MATLAB: I want to solve definite integral with variable limits . can i apply trapezoidal rule for the same

variable limits

t0 = Id/(G0*(Vg-Vt-Id*Rs))
t1 = Id/(G0*(Vg-Vt-Vd+Id*Rd))
r = integral(@(t)1./(t.^2.*log(1-t)),t0,t1);
Id=A/r
where,
G0 = 0.132;
Vg = 0;
Vt = -.485;
Rs = 0.023;
Rd = 0.022;
Id = .003

Best Answer

Can you generate a set of values for t between t0 and t1? Yes. Use linspace.

Can you evaluate that function at those points? Why not?

t = linspace(t0,t1,100);
fun = @(t)1./(t.^2.*log(1-t));
trapz(t,fun(t))

Your code is incomplete, since it fails to define Vd. So I cannot run your code to show that it works.

Related Solutions

MATLAB: How to solve a definite integral that contains a variable same as that of one of its limits

q = 1.6*10^-19;
epsi = 12.47*10^-12*8.85;
Dd = 5*10^-9;
Di = 5*10^-9;
a = 0.125*10^-20*1.6*10^-19;
z = 100*10^-6;
Vs = 2.63*10^5;
G0 = (q^2*epsi*z*Vs)/(q^2*(Dd+Di)+epsi*a);
Vg = 0;
Vt = -0.485;
Rs = 12;
Rd = 12;
Id = 0.002;
Vd = 0;
t0 = Id/(G0*(Vg-Vt-Id*Rs));
t1 = Id/(G0*(Vg-Vt-Vd+Id*Rd));
mu = 0.93;
L = 100*10^-9;
A = -(Vs*L*G0)/mu;
r = integral(@(t)1./(t.^2.*log(1-t)),t0,t1)

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

Best Answer

Related Solutions

MATLAB: How to solve a definite integral that contains a variable same as that of one of its limits

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

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