ECEn Matlab

Read and follow along with the document to get an introduction to MATLAB.

matlab_intro.docx

After completing the document, make sure that you feel comfortable with the following MATLAB topics:

Matlab Basic Operations
Matrix Operations
Array Operations
Script Files

Even if you feel comfortable, click on the links above and become familiar with the MATLAB guide
provided on the wiki page. You may need to reference it later in the course.

mt240_nr_1_6_1_power.pdf

mt240_nr_3_2_1_parallelresistors.pdf

mt240_nr_3_4_1_voltage_division.pdf

mt240_nr_4_3_1_node_voltage_method.pdf

mt240_nr_4_12_1_max_power_transfer.pdf

mt240_nr_5_3_1_inverting_op_amp.pdf
mt240_nr_5_3_1_inverting_op_amp_function.pdf

mt240_nr_5_4_1_sum_op_amp.pdf
mt240_nr_5_4_1_sum_op_amp_function.pdf

(Not required, but for fun)

 Fun application
 Any wave or signal can be made up of tons of sinusoidal signals composed of different frequencies and
 amplitudes. The program below creates a square wave from n-number of input signals. Play around with 
 the number of input signals to see the effect of adding more and more input signals.

funapplication_sumopamp.m

To run this program you will need to edit the code and use your summing op amp function.

mt240_nr_6_3_1_capacitor.pdf

mt240_nr_7_2_1_nat_tesp_rc_circuit.pdf

mt240_nr_8_2_1_rlc_circuit.pdf

mt240_nr_9_1_1_sinusoidal_source.pdf

mt240_9_9_1_mesh_current_method.pdf

   MT240_10_4_1 Complex Power
  
   Objective: Gain a visual understanding of complex power
  
   Functions to learn: refline (this could be useful) to plot avg P and
   reactive P. text (this could be useful) to label your average and
   reactive power.
  
   Exercise: You have seven black boxes(representing unknown circuits), each with terminals 
   coming out of them. You are curious to identify which circuits are more inductive, capacitive, or neither. 
   You begin by measuring the voltage and current across each terminal and measure the voltage phase shift in   
   reference to the current phase shift by setting the current phase shift to zero. From your measurements you 
   gather the following parameters: 
   V = 5*cos(w*t + thetaV), with 'w' being the frequency in rads/s (w = 100*pi),
   't' being the duration of time (t = 0:T/100:2*T - T/100), 'T' being the period 
   of the signal (T = 2*pi/w), thetaV being the voltage phase shift, 
   (thetaV = [-pi/2, -pi/4, -pi/6, 0, pi/6, pi/4, pi/2]. thetaV(1) represents the first
   black box, thetaV(2) the second and so on), and a current I = 1.25*cos(w*t). To gain a visual 
   understanding you decide to calculate and plot the average power, reactive power, and instantaneous
   power for the different voltage phase shifts using the parameters given.
   a) Calculate the voltages as a function of time for all values of thetaV.
   b) Calculate the Vrms and Irms using a for-loop to approximate an integral 
      Vrms = sqrt((1/T)*integral(V(t), from 0 to T)dt) bounds of integration are
      from 0 to T. Verify your calculation using the equation Vrms =
      Vm/sqrt(2).
   c) Calculate average, reactive, and instantaneous power for every thetaV.
   d) Plot voltage, current, average, reactive, and instantaneous power obtained from part c.
      It might be best to create a single plot for each theta since you are
      plotting a lot of information on each graph. Using a legend, titles,
      and labels will help you sort through the information.
   e) Why are all of the calculated Vrms values the same even though the
      phase shift was different?
   f) When the reactant power is zero what is the relationship between the
      phases of voltage and current? What does this tell you about the
      circuit.
   g) When the reactant power is below zero does the voltage lead or lag the current.
      Is the circuit more inductive or capacitive?
   h) When the current and voltage are in phase, why is the instantaneous
      power never below 0? When it is below zero what is happening to the
      power?

mt240_10_4_1_t_complexpowertemplate.m

   MT240_14_4_1 Cross over network

  Objective: Gain an understanding how you can use matlab to help you
  design lowpass, bandpass, and highpass filters.

  functions to learn: log10, semilogx

  Introduction: A crossover network consists of a highpass, lowpass, and
  bandpass filter. They are often used in stereo systems that separates
  a signal into three signals (bass, treble, and midrange). You will design
  a basic crossover network as depicted in the image below. 

  Exercise: Design a crossover network with the following specifications:
  |                        | Low pass | Bandpass | High pass |
  |Lower cut off frequency | N/A      |  250Hz   | 2000Hz    |
  |Upper cut off frequency | 250Hz    |  2000Hz  | N/A       | 
  a) For each filter design you will be calculating the transfer function
     of the voltage across each resistor. The equations should be simple 
     voltage division as shown in the book. See chapter 14. Design your 
     circuits choosing appropriate values for the capacitors and inductors.
  b) Find the magnitudes (|H(jw)|) for v1, v2, and v3 as a function of 'w'
    (frequency) with w being w = 0:10*2*pi:3e5*2*pi. Note that this is the 
     transfer function (H(jw) = vout/vin) thus the amplitude of the input voltage
     source isn't needed in your calculations.
    1) The midrange is a little more difficult so I provided you with the
       steps.
       a) Calculate the bandwidth. B = upper corner frequency - lower fc
       b) Solve for the inductor using the relationship B = R/L
       c) Solve for the capacitor value.
  c) Plot the magnitude in decibels vs the frequency(Hz) using a
     logarithmic scale. (use semilogx for this).
  d) How could you design a bandreject filter that rejects frequencies
     between 250Hz and 2000Hz?

mt240_14_4_1_t_crossover_networktemplate.m

   MT240_15_1_1 Active Filter

  Objective: Design a an active, low-pass filter using an op-amp

  Commands: none

  Background: While designing your crossover network you realized that
  the bass speaker's (low pass) amplifier has broken. You then decide to
  build the low pass filter and amplifier as one unit using an op-amp. 
  You decide to get fancy and use a variable capacitor so that you can
  change the corner frequency.


  Exercise: You decide to have design according to the topology shown in
  the image below.
  a) Design your circuit to have a max gain of 10.
  b) Your variable capacitor can assume values within the range: C = 1e-8:1e-7:1e-6;
  c) For every capacitor value calculate the transfer function |H(jw)| as a 
     a function of frequency using w(rads/sec) = 0:5*2*pi:3e5*2*pi;
  d) Create a bode plot of the results obtained in part c. Plot them all on
     the same graph.
  d) What value should the capacitor be if you want a corner frequency of
     about 140 Hz?
  e) What affect does the size of the capacitor have on the bandwidth?
  

mt240_15_1_1_t_activefiltertemplate.m