MATLAB: Placing a tangential line at point of inflection for a data set.

inflectioninflexioninterceptMATLABslope

I have a graph where I need to find a point with the maximum slope and draw a tangient line there that crosses the x-axis. The value I want should be around 0.6.

I'm using a data set from excel.

% PLOTTING Id vs Vd
clear all;
clc;
%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')
figure('Name','Graph to get Vt')
IdVg = plot(Vg, VtId)
xlabel('Gate Voltage (V)');
ylabel('Drain Current (A)');
legend({'Vd = 0.2040816V'},'Location','northwest')
hold all;

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How to draw tangent line at infleciton point? can provide you with one approach.

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MATLAB: How to extract values from fitting the custom equation to a data set with multiple data entries

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

MATLAB: Plot Y derivative and find resulting X value minimum

Use the gradient function to calculate the first derivative, the del2 function to calculate the second derivative, and the min function to find the minimum.

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MATLAB: How to extract values from fitting the custom equation to a data set with multiple data entries

MATLAB: Plot Y derivative and find resulting X value minimum

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