Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Authors:
Denard Lynch
Date:
July, 16, 2012
Corrections: Sep 16, 2012 – D. Lynch, M. R. Avendi
Revised: Sep 22, 2012 – D. Lynch
Revised: Sep 9, 2013
Description:
This laboratory exercise explores resistance – capacitance (R-C) and resistance –
inductance (R-L) static and transient behaviour in Direct Current (DC) circuits. The
student will assemble circuits composed of resistive, capacitive and inductive elements
and energize them with a DC source. Theoretical circuit behavior will be predicted and
then verified within practical limits.
Learning Objectives:
In this laboratory, the student will:
• Understand and learn how to use a solderless breadboard and construct simple
circuits;
• Learn how to measure circuit parameters using a digital multimeter and the
Digilent ‘Discovery’ module;
• Verify the behaviour of capacitors and inductors in a static (steady-state) DC
circuit
• Verify the transient behavior of R-C and R-L circuits in response to a step change
in potential in a DC circuit
Reporting:
Use your lab notebook (logbook) to document
• the key objectives of this laboratory,
• your theoretical calculations (note what you would expect to see)
• Parts List: your equipment and circuit components used, including circuit and test
equipment set up
• any measured values of components
• your measurements verifying your theoretical expectations (you can paste in
screen shots from your ADM where appropriate, or use annotated hand sketches),
• your observations and comments about how closely your observations matched
your expectations,
• related comments on practical limitations for your observations and comments on
possible sources of error
Denard Lynch
Page 1 of 11
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Safety Considerations:
In addition to general electrical safety considerations, the student should also be aware of
the following considerations specific to this laboratory exercise:
• Resistors carrying current will generate heat energy, which can raise the
temperature of the component significantly, especially when over-driven. Use
your olfactory sense (smell) to alert you to overloaded components; remove the
energy source immediately if you suspect any overheating and check your circuit.
You can check for heat by feeling carefully in the proximity of a suspected
component, but don’t touch anything directly!
• Capacitors generally shouldn’t generate significant heat unless they are subjected
to potentials above their rating and suffer dielectric breakdown. If this happens,
the same considerations as over-loaded resistors apply. In addition, capacitors
can store a significant amount of energy, even after the circuit is de-energized. Or
even when the capacitor is removed from the circuit! Be sure to discharge
capacitors before contacting the leads.
• Inductors usually have some resistance in the wire from which they are made.
This can lead to some heating affect as mentioned for resistors. Subjecting
inductors to potentials or other conditions above their rating can also cause
breakdown of the insulation inside the component leading to partial short circuits
and rapid heating. In addition, when the flow of current through an inductor is
interrupted or stopped for any reason, the collapsing magnetic field will cause an
induced voltage across the inductor which can be many times greater than the
source voltage! This can cause sparks, shocks (if touched) or component
breakdown if not handled appropriately in circuit design and laboratory procedure.
Be sure to allow sufficient time for fields to dissipate before handling circuit
components.
Background and Preparation:
In preparation, especially for your first lab, become familiar with the items in your Lab
Kit and how to use them. Pay particular attention to the following three items:
1. Solderless breadboard – you will use this to assemble experimental circuits
throughout the course. It is used in conjunction with a “wire kit” or other 22ga
(~.67mm / .025” diameter) wire with 7.5mm (.33”) insulation stripped for
insertion into the board connectors. Please consult this brief and very helpful
tutorial by Hernando Baragan about the use of solderless breadboard like the ones
supplied in your Lab Kit.
http://www.wiring.org.co/learning/tutorials/breadboard/index.html
2. Digital Multimeter (DMM) – you will use this to check various circuit conditions
and components, including resistance, continuity, voltage and current. Be very
cautious to select the correct scale (volts, amperes, milliamperes, resistance or
continuity etc.) and an appropriate range. If in doubt, always start with the
highest range for voltage and current and the lowest range for resistance, and then
adjust downward if necessary. Never connect a DMM set on the current scale
directly across a source – it will almost certainly destroy the meter and cause a
Denard Lynch
Page 2 of 11
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
safety incident! View the following YouTube video (title: “THE BEST
Multimemeter Tutorial” at:
http://www.youtube.com/watch?v=bF3OyQ3HwfU&feature=related Note:
NEVER CONNECT THE PROBES TO YOUR SKIN TO MEASURE
RESISTANCE AS SHOWN IN THIS VIDEO – THIS IS AN UNSAFE
PRACTICE AND COULD LEAD TO ELECTROCUTION!) Otherwise, it is a
good explanation of basic DMM operation.
3. Digilent Analog Discovery Module – this will be your main piece of test gear. In
conjunction with the associated Waveforms software and a computer running
Windows XP or later, this will provide virtual instrument capability for your
experiments. This module is USB port connected and powered; provides a 2channell oscilloscope with differential inputs, a 2-channel signal generator, a ±
5VDC supply and 16 digital lines that can be used to monitor digital signals or for
static digital input and output. More information on the specifications and use can
be found at:
http://www.digilentinc.com/Products/Detail.cfm?NavPath=2,842,1018&Prod=AN
ALOG-DISCOVERY . The associated Waveforms software can be downloaded
at no cost from here:
http://www.digilentinc.com/Products/Detail.cfm?NavPath=2,66,849&Prod=WAV
EFORMS
Please refer to the Class Notes for background theory on capacitive and inductive
transients. (There is a summary of key points in Appendix A at the end of this
Laboratory.)
Terms:
ADM
DMM
Steady-state
WVDC
Nominal value
Trigger Level
‘scope
Denard Lynch
Digilent’s Analog Discovery Module
Digital Multimeter – separate instrument often used to
measure voltage, current, resistance, capacitance,
continuity and occasionally other parameters
A circuit condition where all relevant parameters (e.g. V,
I) are “Steady – not changing over time.
Working Volts DC, often used to specify the voltage
conditions for which a capacitor, or other component, was
designed
The target value for a component. Due to manufacturing
tolerances, each part may vary by a specified amount (e.g.
a resistor specified as having a 5% tolerance, may in fact
actually be any value between ~ 950Ω and 1050Ω)
On an oscilloscope, the level at which it will initiate
drawing a trace of a signal on the screen (e.g. if set to +1V,
it will start drawing the signal on the screen once the input
level goes above 1V)
Common abbreviation for oscilloscope
Page 3 of 11
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Procedure:
The procedure will involve three phases. In each part, the student will use a solderless
breadboard to assemble a simple circuit using resistive, capacitive or inductive
components. Theoretical calculations of various circuit parameters should be performed
as part of the lab preparation (i.e. prior to your lab period). During the lab procedure, you
will use your test equipment to measure the same circuit parameters and compare the
results to your theoretical expectations.
A note on measuring current:
A simple way to measure current with your ADM is to measure the voltage across a
resistor that happens to be in series in the circuit leg of interest. If a suitable series
resistor is not already in the circuit, you can insert a small “sense” resistor (say 10Ω) in
series where you want to measure current and then use the differential oscilloscope inputs
from one channel of your ADM (e.g. 1+ and 1-). The differential inputs essentially
measure each point with reference to ground, and then “subtract” the two so you read the
voltage difference between the two points of interest. You can display the measurement
directly in current terms by adding a Mathematical Channel:
and in the “Enter Function” box, typing “C1/4700” (or C2 if you wish to use that
channel; you should also use the actual value of your resistor if not 4700Ω) (you can also
change the units of display under the settings icon on the ‘M?’ dialog box).
Alternately, for static conditions, an ammeter (DMM on one of the current scales) can be
inserted in series where you want to measure the current. Be sure you have the leads
plugged into the appropriate jacks on the DMM and that you’ve selected the right scale.
If in doubt, always start with a high scale and then increase the sensitivity if necessary.
If you don’t have a multimeter, or for dynamic conditions, as in a transient circuit where
you want to observe the change in current over time, you can measure the voltage across
a resistor in the circuit and calculate the current.
Parts List
The following parts, or suitable substitutes, are required for this laboratory:
Item
Quantity
ADM
1
Solderless breadboard
1
1
100Ω ¼ W
2
1000Ω ¼ W
1
3300Ω ¼ W
1
4700Ω ¼ W
1
0.1 µF capacitor
10 mH inductor
1
Denard Lynch
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Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Modeling- (determining what you would expect to see)
This simply means using circuit theory to predict the circuit parameters for each circuit
(e.g. v(t), i(t), τ). The required parameters are given in each section below. Calculating
the expected currents and voltages will also allow you to determine the required ratings
for your components (i.e. how much power they must dissipate, how much voltage they
must withstand etc.).
Note that in this case, you are using a “practical inductor”, which has some internal
resistance. You should account for this fact in your theoretical calculations as much as
possible, and adjust your predictions accordingly.
MeasurementsI. I R-L-C Circuit Static Behaviour
Use your solderless breadboard and set up the circuit shown in Figure 1 below. A
good first step is to examine the circuit, make a list of the parts you will need,
obtain the necessary parts and construct the circuit (again, refer to the brief tutorial
linked above if you are unfamiliar with use of these boards). You may also need to
measure the actual value of your components versus their nominal value, and note
it for calculations and future reference (many times the nominal value will be
sufficiently accurate to allow you to verify the principles involved). For example:
Component
1/4W resistor
Nominal Value
Measured Value
1000Ω
986Ω
Capacitor 100WVDC
0.1µF
0.092µF
Etc.
Your instructor will indicate where to obtain the necessary parts if they are not
already in your parts kit, and how to measure their actual value using a DMM or the
component tester in the lab. You can generally use the power supply provided in
your Analog Discovery Module (ADM). (Note: there is a very limited amount of
current available from the ADM; ~90mA maximum. Check your theoretical
calculation to make sure this supply isn’t overloaded whenever you use it.)
Assemble the components as shown in Figure 1. Place the components as close as
possible to each other, but with enough spacing to allow for insertion of
measurement leads; you can use connectors from your wiring kit to connect
components on the board if required. Your lab instructors can help with layout
suggestions.
Denard Lynch
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Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Digilent
ADM
+5V
Figure 1: Static DC R-L-C Circuit
Once you have checked your breadboarded circuit for correctness, energize the
circuit and measure the voltages and currents indicated using the Voltmeter on your
ADM, as well as verify Kirchhoff’s voltage and current laws by measuring the
voltages around each loop (e.g. 5V source – R1 – R3 – C1 – GND, etc.), and to
verify that the total current drawn from the source is equal to the sum of the
currents in each leg (IS = I1 + I2 + I3)
You may want to use a table similar to Table 1 to record your measurements and
results in your laboratory notebook (logbook).
Table 1
Circuit
Parameter
V1
V2
V3
VR1…
I1
I2
I3
IT
Expected
Value
Measured
Value
Comments
Note: It may not be useful to try to determine an “Expected Value” in every case.
Try to determine what you should see at relevant points in the circuit that will help
you verify the theoretical operation.
II. Resistive – Capacitive Transient Behaviour
Modify your breadboard circuit so that it reflects the circuit shown in Figure 2.
Again, inventory and measure any new components if needed. Use one of the
signal generator outputs on your Analog Discovery Module (ADM) (e.g. W1 or
W2) as an input to this circuit. Set the output for a 0 – 5V square wave (e.g. 2.5V
with an offset 2.5V). Select a suitable frequency so you can observe and measure
the charging and discharging transients. (Based on your theoretical calculation of
the time constant, τ, select a frequency that will result in a “high” signal between
about 5 – 10 time constants. Connect the oscilloscope inputs from your ADM to
Denard Lynch
Page 6 of 11
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
monitor and measure the driving signal, and the resulting voltage across the
capacitor. Be sure to make good ground connections between your ADM (⇓, any
black wire) and your circuit board.
Digilent
ADM
WaveGen (W1)
Amplitude: 2.5V
Offset: 2.5V
-1
f ~ (10τ)
›
Figure 2: R - C Transient Circuit
Adjust the trace on your oscilloscope display so you can measure the observed time
constant as accurately as possible for both the charging and discharging phases.
There are two ways to verify your theoretical calculations: 1) determine the
expected voltage across the capacitor at t = one time constant and then measure the
actual time observed when it reaches that voltage, or 2) measure the voltage at one
(calculated) time constant on the horizontal (time) axis and compare it to the
expected value. Use the X1, X2 and Y1, Y2 cursors on your ADM oscilloscope to
aid with your measurements.
Table 2
Circuit
Parameter
Vi charge
Vf charge
Ii charge
If charge
Expected
Value
Measured
Value
Comments
τ charge
Vi decay
Vf decay
Ii decay
If decay
τ decay
Note: You can add a “Measurement” to your ‘scope display to measure various
parameters of the input signals. If the ADM cannot adequately determine the
values, a “? --” will be shown in the display. In these cases, read the values off the
display visually or using the X, Y cursors.
III. Resistive – Inductive Transient Behaviour
(This is very similar in procedure to part II except that you are using a practical
inductor instead of the capacitor) Modify your breadboard circuit so that it reflects
Denard Lynch
Page 7 of 11
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
the circuit shown in Figure 3. Again, inventory and measure any new components
if needed. Use one of the signal generator outputs on your Analog Discovery
Module (ADM) (e.g. W1 or W2) as an input to this circuit. Again set the output for
a 0 – 5V square wave (e.g. 2.5V with 2.5V offset). This simulates a DC source
alternating periodically between 5V and 0V. Again select a suitable frequency so
you can observe and measure the charging and discharging transients. (Based on
your theoretical calculation of the time constant, τ, select a frequency that will
result in a “high” signal for 5 – 10 time constants. First use one of the oscilloscope
inputs to check your input. Then use the oscilloscope inputs to monitor the
resulting voltage across the inductor and the voltage across the resistor (again using
a Mathematical channel) to observe the current through the inductor. Be sure to
make good ground connections between your ADM (⇓) and your circuit board.
Digilent
ADM
WaveGen (W1)
Amplitude: 2.5V
Offset: 2.5V
-1
f ~ (10τ)
Figure 3: R - L Transient Circuit
Adjust the trace on your oscilloscope display so you can measure the observed time
constant as accurately as possible for both the charging and discharging phases.
Again make use of the X1, X2 and Y2, Y2 cursors on your ADM oscilloscope to
aid with your measurements.
As mentioned above, you are using a “practical inductor”, which has some internal
resistance. You should account for this fact in your theoretical calculations, and
adjust your observed expectations accordingly. For the purposes of this lab, the
following model will adequately represent your practical inductor:
Be sure to account for the extra resistance in your time (τ) and voltage expectations.
(E.g., during the charging phase, the final current will cause a voltage drop across
the inductor resistance, so you may not measure ‘0V’ as you would theoretically
expect. You should verify and explain. You can also estimate the internal
resistance using the voltage measurements you have taken.)
Denard Lynch
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Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Table 3
Circuit
Parameter
Vi charge
Vf charge
Ii charge
If charge
Expected
Value
Measured
Value
Comments
τ charge
Vi decay
Vf decay
Ii decay
If decay
τ decay
APPENDIX A: Background Theory
As discussed in class, the three basic electrical elements, resistors, inductors and
capacitors, exhibit certain characteristic behaviour in Direct Current (DC) circuits. In a
“steady-state” or static DC circuit, a resistor obeys Ohm’s Law, a capacitor looks like an
“open” circuit”, and an inductor looks like a “short” circuit (assuming ideal components).
When subjected to non-static (i.e. changing or “transient”) conditions, these elements,
especially in combination, can act quite differently. The subsequent parts of this lab will
investigate and verify this non-static or “transient” behaviour. You will be using the
signal generator in your Anaolog Discovery Module (ADM) to impose instantaneous
(well, very fast at least) changes to the source voltage impressed across a simple R – L or
R – C circuit.
Internal Impedance of Sources:
Although the output impedance of the Digilent Arbitrary Waveform Generator (AWG) is
not a factor for any of the experiments in this course, its affect should generally be
considered in other cases. The following discussion provides an overview on this topic
which can be used to assess whether or not it shoud be considered.
An “ideal” voltage source has an internal resistance of 0Ω,. However, a real source,
when it is providing, say, 5V DC, will look like an ideal 5V battery with a series
resistance of Rint, as shown in (a) in Figure 4. When this source changes to 0V, it will
still have the internal resistance of the practical source, as shown in (b), even though
there would be no voltage output at the terminals.
Denard Lynch
Page 9 of 11
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Figure 4: Practical Voltage Source
This internal resistance can affect the behavior (and measurements) in both static and
transient conditions. You can estimate the internal resistance of your source by
measuring the difference in output voltage with different load resistances (c). If your
load resistances have a ratio of 2 (e.g. 200Ω and 100Ω), you can use the following
estimate for Rint of the source:
R int =
2Δ
RLoad
1− 3Δ
V 2 RL − VRL
, is the difference in measured voltage as a ratio of the source
E
voltage, E, and RLoad is the smaller load value (e.g. use 100Ω and 200Ω). Of course the
lower the test load resistance, the greater the ΔV, but also the more inaccurate the
estimate is. If the Rint turns out ~2-3% of the RLoad, the estimate is satisfactory. The
internal resistance of modern sources is usually quite low and can often be ignored, but it
should be considered and checked if necessary.
Where Δ =
R-L and R-C Transient Behaviour
The time constants in R-C and R-L circuits respectively is τ=RTC and τ= L RT , where RT
in both cases is really the Thévènin equivalent resistance of the circuit, and should take
into account the internal resistance of the source and the component. While the internal
resistance of a capacitor in these circuits is probably negligible, the internal resistance of
an inductor is probably not and will noticeably affect both the time constant and the end
voltages (because of a “voltage divider” effect).
The expressions describe the transient behaviour for Thévènin equivalent R-C and R-L
circuits (for the charging phase) are summarized in Table 4 and Table 5 for reference.
Table 4: Charging Transient Expressions
i
L
C
Denard Lynch
(
iL (t) = If 1− e
iC (t) = Iie
−t
−t
τ
τ
v
)
vL (t) = Vie
(
−t
τ
vC (t) = Vf 1− e
Page 10 of 11
−t
τ
)
Sep 9, 2013
Laboratory #1: Inductive and Capacitive Transients
Electrical and Computer Engineering
EE 204.3
University of Saskatchewan
Table 5: Discharging Transient Expressions
i
L
C
iL (t) = Iie
v
−t
vL (t) = Vie
τ'
iC (t) = Iie
−t
τ'
−t
vC (t) = Vie
−t
τ'
τ'
In both cases, use KVL, KCL and Ohm’s law to determine the required initial or final
(static) values for current or voltage during the period of interest (i.e. from just after the
circuit changes until it either reaches a steady-date or the circuit is changed again).
References:
(Lynch, 2011), EE201 Supplementary Course Notes p 29 - 51
Denard Lynch
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