MATLAB basics

Getting it

Students can usually use MATLAB through the university licence, either installed or in the browser (MATLAB Online). Check the IT services pages for the current way to sign in. MATLAB Onramp, MathWorks’ free two-hour course, is worth doing first.

The essentials

x = 5;                 % semicolon hides the output
v = [1, 2, 3];         % row vector (commas or spaces)
c = [1; 2; 3];         % column vector (semicolons)
A = [2, 1, -1; 1, 3, 2; 2, -1, 4];   % 3x3 matrix: commas split columns, semicolons split rows
A(2,3)                 % row 2, column 3 -> 2
A'                     % transpose
det(A)                 % determinant
inv(A)                 % inverse

Element-wise vs matrix operations: A*B is matrix multiplication; A.*B multiplies element by element. The same goes for .^ and ./. You need the dot when applying a formula to a whole vector of values, like t.^2.

Solving a circuit

The Mesh analysis worked example in three lines:

R = [10, -6, 0; -6, 17, -8; 0, -8, 10];
V = [24; 0; 12];        % must be a column
I = R \ V               % backslash solves R*I = V

Use \, not inv(R)*V. It’s faster and more accurate. A common error is writing V = [24, 0, 12] (a row), which gives a dimension error.

Plotting an RC transient

R = 47e3;  C = 100e-6;  V = 12;
tau = R*C;
t = linspace(0, 5*tau, 500);      % 500 points from 0 to 5 tau
u = V*(1 - exp(-t/tau));          % note: exp works element-wise
i = (V/R)*exp(-t/tau);
 
yyaxis left;  plot(t, u); ylabel('u_C (V)');
yyaxis right; plot(t, i*1e3); ylabel('i (mA)');
xlabel('t (s)'); title('RC charging'); grid on

Printing results neatly

fprintf('tau = %.2f s\n', tau);
fprintf('I1 = %.3f A, I2 = %.3f A, I3 = %.3f A\n', I);

Scripts and functions

• A script (.m file) is a list of commands. Put clear; clc; at the top so old variables don’t interfere.
• A function goes in its own file named after it:

function P = mosfet_loss(Rds, I, V, ton, toff, f)
    P = Rds*I^2 + (V*I/2)*(ton + toff)*f;
end

Call it with mosfet_loss(0.075, 10, 24, 57e-9, 74e-9, 13e3) and you get 7.70 W, matching MOSFET power loss.

Common errors

Message	Usual cause
Dimensions of arrays being concatenated are not consistent	Rows of different lengths in a matrix
Incorrect dimensions for matrix multiplication	Used * where you needed .*
Undefined function or variable	Typo, or the script ran before the variable was set
Matrix is singular	Determinant is zero: check your equations