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Instructions. This document comprises the lab manual for Lab 6: AC Measurements. Complete the pre-lab exercises, perform the lab experiment, record your results, and prepare your lab report by following the instructions contained in this document. Save only the pages comprising the lab report into a new document using the naming convention

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EEE 202

Lab 6: AC Measurements

Instructions.  This document comprises the lab manual for Lab 6: AC Measurements.  Complete the pre-lab exercises, perform the lab experiment, record your results, and prepare your lab report by following the instructions contained in this document.  Save only the pages comprising the lab report into a new document using the naming convention YourLastName_EEE202_Lab6.doc and then export the new document to PDF.  Submit the PDF file using the link on BB.

Overview

AC steady-state analysis applies to circuits that contain only linear elements (active or passive) and sinusoidal voltage and/or current sources. We can use phasor analysis to solve AC steady-state problems.

In the pre-lab exercises, you will be analyzing AC circuits as well as simulating them in LTSPICE using both transient and AC (steady-state) analysis.  Linear Technology has produced a video that shows you how to perform AC analysis in LTSPICE.  The link for this video is http://www.linear.com/solutions/4581.  (Only the first 4:10 of this video is relevant to this lab.)

In the lab exercises, you will be analyzing AC circuits using your EIC-106 Breadboard, the Analog Parts Kit, and ADK. We will use the waveform generator and oscilloscope functions as well as the network analyzer instrument of the ADK.  Digilent Inc. has produced a video available on YouTube that describes Bode plots and their creation using the Analog Discovery Network Analyzer, and you should watch this video in its entirety prior to attempting the lab.  The link is https://www.youtube.com/watch?v=y-KQ2NMxws0.

Prelab Exercises

  1. Consider the RC Circuit shown below.  Assume the excitation is a 10 kHz sine wave with amplitude of 1 volt.   Derive expressions for the voltages across the resistor and the capacitor as time functions.  Plot the voltages across the resistor and the capacitor over two periods using MATLAB and a reasonable time interval (e.g., Dt = T/20). Capture the plot and paste it as Figure 1 in the report form below.  Compute the phase difference between the current through and the voltage across the capacitor, and record this result in Table 1 of the report form below.

RC Circuit

  • Simulate the RC Circuit in LTSPICE using transient analysis.  Plot the voltages across the resistor and the capacitor over two periods in steady state.Capture the plot and paste it as Figure 2 in the report form below.  Compute the phase difference between the current through and the voltage across the capacitor, and record this result in Table 1 of the report form below.
  • Derive the transfer function for the RC circuit assuming the transfer function is defined as the ratio of the voltage across the capacitor to the input voltage, i.e.,

Using MATLAB, produce a Bode plot of the magnitude and phase of this transfer function as a function of frequency from 100 Hz to 1 MHz.  Capture the plot and paste it as Figure 3 in the report form below.

  • Use AC analysis in LTSPICE to produce a Bode plot of the magnitude and phase of the transfer function described in Question 3.  Capture the plot and paste it as Figure 4 in the report form below.
  • Consider the RL Circuit shown below.  Assume the excitation is a 10 kHz sine wave with amplitude of 1 volt.   Derive expressions for the voltages across the resistor and the inductor as time functions.  Plot the voltages across the resistor and the inductor over two periods using MATLAB and a reasonable time interval (e.g., Dt = T/20). Capture the plot and paste it as Figure 5 in the report form below.  Compute the phase difference between the current through and the voltage across the inductor, and record this result in Table 2 of the report form below.

Fig. 2. RL Circuit

  • Simulate the RL Circuit in LTSPICE using transient analysis.  Plot the voltages across the resistor and the inductor over two periods in steady state. Capture the plot and paste it as Figure 6 in the report form below.  Compute the phase difference between the current through and the voltage across the inductor, and record this result in Table 2 of the report form below.
  • Derive the transfer function for the RL circuit assuming the transfer function is defined as the ratio of the voltage across the inductor to the input voltage, i.e.,

Using MATLAB, produce a Bode plot of the magnitude and phase of this transfer function as a function of frequency from 100 Hz to 1 MHz.  Capture the plot and paste it as Figure 7 in the report form below.

  • Use AC analysis in LTSPICE to produce a Bode plot of the magnitude and phase of the transfer function described in Question 7.  Capture the plot and paste it as Figure 8 in the report form below.

Lab Work

  1. Build the RC Circuit on your breadboard.  Measure the circuit with a 10 kHz sine wave with amplitude of 1 volt (2 volt peak-to-peak). Plot the voltage waveforms across the resistor and the capacitor over two periods in steady state.  Capture the plot and paste it as Figure 9 in the report form below.  Measure the phase difference between the current through and the voltage across the capacitor (in the direction of assumed current flow).  (Note that the current through the capacitoris proportional to the voltage across the resistor, and thus the phase of the current through the capacitor is equal to the phase of the voltage across the resistor.)Record your result in Table 1 of the report form below.
  • In this part of the lab, you will make measurements of the RC circuit using the network analyzer instrument feature of the Analog Discovery.  Use waveform generator channel 1 (the solid yellow wire numbered W1) as the stimulus for the circuit. (Don’t forget the ground connection!)  Connect oscilloscope input channel 1 so as to monitor the output of the AWG (i.e., the source).  Connect oscilloscope input channel 2 across the capacitor.  In the control area of the instrument, set the Start and Stop frequencies to 100 Hz and 1 MHz respectively.  Ensure that the scope channels are set so as to use ‘Channel 1 as Reference’.  Capture the Bode plot (magnitude and phase) of the voltage across the capacitor and paste it as Figure 10 in the report form below. 
  • Build the RL Circuit on your breadboard.  Measure the circuit with a 10 kHz sine wave with amplitude of 1 volt (2 volt peak-to-peak).   Plot the voltage waveforms across the resistor and the inductor over two periods in steady state.  Capture the plot and paste it as Figure 11 in the report form below.  Measure the phase difference between the current through and the voltage across the inductor (in the direction of assumed current flow).  (Note that the current through the inductor is proportional to the voltage across the resistor, and thus the phase of the current through the inductor is equal to the phase of the voltage across the resistor.)  Record your result in Table 2 of the report form below.
  • In this part of the lab, you will make measurements of the RL circuit using the network analyzer instrument feature of the Analog Discovery.  Use waveform generator channel 1 (the solid yellow wire numbered W1) as the stimulus for the circuit. (Don’t forget the ground connection!)  Connect oscilloscope input channel 1 so as to monitor the output of the AWG (i.e., the source).  Connect oscilloscope input channel 2 across the inductor.  In the control area of the instrument, set the Start and Stop frequencies to 100 Hz and 1 MHz respectively.  Ensure that the scope channels are set so as to use ‘Channel 1 as Reference’.  Capture the Bode plot (magnitude and phase) of the voltage across the inductor and paste it as Figure 12 in the report form below. 
 

EEE 202 Lab 6 Report Form

Name: _______________________________________________

ASU ID: _____________________________________________

Lab 6 Grade

Question Score
Figure 1                                           /5
Figure 2                                           /5
Figure 3                                           /5
Figure 4                                           /5
Figure 5                                           /5
Figure 6                                           /5
Figure 7                                           /5
Figure 8                                           /5
Figure 9                                           /5
Figure 10                                           /10
Figure 11                                           /5
Figure 12                                           /10
Table 1                                           /5
Table 2                                           /5
   
TOTAL                                           /80


Figure 1. Voltages across the resistor and the capacitor (in the direction of assumed current flow) in the RC circuit obtained using the analytical expressions in MATLAB.  (5pts)

Figure 2. Voltages across the resistor and the capacitor (in the direction of assumed current flow) in the RC circuit obtained using simulation in LTSPICE.  (5 pts)

Figure 3. Bode plot (magnitude and phase) of the voltage across the capacitor (in the direction of assumed current flow) in the RC circuit obtained using the analytical expressions in MATLAB.  (5pts)

Figure 4.Bode plot (magnitude and phase) of the voltage across the capacitor (in the direction of assumed current flow) in the RC circuit obtained using simulation in LTSPICE. (5 pts)

Figure 5. Voltages across the resistor and the inductor (in the direction of assumed current flow) in the RL circuit obtained using the analytical expressions in MATLAB.  (5pts)

Figure 6. Voltages across the resistor and the inductor (in the direction of assumed current flow) in the RL circuit obtained using simulation in LTSPICE.  (5 pts)

Figure 7. Bode plot (magnitude and phase) of the voltage across the inductor (in the direction of assumed current flow) in the RL circuit obtained using the analytical expressions in MATLAB.  (5pts)

Figure 8.  Bode plot (magnitude and phase) of the voltage across the inductor (in the direction of assumed current flow) in the RL circuit obtained using simulation in LTSPICE. (5 pts)

Figure 9. Voltages across the resistor and the capacitor (in the direction of assumed current flow) in the RC circuit obtained in the measurement.  (5pts)

Figure 10. Bode plot (magnitude and phase) of the voltage across the capacitor (in the direction of assumed current flow) in the RC circuit in the measurement.  (10pts)

Figure 11. Voltages across the resistor and the inductor (in the direction of assumed current flow) in the RL circuit obtained in the measurement.  (5pts)

Figure 12. Bode plot (magnitude and phase) of the voltage across the inductor (in the direction of assumed current flow) in the RL circuit obtained in the measurement.  (10pts)

Table 1.  Comparison from analysis, simulation and measurement of RC circuit for phase difference between the current through and the voltage across the capacitor. (5 pts)

  <I – <V (deg)
Analysis    
LTSPICE Simulation  
Measurement    

Table 2.  Comparison from analysis, simulation and measurement of RL circuit for phase difference between the current through and the voltage across the inductor. (5 pts)

  <I – <V (deg)
Analysis    
LTSPICE Simulation  
Measurement    
 
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