cpet190_lect10

8/12/2019 CPET190_Lect10

1/19

February 21, 2005 Lecture 10 - By Paul Lin 1

CPET 190

Problem Solving with MATLAB

Lecture 10

http://www.etcs.ipfw.edu/~lin

8/12/2019 CPET190_Lect10

2/19


Lecture 10: MATLAB Program

Design & Flow Control - III

10-1 SWITCH Construct

10-2 Problem Solving - MATH Applications

10-3 Problem Solving - Electrical CircuitApplications

8/12/2019 CPET190_Lect10

3/19


10-1 SWITCH, CASE, WHATEVER

SWITCH Construct

Another form of flow control or branching General form

switch (expression)

case exp_1,

statement 1-1

statement 1-2****

case exp_2,

statement 2-1

statement 2-2

****case exp_3,

statement 3-1

statement 3-2

****

end

8/12/2019 CPET190_Lect10

4/19


10-1 SWITCH, CASE, WHATEVER

SWITCH Construct

Example

N = input(Enter a number - less than 10-: );

switch (N)

case {1, 3, 5, 7, 9},

disp(Odd number is matched);,

case {2, 4, 6, 8, 10},

disp(Even number is matched);

otherwise,

disp(No match is found);

end

8/12/2019 CPET190_Lect10

5/19


10-2 Problem Solving - MATH

Applications

Example 10-1: Evaluating a Function of Two

Variables

Write a MATLAB program to evaluate a function

f(x,y) for any two user-specified values x and y.The function is defined as follows:

00,00,

00,00,

),(22

2

2

yandxyxyandxyx

yandxyxyandxyx

yxf

8/12/2019 CPET190_Lect10

6/19



Applications

Example 10-1: Evaluating a Function of

Two Variables

Solution:

1. State the problem2. Define the inputs and outputs

3. Design the algorithm

4. Translate the algorithm into MATLAB

statements

5. Test the program

6. Document the process and solution.

8/12/2019 CPET190_Lect10

7/19



Applications

Example 10-1: Evaluating a Function of TwoVariables (continue)

Solution:

1. State the problemas the question

2. Define the inputs and outputs

User input two values for X and Y

Output is a function value

3. Design the algorithm Read the input X and Y

Calculate f(x,y), based on the X and Y values

Print output

8/12/2019 CPET190_Lect10

8/19



Applications

Example 10-1:Evaluating a Function of

Two Variables (continue)

4. Translate the

algorithm intoMATLABstatements

%func_evs.m

%

n = true;

while n == truex = input('Enter the x

coefficient: ');

y = input('Enter the ycoefficient: ');

if x >= 0 && y >= 0f_xy = x + y;

elseif x >= 0 && y < 0

f_xy = x + y^2;

elseif x == 0 && y >= 0

f_xy = x^2 + y;else

f_xy = x^2 + y^2;

end

fprintf('x = %f, y = %f,

f(x,y) = %f\n', x, y, f_xy);disp('Enter Ctrl C one or

two times to exit the

program');

disp('');

end

8/12/2019 CPET190_Lect10

9/19



Applications

Example 10-1: Evaluating a Function of Two

Variables (continue)

5. Test the program

(x,y) f(x,y)

(2,3) -> f(x,y) = 5

(2, -3) -> f(x, y) = 11

(-2, 3) -> f(x,y) = 7

(-2,-3) -> 13

How about x, y => a very large number, and a

very small number (accuracy, and computers

limit)

8/12/2019 CPET190_Lect10

10/19


10-3 Problem Solving - Electrical

Circuit Applications

Example 10-2: CardioidMicrophone

Domain Knowledge onMicrophone Pick-up

patterns Omni patternthe most

common pattern

Cardioid patternAdirectional sound pick-uppattern for use on a stage

Super Cardioid pattern

Source: http://homerecording.about.com/library/weekly/aa032597.htm

8/12/2019 CPET190_Lect10

11/19




Example 10-2: CardioidMicrophone

Cardioid patternAdirectional sound pick-uppattern for use on a stage

Gain Equation

It varies as a function ofangle according to theequation

g is the constantassociated with aparticular microphone;

(value of g?; assume g =0.5)

is the angle from theaxis of the microphoneto the sound source(range of angle?)

)cos1(2 gGain

Questions Calculate gain

versus angle and

prepare a polar

plot (what is this?)

8/12/2019 CPET190_Lect10

12/19

February 21, 2005Lecture 10 - By Paul Lin

12



Example 10-2: Cardioid Microphone - continue

)cos1(2

gGain

POLAR(THETA, RHO)

THETA theta in Gainequation RHO -> Gain value

POLAR Polar coordinate

plot. POLAR(THETA, RHO)

makes a plot using polar

coordinates of the angle

THETA, in radians, versus

the radius RHO. POLAR(THETA,RHO,S)

uses the linestyle specified

in string S.

8/12/2019 CPET190_Lect10

13/19

February 21, 2005Lecture 10 - By Paul Lin

13


Circuit Applications Example 10-2: Cardioid

Microphonethe Program%cardioid_mic.m

%Define Variables:

% g -- Microphone gain constant

% gain - Gain(theta) of the

microphone% theta - Angle in radians from

% microphone axis

% Calculate gain versus angle

g = 0.5;

theta = 0:pi/20:2*pi;

gain = 2*g*(1 +cos(theta));% Polar plot Gain vs Angle

polar(theta, gain, 'r-');

title('\bfGain vs Angle \theta');

Verifying Answrs

0.5

1

1.5

2

30

210

60

240

90

270

120

300

150

330

180 0

Gain vs Angle

8/12/2019 CPET190_Lect10

14/19




Example 10-2: Cardioid

MicrophoneVerifying

the answer

Verifying Answers: Gain =

2*g*(1+cos(theta)) g = 0.5, theta = 0, gain =

2*0.5*(1+1) = 2

g = 0.5, theta = 60 degree,

gain = 2*0.5*(1 +0.5) = 1.5

0.5

1

1.5

2

30

210

60

240

90

270

120

300

150

330

180 0

Gain vs Angle

Theta = 0,gain = 2

Theta = 60 degree,gain = 2

8/12/2019 CPET190_Lect10

15/19




Example 10-3: Plot theamplitude andfrequency responseof Low-Pass Filter

A simple RC low-

pass filter Components: Vi, R

and C are in series

R = 16 k, C = 1 F,

Xc = 1/(2*pi*f*C)

Complex number

calculation onAmplitude and Phaseangle of the Gain =Vo/Vi

Circuit Equations?

Xc

R= 16 k

VoVi

Vr

VcC = 1F

8/12/2019 CPET190_Lect10

16/19




Example 10-3: CircuitEquations?

Xc = -j*1/(2*pi*f*C);

as f , Xc

Vo = Vc = Vi/(RjXc) * (-

jXc) Gain of response is

Vo/Vi = (-jXc)/(R-jXc)

Vo/Vi = 1/(1 + j2fRC)

Frequency range?

R*C = 16k * 1 uF = 16milli-seconds

F = 1/RC about 60 Hz

Use 0 to 1000 Hz asrange

Xc

R= 16 k

VoVi

Vr

VcC = 1F

8/12/2019 CPET190_Lect10

17/19




Example 3: MATLABProgram

%rc_lpf.m

%

R = 1600; % 1600 ohms

C = 1E-6; % 1 uFf = 1:2: 1000;

% Frequency varies from

% 1 to 1000 Hz

% Response

Av = 1 ./ (1 + j*2*pi*f*R*C);

Av_amp = abs(Av);% amplitude

% Phase angle

phase = angle(Av)

% Plotsfigure(1), subplot(2,1,1), loglog(f,Av_amp);title('Amplitude Response - Gain');xlabel('Frequency - Hz');ylabel('Av = Vo/Vi');grid onfigure(1), subplot(2,1,2),semilogx(f, phase);title('Phase Response');xlabel('Frequency - Hz');ylabel('Angle of Av = Vo/Vi inRadians');grid on

8/12/2019 CPET190_Lect10

18/19

8/12/2019 CPET190_Lect10

19/19


Summary

SWITCH, CASE, WHATEVER

Problem Solving - MATH Applications

Problem Solving - Electrical Circuit

Applications

cpet190_lect10

Documents