Laboratory Experiments - Valencia Collegefd.valenciacollege.edu/file/mejaz/Lab Experiments EET...
Transcript of Laboratory Experiments - Valencia Collegefd.valenciacollege.edu/file/mejaz/Lab Experiments EET...
Department of Electrical & Computer
Engineering Technology
EET 3086C – Circuit Analysis
Laboratory Experiments
Masood Ejaz
EET 3086C – Circuit Analysis Valencia College
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Experiment # 1
DC Measurements of a Resistive Circuit and Proof of Thevenin Theorem
Prelab: Solve the circuits theoretically (steps 1, 2, and 3) and then perform PSpice simulations
to fill out appropriate tables under procedure section.
Objective: To build a resistive circuit and its Thevenin equivalent to prove their equivalency for
the load.
Procedure:
1. Build the following resistive circuit on the breadboard and measure the indicated variables
Figure 1: Resistive Circuit for Step 1
VR4 IR3 VR6 IR6
Theory
Simulation
Lab
2. Suppose your load is comprised of resistors R4, R5, and R6. Draw the Thevenin equivalent
circuit and then build it on the breadboard. Measure load current and load voltage and
compare them to the corresponding values that you obtained in step 1 to show the
equivalency of both the circuits for this load (Note: if exact value of RTH is not available, use
the closest value or make a series combination of resistors to get to the closest value)
VTH = _____________________________; RTH = ____________________________
R1
1.0k
R22.0k
R3
3.0k
R44.7k
R5
1.0k
R62.2k
V110 V
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VLOAD ILOAD
Theory
Simulation
Lab
3. Now assume that load is just resistor R6. Repeat step 2.
VTH = _____________________________; RTH = ____________________________
VLOAD ILOAD
Theory
Simulation
Lab
Thevenin Circuit
Thevenin Circuit
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Discussion: You lab report discussion should include an explanation and importance of
Thevenin theorem and explanation of your Thevenin equivalent circuits. If there is any
discrepancy in your results, make sure to discuss that too.
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Experiment # 2
Transient Response of RC and RL Circuits
Prelab: Perform lab simulation using PSpice. Also, find the response equations as being asked in
the lab and fill out the corresponding tables to compare simulated and theoretical results.
Objective: To design first-order RC and RL circuits to observe their transient response
RC Circuit
Procedure:
1. For the first-order RC cicuit as shown in figure 1, derive the equations for the capacitor
voltage when input is 5V (complete or step response) and when it is 0V (source-free or
natural response).
vc(t) [step response] = ____________________________________________
vc(t) [natural response] = ____________________________________________
2. Build a first-order RC circuit as shown in figure 1. Use square wave as your input and choose
its frequency such that pulse width of the square wave (tp) is six times the time constant () of
the circuit, i.e. 6pt . It can safely be assumed that this pulse width time is long enough for
the circuit to get to its steady-state value. Remember that pulse width is half of the time
period of the square wave. Set input voltage to be 5Vp-p (high voltage = 5V, low voltage =
0V)
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Figure 1: First-Order RC Circuit
3. Connect your oscilloscope to observe both input signal and voltage across capacitor
simultaneously. Fill out the following table with your theoretical, simulated, and observed
values from oscilloscope. Save your waveform.
vc(t) [step response] vc(t) [natural response]
Theory Simulation Lab Theory Simulation Lab
t =
t = 2
t = 3
RL Circuit
Procedure:
1. A first-order RL circuit is shown in figure 2. Derive the equations for the inductor current
when input is 5V (complete or step response) and when it is 0V (source-free or natural
response).
iL(t) [step response] = ____________________________________________
iL(t) [natural response] = ____________________________________________
C1
10n
R1
1k
R2
2k
R3
2k
V1
TD = 0
TF = 1p
V1 = 0
TR = 1p
V2 = 5V
0
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Figure # 2: First-Order RL Circuit
2. Build the circuit from figure 2. Use square wave as your input and choose its frequency such
that pulse width of the square wave (tp) is six times the time constant () of the circuit, i.e.
6pt . It can safely be assumed that this pulse width time is long enough for the circuit to
get to its steady-state value. Remember that pulse width is half of the time period of the
square wave. Set input voltage to be 5Vp-p (high voltage = 5V, low voltage = 0V)
3. Observe the current passing through the inductor. For hands-on, measure the voltage across
R3 on the oscilloscope and calculate current from that. PSpice simulation can plot the current
using a current probe. Fill out the following table with your theoretical, simulated, and
observed values. Save your waveform.
iL(t) [step response] iL(t) [natural response]
Theory Simulation Lab Theory Simulation Lab
t =
t = 2
t = 3
Discussion:
Your lab report should show the derivation of the equations. Discussion should focus on the
transients in RL and RC circuits. Also discuss about discrepancies between lab and expected
results. Discuss why it is important to study transient analysis of RL and RC circuits, i.e. their
practical implication.
L1
1mH
R1
100
R2
100
R3
100
V1
TD = 0
TF = 1p
V1 = 0
TR = 1p
V2 = 5V
0
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Experiment # 3
Transient Response of RLC Circuits
Prelab: Solve circuits theoretically and perform simulation using PSpice. Write down your
prelab calculations and observations as required in the following procedure.
Objective: To design two different RLC circuits to study the response characteristics.
Procedure:
4. For the first RLC circuit as shown in figure 1, calculate the values for neper frequency ()
and resonant frequency (o). Determine the type of damping and calculate the root(s) of the
characteristic equation.
Figure # 1: First RLC Circuit
Neper
Frequency ()
Resonant
Frequency (o)
Damping Type s1 s2
5. Assume that input is a square wave with values from 0 to 5V with level zero representing
source-free circuit and 5V representing step circuit. Perform the analysis to calculate the
capacitor voltage for both step and source-free circuits.
vc(t) (step) = _____________________________________________________________
vc(t) (source-free) = _______________________________________________________
6. Simulate your circuit with PSpice. Take pulse width (half of the time period) of the square
wave to be around six times the time constant (reciprocal of the dominant neper frequency,
C
10nF
L
100mH
R21k
R1
1k
V1
TD = 0
TF = 1p
V1 = 0V
TR = 1p
V2 = 5V
0
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i.e. dominant root). Observe the voltage across capacitor. Make sure to keep your simulation
interval small enough to have a smooth graph.
7. Use MATLAB to plot the step and source-free responses from your expressions of capacitor
voltage (one plot will be preferred else plot separately). Compare your plot with the
simulated results to check the accuracy of your derived expressions. Fill out the following
table. Make sure to put the simulated and MATLAB plots in your lab report.
Step Response Source-free Response
First Peak
Time
First Peak
Value
(positive
or
negative)
Steady-
State
Value
First Peak
Time
First Peak
Value
(positive or
negative)
Steady-
State
Value
Simulation
MATLAB
8. Build your circuit on bench and observe capacitor voltage to fill out the following table.
Compare your results with the simulated and theoretical responses for validation.
Step Response Source-free Response
First Peak
Time
First Peak
Value
(positive or
negative)
Steady-
State
Value
First Peak
Time
First Peak
Value
(positive or
negative)
Steady-
State
Value
Bench
9. Now, for the second RLC circuit as shown in figure 2, calculate the values for neper
frequency () and resonant frequency (o). Determine the type of damping and calculate the
root(s) of the characteristic equation.
Neper
Frequency ()
Resonant
Frequency (o)
Damping Type s1 s2
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Figure # 2: Second RLC Circuit
10. Assume that input is a square wave with values from 0 to 5V with level zero representing
source-free circuit and 5V representing step circuit. Perform the analysis to calculate the
voltage across R2 for both step and source-free circuits.
VR2(t) (step) = _____________________________________________________________
VR2(t) (source-free) = _______________________________________________________
11. Simulate your circuit with PSpice. Take pulse width (half of the time period) of the square
wave to be around six times the time constant (reciprocal of the dominant neper frequency,
i.e. dominant root). Observe the voltage across capacitor. Make sure to keep your simulation
interval small enough to have a smooth graph.
12. Use MATLAB to plot the step and source-free responses from your expressions of the
voltage across R2 (one plot will be preferred else plot separately). Compare your plot with
the simulated results to check the accuracy of your derived expressions. Fill out the following
table. Make sure to put the simulated and MATLAB plots in your lab report.
Step Response Source-free Response
First Peak
Time
First Peak
Value
(positive
or
negative)
Steady-
State
Value
First Peak
Time
First Peak
Value
(positive or
negative)
Steady-
State
Value
Simulation
MATLAB
C1
100nF
L1
100mH
R11k
R22k
V1
TD = 0
TF = 1p
V1 = 0V
TR = 1p
V2 = 5VR3
3k
0
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13. Build your circuit on bench (if required) and observe voltage across R2 to fill out the
following table. Compare your results with the simulated and theoretical responses for
validation.
Step Response Source-free Response
First Peak
Time
First Peak
Value
(positive or
negative)
Steady-
State
Value
First Peak
Time
First Peak
Value
(positive or
negative)
Steady-
State
Value
Bench
Discussion:
Your lab report discussion should focus on the transients in RLC circuits. Discuss different types
of damping, effect of neper (), resonant (o), and natural resonant (d) on the circuit response,
and practical implication of this study. Compare your theoretical, simulated, and lab results and
discuss if there are any discrepancies.
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Experiment # 4
Sinusoidal Response of an RLC Circuit
Prelab: Solve circuit theoretically and perform simulation using PSpice. Write down your prelab
calculations and observations as required in the following procedure.
Objective: To observe amplitude and phase change in an RLC circuit under a sinusoidal forcing
function.
Procedure:
1. Solve for the voltage expressions across inductor and capacitor in figure 1
Figure 1: RLC Circuit for the Experiment
VL(j) = __________; vL(t) = _________________________________________________
Vc(j) = __________; vc(t) = _________________________________________________
2. Simulate the circuit in PSpice and observe waveforms across source, capacitor, and inductor.
Fill out the following table with the observed values from the simulated results.
VL(peak) (Volt) Phase angle L(degree) VC(peak) (Volt) Phase angle C(degree)
Vs
5 V
100kHz
0Deg
L1330uH
R1
100
R2
510
R31.0k
R4
1.0k
C11.0nF
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Note:
(i) To measure phase angle of VL and VC from the simulation and oscilloscope, measure the
time difference between the zero-crossing of your source waveform and the respective
voltage waveforms using cursors (figure 2). Let this time be t, then using the following
relationship, phase angle for each of the waveform can easily be found,
360T
t
where T is the time period of each waveform (constant as long as f is constant), and is
the phase angle.
(ii) When you use PSpice to simulate your circuit, make sure to use fourth or fifth cycle of
your voltage waveforms to measure peak voltage and phase angle, i.e. when voltages are
settled down to their steady-state. From the simulation, you will see that for the first
couple of cycles, vLand vC will still be in the process of settling down to their steady-state.
Figure 2: Measurement of t from simulation
t
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3. Build circuit on the breadboard and repeat step 2. Fill out the following table with your lab
results
VL(peak) (Volt) Phase angle L(degree) VC(peak) (Volt) Phase angle C(degree)
4. Show the phasor relationship of the three voltages using phasor diagram
Discussion:
Your discussion should encompass the importance of sinusoidal analysis as well as reason to
perform analysis in complex frequency domain versus time domain. You should also discuss the
concept of lagging waveforms versus leading waveforms and effect of the inclusion of capacitors
and inductors in the sinusoidal circuits.
Exercise:
Make Thevenin equivalent of your circuit assuming load to be C1. Find load voltage and load
current and show their phasor relationship.
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Experiment # 5
Analysis of Series RLC Band-pass Filter
Prelab: Solve circuit theoretically and perform simulation using PSpice (AC sweep with both
linear and logarithmic sweep type). Write down your prelab calculations and observations as
required in the following procedure.
Objective: To observe the frequency response of a series RLC bandpass filter or series resonant
circuit
Procedure:
1. For the bandpass filter design shown in figure 1, let resonant frequency fo be 159.15 KHz and
required bandwidth is approximately 15.915 KHz. Complete the design by calculating the
following quantities:
Inductance L Capacitance C Quality factor Q Lower cut-off f1 Upper cut-off f2
Figure 1: Series RLC Band-pass filter
2. Fill out the following table from your calculated and simulated values. Note that the input
sinusoidal source has 5Vp output.
Calculated Simulated
VR (fo)
VR (f1)
VR (f2)
Vin
5Vac
0Vdc
0
+
Vout
-
C1L1
R1
10k
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3. From your simulation, figure out the upper and lower frequencies corresponding to 10% of
the maximum output and write them down. These will be considered as stop-band
frequencies
flower_10% = _________________________; fupper_10% = _________________________
4. Build circuit on the bench and fill out the following table with your observations.
Hz Volt
fo v(fo)
f1 v(f1)
f2 v(f1)
flower_10% v(flower_10%)
fupper_10% v(fupper_10%)
5. From your observations, draw a rough sketch of frequency response of the circuit (vR vs. f)
Discussion: In your lab report, discuss band-pass filter, its equations, its practical applications,
and discrepancies between theoretical, simulated and lab results and their possible explanation.
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Exercises:
(i) Derive circuit equations to find out flower_10% and fupper_10%
(ii) Create two MATLAB programs to calculate different parameters for series band-pass
filter as follows:
Program 1 should be a function based on this lab, i.e., given the center frequency,
required bandwidth, and resistor value, it should calculate values for inductor and
capacitor, upper and lower cut-off frequency and quality factor. Further, it should also
plot the frequency response of the circuit. Plot should be properly labeled.
Program 2 should be a function that calculates center frequency, quality factor,
bandwidth, upper, and lower cut-off frequencies based on the input values of resistor,
capacitor and inductor. Plot the frequency response of the circuit and properly label your
plot.