interested in the answer. Here is the code I'm using. I've commented some things out so I could plot them all together. I used a curve fitting app but generated the code for it.

clc;
%Long Channel
Vd = xlsread('W1umL3um.xlsx', 'C4:C43');
Id0 = xlsread('W1umL3um.xlsx', 'D56:D95');
Id2 = xlsread('W1umL3um.xlsx', 'F56:F95');
Id4 = xlsread('W1umL3um.xlsx', 'H56:H95');
Id6 = xlsread('W1umL3um.xlsx', 'J56:J95');
Id8 = xlsread('W1umL3um.xlsx', 'L56:L95');
Id10 = xlsread('W1umL3um.xlsx', 'N56:N95');
Id12 = xlsread('W1umL3um.xlsx', 'P56:P95');
% Fit: 'Vg = 0V'.
[xData, yData] = prepareCurveData( Vd, Id0 );
% Set up fittype and options.
ft = fittype( '(a1.*0.00575.*((0-b1).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off'
opts.StartPoint = [0.196595250431208 0.251083857976031];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 0V' );
h1 = plot( fitresult, xData, yData, 'ok')
h1(1).LineWidth = 1;
h1(2).LineWidth = 2;
%legend( h1, 'Id0 vs. Vd', 'Vg = 0V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id0
%grid on
hold on
%Fit: 'Vg = 0.2V'.
[xData, yData] = prepareCurveData( Vd, Id2 );
% Set up fittype and options.
ft = fittype( '(a2.*0.00575.*((0.2-b2).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.162182308193243 0.794284540683907];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
%figure( 'Name', 'Vg = 10.2V' );
h2 = plot( fitresult, xData, yData, 'ok')
h2(1).LineWidth = 1;
h2(2).LineWidth = 2;
%legend( h2, 'Id2 vs. Vd', 'Vg = 10.2V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id2
grid on
% Fit: 'Vg = 0.4V'.
[xData, yData] = prepareCurveData( Vd, Id4 );
% Set up fittype and options.
ft = fittype( '(a3.*0.00575.*((0.4-b3).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.311215042044805 0.528533135506213];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
%figure( 'Name', 'Vg = 0.4V' );
h3 = plot( fitresult, xData, yData, 'ok')
h3(1).LineWidth = 1;
h3(2).LineWidth = 2;
%legend( h3, 'Id4 vs. Vd', 'Vg = 0.4V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id4
%grid on
% Fit: 'Vg = 0.6V'.
[xData, yData] = prepareCurveData( Vd, Id6 );
% Set up fittype and options.
ft = fittype( '(a4.*0.00575.*((0.6-b4).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.165648729499781 0.601981941401637];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
%figure( 'Name', 'Vg = 0.6V' );
h4 = plot( fitresult, xData, yData, 'ok')
h4(1).LineWidth = 1;
h4(2).LineWidth = 2;
%legend( h4, 'Id6 vs. Vd', 'Vg = 0.6V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id6
%grid on
% Fit: 'Vg = 0.8V'.
[xData, yData] = prepareCurveData( Vd, Id8 );
% Set up fittype and options.
ft = fittype( '(a5.*0.00575.*((0.8-b5).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.262971284540144 0.654079098476782];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
%figure( 'Name', 'Vg = 0.8V' );
h5 = plot( fitresult, xData, yData, 'ok')
h5(1).LineWidth = 1;
h5(2).LineWidth = 2;
%legend( h5, 'Id8 vs. Vd', 'Vg = 0.8V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id8
%grid on
% Fit: 'Vg = 1.0V'.
[xData, yData] = prepareCurveData( Vd, Id10 );
% Set up fittype and options.
ft = fittype( '(a6.*0.00575.*((1.0-b6).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.689214503140008 0.748151592823709];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
%figure( 'Name', 'Vg = 1.0V' );
h6 = plot( fitresult, xData, yData, 'ok')
h6(1).LineWidth = 1;
h6(2).LineWidth = 3;
%legend( h6, 'Id10 vs. Vd', 'Vg = 1.0V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id10
%grid on
% Fit: 'Vg = 1.2V'.
[xData, yData] = prepareCurveData( Vd, Id12 );
% Set up fittype and options.
ft = fittype( '(a7.*0.00575.*((1.2-b7).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id12' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.380445846975357 0.567821640725221];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
%figure( 'Name', 'Vg = 1.2V' );
h7 = plot( fitresult, xData, yData, 'ok')
h7(1).LineWidth = 1;
h7(2).LineWidth = 2;
%legend( h7, 'Id vs. Vd', 'Vg = 1.2V', 'Location', 'NorthEast' );
% Label axes
%xlabel Vd
%ylabel Id12
%grid on
grid on
xlabel ('Drain Voltage (V)')
ylabel ('Drain Current (mA/um)')
title ('Drain Current vs Drain Voltage w/ varying Gate Voltage')
hold off

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Answer 2

Star Strider 2018-12-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/432870-how-do-i-extract-values-from-fitting-my-custom-equation-to-a-data-set-with-multiple-data-entries#answer_349938

在 MATLAB Online 中打开

I am using this code to estimate your parameters:

Vd = xlsread('W1umL3um.xlsx', 'C4:C53');
Id0 = xlsread('W1umL3um.xlsx', 'D56:D5105');
SVd = xlsread('W1umL60nm.xlsx', 'C4:C53');
SId0 = xlsread('W1umL60nm.xlsx', 'D56:D105');
Vg = 0:0.2:1.2;
% % % b(1) = mu,    b(2) = Vt
% Idfcn = @(b,Vd) b(1).*Z*Ci.*(Vg-b(2)).*Vd - Vd.^2/2)./L;
ZCiL = 0.00575;
Idfcn = @(b,Vd) b(1).*ZCiL.*(Vg(1)-b(2)).*Vd - Vd.^2/2;
% [B,fv] = fminsearch(@(b) norm(Id0 - Idfcn(b,Vd)), [1;1]);
[B,fv] = fminsearch(@(b) norm(SId0 - Idfcn(b,SVd)), 1000*rand(2,1));
figure
plot(SVd, SId0, 'p')
hold on
plot(SVd, Idfcn(B,SVd), '-g')
hold off
grid

However, since I cannot use your data (it is either nonexistend or apparently random), I can go not further.

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Ausamah Hobbi 2018-12-2

在 MATLAB Online 中打开

This is what I'm getting when I run your code. Not getting anything for mu or Vt yet though. Code is below.

Here's the code:

clear all;
clc;
%Long Channel
Vd = xlsread('W1umL3um.xlsx', 'C4:C53');
Id0 = xlsread('W1umL3um.xlsx', 'D56:D5105');
Id2 = xlsread('W1umL3um.xlsx', 'F56:F105');
Id4 = xlsread('W1umL3um.xlsx', 'H56:H105');
Id6 = xlsread('W1umL3um.xlsx', 'J56:J105');
Id8 = xlsread('W1umL3um.xlsx', 'L56:L105');
Id10 = xlsread('W1umL3um.xlsx', 'N56:N105');
Id12 = xlsread('W1umL3um.xlsx', 'P56:P105');
%Short Channel
SVd = xlsread('W1umL60nm.xlsx', 'C4:C53');
SId0 = xlsread('W1umL60nm.xlsx', 'D56:D105');
SId2 = xlsread('W1umL60nm.xlsx', 'F56:F105');
SId4 = xlsread('W1umL60nm.xlsx', 'H56:H105');
SId6 = xlsread('W1umL60nm.xlsx', 'J56:J105');
SId8 = xlsread('W1umL60nm.xlsx', 'L56:L105');
SId10 = xlsread('W1umL60nm.xlsx', 'N56:N105');
SId12 = xlsread('W1umL60nm.xlsx', 'P56:P5105');
Vg = 0:0.2:1.2;
% % % b(1) = mu,    b(2) = Vt
% Idfcn = @(b,Vd) b(1).*Z*Ci.*(Vg-b(2)).*Vd - Vd.^2/2)./L;
ZCiL = 0.00575;
Idfcn = @(b,Vd) b(1).*ZCiL.*(Vg(1)-b(2)).*Vd - Vd.^2/2;
% [B,fv] = fminsearch(@(b) norm(Id0 - Idfcn(b,Vd)), [1;1]);
[B,fv] = fminsearch(@(b) norm(SId0 - Idfcn(b,SVd)), 1000*rand(2,1));
figure
plot(SVd, SId0, 'p')
hold on
plot(SVd, Idfcn(B,SVd), '-g')
hold off
grid

Ausamah Hobbi 2018-12-2

在 MATLAB Online 中打开

W1umL3um.xlsx

Here is an updated excel spreadsheet with (I'm pretty sure) with the correct values. I went back and made sure the units in the .xls was correlating correctly to the units of the equation.

Here are some alterations I did to the code you provided me with. You do not need the "Short Channel" values such as SVd or SId. Sorry for any confusion. I just want the equation to fit to the "Long Channel" data.

clear all;
clc;
%Long Channel
Vd = xlsread('W1umL3um.xlsx', 'C4:C53');
Id0 = xlsread('W1umL3um.xlsx', 'R56:R105');
Id2 = xlsread('W1umL3um.xlsx', 'T56:T105');
Id4 = xlsread('W1umL3um.xlsx', 'V56:V105');
Id6 = xlsread('W1umL3um.xlsx', 'X56:X105');
Id8 = xlsread('W1umL3um.xlsx', 'Z56:Z105');
Id10 = xlsread('W1umL3um.xlsx', 'AB56:AB105');
Id12 = xlsread('W1umL3um.xlsx', 'AD56:AD105');
Vg = 0:0.2:1.2;
%%%b(1) = mu,    b(2) = Vt
% Idfcn = @(b,Vd) b(1).*Z*Ci.*(Vg-b(2)).*Vd - Vd.^2/2)./L;
ZCiL = 0.00575;
Idfcn = @(b,Vd) (b(1).*ZCiL.*((Vg(7)-b(2)).*Vd - Vd.^2/2)).*1000;
% [B,fv] = fminsearch(@(b) norm(Id0 - Idfcn(b,Vd)), [1;1]);
[B,fv] = fminsearch(@(b) norm(Id0 - Idfcn(b,Vd)), 1000*rand(2,1));
figure
plot(Vd, Id0, '.')
hold on
plot(Vd, Idfcn(B,Vd), '-g')
hold off
grid

Ausamah Hobbi 2018-12-3

在 MATLAB Online 中打开

Hey Star Strider! I figured it out! I got the fits I need! I wouldn't have gone this far without you!

Here's my final code. I... however have one question. How do I combine all these plots together? I can't figure out how to implement the 'hold'.

clear all;
clc;
%Long Channel
Vd = xlsread('W1umL3um.xlsx', 'C4:C53');
Id0 = xlsread('W1umL3um.xlsx', 'R56:R105');
Id2 = xlsread('W1umL3um.xlsx', 'T56:T105');
Id4 = xlsread('W1umL3um.xlsx', 'V56:V105');
Id6 = xlsread('W1umL3um.xlsx', 'X56:X105');
Id8 = xlsread('W1umL3um.xlsx', 'Z56:Z105');
Id10 = xlsread('W1umL3um.xlsx', 'AB56:AB105');
Id12 = xlsread('W1umL3um.xlsx', 'AD56:AD105');
%{
Vg = 0:0.2:1.2;
%%%b(1) = mu,    b(2) = Vt
% Idfcn = @(b,Vd) b(1).*Z*Ci.*(Vg-b(2)).*Vd - Vd.^2/2)./L;
ZCiL = 0.00575;
Idfcn = @(b,Vd) (b(1).*ZCiL.*((Vg(1)-b(2)).*Vd - Vd.^2/2)).*1000;
[B,fv] = fminsearch(@(b) norm(Id0 - Idfcn(b,Vd)), [1;1]);
% [B,fv] = fminsearch(@(b) norm(Id0 - Idfcn(b,Vd)), 1000*rand(2,1));
figure
plot(Vd, Id0, '.')
hold on
plot(Vd, Idfcn(B,Vd), '-g')
hold off
grid
%}
% Fit: 'Vg = 0V'.
[xData, yData] = prepareCurveData( Vd, Id0 );
% Set up fittype and options.
ft = fittype( '(a1.*0.00575.*((0-b1).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off'
opts.StartPoint = [0.196595250431208 0.251083857976031];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 0V' );
h1 = plot( fitresult, xData, yData );
legend( h1, 'Id0 vs. Vd', 'Vg = 0V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id0
grid on
%Fit: 'Vg = 0.2V'.
[xData, yData] = prepareCurveData( Vd, Id2 );
% Set up fittype and options.
ft = fittype( '(a2.*0.00575.*((0.2-b2).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.162182308193243 0.794284540683907];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 10.2V' );
h2 = plot( fitresult, xData, yData );
legend( h2, 'Id2 vs. Vd', 'Vg = 10.2V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id2
grid on
% Fit: 'Vg = 0.4V'.
[xData, yData] = prepareCurveData( Vd, Id4 );
% Set up fittype and options.
ft = fittype( '(a3.*0.00575.*((0.4-b3).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.311215042044805 0.528533135506213];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 0.4V' );
h3 = plot( fitresult, xData, yData );
legend( h3, 'Id4 vs. Vd', 'Vg = 0.4V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id4
grid on
% Fit: 'Vg = 0.6V'.
[xData, yData] = prepareCurveData( Vd, Id6 );
% Set up fittype and options.
ft = fittype( '(a4.*0.00575.*((0.6-b4).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.165648729499781 0.601981941401637];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 0.6V' );
h4 = plot( fitresult, xData, yData );
legend( h4, 'Id6 vs. Vd', 'Vg = 0.6V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id6
grid on
% Fit: 'Vg = 0.8V'.
[xData, yData] = prepareCurveData( Vd, Id8 );
% Set up fittype and options.
ft = fittype( '(a5.*0.00575.*((0.8-b5).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.262971284540144 0.654079098476782];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 0.8V' );
h5 = plot( fitresult, xData, yData );
legend( h5, 'Id8 vs. Vd', 'Vg = 0.8V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id8
grid on
% Fit: 'Vg = 1.0V'.
[xData, yData] = prepareCurveData( Vd, Id10 );
% Set up fittype and options.
ft = fittype( '(a6.*0.00575.*((1.0-b6).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.689214503140008 0.748151592823709];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 1.0V' );
h6 = plot( fitresult, xData, yData );
legend( h6, 'Id10 vs. Vd', 'Vg = 1.0V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id10
grid on
% Fit: 'Vg = 1.2V'.
[xData, yData] = prepareCurveData( Vd, Id12 );
% Set up fittype and options.
ft = fittype( '(a7.*0.00575.*((1.2-b7).*Vd - (Vd.^2/2)))*1000', 'independent', 'Vd', 'dependent', 'Id12' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.StartPoint = [0.380445846975357 0.567821640725221];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts )
% Plot fit with data.
figure( 'Name', 'Vg = 1.2V' );
h7 = plot( fitresult, xData, yData );
legend( h7, 'Id12 vs. Vd', 'Vg = 1.2V', 'Location', 'NorthEast' );
% Label axes
xlabel Vd
ylabel Id12
grid on

Star Strider 2018-12-3

在 MATLAB Online 中打开

Congratulations! Thank you!

I do not have the Curve Fitting Toolbox, so I cannot run your code.

You appear to have several different plots with different legend entries and figure names, so I am not certain what you want to do with all of them. The easiest way may be to combine them as different axes in the same figure, using the subplot (link) function.

If you want them all in the same figure, do something like this:

figure
h1 = plot( fitresult_1, xData, yData, 'DisplayName', 'Vg = 0V');
hold on
h2 = plot( fitresult_2, xData, yData, 'DisplayName', 'Vg = 10.2V');
h3 = plot( fitresult_3, xData, yData, 'DisplayName', 'Vg = 0.4V');
h4 = plot( fitresult_4, xData, yData, 'DisplayName','Vg = 0.6V');
h5 = plot( fitresult_5, xData, yData, 'DisplayName','Vg = 0.8V');
h6 = plot( fitresult_6, xData, yData, 'DisplayName','Vg = 1.0V');
h7 = plot( fitresult_7, xData, yData, 'DisplayName','Vg = 1.2V');
hold off
hl = legend;
hl.Location = 'NE';
grid

That should work. However, since I cannot run your code, I am specifying that my code here is UNTESTED.

Note that this requires that you label each ‘fitresult’ and probably ‘gof’ uniquely. (You might be able to store these as numeric or cell array elements instead. I do not know the variable class the are, so I cannot specify that.)

I will consider running your code with fitting procedures that I have available (Statistics and Machine Learning Toolbox, Optimization Toolbox) to see what the result is, simply out of curiosity.

Ausamah Hobbi 2018-12-3

编辑：Ausamah Hobbi 2018-12-3

在 MATLAB Online 中打开

I do have the Symbolic math toolbox. How would it change it?

I have updated the code to what you mentioned.

clc;
% INITIALIZE MATLAB
close all;
clc;
clear all;
syms Vt
syms x
syms Vd
syms Vg
syms Cop %Constant of p
syms r
%Short Channel
SVd = xlsread('W1umL60nm.xlsx', 'C4:C53');
SId0 = xlsread('W1umL60nm.xlsx', 'D56:D105');
SId2 = xlsread('W1umL60nm.xlsx', 'F56:F105');
SId4 = xlsread('W1umL60nm.xlsx', 'H56:H105');
SId6 = xlsread('W1umL60nm.xlsx', 'J56:J105');
SId8 = xlsread('W1umL60nm.xlsx', 'L56:L105');
SId10 = xlsread('W1umL60nm.xlsx', 'N56:N105');
SId12 = xlsread('W1umL60nm.xlsx', 'P56:P105');
%Vg = 0:0.2:1.2;
vd = @(SVd, r) (1/0.026).*r.*SVd; %r is the fitting parameter
% Ro (Density)
Cop = 1.652e+16; %Coefficient of Ro
p = @(Vg, Vt) Cop*(Vg-Vt);  %Vt is the fitting parameter
% Breaking down the Integral
a = @(SVd,r) 1+exp(vd(SVd, r));
b = @(SVd,Vg,Vt,r)sqrt(a(SVd,r)^2+4*exp(vd(SVd,r))*(exp(p(Vg, Vt))-1));
u = @(SVd,Vg,Vt,r) log(b(SVd,Vg,Vt)-(1+exp(vd(SVd,r)))-log(2));
f = @(SVd,Vg,Vt,r,x)sqrt(u(SVd,Vg,Vt,r))./(1+exp(u(SVd,Vg,Vt,r)-x));
%F = @(x)integral(@(u)f(u,x),0,inf, 'ArrayValued', true);
int(f, SVd, Vg, r, [0 inf])

Ausamah Hobbi 2018-12-4

在 MATLAB Online 中打开

Hey Star, here's an updated version of my code. Of course there are errors.

% INITIALIZE MATLAB
close all;
clc;
clear all;
syms Vt
syms x
syms Vd
syms Vg
syms Cop %Constant of p
syms r
Z = 1e-6;
q = 1.6e-19;
kT = 4.11e-21;
m0 = 9.1e-31;
hbar = 1.054e-34;
mt = .2 * m0;
mv = 2.5;
e0 = 8.85e-12;
er = 3.7;
Ci = .0163725;
%Defining Vg
Vg0 = 0;
Vg2 = 0.2;
Vg4 = 0.4;
Vg6 = 0.6;
Vg8 = 0.8;
Vg10 = 1.0;
Vg12 = 1.2;
%Short Channel
SVd = xlsread('W1umL60nm.xlsx', 'C4:C53');
SId0 = xlsread('W1umL60nm.xlsx', 'D56:D105');
SId2 = xlsread('W1umL60nm.xlsx', 'F56:F105');
SId4 = xlsread('W1umL60nm.xlsx', 'H56:H105');
SId6 = xlsread('W1umL60nm.xlsx', 'J56:J105');
SId8 = xlsread('W1umL60nm.xlsx', 'L56:L105');
SId10 = xlsread('W1umL60nm.xlsx', 'N56:N105');
SId12 = xlsread('W1umL60nm.xlsx', 'P56:P105');
Io = (sqrt(2).*q.*((kT)^1.5).*mv.*sqrt(mt))/((pi.^2).*(hbar).^2);
vd = @(Vd) (q.*r.*SVd)/(kT);
Ro = @(Vg) (2.*pi.*(hbar.^2).*Ci.*(Vg-Vt))./(q.*kT.*mt.*mv);
fermi_half = @(x) (x.^0.5)/(1+exp.^(x-a));
fermi_half_vd = @(x) (x.^0.5)/(1+exp.^(x-a+vd(Vd)));
%To get u(Vd, Vg)
a = @(Vd, Vg) sqrt((1 + exp.^(vd(Vd))).^2 + 4.*exp(vd(Vd)).*(math.exp(p(Vg)) - 1));
b = @(Vd)(1 + exp.^(vd(Vd)));
c = log(2);
u = @(Vd, Vg) log(a-b)-c
fermi_half_int = quadgk(fermi_half(x), 0, inf)
fermi_half_vd_int = quadgk(fermi_half_vd(x), 0, inf)

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How do I extract values from fitting my custom equation to a data set with multiple data entries?

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