Faculty of Engineering and Applied Science
Department of Electrical and Computer Engineering
ECE 3300: Circuit Analysis
Instructions
1. Full participation in all labs in the course is compulsory for all students. Failure to participate
in all labs and complete all laboratory tasks will result in an INCOMPLETE grade.
2. Please carefully read the lab schedule and attend the correct session you are assigned to.
3. Labs include prelabs which are to be completed prior to the lab session. Each student must
complete their own prelab individually and submit it at the beginning of the lab session.
4. Each experiment will be undertaken in groups of 2 students. Only one report per experiment is
expected from each group but both students are required to contribute equally to every report
and lab activities.
5. Submit the lab report to the corresponding assignment submission folder in D2L.
Submitting to a wrong submission folder or submitting in any other way (e-mailed)
will be discarded.
6. Note that there is separate submission folder for Tuesday group and Thursday group as
they have different submission due dates.
7. It is required to create a single PDF file of the lab report and prelabs before submitting
to the Brightspace’s assignment submission folder.
8. Lab reports submission are due in one week after the lab at midnight.
9. Late submission is penalized by 10% per day.
10. The lab report must include a cover page identical to the sample cover page shown
in the next page.
11. See, Annex 1 for rubric. Every element in the rubric MUST be presented on the LAB
REPORT.
1
FACULTY OF ENGINEERING AND APPLIED SCIENCE
Department of Electrical and Computer Engineering
ECE 3300 – Circuit Analysis
Lab 7 - Step and Frequency Response of RLC Circuits
Student 1
Student 2
Name
Student ID
Date
2
FACULTY OF ENGINEERING AND APPLIED SCIENCE
Department of Electrical and Computer Engineering
Exp. 3300-7 Step and Frequency Response of RLC Circuits
(Prepared by Dr. John Quaicoe and updated by Andrew Peddle)
Purpose
•
To determine the step response of RLC circuits, and
•
To explore the frequency response of RLC circuits.
1.0
Introduction
It was observed in the previous lab that when an RC or RL circuit is suddenly energized or deenergized, a transient phenomenon occurs which dies out as the circuit approaches the steady-state
operation. The nature of the transients depends on the values of R, L and C as well as on how they
are combined in a circuit. The steady state response of the circuit, which is determined by the external
source, is reached only after a transient time interval.
The response of RLC circuits may be classified as under damped, critically damped, or over damped.
In this lab session, we will explore the time-dependent response of the series RLC circuit.
The current and voltage responses in circuits containing inductors and capacitors (besides resistors)
are also frequency-dependent because the impedances of the elements vary with frequency. Such
circuits can be used as "frequency-selective circuits" or filters - that is, they respond to signals of
different frequencies differently and can therefore be designed to "pass" certain frequencies to a
load or other parts of the circuit and to attenuate others. The study of the frequency response of a
circuit involves the consideration of the magnitude and phase of the steady state voltages and
currents as the frequency varies. In this lab a study the frequency response of a particular RLC
circuit configuration is examined through PSpice simulation and by experimental measurements.
2.0
Prelab
Read Section 8.4, pg. 296-303 (or pg. 285-288 of 10th edition) and Section 14.4, pg. 550560 (or pg. 534 – 543 of 10th edition) of the Textbook for the theory behind the
experiment.
The circuit of Figure 1 is excited by a square wave voltage of 4 V peak (zero to peak)
with a frequency of 500 Hz. Create the square wave voltage so that the pulse width is
half the period.
For R = 1.5 Ω, L = 2.2 mH, and C = 0.1 µF, use PSpice to obtain the plot of the variation of the
voltage across the capacitor (vc). Assume zero initial conditions. Limit the response to two
cycles only. Indicate the nature of the response as overdamped, underdamped, or critically
damped.
3
Repeat 2.2.1 for R = 100 Ω, L = 2.2 mH, and C = 0.1 µF.
Repeat 2.2.1 for R = 220 Ω, L = 2.2 mH, and C = 0.1 µF.
From the plots for 2.2.1 and 2.2.2, determine the frequency of oscillations. Also, determine
the frequency of oscillations using the circuit parameters. Refer to equations 8.14 (pg. 282)
and 8.29 and 8.30 (pg. 297) of the Textbook [or 8.27 (pg. 274) and equations 8.58 and 8.59
(pg. 286) of the 10th edition of the Textbook].
Figure 1 - Step response of a series RLC circuit
General Guidelines: Frequency response of RLC circuits using PSpice: Draw the
PSpice schematic for the circuit indicated in Figure 2 with R1 = 1 kΩ and C1 = 0.1
µF. Use source, VSRC with AC = 1 V. Set the other parameters as follows: DC= 0
and TRAN=0. With vin set to 1 V, vo is the desired response.
Figure 2 - RC circuit for sweep analysis
On the Simulation Settings screen, select AC Sweep, Logarithmic, and specify the frequency
range as shown in Figure 3. Refer to the PSpice Presentation file. Set the number of points
to 1000 to get better and smoother plots, especially for section 2.3.2.
Let the circuit of Figure 2 be excited by a sinusoidal source whose frequency varies from 10
Hz to 40 kHz. Use PSpice to obtain a plot of |v0/vin| versus frequency. In Probe, set the
x-axis setting of the plot to log scale.
4
Figure 3 - PSpice simulation profile for AC frequency sweep
Consider the circuit of Figure 4. L1 = 1 mH and C1 = 0.47 µF. Let the circuit be excited by
a sinusoidal source whose frequency can be varied from 100 Hz to 100 kHz. Use PSpice to
obtain plots of |v0/vin| versus frequency for two different values of R1 (i.e. R1 = 47 Ω, and R1
= 220 Ω). Obtain the two required plots on the same graph (by creating two circuits in the
same Schematic file). In Probe, set the x- axis setting of the plot to log scale.
Figure 4 - Frequency Response of a Series RLC Circuit
3.0
Experiment
Refer to your notes on the Oscilloscope and use the relevant features for these experiments.
Step response of a series RLC circuit.
Construct the circuit of Figure 1 using RLC values in 2.2.1. Adjust the Wavegen on the AD2
(W1) to provide 4 V (peak), 500 Hz symmetrical square wave after connecting all the
elements. Note that the use of this signal enables you to simulate the effect of repeatedly
energizing the RLC circuit and the waveform in the AD2’s oscilloscope may be considered
similar to the step response of this circuit.
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Sketch to scale one-half of the input square wave and the voltage across the capacitor.
Complete the experiment for the remaining two combinations of the circuit elements as in the
prelab 2.2.2 and 2.2.3. Estimate the frequency of oscillation for the three combinations of the
circuit element.
Frequency Response of RC and series RLC circuits.
Connect the circuit of Figure 2. Adjust the Wavegen on the AD2 (W1) to provide 3 V (6V peakpeak) sinusoidal wave. For the source frequency varying from 60 Hz to 20 kHz, measure v0 and
vin for 12 different frequencies. Use the AD2s oscilloscope or counter to measure the frequency
accurately.
Experimentally determine |v0/vin| as a function of frequency for the circuit of Figure 4 for R1
equal to 47 Ω. Take more readings near the frequency of interest.
Repeat 3.2.2 for R1 = 220 Ω.
4.0
Lab Writeup
Plots: Since the range of the x-axis is large, plot the experimental results using a semi-log graph.
Compare the response of the RLC circuits obtained from the experiment with the PSpice
simulation. Discuss the differences between the types of response for the three circuits.
Compare the experimentally determined frequency of oscillation with the theoretical
values.
Draw the frequency response of the RC circuit using your measurements. From your
plot, determine the half-power frequency and compare it with the theoretical value.
Compare the experimental plot with that obtained using PSpice. Suggest a possible
application of this circuit.
Draw the frequency response for the series RLC circuit. Compare this plot with the plot
obtained by the PSpice simulation. Discuss the influence of the value of the resistance
on the frequency response of the circuit. Suggest an application for this circuit.
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ANNEX I
2.2.1
2.2.2
2.2.3
2.2.4
2.3
2.3.1
2.3.2
3.1
Prelab
R=1.5; L=2.2mH; C=0.1uF
Pspice circuit diagram
Vc plot - 2 cycles
Nature of oscillation
R=100; L=2.2mH; C=0.1uF
Pspice circuit diagram
Vc plot - 2 cycles
Nature of oscillation
R=220; L=2.2mH; C=0.1uF
Pspice circuit diagram
Vc plot - 2 cycles
Nature of oscillation
Freq of oscillation
Measure from graph (both 2.2.1, 2.2.2)
Calculated values
Frequency Response- AC sweep
Pspice circuit diagram
Freq response plot
Freq response plot for L=1mH; C=0.47uF; R=47
Freq response plot for L=1mH; C=0.47uF; R=220
LAB report
Step response
3.1.2 Sketch of input and Vc for RLC values in 2.2.1
3.1.3 Repeat 3.2.2 for RLC values in 2.2.2 and 2.2.3
Measured frequency of oscillation for each case
30
7
2
4
1
7
2
4
1
7
2
4
1
3
2
1
6
1
1
2
2
70
16
4
8
4
15
3.3. Frequency response
5
3.2.1 Vo and Vin values for 12 frequency points
3.2.2 |Vo/Vin| for R=47 ohms
3.2.3 |Vo/Vin| for R= 220 ohms
5
5
34
4 Lab write up
4
8
3
2
2
8
3
2
2
4.1 Comparison; nature of response discussion
4.2 Freq response plot from 3.2.1
measure Half power frequency from plot
Compare with prelab results
Suitable application
4.3 Freq response plot from 3.2.2 and 3.2.3
Comparison with prelab
Discussion on value of R
Suitable application
5
Report quality
1.
7