CPET 190

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CPET 190

• Lecture 6
• Problem Solving with MATLAB
• http//www.etcs.ipfw.edu/lin

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Lecture 6 MATLAB Plotting

• 6-1 Introduction to Plotting
• 6-2 Simple X-Y Plots
• Printing a Plot
• Exporting a Plot as a Graphical Image
• Line Color, Style, Marker and Legends
• 6-3 Multiple Plot
• 6-4 Logarithmic Scales
• 6-5 Plotting Applications

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6.1 Introduction to Plotting

• Data or Numerical facts
• For making decision making
• Pictures, Graphs, or Plots
• Describe data
• Ohms Laws V R I
• MATLAB Plotting Capabilities
• 2-D XY Plot
• Semilog Plot
• 3-D Plot
• More

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6.2 Simple XY Plots

• Basic Steps for Preparing a XY Graph
• Prepare data for x-axis and y-axis in row vector
  or column vector format
• Select a window with a figure number and plot
  position (if multiple sub-plot)
• Call plot() function
• Select plot line, color, etc
• Set Axis range and grid
• Annotate the plot
• Export graph
• MATLAB XY Plot Related Functions
• figure, plot, subplot, set, grid on, axis,
  xlabel, ylabel, title, legend, text

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6.2 Simple XY Plots (cont.)

• Example 6.1 Plot the function y x2 10x 15
  (from page 56-57 of MATLAB Programming for
  Engineers, 3rd, by Stephen J. Chapman, published
  by Thomson-Learning)
• Solution
• Planning
• Prepare x vector, with reasonable range, and
  compute y vector
• Use a default window ( without figure), and call
  plot(x,y) function
• Add title(), xlabel(), ylabel(), grid on, etc to
  fine-tune the graph

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6.2 Simple XY Plots (cont.)

• Example 6-1 (cont.)
• MATLAB Solution
• Start MATLAB, and invoke M-File Editor
• Write the following MATLAB statements

plotxy_p56.m x 0110 NOT y x2 - 10x
15 y x.2 - 10.x 15 plot(x, y) title('y
x.2 - 10.x 15') xlabel('x axis'), ylabel('y
axis') grid on
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6.2 Simple XY Plots (cont.)

• Example 6-1 (cont.)

• Verifying Data
• X 0, Y 15
• Y 0 0 15 15
• X 10, Y 15
• Y 102 - 1010 15 15
• Exporting Figure
• Copy Figure for Exporting

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6.2 Simple XY Plots (cont.)

• Example 6-1 (cont.)

Exporting TIFF Figure to PowerPoint applications
like this one 1. On MATLAB Command Windows we
type gtgt print dtiff plotxy_56.tif for creating
graphic files 2. We locate the plotxy_56.tif in
the current directory OK. 3. We start and setup
PowerPoint, then Insert -gt Picture to locate
plotxy_56.tif file.
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6.3 Multiple Plots

• Multiple Plots
• On the same Graph using plot function, or
• Arranged in m x n matrix format
• subplot(2,1,1) 2 subplots, two rows, one
  column, the first plot
• subplot(2,2,1) 4 subplots, two rows, two
  column, the first plot
• gtgt help subplot
• Examples
• gtgt subplot(2,1,1), plot(sine)
• gtgt subplot(2,1,2), plot(cosine)

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6.3 Multiple Plots

• Example 6-2. Multiple plots of sine and cosine
  from the equation (from page 56-57 of MATLAB
  Programming for Engineers, 3rd, by Stephen J.
  Chapman, published by Thomson-Learning)
• Analysis
• Data preparation
• X vector from 0 to 2pi
• Y1 sin2x
• Y2 2cos2x
• Two plots subplot(2,1,1), and subplot(2,1,2)

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6.3 Multiple Plots

• Example 6-2 (cont.)
• MATLAB Program

plot_sine_cosine.m x 0pi/1002pi y1
sin(2x) y2 2cos(2x) figure(1), plot(x,y1,
x, y2) figure(2),subplot(2,1,1),plot(x,y1),title('
sin 2x') figure(2),subplot(2,1,2),plot(x,y2),titl
e('2cos 2x')
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6.3 Multiple Plots

• Distinguish different plots
• Line Color
• Line Style
• Marker Style and
• Legends
• help plot for more info
• Example 6-3
• plot_p60.m
• x 0 1 10
• y x.2 - 10.x 15
• plot(x,y,'r--', x, y, 'bo')

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6.3 Multiple Plots

• Legends
• Name and its line style
• Example 6-4

plot_sine_cosine_legend.m x 0pi/1002pi y1
sin(2x) y2 2cos(2x) plot(x,y1,'k-', x,
y2,'b--'), grid on title('f(x) sin(2x) and
its Derivative') xlabel('x') ylabel('y') legend
('f(x)', 'd/dx (fx)')
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6.4 Logarithmic Scales

• Log Scale plots
• Decibel Db 10log(Pout/Pin)
• Frequency response plot
• MATLAB Functions
• semilogx(x,y) plot x data on log scale and y
  data on linear scale
• semilogy(x,y) plot x data on linear scale and y
  on log scale
• Loglog(x,y) plot both x and y data on log scale

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6.5 Plotting Applications

• Example 6-5 Mr. A performed an electrical
  circuit experiment and collected the following
  measured resistance values (ohms) and current
  values (amperes)
• R 0.5, 0.75, 1.0, 2.0, 3.0, 4.0
• I 10, 7, 5.2, 3, 1.8, 1.5
• You are asked to help Mr. A to prepare data and
  generate a plot that shows red circles on all
  data points

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6.5 Plotting Applications (continue)

• Example 6-5 Solution

plotRI.m Author M. Lin Date 9/1/04 Version
1.0 Description R 0.5 0.75 1.0 2.0 3.0
4.0 I 10 7 5.2 3 1.8 1.5 R 0.5 0.75
1.0 2.0 3.0 4.0 I 10 7 5.2 3 1.8
1.5 plot(R,I, 'ro--') show red circles at
the data points xlabel('Resistance'),
ylabel('Current') title('R vs I Plot')
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6.5 Plotting Application (continue)

• Example 6-6 Mr. A performed an Ohms experiment
  and collected the following measured voltage
  values (volts) and current values
  (milli-amperes)
• V 0, 1, 2, 3, 4, 5, 6, 7, 8
• I 10, 8, 7, 7, 6, 4. 3, 2, 0
• You are asked to help Mr. A to prepare data and
  generate a plot that shows red-lines and blue
  circles on all data points

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6.5 Plotting Applications (continue)

• Example 6-6 Solution
• plotVI.m
• Author M. Lin
• Date 9/1/04
• Version 1.0
• Description
• V (volts) 0 1 2 3 4 5 6 7 8
• I (milliamps) 10 8 7 7 6 4 3 2 0
• V 0 1 2 3 4 5 6 7 8
• I 10 8 7 7 6 4 3 2 0
• plot(V,I, 'r--', V, I, 'bo')
• show red cicrles at the data points
• xlabel('Voltage - Volt'), ylabel('Current -
  milliamps')
• title(E - I Plot')

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6.5 Plotting Applications

• Example 6-7 Maximum Power Transfer. A voltage
  source E 120 v with an internal resistance of
  Rs of 50 ohms supplying a load of resistance RL .
  
• Q1 - Find the value of load resistance RL that
  will result in the maximum possible power being
  supplied by the source to the load.
• Q2 How much power be supplied in this case?
• Q3 Plot the power supply to the load as a
  function of the load resistance RL.

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6.5 Plotting Applications

• Example 6-7 Solution
• Circuit Diagram
• Equations
• PL I2 RL,
• where I is the current passing through the
  circuit.
• I E/Rtotal E/(Rs RL)
• Array data for MALAB plotting
• RL a vector
• E and Rs are scalars

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6.5 Plotting Applications

• Example 6-7 Solution
• MATLAB Program

maxPower_p67.m Rs 50 E 120 RL 11100 I
E./(Rs RL) NOT I R/(Rs RL) -- for
Scalar calculation PL (I.2) . RL NOT PL
I2 RL -- for Scalar calculation plot(RL,
PL), grid on title('Max Power Transfer') xlabel('
Load resistance RL') ylabel('Power - Watts')
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6.5 Plotting Applications
72 watts

• Example 6-7 Solution
• Answers
• Q1 Find the value of RL for Pmax to occur
• RL 50 ohms results a PL max of 72 watts
• Q2 How much power be supplied in this case?
• PL consume 72 Watt,
• Rs will also receive the same 72 Watts inside the
  power supply
• Power supplied is 144 watts
• Q3 Plot the PL(RL)

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Summary

• Introduction to Plotting
• Simple X-Y Plots
• Printing a Plot
• Exporting a Plot as a Graphical Image
• Line Color, Style, Marker and Legends
• Multiple Plot
• Logarithmic Scales
• Plotting Applications