ECEN 3714----Network Analysis
Section 3
Laboratory Manual
LAB 5: RLC circuit with the L and C in Parallel
Oklahoma State University
School of Electrical and Computer Engineering.
Laboratory manual
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Fall 2016
1. OBJECTIVE
The objective of this laboratory section is to examine the resonance and damping features of the RLC circuits.
You will measure the response of an RLC circuit, with the L and C in parallel, to a step input, and to learn the similarity
and difference of the response of this LC-parallel circuit with that of the series RLC circuit of the last lab. After this lab, you
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will be able to quantify the under-damped natural frequency and the damping time constant of a 2 -order circuit.
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2. RLC CIRCUIT AND STEP RESPONSE
order circuit composed of R, L and C with the L and C in parallel has a natural (resonant) frequency of
√
and a damping factor of
Depending on the values of R, L, and C, the circuit can be over-damped (when > ), critically damped (when = );
or under-damped (when < ). For under-damped case, the voltage or current for the passive elements all have the
pattern of oscillating with decaying amplitude similar to the one shown in below
which can be described in a general form by:
X (t )  e t  A cos d t + Bsin d t

d  o 2   2
Where the coefficients A and B are determined by the initial conditions of the circuit. The exponential envelope is
described as
e- t / where = 1/is the time constant for the decay. The damped frequency d is just 2 times the
inverse of the period T.
3. PRE-LABORATORY ASSIGNMENT
The pre-lab assignment MUST be completed before you perform the hands-on laboratory measurement. The pre-lab accounts
for 40% of the lab-6 grade.
Figure 1
3.1 Pre-Lab Assignments7:
3.1.1 Convert the circuit to s-domain, assuming zero initial capacitor voltage and zero initial inductor current.
Derive Vout(s) of the s-domain circuit---it will be expressed by Vin(s) and a fraction involving “s”--------10%
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3.1.2
Choose three resistor values (or ranges, you are going to use those values in the lab) for the circuit to
become under-damped, critically damped, and over-damped. Confirm using PSpice with an input of
in (t )  5u(t ) , ------------------------------------------------15%
3.1.3
Find Vout(s)/ Vin(s) for the L, C values and the three respective resistor values chosen above. The result will
be three functions (involving “s”) that determine system response---the “transfer function”------------ 5%
Design an RL first order circuit that has a SIMILAR (as close as possible) time-constant as the damping of
the under-damped circuit that you have chosen in 3.1.2. Verify with PSpice--------------------------- 5%
Derive Vout(s)/ Vin(s) of the circuit you designed in 3.1.4. The Vout is taken across the resistor.
------------------------ 5%
3.1.4
3.1.5
Bring your own thumb drive, and check the data is saved in the drive before leaving lab.
4.1
4. LABORATORY ASSIGNMENT
Activities:
4.1.1 Implement the circuit in Fig. 1 using the three different resistor values you have chosen in 3.1.2. Record the
responses (waveforms) of the circuit in all three conditions to the same input of in (t )  5u (t ) .
4.1.2 For only the under-damped circuit implemented in 4.1.1, quantify the damped natural frequency and the
decay time-constant. You may use this format to keep record of the circuit parameter.
Parameter
Measured
Calculated
% Error
, time constant
d
4.1.3 Implement the first-order circuit you designed in 3.1.4 and measure voltage across the resistor in response to
in (t )  5u(t ) . Record the response, and measure the time-constant.
4.2 Laboratory Report:4.2.1 Cover page-------------------------2%
The cover page should include (1) the course name, lab-sections, dates, lab numbers, etc. that indicate the
comprehensive lab information, (2) the names of the group members, and the signatures of the members. The lab
should be the work of the lab-group only, no discussion with other group members is allowed.
4.2.2 Introduction- ----------------------3%
Describe the objective of this laboratory section
4.2.3 Completed pre-lab (with the signature of TA): ----------------
40%
4.2.4 Results and data analysis by referring to pre-lab results: ------- 40%
Based on the order of the laboratory activities defined in 4.1, organize the predicted and observed responses of the
circuits. This section shall include the following components for each experimental set up of 4.1.1—4.1.3:






The S-domain representation of the circuit in Fig, 1--------------------------------------------------------------5%
Results of 4.1.1, including the predicted and measured responses at the three cases, under-damped,
critically damped, and over-damped cases.
15%
The method of measuring the damping factor in under-damped case, show with figure -5%
The method of measuring the damped natural frequency, show with figure ---5%
The tabular results of 4.1.2,
5%
Results of 4.1.3, including the predicted and measured responses and the time-constant
5%
4.3.5 Discussions: -----------15%
 For a 2nd order RLC circuit as shown in Fig. 1, which parameters determine the oscillation of the current
through the L? Which parameters determine the damping of the voltage across the resistor? --------5%
 What are the similarity and difference of the response of RLC in-series and RLC in-parallel? ---------5%
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
What general conclusion can you made for a 2nd-order circuit? Use relevant equations to support your
findings if necessary.-------------------------------------------------------------------------------------------------------5%
Laboratory manual
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Fall 2016