ET310 GU Laplace Transform and Analysis in S Domain Lab Report

Description

Circuit Analysis – Week #6 Lab Laplace Transform and Analysis in S-Domain
Rules for lab submissions: 1. The lab document must be a Word document. PDF files are NOT accepted. 2. All screenshots must be included. 3. All screenshots must include the Multisim time stamp. 4. Any and all Multisim files must be submitted. 5. Any equations used must be typed in Word. Copy and paste of equations from outside sources is prohibited. 6. No graphics are allowed in the Word document other than screenshots of circuits from Multisim with the time stamp. 7. The lab template should be used. Specifically, it is brought to your attention that a summary MUST be provided explaining the results of the labs, the relationship of the results to expected results, and any challenges encountered. 8. All resistors in must be have a tolerance of at least 5% set. Thus, your measured values should NOT be exactly equal to your calculated values.

Circuit Analysis – Week #6 Lab
Laplace Transform and Analysis in S-Domain
This week’s lab is based on the application of circuit analysis techniques to a capacitive circuit
with Multisim. You will learn to utilize Multisim to perform the mesh analysis.
1. See file “Design of Oscillator Circuits” (click link)
2. Design a Wein bridge Oscillator shown in the figure below in Multisim to generate a
sinusoidal signal at frequency of 300Hz. Consider a capacitor of 1uF, resistor R =
5950Ω, R1 = 3Ω, Rf = 6.05Ω for the oscillator circuit.
a. Determine output voltage ‘Vo’ and run the simulation to plot the output of the
oscillations at frequency of 300 Hz using an oscilloscope.
b. Increase the frequency to 500Hz, 800Hz and 1000Hz and plot the output of the
oscillator at these multiple frequencies.
c. Take the screen capture of the oscilloscope readings for all the frequencies.
a. What is the requirement to generate oscillation in the circuit? Is the circuit stable
or unstable?
b. What do you observe in the oscillations when the frequency is increased?
c. With increased frequency, did you observe the oscillations? If not what did you
d. Explore different practical applications of oscillator circuits and explain.
4. Create a new word document called “Lab6_StudentID.docx” with your GID substituted
into the file name.
5. Save the simulation results from step 2 along with the measurements and screen
captures. Make sure to answer the questions in step 6.
Rules for lab submissions:
1. The lab document must be a Word document. PDF files are NOT accepted.
2. All screenshots must be included.
3. All screenshots must include the Multisim time stamp.
4. Any and all Multisim files must be submitted.
5. Any equations used must be typed in Word. Copy and paste of equations from outside
sources is prohibited.
6. No graphics are allowed in the Word document other than screenshots of circuits from
Multisim with the time stamp.
7. The lab template should be used. Specifically, it is brought to your attention that a
summary MUST be provided explaining the results of the labs, the relationship of the
results to expected results, and any challenges encountered.
8. All resistors in must be have a tolerance of at least 5% set. Thus, your measured
values should NOT be exactly equal to your calculated values.
Any violation of the submission rules above will result in a grade of 1.
Lab 6
Demonstrate understanding of Circuit Analysis in s-domain
10 points
Analyze the circuit in to compute the output of the oscillator circuit
20 points
10 points
Measurement of oscillations for different frequencies
30 points
20 points
Lab Report (includes table, measurement with proper units, screenshots, APA
guidelines)
10 points
Total
100
points
KINGSLEY OTENG
GRANTHAM UNIVERSITY
G00160809
ET 310
WEEK 4 LAB
Introduction:
Main intention of implementing this lab is to apply the circuit analysis techniques for evaluating
RLC circuits. I expect to learn about the functionality of RLC circuits and evaluate them based
on the values obtained from calculations as well as measurements. Multisim software will be
used to carry out the constructing task of the circuit and measuring the current flow (i) through
the inductor.
Equipment/Components:
In this experiment, 1 DC Power supply (24V), 2 Resistors (350Ω, 125Ω), 1 Electrolytic
Capacitor (500nF), 1 DC Current source (20mA) will be used. Multisim software provides a
variety of list which contains all the components that are needed. By selecting the category and
the component from the master database, components can be added to the circuit design. After
adding the components, the values can be changed by double clicking on it. There will be a popup window to make the changes of the values. Specially in this lab it is mentioned that the
tolerance values of the resistors should be at least 5%. Tolerance values can be changed by
double clicking on each resistor and adding 5% to tolerance field indicated in the value tab of the
pop-up window.
Procedure:
After constructing the circuit in Multisim, an ammeter and current indicator were used to find the
current flow through the inductor. Current measurements were taken for open switch and close
switch conditions. Screen captures were taken to present the measured values. Then the
measured values were compared with the calculated values.
In this experiment, Ohm’s law and Kirchhoff’s Current law were used to compute the values for
the current flow. Ohm’s law is algebraic relationship between voltage and current for a resistor.
Kirchhoff’s Current law states that algebraic sum of all the current at any node in a circuit equals
to zero (Nilsson & Riedel, 2008).
Resonant radian frequency can be measured by using following formula.
1
𝜔0 =
√𝐿𝐶
1
To measure Neper frequency for parallel RLC circuit, 𝛼0 = 2𝑅𝐶 formula can be used.
Circuit design:
Circuit design
Execution/Results:
Finding the iL (0), current through inductor
Finding the iL(∞) current through the inductor
Finding the iL(t) current through the inductor
Analysis:
Circuit design
A
i1
i2
i3
Since the switch has been open for a long time, the current flow through the inductor is equal to
current flow through the resistor (350Ω). Immediately after closing the switch, current source
(20mA) is not affecting the value. Inductor acts as a short circuit and capacitor acts as an open
circuit. Hence, we can calculate the current flow by considering only the value of resistor.
Applying Ohm’s law to find the current flow through the inductor.
𝑉 = 𝐼. 𝑅
Let Vs = Source Voltage, R1 = Resistance value of R1, iL = Current through the inductor
𝑖𝐿 =
𝑉𝑠
𝑅
When t = 0,
𝑖𝐿 (0) =
24𝑉
350Ω
𝑖𝐿 (0) = 0.068571𝐴 = 68.571𝑚𝐴
When t = ∞, the 20mA current flow goes in the opposite direction of iL.
Applying Kirchhoff’s Current Law to node A,
When t = ∞,
𝑖𝐿 (∞) = (
24𝑉
− 20𝑚𝐴)
350Ω
𝑖𝐿 (∞) = 0.48571𝐴 = 48.571𝑚𝐴
When t ≥0,
Applying Kirchhoff’s current law to node A,
𝑖1 + 𝑖2 + 𝑖3 = 0
68.571𝑚𝐴 − 𝑖3 − 20𝑚𝐴 = 0
𝑖3 = 48.571𝑚𝐴
Finding the resonant (natural) frequency,
𝜔0 =
𝜔0 =
1
√𝐿𝐶
1
√(20 ∗ 10−3 ) ∗ (500 ∗ 10−9 )
𝜔0 = 10000 𝑟𝑎𝑑𝑠 −1
Following table indicates the computed and measured values for current flow through the
inductor. And the resonant radian frequency is included in the last row.
iL(0)
iL(∞)
iL(t) for t≥0
ω0
Calculated
68.571mA
48.571mA
48.571mA
Measured
68.6mA
48.6mA
48.6mA
Measured values are different from calculated values. When the current flow value is rounded
off, there may be changes in final value. It is clear by observing the ammeter value and the value
displayed in indicator. This may be due to the tolerances of the resistor that we included. When
the tolerance of resistor value is 5%, that implies there will be 5% more or less to the exact value
of resistor. 350Ω resistor can vary from approximately 333Ω to 368Ω. (350*0.05=17.5).
Conclusion:
Neper frequency can be found by using following formula.
Neper frequency = α0
𝛼0 =
𝛼0 =
1
2𝑅𝐶
1
2 ∗ (125) ∗ (500 ∗ 10−3 )
𝛼0 = 16000 𝑟𝑎𝑑𝑠 −1
Since ω0 = 10000 rads-1 and ω02