ENGR 43
Lab Activity
Student Guide
LAB 7 – Skin Effect and Transmission Lines
Student Name: ___________________________________________________
summary of the effects of frequency
and termination impedance on signals
transmitted through cables.
Overview
In this lab, you will collect data on
measurements, observe skin effect in wires
and propagation delay in a cable, and
summarize your findings.
Before Starting This Activity
You should be able to perform the following
tasks before starting this activity:
 Basic operation of the function
generator: setting frequency, waveform,
and amplitude.
 Operate a digital oscilloscope to trigger
and measure voltage and time of
waveforms.
 Calculate series voltage drops using the
voltage divider formula.
 Calculate attenuation (logarithms).
 Enter data and create charts using
Microsoft Excel spreadsheets.
Learning Outcomes For Activity
Relevant knowledge (K), skill (S), or
attitude (A) student learning outcomes
K1. Identify situations where wire and cable
can have a significant effect on the
operation of an electronic system.
S1. Measure voltage and phase of lowamplitude signals with an oscilloscope.
S2. Compare measured data with the
preparatory calculations, and describe
how the data show the effects of
resistance and inductance in wires, and
propagation time and impedance in
cables.
A1. Appreciate that secondary effects, such
as skin effect and cable impedance,
can have significant effects of circuits.
Getting Started
Lab Activity and Deliverables:
It should take students approximately 3
hours to complete the lab activity, and 1
hour of homework time to complete the lab
report.
Equipment & Supplies
Item
Tek MSO2014 scope
Fluke 271 function generator
BNC-clip cable
1x/10x scope probes
100-foot roll of CAT 5e cable
2-foot wire sample bundle
51 Ω, ¼ W resistor
(green, brown, black, gold)
100 Ω, ¼ W W resistor
(brown, black, brown, gold)
Quantity
1
1
1
3
1
1
1
1
Special Safety Requirements
None
Lab Preparation
You may start with Task #1 or Task #2,
depending on the availability of the wire
bundles or CAT 5e cable rolls.
S3. Prepare a presentation that includes a
table and chart to show resistive and
skin effects in multiple wires and a
Lab 7 – Skin Effect and Transmission Lines
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Lab Activity
Student Guide
Task #1 – Skin Effect
When we first learned about electric circuits,
we learned that the solid lines on the
schematic diagram represented wires, all
points connected by a wire were always at
the same voltage potential, and current
flowing through a wire did not produce a
voltage drop because wires had zero
resistance. While this may be close enough
to the truth for short wires and low
frequency AC and DC circuits, the highspeed circuitry in today’s electronics
requires greater recognition of the effects
wire and cable can have in a circuit.
1. Locate an American wire gauge table
that lists the milohms per foot resistance
and diameter (in millimeters) for solid
conductors. An easy place to find such a
table is at Wikipedia
(http://en.wikipedia.org/wiki/American_
wire_gage). Although we are using
stranded wire for the larger gauges, the
performance is similar to solid wire.
Enter the diameter and resistance for
each gauge wire in Table 1 of the Excel
worksheet.
2. For each of the 2-foot lengths of wire,
use the wire gauge table from step 1 to
calculate the resistance in milohms
(thousandths of an ohm). Enter these
values in Table 1.
3. Calculate the frequency where skin
effect will add approximately 10% to the
total impedance using the following
formula (derived from Terman, F. E.
Radio Engineers' Handbook. New York:
McGraw-Hill, 1943)
æ 200mm ö2
freq = ç
÷
è Dw ø , where Dw is the wire
diameter, in millimeters. Enter your
values in Table 1.
Lab 7 – Skin Effect and Transmission Lines
ENGR 43
4. Refer to the test circuit schematic in
figure 1, shown below.
5. Using the voltage divider formula,
calculate the expected voltage drop
across the wire under test (TP2 to
ground) when a low-frequency 5 VPP
sine wave is applied, as measured at
TP1. Enter these values in Table 1.
6. Connect the skin effect test circuit
shown in figure 1, above. Start with the
28 AWG 2-foot wire. Ensure that the
ground connections for the function
generator and scope probes are as close
as practical.
7. Set the function generator to apply a 1
kHz, 5 VPP, sine wave as measured at
TP1. Measure the voltage at TP2. Enter
this value in Table 2 of the Excel
worksheet. Compare with your
calculated value in Table 1. Are you
able to measure a stable voltage at TP2?
What is degrading your measurement?
_______________________________
_______________________________
_______________________________
_______________________________
8. In order to measure small voltages and
minimize the background noise, change
the acquisition mode of the digital oscope to sample mode, and increase the
number of samples until the noise is
reduced on the TP2 waveform and the
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Lab Activity
Student Guide
measurement is stable within 1 mV. Set
the trigger mode to trigger on the input
voltage at TP1. You should be able to
see voltages down to a few millivolts.
Why is it necessary to trigger the scope
on TP1?
12. After you have entered all of your
measurement data, click on the Linear
Chart tab to see the data plotted on linear
scale X/Y axes. Can you easily
determine where the skin effect begins
for each wire? Why not?
_______________________________
_______________________________
_______________________________
_______________________________
_______________________________
_______________________________
9. Measure the p-p voltage at TP2.
Compare the phase of the waveforms at
TP1 and TP2 by measuring time delta,
∆, (difference) between the rising zerocrossing points on each waveform (or by
selecting “phase” from the measure
menu). For the low-amplitude voltages
at TP2 you may note “in phase,”
“leading,” or “lagging” instead of a
specific number of degrees of phase
shift. When voltages at TP2 are at least 4
divisions vertically, measure the time
delta between waveforms and calculate
phase with the following formula:
phase=0.360• ∆(µs)•freq(kHz)
Enter your measurements in Table 2.
10. Repeat the voltage and phase
measuerments at frequencies of 2kHz, 5
kHz, 10 kHz, 20 kHz, 50 kHz, 100 kHz,
200 kHz, 500 kHz, and 1 MHz. At each
frequency, adjust the output level of the
function generator as needed to maintain
the 5 VPP at TP1.
11. Repeat the voltage and phase
measurements at the same frequencies
for each of the other 2-foot test wires.
Remember to check and adjust the
voltage at TP1 for each frequency.
13. Click on the Log-Log tab to see the same
data plotted on logarithmic X/Y axes.
What can you determine about skin
effect frequency and wire gauge?
_______________________________
_______________________________
_______________________________
14. Compare the 28 gauge wire-wrap wire
plotted data with all the other wires.
What was different about this wire, and
why? (hint: wire-wrap wire is silverplated copper.)
_______________________________
_______________________________
_______________________________
15. What does the phase data tell you about
skin effect?
_______________________________
_______________________________
_______________________________
Lab 7 – Skin Effect and Transmission Lines
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Lab Activity
Student Guide
Task #2 – Transmission Line Pulse
Reflection
For most circuits we assume that electrons
flow through a wire at the speed of light.
When the combination of wire length and
signal frequency result in the distance
through the wire being ¼ of the wavelength
of that frequency, we must account for the
time that it takes for a signal to travel
through the wire. When we reach the ¼
wavelength threshold, we refer to the wire or
cable (two or more wires) as being a
transmission line.
TP1 = ______________
TP2 = ______________
TP3 = ______________
What is the shape of the waveform at
each test point? Is there any severe
distortion at the rising and falling edges?
Save the screen image to your flash
drive, showing the three test point
waveforms. This it the “100Ω
termination” data.
_________________________________
_________________________________
_________________________________
2. Remove the 100Ω termination load,
leaving the scope probe and ground
connected. What are the p-p voltages at
TP1, TP2, and TP3?
TP1 = ______________
TP2 = ______________
Part 1: Square Wave Transmission
1. Connect the circuit shown in Figure 2.
Use any one of the four twisted pairs,
such as the blue and blue/white wires.
Set the function generator for a 5 Vp-p,
250 kHz squarewave output. Verify the
generator output impedance is set to
50Ω. With the 100 Ω termination load
RL and the 51Ω series source resistor RS,
what are the p-p voltages at TP1, TP2,
and TP3?
Lab 7 – Skin Effect and Transmission Lines
ENGR 43
TP3 = ______________
What is the shape of the waveform at
each test point? Is there any severe
distortion at the rising and falling edges?
With the 100Ω termination removed, the
signal travels down the wire, has no load
to deliver its energy, so it travels back up
the wire where it is dissipated in the
source resistance. Save the screen image
to your flash drive, showing the three
test point waveforms. This is your
“open termination” data.
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Lab Activity
Student Guide
3. Looking at TP2, can you determine the
time needed to “charge the line” (the
delay between the transmitted signal and
the reflected signal)? Taking in to
account that the signal has traveled
double the distance of the cable (down
and back), divide the “line charging”
time by 2 to determine the propagation
delay (the time to travel through the
transmission line). You will need the
propagation time value for step 5.
Charge time ÷ 2 = propagation delay
__________÷2 = _______________
4. Short the end of the transmission line.
Save the screen image of TP1 and TP2
(TP 3 is shorted to ground). This is your
“shorted termination” data. Compare this
with your open termination waveforms.
Can you describe what is happening at
TP2?
_______________________________
5. Calculate the time needed for a pulse to
travel 100 feet (30.5 m) at the speed of
light (c = 3x108 m/s).
30.5 m ÷ 3x108 m/s = ___________
Calculate the propagation velocity vp by
dividing the length of the transmission
line by the propagation delay
30.5 m ÷ ___________=_____________
Calculate the velocity factor VF for the
CAT5e cable by dividing the
propagation velocity vp by the speed of
light (VF should be around 0.75).
VF = ___________÷3x108 m/s=_______
6. Bonus question: Measure the
capacitance of the 100 ft transmission
line, then use the formula
vp=(LC)-1/2 to find the inductance.
L = ______________
Deliverable(s)
_______________________________
_______________________________
Did this effect the propagation time?
Print and label the saved screen images for
100Ω, open, and shorted terminations from
Task #2, Part 1. Print the Excel worksheet
and the log-log chart. Save these documents
along with this activity sheet in your lab
activity binder.
_______________________________
Lab 7 – Skin Effect and Transmission Lines
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Lab Activity
Student Guide
Notes:
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© 2012