BlogSheet Week 10

Blogsheet week 10

In this week’s lab, you will collect more data on low pass and high pass filters and “process” them using MATLAB.

PART A: MATLAB practice.

   1.     Open MATLAB. Open the editor and copy paste the following code. Name your code as FirstCode.m

Save the resulting plot as a JPEG image and put it here.

clear all;

close all;

x = [1 2 3 4 5];

y = 2.^x;

plot(x, y, 'LineWidth', 6)

xlabel('Numbers', 'FontSize', 12)

ylabel('Results', 'FontSize', 12)

Image 1.1 Graph of Code above in Matlab

   2.     What does clear all do?

Clears all objects in the Matlab workspace and closes the Mupad engine that is associated with the workspace and resets all the assumptions.

   3.     What does close all do?

Close all is the equivalent of clear all and will do the same as clear all.

   4.     In the command line, type x and press enter. This is a matrix. How many rows and columns are there in the matrix?

There are 5 columns and 1 row in the matrix created in x.

   5.     Why is there a semicolon at the end of the line of x and y?

Semicolons are used to seperate rows to create an array, they can also be used to suppress code output, and also suppress code on a single line.

   6.     Remove the dot on the y = 2.^x; line and execute the code again. What does the error message mean?

The . is used for elementwise power. Without the '.' is using power in matrix form. So the matrix must be a square matrix meaning it must have the same number or rows and columns.

   7.     How does the LineWidth affect the plot? Explain.

Changing the LineWidth makes the graphs line objects thicker or thinner, and the lines cannot be made invisible by making the linewidth zero, linesvisible=False would have to be used. Note that changing the linewidth does not affect the width of the lines in the axes.

   8.     Type help plot on the command line and study the options for plot command. Provide how you would change the line for plot command to obtain the following figure (Hint: Like ‘LineWidth’, there is another property called ‘MarkerSize’)

In the code line with plot we added 'ro-' and 'Markersize', 12 and changed to 'Linewidth', 4 to obtain this plot below.

   9.     What happens if you change the line for x to x = [1; 2; 3; 4; 5]; ? Explain.

When it is typed in this way x = [1 2 3 4 5];, x and y values will be in row. By adding (;) between the values it will make appear as a column.  

  10.  Provide the code for the following figure. You need to figure out the function for y. Notice there are grids on the plot.

Here is the code we used to achieve the graph below.

clear all;
close all;
x = [1; 2; 3; 4; 5];
y = x.^2;
plot(x, y, 'ks:', 'LineWidth', 5, 'MarkerSize', 16)
xlabel('Numbers', 'FontSize', 12)
ylabel('Results', 'FontSize', 12)
grid on;

  11.  Degree vs. radian in MATLAB:

a.     Calculate sinus of 30 degrees using a calculator or internet.

Using a calculator,

Sin(30)=0.5 degree.

Sin(30)=-0.988 radian.

b.     Type sin(30) in the command line of the MATLAB. Why is this number different? (Hint: MATLAB treats angles as radians).

If it is typed sin(30) it will be treated as radians, and by typing it sind(30) we will get the same answer that we got in the calculator  which is 0.5 degree.

c.     How can you modify sin(30) so we get the correct number?

By adding d which is referring to degree. So, it will look like this sind(30).

  12.  Plot y = 10 sin (100 t) using Matlab with two different resolutions on the same plot: 10 points per period and 1000 points per period. The plot needs to show only two periods. Commands you might need to use are linspace, plot, hold on, legend, xlabel, and ylabel. Provide your code and resulting figure. The output figure should look like the following:

This is our code to provide the same plot with different resolutions. This code should create the plot below.

t1 = linspace(0, .125, 10),
t2 = linspace(0, .125, 1000),
y1 = 10*sin(100*t1);
y2 = 10*sin(100*t2);

plot(t1, y1, 'ro-',t2, y2, 'k')
xlabel('Time(s)');
ylabel('y function');
axis([0 .14 -10 10])

legend('Coarse','Fine')

  13.  Explain what is changed in the following plot comparing to the previous one.

The 'fine' line plot is for when y is greater than 5 then y = 5. So it caps the value of y on the 'fine' line to a maximum value of 5.

  14.  The command find was used to create this code. Study the use of find (help find) and try to replicate the plot above. Provide your code.

t1 = linspace(0, .125, 10),
t2 = linspace(0, .125, 1000),
y1 = 10*sin(100*t1);
y2 = 10*sin(100*t2);

f=find(y2>5);
y2(f)=5;

plot(t1, y1, 'ro-',t2, y2, 'k')
xlabel('Time(s)');
ylabel('y function');
axis([0 .14 -10 10])
legend('Coarse','Fine')

PART B: Filters and MATLAB

   1.     Build a low pass filter using a resistor and capacitor in which the cut off frequency is 1 kHz. Observe the output signal using the oscilloscope. Collect several data points particularly around the cut off frequency. Provide your data in a table.

Table 1.1 Low Pass Filter

   2.     Plot your data using MATLAB. Make sure to use proper labels for the plot and make your plot line and fonts readable. Provide your code and the plot.

Frequency = [100 200 300 400 500 600 700 800 900 1000 1100 1200];

Output = [0.98 0.96 0.94 0.90 0.86 0.79 0.78 0.74 0.70 0.66 0.63 0.6];

plot(Frequency, Output, 'o-r')

xlabel('Frequency');

ylabel('Vout/Vin'); 

Graph 2.1 Low Pass Filter

   3.     Calculate the cut off frequency using MATLAB. find command will be used. Provide your code.

Frequency = [100 200 300 400 500 600 700 800 900 1000 1100 1200];

Output = [0.98 0.96 0.94 0.90 0.86 0.79 0.78 0.74 0.70 0.66 0.63 0.6];

plot(Frequency, Output, 'o-r')

xlabel('Frequency');

ylabel('Vout/Vin'); 

s=find(y>0.7);

s=find(y<0.72);

a=x(s);

cutoff=min(a)

Photo 3.1 calculating cut of frequency using MATLAB (Low Pass)

   4.     Put a horizontal dashed line on the previous plot that passes through the cutoff frequency.

Frequency = [100 200 300 400 500 600 700 800 900 1000 1100 1200];

Output = [0.98 0.96 0.94 0.90 0.86 0.79 0.78 0.74 0.70 0.66 0.63 0.6];

plot(Frequency, Output,'o-r')

xlabel('Frequency');

ylabel('Vout/Vin');

hold on

hline = refline(0,0.7);

set(hline, 'linestyle','--')

xlabel('Frequency');

ylabel('Vout/Vin');

Graph 4.1 shows the horizontal dashed line passes through the cutoff frequency

   5.     Repeat 1-3 by modifying the circuit to a high pass filter.

Table 5.1 High Pass Filter 

Frequency = [100 200 300 400 500 600 700 800 900 1000 1100 1200];

Output= [0.10 0.21 0.30 0.39 0.47 0.54 0.60 0.65 0.69 0.71 0.73 0.76];

plot(Frequency, Output, 'o-r')

xlabel('Frequency');

ylabel('Vout/Vin');

Graph 5.1 High Pass Filter 

requency = [100 200 300 400 500 600 700 800 900 1000 1100 1200];

Output= [0.10 0.21 0.30 0.39 0.47 0.54 0.60 0.65 0.69 0.71 0.73 0.76];

plot(Frequency, Output, 'o-r')

xlabel('Frequency');

ylabel('Vout/Vin');

s=find(y>0.7);

s=find(y<0.72);

a=x(s);

cutoff=min(a)

Photo 5.1 calculating cut of frequency using MATLAB (High Pass)