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