33
2OBJECTIVES
Computer Tools for Electrical Engineers
MATLAB AS A CALCULATOR
34
ROUNDING AND SEPARATING NUMBERS
round()
round(3.4) 3
�oor(�
�oor(-2.�� -2
�.�����oor(�.�� 0.7
VECTORS
CREATING VECTORS
Computer Tools for Electrical Engineers
35
[3 -2.4 pi sqrt(3) 7-2*j]
Chapter 2: Matlab as a Calculator
zeros(1,5)
[0 0 0 0 0]
ones(1,12)
[1 1 1 1 1 1 1 1 1 1 1 1]
NOTE
pi
sqrt�3� 7-j*2
NOTE
ones()
4*ones(1,5) [4 4 4 4 4]
-pi*ones(1,2) [-3.14159 -3.14159]
36
[1 2 3
4])
:
[start:increment:end]
0:0.5:3 [0 0.5 1 1.5 2 2.5 3]
3:-1:0 [3 2 1 0]
[start:end]
-2:2 -2:1:2 [-2 -1 0 1 2]
linspace linspace(start, end, number_of_values)
linspace(0,3,7) [0 0.5 1 1.5 2 2.5 3]
linspace()
linspace(10,0,5) [10 7.5 5 2.5 0]
logspace
logspace(2,5,75)
logspace(0,4,5) [1 10 100 1000 10000]
logspace(a,b,N)
Computer Tools for Electrical Engineers
37Chapter 2: Matlab as a Calculator
v = rand(1,10)
rand()
10*rand(1,20)-5
NOTE
logspace(a,b,N)
linspace
DIGGING DEEPER
38 Computer Tools for Electrical Engineers
PRACTICE PROBLEMS
TECH TIP: MEASURING RESISTANCE
39Chapter 2: Matlab as a Calculator
40 Computer Tools for Electrical Engineers
WORKING WITH VECTORS
v
v
v = ones(1,1000);
length(v)
length([7 6 1]) 3
N = length(y) N y
NOTE
v
41Chapter 2: Matlab as a Calculator
v
v
x
x = v(4)
v �
v(2) = pi
v
v(3:7)
v
v(3:5) = [1 pi sqrt(2)]
v
v(1:5)
42 Computer Tools for Electrical Engineers
length(v)
v(3:length(v))
v(3:end)
x = v(end-4:end)
v(end-4:end)=[1 2 3 4]
v(1) = 0;
v(1) = [ ]
length(v) 2
z = [x 7.5 y]
43Chapter 2: Matlab as a Calculator
v
v = [5 v]
v
v
v = [v 7]
v
v
v = [v(1:2) 5 v(3:4)]
v
v
v
x v
PRACTICE PROBLEMS
x
x
x
x
y x
����x
x y y
x
44
PRO TIP: BUYING A DIGITAL MULTIMETER (DMM)
Computer Tools for Electrical Engineers
45Chapter 2: Matlab as a Calculator
COMPLEX NUMBERS
DIGGING DEEPER
46 Computer Tools for Electrical Engineers
� �
z = 4 + j*3
47Chapter 2: Matlab as a Calculator
real(z)
imag(z)
abs(z)
angle(z)
angle(z)*180/pi
ma�nit�d�� �� an�l�
ma�nit�d����an�l�� �37�
�
z = mag*cos(ang) + j*mag*sin(ang)
ang
z = mag*cosd(ang) + j*mag*sind(ang)
ang
48 Computer Tools for Electrical Engineers
z = 3*exp(j*pi);
z = 3*exp(j+22*pi/180);
�
NOTE
� � �
� ��
� �
� � � �
� � �
49Chapter 2: Matlab as a Calculator
VECTOR MATHEMATICS
cos()
+
x = [2 4 7] cos(x)
x + x [4 8 14]
sqrt() exp()
sin()
[5 3]–[1 2] =[4 1]
* /
[5 3]*[1 2]
[5 3].*[1 2] [4 8]./[2 4] [5 6] [2 2]
PRACTICE PROBLEMS
z = 5+j12
�
z = 5+j12
�
14�45� �
50 Computer Tools for Electrical Engineers
PRACTICE PROBLEMS
[2 4 9] - 1
[1 3 8]
[2 4 9] – [1 1 1]
[2 8 16]/2
[2 8 16]./[2 2 2]
[1 4 8]
STRINGS
s1 = 'Hello, there!';
s1
s1(2)
x = [4 2 6]
x = [4 2 6] y = [2 4 8]
51Chapter 2: Matlab as a Calculator
s1(1:5)
[ s1(1:12) ' Laura' s1(13)]
s1(6:14) = [];
string2 = '521';
string2
string2 + 0
[53 50 49]
['5' '2' '1']
str2num
str2num('521') + 3
524
PRACTICE PROBLEMS
str = 'R1 = 47 ohms'
52 Computer Tools for Electrical Engineers
TECH TIP: RESISTORS IN SERIES AND PARALLEL
53Chapter 2: Matlab as a Calculator
MATRICES
PRACTICE PROBLEMS
R6+R7
54 Computer Tools for Electrical Engineers
CREATING MATRICES
x = [2 -3; 1 0]
y = [2 -3]
[]
zeros() ones()
zeros(2,4)
[0 0 0 0; 0 0 0 0]
RECALL
55Chapter 2: Matlab as a Calculator
ones(3,5)
[1 1 1 1 1; 1 1 1 1 1; 1 1 1 1 1]
big
big = 7 * ones(20,30);
x = [1 2 3] y = [4 5 6] z
z = [x y] z = [x; y]
z = [1 2 3; 4 5 6]
rand() mrand
mrand = 2*rand(3,3) – 1;
NOTE
ones(1,5)
56 Computer Tools for Electrical Engineers
CHANGING MATRIX VALUES
m = [-5 7 2.4; 8 0 9]
x = m(2,3)
m(2,3) = pi
PRACTICE PROBLEMS
57Chapter 2: Matlab as a Calculator
v = [-2 -4 -6 -8 -10]
v(2:4)
[-4 -6 -8] :
m(1:2, 1:2)
m(:,:)
x = m(2, :);
m = (1, :);
[]
m(:,4) = []
m(2:3,:)=[]
m(:, 3:end)=[]
m([1:2:end,:])=[]
58 Computer Tools for Electrical Engineers
PRACTICE PROBLEMS
m
m
PRO TIP: BUYING A CALCULATOR
x
m
m
m
m
rand()
v m
59Chapter 2: Matlab as a Calculator
WORKING WITH MATRICES
length()
size()
x = [4 3; 2 -4; 5 7]
[rows, cols] = size(x)
rows cols size()
size()
size([10 20 30 40 50])
size([10; 20; 30; 40; 50])
'
x = [4 3; 2 -4; 5 7]
y = x'
resistors = [10; 11; 12; 13; 15]
60 Computer Tools for Electrical Engineers
PRACTICE PROBLEMS
resistors = [10 11 12 13 15]'
* /
[2 15; 0 3].*[-1 3; 2 1]
[-2 45; 0 3]
* /
[2 -3; 0 4]*2 [4 -6; 0 8]
t=0:5 ���
�
61Chapter 2: Matlab as a Calculator
TECH TIP: MESH AND NODAL ANALYSIS METHODS
62 Computer Tools for Electrical Engineers
SOLVING SIMULTANEOUS EQUATIONS USING MATRICES
V1 + 2V
2 + V
3 = 5
3V1 – V
2 + 2V
3 = 2
-V1 + V
2 – 2V
3 = -4
A = [1 2 1;3 -1 2;-1 1 -2];
b = [5; 2; -4];
V = A\b
A = [1+j 2-j*2; -3+j 3];
b = [j; 2-j];
I = A\b;
DIGGING DEEPER
63Chapter 2: Matlab as a Calculator
TECH TIP: VOLTAGE DIVIDERS
PRACTICE PROBLEMS
I1I2
I3
�
2I1 + 6I
2 - 3I
3 = 3
4I1 - I
2 + I
3 = 25
I1 + 2I
2 - I
3 = 8
64 Computer Tools for Electrical Engineers
PRACTICE PROBLEMS
�
65Chapter 2: Matlab as a Calculator
COMMAND REVIEW
[] m = [2 4; 1 5]
zeros(r,c)
ones(r,c)
[a:b]
[a:inc:b]
linspace(a,b,N)
logspace(a,b,N)
rand(r,c)
round(n)
�oor(n�
ceil(n)
length(v)
[r,c]=size(m)
m(r,c)
m(:, c)
m(1:4, :)
m(:, 3:end)
v(4) = []
m(:,1) = []
66 Computer Tools for Electrical Engineers
pi
+ - * /
+ -
.* ./
A\b
i, j
real(z)
imag(z)
abs(z)
angle(z)
v = 'Hello'
x = str2num('42')
67Chapter 2: Matlab as a Calculator
LAB PROBLEMS
�
�
�
�
68 Computer Tools for Electrical Engineers
�
�
2i1 - i
2 + i
3 + 6i
4 = 22
-i1 + 3i
2 = -12
i3 + i
4 = 1
2i1 – i
3 = 12
�
(1+j2) V1 + j3 V2 = 7
2 V1 - 4 V2 = -2+j4