Summary EE Science II Laboratory #7 RLC Circuits and Build an Inductor You will build an inductor and determine its

Summary

EE Science II Laboratory #7

RLC Circuits and Build an Inductor

You will build an inductor and determine its inductance by using it in an RLC circuit. RLC circuits are commonly used in oscillator design, tuning and filter circuits. These circuits exhibit resonance at a certain frequency making them ideal for applications that desire frequency selectivity. You will use this property to measure the inductance.

Let us approach this experiment as a problem –

The Problem Statement:

How will you construct an inductor and measure its inductance using an oscilloscope?

Solution Outline:

Break problem into smaller steps The problem has two main questions:
a) Build an inductor
b) Measure the inductance with an oscilloscope – we will use an RLC circuit
What you need to find out
For (1.a), we will need to identify / review the constructional features of an inductor. A simple inductor can be constructed by winding a wire around a core of some sort. Which material would we use for the core? The material should be chosen such that the inductor has sufficient inductance. It should be easy to handle – should have a known permeability and it should be easy to wind a wire around it.
For (1.b), we will need to build out a circuit – with known circuit elements, and characterize the response. In effect we will use the unknown inductor for an application, and based on our knowledge of how RLC circuits should behave specifically its resonance frequency, calculate the inductance.
How you will obtain the data a. Circuit elements – so use an oscilloscope, multimeter, etc — what other equipment will we need? b. We will need to find a way to measure resonance accurately –
How you will validate the test setup a. Recreate the circuit with a known inductance and check
How will you know if your answers are correct? a. Compare with theoretical expectation b. What are the sources of error?

so I want A post lab see what you need

1. see the summary to get idea

2. see the experment pdf and on page 10 you will see Laboratory Report 5 steps (this what should the post lab enclude)

3. see the tamplet to know how the post lab shold be formed and looks like.


EEL3472C: EE SCIENCE II – EM
Lab: __#___Title:__(10 pt font)_____
Date: 00/00/2017
Name: ____(10 pt font) ________
Lab Partner(s):__(10 pt font)__________
SUMMARY OF RESULTS AND DISCUSSION (PARAGRAPH STYLE , 12 PT FONT, SINGLE SPACE )
In this section, you should summarize and analyze your results. In other words, tell me what you
learned and what the results mean to you.
Things to avoid:


Don’t write EVERY step you did in class (I connected the function generator to the
oscilloscope, then I turned it on…etc)
Do not rewrite the lab manuscript
Things to include






Knowledge about the equipment and attachments (Eg: “Channel 1 of the oscilloscope is
connected across the input of the circuit and channel 2 across the capacitor. The
configuration allows you to compare the output with the input.”)
Understand results (what each or group of values mean to you)
If there are too many results you can create a table
Graphs and equations are also acceptable (reference them in your text)
Guide me though the whole lab exercise using your own words and understanding
Something in the lab that you did not understand or results not clear to you
EXPERIMENTAL QUESTIONS (PARAGRAPH STYLE , 12 PT FONT, SINGLE SPACE )

Answer/complete any additional questions asked during/ at the end of the lab experiment
LAB IMPROVEMENTS (THIS IS OPTIONAL , BUT HELP US IMPROVE THE LABS!)


Tell us what went wrong and what can be done to avoid those mistakes in the future
Mention any lab procedures that were confusing
General rules:
Minimum of 1/2 page written (be creative, I don’t want to see reports less than one full page)
Maximum of 1 page written (include figures/graphs/tables on extra pages)
Body Format: font size – 12pt (Times New Roman), Spacing – Single
This post lab report must be stapled on the front of the completed lab experience. Additionally, a
copy of this report must be submitted online via canvas (you do not have to submit the
completed lab experience online).
Maximum grade of 50% (5/10) if signed lab experience not included.
Laboratory #7
EE Science II Laboratory #7
RLC Circuits and Build an Inductor
Summary
You will build an inductor and determine its inductance by using it in an RLC circuit. RLC circuits are commonly
used in oscillator design, tuning and filter circuits. These circuits exhibit resonance at a certain frequency making them
ideal for applications that desire frequency selectivity. You will use this property to measure the inductance.
Let us approach this experiment as a problem –
The Problem Statement:
How will you construct an inductor and measure its inductance using an oscilloscope?
Solution Outline:
1. Break problem into smaller steps
The problem has two main questions:
a) Build an inductor
b) Measure the inductance with an oscilloscope – we will use an RLC circuit
2. What you need to find out
a. For (1.a), we will need to identify / review the constructional features of an inductor. A simple
inductor can be constructed by winding a wire around a core of some sort. Which material would
we use for the core? The material should be chosen such that the inductor has sufficient inductance.
It should be easy to handle – should have a known permeability and it should be easy to wind a wire
around it.
b. For (1.b), we will need to build out a circuit – with known circuit elements, and characterize the
response. In effect we will use the unknown inductor for an application, and based on our
knowledge of how RLC circuits should behave specifically its resonance frequency, calculate the
inductance.
3. How you will obtain the data
a. Circuit elements – so use an oscilloscope, multimeter, etc — what other equipment will we need?
b. We will need to find a way to measure resonance accurately 4. How you will validate the test setup
a. Recreate the circuit with a known inductance and check
5. How will you know if your answers are correct?
a. Compare with theoretical expectation
b. What are the sources of error?
Objectives

Build an inductor and measure its inductance

Gain an understanding of RLC circuits and study the frequency behavior of a series RLC circuit through
measurement
Equipment and Software

Oscilloscope

Function generator

Ferrite rod, magnet wire, rubber bands, jumper wires, R,C, breadboard
 University of South Florida
1
EE207-sum.docx
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EE Science II Laboratory #7
RLC Circuits and Build an Inductor
Printed Name:
~ YY 0i:
Bench# Used
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Please read the reminder on general policies and sign the statement below. Attach this page
to your Post-Laboratory report.
General Policies for Completing Laboratory Assignments:
For each laboratory assignment, you will also have to complete a Post-Laboratory report. For this report, you are
strongly encouraged to collaborate with your partner and discuss the results, but the descriptions and conclusions must
be completed individually. You will be graded primarily on the quality of the technical content, not the quantity or
style of presentation. Your reports should be neat, accurate and concise (the Summary portion must be less than one
page). Laboratory reports are due the week following the laboratory experiment unless notified otherwise, and should
be turned in to the TA at the start of the laboratory period. See the syllabus for additional instructions regarding the
report format.
Cheating: University Policies on cheating can be found in your student catalog. The standard penalty for cheating
is an automatic 2-letter reduction in the overall course grade; however, more severe penalties are possible. Do your
own work; discuss the lab concepts with others as allowed, and learn everything you can.
This laboratory report represents my own work, completed according to the guidelines described above. I have
not improper used previous semester laboratory reports, or cheated in any other way.
;/

Signed: – –,+-::t’d”-=’—=.,,,.__ _ _ _ __
Please get TA signatures for individual sections below. Please upload this page along with
the post lab report
Part I
Part I(b)
Part II
Part II(b)
I AlJ V I OLV l J
EE Science II Laboratory #7
RLC Circuits and Build an Inductor
Laboratory Assignment
Identify the model of the function generator and oscilloscope on your bench.
Function Generator (Model no.): _ _ _ _ _ __
Oscilloscope (Model no.): _ _ _ _ _ _ __
Part I: Build the Inductor

Inductor design from prelab:
. from thepre1a b
Table 1: Inductor d esum
Length of inductor, le
Cross sectional area, S
Diameter of wire, d
Number of turns, N
Relative permeability of
ferrite, µr
Calculated inductance (JlH)

Identify the components given to your group •
The resistor – a through-hole, metal film, 10 0 resistor.

The capacitor – a through-hole, electrolytic, 10 µF capacitor

Magnet Wire-to create the coil (Figure l(a))


22AWG wire of diameter 0.645 mm
Ferrite Rod- core of the inductor (Figure l{b))

MnZn ferrite rod from Fair-Rite Corp (Part No: #4077375411)

µr = 13 (the value is called Jlrod in the data sheet)

Length of rod,/= 41.30mm, Diameter of Cross Section= 9.45mm

Sandpaper – to strip the ends of the magnet wire

Rubber band – to hold the coils in place
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7 • ‘-•
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Figure l : (a) 22 AWG magnet wire (b) ferrite rod

Build the inductor •
Tie two rubber bands on the ferrite such that the distance between them is roughly equal to le in
Table I (Figure 2(a)). The rubber bands will prevent the magnet wire from slipping.

Wind N = 12 turns of the magnet wire around the ferrite rod in between the two rubber bands as
shown in Figure 2 (b). As much as possible, try to wind the wire without leaving any air gaps.

Remove the insulation at the ends of the wire using sandpaper. Once the insulation in removed, you
should be able to see copper conductors clearly.
Remove
insulation
using
sandpaper
(a)
(b)
Figure 2: Building the inductor: (a) try rubber bands to act as retainers with distance between them equal to lc(b)
wind N turns of magnet wire between the rubber bands and use sandpaper to remove the insulation from the ends
of the wire.
Part II: Assemble and Test the RLC Circuit
Use a multimeter to measure the resistor and capacitor and note them below:
Measured resistance, R =
10 . ffl,
Measured capacitance, C = 10 · ]J.. tf

Connect the RLC circuit as shown in Figure 3.
0

Connect channel 1 ofthe oscilloscope across the input of the circuit and channel 2 of the oscilloscope
across the resistor. NOTE: one end of the resistor should be connected to the ground.
Before proceeding to the next part of the laboratory, ask your TA to check your circuit and obtain
bis/her signature on the first page

Generate a sine wave using the function generator:
o
Set the impedance to HiZ, frequency to I 00 Hz, and amplitude to I Vpp.
Note: a sine wave has a single frequency and will help study the frequency dependent behavior of the circuit. In
labs 5 and 6, the input waveform was a square wave in order to create a pulsed DC signal (to measure RC
time constant). A square wave consists of an infinite number of sine waves.

Restore the oscilloscope to factory setup:
0
0
DPO305 Series: Press Default Setup (#3 in Figure DPO 1 – WAMI Lab Oscilloscopes Operation
Guide).
TDS 3052: Press Save/Recall (#3 in Figure TDSI- WAMl La.b Oscilloscopes Operation Guide).
Use the horizontal softkeys (#2 in Figure TDSl) to select Recall Factory Setup and then use the
vertical softkeys (#5 in Figure TDSl) to select OK Confirm Factory /nit.

Ensure that the impedance of both channels is set to I MO.

Turn on the output of the function generator by pressing ‘ Channel ‘ –

Adjust the oscilloscope to display both the signals on the screen and make the measurements in Table 2.
‘ Output on’
Oscilloscope
□ 12
l
I
!I
: I
!I
‘ – – – – – – – – – – – – – ~ ~ __ J__;
Figure 3: Assemble the RLC circuit as shown. Connect channel I of the oscilloscope to the input and channel 2
across the resistor.
. tior lOOHz mput

Ta ble 2 .. Measure th e crrcmt
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~(r&
{),~ ,Cb
ii “‘,
Frequency of the waveform on Channel I
Frequency of the waveform on Channel 2
Peak to peak voltage of the waveform at the input
(Channel 1), V;n,t
Peak to peak voltage of the waveform across the
resistor (Channel), V R,t
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Observations:
From the values measured in channel, what is the ratio between VR.I and V;n,1? o
(3 . r !>/2.J-:..
vR,,v,n.,= _____
C>-
81 9-
Is this value close to 0? Explain why the value should be close to 0 (Hint: what happens to the impedances of the
inductor and the capacitor at low frequencies).
.
_ __
f ~ let..
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~ ~$/1.L l S 0pe.n_. , l” C~J /-1- ½,e…_ J.(“Di(XcHU

Vi
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Before proceeding to the next part of the laboratory, ask your TA to check your observations and obtain his/her
signature on the first page
Consider that a current I= / 0 sin(mt )flows through the RLC circuit. Since the impedance of the resistor is real
(resistive), the voltage across the resistor will be in phase with the current. Therefore, we will use the voltage across
the resistor to be the reference for all phase measurements in this lab.

Set the oscilloscope mode to Average – 64. Refer to the oscilloscope manual for detailed instructions on how
to tum on averaging.

Measure the phase difference between the waveforms with the voltage across the resistor as the reference:
o
DPO 305 Series: Press Measure -+Add Measurement -+ Select Phase for Measurement Type and
set ‘Source’to 1 and ‘Phase To ‘ 2
o
IDS 3052 Series: Select CH1 to make it the active channel. Then, press Measure -+ Select
Measurement for CH1 -+ Phase -+ Measure phase from CH 1 to CH2
base observations
Observations:
Frequency of the waveforms= – +/_
O_fJ_,”””‘(y_
l’ _
Phase of waveform on channel 1 (the input) with respect to channel 2 (the resistor) =
Is the angle positive or negative?
r-“16j
rJ
n~~ lo’1J..,,.
v
~fthe angle ~bove i~ positive, then the voltage on channel 1 (input) leads the voltage on channel 2 (the resistor);
1fthe angle JS negative, the voltage on channel ](input voltage) lags the voltage on channel 2 (resistor).
Recall that the voltage across the resistor (Channel 2) is in-phase with the current in the circuit d ·
th
components . th . .t
.
. th
an smce e
.
m. e crrcut are ~ s:ry_es, , e ~~urrent flows through. all the components. Comment whether
the mput ~~~.J~ the RLc ctrcmt ~e-~ or:~•e current in the circj t.
1
1
5
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Is the net impedance of the circuit inductive or capacitive?

Set the oscilloscope back to Sample mode. To do so, follow the same steps
d’d ti turrun·
·
· tead .
as you 1 or
g on averagmg
but select SampIe IIlS
LCI UJI B l V I

O n the function generator, change the frequency of the sine wave to 2 MHz.

Adj ust the oscilloscope to display the waveforms and turn on averaging (64).
y
ff
I
T able 4: Measure the circuit for 2ritHz input
Frequency of the waveform on Channel l
;2_ , O O
Frequency of the waveform on Channel 2
I . q q q,
Peak to peak voltage of the waveform at the input
(Channel 1), V1n,H
o -ct4 oJ
Peak to peak voltage of the waveform across the
resistor (Channel), V lf,H
o ,D9)b ,/
I
Observations:
What is the ratio between VR.H and Vin.H?
VR.H I V ;n,H= – – – – – –
Is this value close to O? Explain why the value should be close to O (Hint: what happens to the impedances of the
inductor and the ca~acitor at high frequencies).
, _ _, ,,,.., L/ ;
()..a.l’2._ t:ff J
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Make phase measurements and fill Table 5.
base observations
Observations:
Frequency of the waveforms = _ ,.,…’I, – •….,f_,,.,’)~·fl
._
/ __
Phase of waveform on channel I (the input) with respect to channel 2 (the resistor) =
7-q . S 0
Is the angle .___/
~ ;iii;? or negative? -.,- – – – –
If the angle above is positive, then the voltage on channel I (input) leads the voltage on channel 2 (the resistor);
if the angle is negative, the voltage on channel !(input voltage) lags the voltage on channel 2 (resistor).
Recall that the voltage across the resistor (Channel 2) is in-phase with the current in the circuit and since the
components in the circuit are in seri~s_,_the same current flows through all the component:;. ~omment whether
the input voltage to the R,LC circuit i ea~ or lags the current in the circQit. ~ c) (l,’J ,,,.
fk JJ h:rt, 1~. · JflY’J : 4t- c;;-r r’t.A- ·~- ‘
——
Is the net impedance of the circuit inductive or capacitive?
I .ctJUI U lUt
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f
From the observation in Tables 3 and 5, complete the phasor diagram in Figure 4 by drawing the phasor representation s
of the input voltage for both the low frequency and high frequency case. Label each case clearly.
_ . . _ _ __::;.;
Im
.AR’, µJ
Figure 4: Phasor diagram – draw the phasor representation of the input voltage for both the low frequency case and
the high frequency case. The phasor representation of the voltage across the resistor and the current has been drawn
for you.
Before proceeding to the next part of the laboratory, ask your TA to check your observations and obtain his/her
signature on the first page
Part III: Determine the Resonance Frequency of the RLC Circuit
At resonance, the impedance of the capacitor becomes equal and opposite to that of the impedance of the inductor. As
a result, the net voltage drop across the inductor and capacitor combined is zero and the input voltage and the current
become in-phase. Therefore, the input voltage and the voltage across the resistor also become in-phase. Additionally,
the impedance of the RLC circuit is minimum at resonance and the current maximizes. In this part of the lab, you will
measure the resonance frequency of the RLC circuit and study its frequency response.

Use the XY mode of the oscilloscope to accurately measure the resonance frequency:
o
Turn off the output of the function generator by pressing Channel –
o
Turn on XY mode in the oscilloscope:
Output off

DPO 305 Series: Press Acquire – XY Display-Triggered XY. The screen will look like the one
shown in Figure 5.

TDS 3052 Series: Press Display – XY Display CHI vs CH2 -Triggered XY. The screen will look
like the one shown in Figure 5.
o
Use the vertical position knobs to align the channels to the center of the screen (refer Figure 5).
o
Set up the oscilloscope to improve accuracy:


o
DPO 305 Series: Acquire – Mode – Hi Res
TDS 3052: Acquire Menu – Mode -Average (64)
Set both channel I and channel 2 to 200mV/div.
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o
Set the frequency on the function generator to 100 Hz and turn on the output. You will see an ellipse
along the x-axis of the oscilloscope screen. If the signals do not appear on the screen, change the
horizontal (time) scale until they are visible on the screen.
o
Use the knob on the function generator and increase the frequency until the ellipse looks like a line at
angle of 45 degrees:

On the function generator, use the arrows below the knob to select the digit you want to change
and then rotate the knob to change it.

The ellipse on the oscilloscope screen will change shape and orientation as the frequency is
increased.

An example for the same is shown in Figure 6.

If needed, you can zoom in by decreasing the scale for both channels. However, ensure that the
scales on both channels are the same.
Observations:
.;~
~-,~Q, ~ r~
Frequency at which the ellipse becomes a line= resonan_c~ frequency ,f= · ~D · ~ 3
Inductance of your inductor =
1·9-
-➔
L=
1
2
2
,
-.:-:

:=t.
where C is the capacitance in the RLC circuit
41r f C
L=1r•2’.72ftoµH
11
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“- ” I0·3ri.,)
~~
.
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Compare this value with the value in Table I: – – – – – – – – – – –
Calculate the percent error in your measurement. What could be some sources of error in your
measurement? ~ q~
-~? –,; 3 5;!,

[p,V-·
1 .r-t·
XV 01, pl,iy
r~·:.r–~}!?-~~/
Align channels to
the center of the
screen
f· ■::
Align channels to
the center of the
screen
r~
Figure 5: Screen of oscilloscope in XY mode – left: DPO 305 Series; right: TDS 3052
Zoom-in equally
if needed

II
111111

r·–=-
Figure 6: An example of the signal measured on DPO Series oscilloscope in XY mode – left: at 100 Hz; right: at
resonance
Press AUTOSET to tum off the XY display. Set the amplitude to 1Vpp on the function generator. Study the frequency
response by changing the frequency of the input sinusoidal wave. Depending on your resonance frequency, select 10
frequency points between 100 Hz and 2 MHz to capture the resonance behavior of your circuit. Note down the peakto-peak voltages across the input and the resistor for each case in Table 6.
Ta ble 6 : Frequency response of the RLC circuit – select frequency to capture the resonance behav1or
. of ,our circuit.
Phase difference
Measured
Peak-to-peak
input peak-toNormalized voltage
between waveforms
Frequency
voltage across
=VRIV;n
peak voltage,
(channel 2 as
resistor, VR (V)
Vm(V)
reference)
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Note: As the frequency of the input changes, the impedance of the circuit changes. At certain frequencies, the function
generator will not see a high impedance. As a result, the measured input voltage will not be what is set on the function
generator. The normalized voltage is studied in Table 6 in order to understand how the voltage across the resistor
varies with frequency for the actual input voltage.
Before leaving the laboratory, ask your TA to check your observations and obtain bis/her signature on the first
page
Laboratory Report
A one paragraph summary of the laboratory assignment.
5 pt
2
How well does your measured inductance compare with your calculations? What is the percent
error in our measurements? List ossible sources of error.
2 pt
3
Summarize the observations from Tables 3 and 5.
1 pt
4
Will the amplitude of the input sine wave affect your measurement? Explain.
1 pt
5
Use MATLAB to plot the normalized voltage across the resistor as a function of frequency
(results from Table 6)- the x-axis should be the measured frequency on channel 1 in kHz and
the y-axis should be the normalized voltage. Submit a copy of your plot-the title of the plot
should our name and ou number. Axis should be labeled clear! for full credit.
I pt
{Optional} – Suggestions to improve the laboratory experience.
-7
LA’.lllUI Q l VI
Appendix
Ferrite Rod: 4077375411 rrom Fair Rite Corp (77 Solid Rod)
Link for datasheet: http://www.fair-rite.com/product/rods-4077375411 /
Calculation of inductance for Fair-Rite ferrites (taken from their website):
Calculate µrod and K from the graphs below:
Rod PtnnealJjlly YI. Rod Lenglh diYkled by Rod Diameter
60
llalwls
,$’

Purchase answer to see full
attachment