Transcript ECE211Prelabs2x - Clemson University

Clemson ECE Laboratories
ECE 211 - Electrical Engineering
Lab VI
Pre-labs for ECE 211
Guneet Bedi
Created: 10/09/2012 Updated: 10/09/2012
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Introduction
• This lab focuses on the Thévenin equivalent and maximum
power transfer theorems.
• Complex circuits are often replaced with their Thévenin
equivalent to simplify analysis.
• Maximum power transfer is also an important concept which
allows the designer to determine an optimal design when
power is a constraint.
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Thévenin Equivalent Circuit
• Thevenin equivalent circuit is an independent voltage source
VTh in series with a resistor RTh, which replaces an
interconnection of sources and resistors.
• This series combination of VTh and RTh is equivalent to the
original circuit in the sense that, if we connect the same load
across the terminals a, b of each circuit, we get the same voltage and current at the terminals of the load.
• This equivalence holds for all possible values of load
resistance.
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Thévenin Equivalent Circuit contd…
• To calculate the Thevenin voltage VTh, we simply calculate the opencircuit voltage in the original circuit.
• If we place a short circuit across the terminals a, b of the Thevenin
equivalent circuit, the short-circuit current directed from a to b is
vTh
isc =
RTh
• This short-circuit current must be identical to the short-circuit current
that exists in a short circuit placed across the terminals a, b of the
original network.
• Thus the Thevenin resistance is the ratio of the open-circuit voltage
to the short-circuit current.
vTh
RTh =
isc
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Maximum Power Transfer
• Maximum power transfer occurs when the load resistance
equals the Thevenin resistance i.e. RL=RTh
• The maximum power delivered to RL is
pmax
2
vTh
=
4RL
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Lab Objective
• By the end of this lab, the student should be able to verify
Thévenin's equivalence theorem and the concept of maximum
power transfer.
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Equipment Needed
• NI-ELVIS workstation
• Resistance substitution box
• Individual resistors (220Ω, 330Ω, 680Ω, 1kΩ)
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Procedure-Thévenin’s Theorem
•
•
•
•
Set up the circuit as shown in figure.
Adjust the output of the DC power supply to 10V.
Measure the open circuit voltage between nodes A and B.
Now connect the ammeter between nodes A and B and measure the short
circuit current between nodes A and B.
• Using these measurements, determine the Thévenin equivalent circuit.
• Set up the newly determined Thévenin equivalent circuit and verify that
this circuit has the same open circuit voltage and short circuit current as
the previous circuit.
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Procedure-Maximum Power Transfer
Theorem
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• Use the Thévenin equivalent circuit developed in Part 1.
• For a resistance substitution box RL between nodes A and B,
measure the current through and voltage across RL for RL=0Ω.
• Repeat for RL=100Ω, 120Ω …… 500Ω (in 20Ω increments).
• Determine the power dissipated by the resistor for each value of RL.
• Plot Power vs. Resistance.
• At which value is the power a maximum?
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Lab 6-Student Tasks
• Students are required to solve the ‘Probing Further’ section,
given in the lab manual, in their laboratory notebooks.
• Lab notebooks are due on the same day as your report for lab
5.
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Preparations for Next Week
• Review 'XYZs of Oscilloscopes', available at: www.tek.com
(60+ pages).
•
o
o
o
o
o
Be familiar with the following:
Voltage scaling (Volts/division)
Time base (seconds/division)
Input coupling
Triggering
Measurement probes
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References
• ECE 211 – Electrical Engineering Lab I. Latest Revised July
2010.
• Electric Circuits 8th Edition by James W. Nilsson & Susan A.
Riedel.
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ECE 211 - Electrical Engineering
Lab VII
Pre-labs for ECE 211
Guneet Bedi
Created: 10/19/2012 Updated: 10/19/2012
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Introduction
• Oscilloscopes are indispensable tools for anyone designing,
manufacturing or repairing electronic equipment.
• The digital oscilloscope allows the engineer to examine time
varying waveforms to determine the magnitude, frequency,
phase angle, and other waveform characteristics which depend
upon the interaction of circuit elements with the sources
driving them.
• The usefulness of an oscilloscope is not limited to the world of
electronics. With the proper sensor, an oscilloscope can
measure all kinds of phenomena.
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The Oscilloscope
• The oscilloscope is basically a
graph-displaying device.
• The graph shows how signals
change over time.
• The vertical (Y) axis represents
voltage and the horizontal (X)
axis represents time. The
intensity or brightness of the
display is sometimes called the Z
axis, as shown in figure.
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Waveforms
• A waveform is a graphic representation of a wave.
• Waveform shapes reveal a great deal about a signal.
• Any time you see a change in the height of the waveform, you
know the voltage has changed.
• Any time there is a flat horizontal line, you know that there is
no change for that length of time.
• Straight, diagonal lines mean a linear change – rise or fall of
voltage at a steady rate.
• Sharp angles on a waveform indicate sudden change.
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Waveform Measurements-Frequency &
Period
• If a signal repeats, it has a
frequency.
• The frequency is measured in Hertz
(Hz) and equals the number of times
the signal repeats itself in one
second, referred to as cycles per
second.
• A repetitive signal also has a period,
which is the amount of time it takes
the signal to complete one cycle.
• Period and frequency are reciprocals
of each other,
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Waveform Measurements-Voltage
• Voltage is the amount of electric
potential, or signal strength, between
two points in a circuit.
• Usually, one of these points is
ground, or zero volts, but not
always.
• One may measure the voltage from
the maximum peak to the minimum
peak of a waveform, referred to as
the peak-to-peak voltage.
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Waveform Measurements-Amplitude
• Amplitude refers to the amount of
voltage between two points in a
circuit.
• Amplitude commonly refers to the
maximum voltage of a signal
measured from ground, or zero
volts.
• The waveform shown in figure has
an amplitude of 1 V.
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Waveform Measurements-Phase
• The voltage level of sine wave is based
on circular motion.
• Given that a circle has 360°, one cycle
of a sine wave has 360°.
• Phase shift describes the difference in
timing between two otherwise similar
signals.
• The waveform in figure labeled
“current” is said to be 90° out of phase
with the waveform labeled “voltage,”
since the waves reach similar points in
their cycles exactly 1/4 of a cycle apart
(360°/4 = 90°).
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Controls of an Oscilloscope
• The front panel of an oscilloscope is
divided into three main sections:
o Vertical:
The
attenuation
or
amplification of the signal. Use the
volts/div control to adjust the
amplitude of the signal to the desired
measurement range.
o Horizontal: The time base. Use the
sec/div control to set the amount of
time per division represented
horizontally across the screen.
o Trigger: The triggering of the
oscilloscope. Use the trigger level to
stabilize a repeating signal.
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Probes
• Even the most advanced instrument can only be as precise as the
data that goes into it.
• A probe functions in conjunction with an oscilloscope as part of
the measurement system.
• Precision measurements start at the probe tip.
• The right probes matched to the oscilloscope and the device-under
test (DUT) not only allow the signal to be brought to the
oscilloscope cleanly, they also amplify and preserve the signal for
the greatest signal integrity and measurement accuracy.
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Probe Types
Passive Probes
Active & Differential Probes
Logic Probes
Specialty Probes
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NI-ELVIS Series II WorkstationAdditional Features
User Configurable
Input/Output
Oscilloscope (Scope)
Connectors
(Input):
o CH 0 BNC Connector: The input
for channel 0 of the oscilloscope.
o CH 1 BNC Connector: The input
for channel 1 of the oscilloscope.
SYNC (Output):
o 5V TTL signal synchronized to
the FGEN signal.
Generator
o This signal isFunction
most used
as a
(FGEN)
trigger signal for the oscilloscope.
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NI ELVIS Instrument Launcher- Scope
(Oscilloscope)
1.
2.
3.
4.
5.
6.
7.
8.
9.
Scope Graph
Channel Settings
Probe & Coupling
Volts/Div (Vertical
sensitivity) & Vertical
Position
Trigger
Log
Timebase (Horizontal
Sensitivity)
Display Measurement
Cursor Settings
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Lab Objective
• By the end of the lab the student should be familiar with the
controls of a digital oscilloscope and be able to use the
instrument to observe periodic waveforms.
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Equipment Needed
• NI-ELVIS workstation
• 100Ω resistor
• 1kΩ resistor
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Procedure-Basic Setup
• Connect a cable with BNC fitting to the BNC jack for CH 0 of the oscilloscope
on the left side of the NI-ELVIS II.
• Connect the cable’s red lead to the FGEN output; connect the cable’s black lead
to GROUND.
• Set the function generator to output a 100Hz sine wave with amplitude = 3.0
VPP and DC offset = 0V.
• Open the oscilloscope window in the NI-ELVIS software.
• “ENABLE” the display for Channel 0.
• “RUN” the function generator and the oscilloscope.
• Turn on the prototype board.
• Record the measured values for RMS voltage, peak-to-peak voltage, and
waveform frequency.
• Sketch the displayed waveform in your laboratory notebook.
• Compare your measurements with the expected values based on the function
generator output.
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Procedure-Source Control
• Connect CH 0 to “SYNC” (adjacent to FGEN).
• Sketch this waveform in your laboratory notebook.
• Reconnect CH 0 to FGEN.
• Change the function generator output to a square wave.
• Record the displayed waveform in your laboratory notebook.
• Measure the peak-to peak output voltage.
• Repeat this measurement for a triangular wave.
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Procedure-Voltage Scaling
• Reset the function generator to output a sine wave.
• Vary the vertical scale control for Channel 0 using either the control
knob or pull-down menu.
• Record the effect that this control has on the displayed waveform.
• Set the control to 500mV/div.
• Measure the peak-to-peak magnitude of the displayed waveform by
counting (estimate) the number of peak-to-peak divisions and
multiplying by the vertical scale.
• Compare this result with the measurement given by the oscilloscope.
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Procedure-Voltage Offset Manipulation
• Vary the vertical position control in the oscilloscope and record the
effects in your laboratory notebook, noting any changes in the measured
RMS voltage.
• Return the offset to zero and add a DC offset of 0.5V to the function
generator output.
• Record the effects in your laboratory notebook, noting any changes in
the measured RMS voltage.
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Procedure-Time Scaling
• Return the DC offset in the function generator to 0V.
• Using either the timebase dial or pulldown menu, adjust the timebase of the
oscilloscope display to the fastest setting (5μs/div).
• Record the effect that this setting has on displayed measurements for the
waveform.
• Gradually increase the timebase through each available setting until the slowest
setting has been reached (200ms/div).
• Record the effect that this control has on the measurement of voltage and
frequency.
• Return the timebase to a setting where 1-3 full cycles of the output sine wave is
viewable.
• Set the Acquisition Mode to ‘RUN ONCE’ and press ‘RUN’ to capture a single
sweep of the output waveform.
• Measure the period of the waveform by counting (estimate) the number of time
divisions for a single cycle and multiplying by the time scale.
• Compare this measurement to the inverse of the frequency measured by the
oscilloscope.
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Procedure-Triggering/Synch Function
• Return the screen update to 'RUN'.
• Adjust the triggering pull-down menu to edge and record the
oscilloscope response.
• Vary the function generator peak amplitude to verify that the
oscilloscope is continuing to update the display in this mode of
operation.
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Procedure-Cursor Function
• Set the function generator to output a 100Hz sine wave with peak amplitude = 3.0
VPP and DC offset = 0V.
• Return the triggering function to 'Immediate'.
• Display a single screen update of between 1-3 cycles of the output function.
• Switch the cursors function on and drag the cursors to appropriate points on the
waveform to measure the period of the sine wave.
• Then adjust the cursors to measure the peak-to-peak voltage of the sine wave.
• Compare these measurements to those expected based on the function generator's
output settings.
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Procedure-Test Circuit
• Connect the voltage divider circuit
shown in figure.
• Set the function generator to output
a 1kHz sine wave with amplitude
2Vp-p and DC offset = 0.
• Display the function generator
output on channel 0 of the
oscilloscope and the voltage across
the 100Ω resistor on channel 1.
• Display and measure these voltages
simultaneously.
• Measure the period of both
waveforms using the cursor
function.
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Procedure-Test Circuit contd…
• Sketch the waveforms in your
laboratory notebook and record your
settings
for
Volts/div
and
seconds/div.
• Compare
your
voltage
measurements
with
theoretical
calculations based on the voltage
divider equation.
• Compare your waveform period
measurement with the theoretical
value obtained from the input
frequency.
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Procedure-Test Circuit contd…
• Reverse the polarity for the output
voltage measurement on Channel 1.
• Repeat your voltage and period
measurements.
• Sketch the resulting waveforms in
your laboratory notebook.
• Record your settings for Volts/div
and seconds/div.
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Lab 7-Student Tasks
• Students are required to solve the ‘Probing Further’ section,
given in the lab manual, in their laboratory notebooks.
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Preparations for Next Week
• Read Appendix C, Fundamentals of Statistical Analysis.
•
o
o
o
o
Become familiar with the following concepts:
Mean
Standard deviation
Variance and
The formulas used for calculating these quantities.
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References
• ECE 211 – Electrical Engineering Lab I. Latest Revised July
2010.
• XYZs of Oscilloscopes-Primer by Tektronix
• Otago University Electronics Group-NI ELVIS II Orientation
Manual.
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ECE 211 - Electrical Engineering
Lab VIII
Pre-labs for ECE 211
Guneet Bedi
Created: 11/09/2012 Updated: 11/09/2012
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Introduction
• A resistor–capacitor circuit (RC
circuit) or RC network, is an
electric circuit composed of
resistors and capacitors driven by
a voltage or current source.
• A resistor–inductor circuit (RL
circuit) or RL network, is an
electric circuit composed of
resistors and inductors driven by a
voltage or current source.
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Time Constant-RC Circuit
• The time taken for the capacitor to charge or discharge to
within a certain percentage of its maximum supply value is
known as its Time Constant ( τ ).
• Mathematically, τ=RC
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Time Constant-RL Circuit
• The time taken for the current in an inductor to grow or decay
to within a certain percentage of its maximum value is known
as its Time Constant ( τ ).
• Mathematically, τ=L/R
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Lab Objective
• By the end of this lab, the student should know how to
measure the time constants of RC and RL circuits.
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Equipment Needed
•
•
•
•
NI-ELVIS workstation
Resistance substitution box
Capacitance substitution box
Inductance substitution box
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Procedure-RC Time Constant
Measurement (1)
• Set up the RC circuit shown in figure.
• Set the function generator to give a
square wave output with magnitude
equal to 500mV.
• Measure both the source voltage and
the voltage across the capacitor with
the digital oscilloscope.
• Adjust the frequency of the function
generator so that the waveform shown
has definite flat sections at the top and
bottom.
• Using the oscilloscope cursors
function, determine when the voltage
reaches 0.632 times its final value.
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Procedure-RC Time Constant
Measurement (1) contd…
• Sketch the waveform for a
complete cycle in your notebook,
recording the voltage scale and
time scale values.
• Clearly label the sketched
waveforms, including the initial
and final values.
• Repeat these steps using
C=0.047μF and C=0.1μF.
• For each circuit the frequency of
the waveform generator may
have to be changed to achieve
the flat sections at top and
bottom of the waveforms.
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Procedure-RC Time Constant
Measurement (2)
• Now modify the circuit as shown in
figure.
• Repeat the measurements in part 1
using C=0.01μF, 0.047μF, 0.1μF while
observing the voltage across the
resistor.
• Find the time when the voltage reaches
0.368 times its initial value.
• Compare your measured values of the
RC circuit time constant in Parts 1 and
2 with the theoretical values.
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Procedure-RL Time Constant
Measurement (1)
• Set up the RL circuit shown in figure.
• Set the function generator to give a
square wave output with magnitude
equal to 500mV.
• Measure both the source voltage and
the voltage across the resistor with the
digital oscilloscope.
• Adjust the frequency of the function
generator so that the waveform has
definite flat sections at the top and
bottom.
• Using the oscilloscope cursors
function, determine when the voltage
reaches 0.632 times its final value.
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Procedure-RL Time Constant
Measurement (1) contd…
• Sketch the waveform for a
complete cycle in your notebook,
recording the voltage scale and
time scale values.
• Clearly label the sketched
waveforms, including the initial
and final values.
• Repeat these steps using
L=400mH, 600mH and 800mH.
• For each circuit the frequency of
the waveform generator may
have to be changed to achieve
the flat sections at top and
bottom of the waveforms.
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Procedure-RL Time Constant
Measurement (2)
• Now modify the circuit as shown in
figure.
• Repeat the measurements in part 1
using C=200mH, 400mH, 600mH and
800mH while observing the voltage
across the inductor.
• Find the time when the voltage reaches
0.368 times its initial value.
• Compare your measured values of the
RC circuit time constant in Parts 1 and
2 with the theoretical values.
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Lab 8-Student Tasks
• Students are required to solve the ‘Probing Further’ section,
given in the lab manual, in their laboratory notebooks.
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Preparations for Next Week
• Review the material in the textbook on the RLC circuit
response.
• Review the concepts of overdamped, underdamped, and
critically damped response.
• Calculate the theoretical parameter values of s1, s2, α, ωd, and
T for the circuit used in the lab (i.e., do Part 0 of the
Procedure).
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References
• ECE 211 – Electrical Engineering Lab I. Latest Revised July
2010.
• Wikipedia
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Clemson ECE Laboratories
ECE 211 - Electrical Engineering
Lab IX
Pre-labs for ECE 211
Guneet Bedi
Created: 11/16/2012 Updated: 11/16/2012
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Introduction
• A series RLC circuit (or LCR circuit) is an electrical circuit
consisting of a resistor, an inductor, and a capacitor, connected
in series with the voltage source.
• The RLC part of the name is due to those letters being the usual
electrical symbols for resistance, inductance and capacitance
respectively.
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Series RLC Circuit Properties-Circuit
Response
• The differential equation for the circuit has the following
characteristic equation
s 2 + 2a s + w 20 = 0
• The circuit response or the roots of the characteristic equation
is given by
s1 = -a + a 2 - w 02
s2 = -a - a 2 - w 02
or
R
R
1
s1, s2 = ±
2
2L
4L LC
2
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Series RLC Circuit Properties-α, ω0 & ζ
• α is called the neper frequency, or attenuation, and is a
measure of how fast the transient response of the circuit will
die away after the stimulus has been removed.
R
a=
2L
• ω0 is the angular resonance frequency.
w0 =
1
LC
• Damping factor, ζ is defined as the ratio of α and ω0
a
V=
w0
R C
V=
2 L
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Series RLC Circuit Properties-Time
Period (T)
• Let us define ωd as
1
R
2p
wd = w -a =
- 2 =
LC 4L
T
2
2
0
Where
T=Time Period
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Transient Response-Overdamped
Response
• If α is large compared with the resonant frequency ωo, the
voltage or current approaches its final value without
oscillation, and the non-oscillatory response is called
overdamped.
• ζ>1
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Transient Response-Underdamped
Response
• If α is small compared to ωo, the response oscillates about its
final value, and this response is called underdamped.
• The smaller the value of α is, the longer the oscillation
persists.
• ζ<1
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Transient Response-Critically Damped
Response
• If the dissipative element is removed from the circuit, α=0 and
the voltage or current response becomes a sustained
oscillation.
• The critical value of α occurs when α = ωo; in this case, the
response is on the verge of oscillation and is called the
critically damped response.
• ζ=1
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Transient Response-Graphical Summary
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Total Resistance Calculation
• Let Rtot is the total resistance of the circuit.
• In practice, part of that resistance is due to the internal
resistance of the function generator (RFGEN) and part is
supplied by the resistance substitution box (RS).
Rtot = RFGEN + RS
where RFGEN is the internal resistance of the function generator,
and RS is the resistance set on the resistance substitution box.
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Lab Objective
• By the end of this lab, the student should be able to relate the
nature of the physical response of a series RLC circuit to the
parameter values α and ωd determined by the component
values.
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Equipment Needed
•
•
•
•
NI-ELVIS workstation
Resistance substitution box
Capacitance substitution box
Inductance substitution box
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Procedure-Theoretical Calculations
• Calculate the values of s1, s2, α, ωd, and T for the circuit shown in
figure.
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Procedure-Part 1 (Measurements across L)
Circuit Setup
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• Set up the circuit as shown in figure.
• Since the function generator has internal resistance RFGEN in the
range of 50Ω to 150Ω, set the resistance substitution box to
RS=100Ω.
• Set the function generator to output a square wave with amplitude
= 2VPP, DC offset = 0V, and frequency in the range of 10Hz to
100Hz.
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Procedure-Part 1 (Measurements across
L) Underdamped Response
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• Connect CH 0 of the oscilloscope to display the voltage across the
inductor. To avoid a grounding error, the inductor must have one lead
connected to ground.
• To get a stable image of the circuit oscillations, connect a lead from the
FGEN output to CH1 of the oscilloscope. Then set the scope’s trigger to
EDGE, CH 1, rising slope.
• Adjust the period of the square wave, if necessary, so that the damped
sinusoidal waveform decreases to a negligible value (i.e., dampens out)
before the next square-wave pulse occurs. Something in the range of 10
Hz to 100 Hz probably will be adequate.
• Draw an accurate representation of the transient sinusoidal waveform
(the damped oscillations) in your laboratory notebook.
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Procedure-Part 1 (Measurements across
L) Measuring T
• Expand the time scale of the oscilloscope to show 3 to 6
peaks of the damped sinusoidal oscillation.
• Using the CURSORS function of the oscilloscope, measure
the period of the damped sinusoidal waveform.
• Compare this value to T obtained in Part 0.
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Procedure-Part 1 (Measurements across
L) Measuring α
• Measure the peak height of the first full peak of the damped
sinusoidal waveform and the peak height at the next peak
(+1 cycle). Measure the time difference Δt between these
two peaks.
• Determine the Neper frequency (damping coefficient), α,
using your measurements and the equation
Vpeak 2 = Vpeak1e
- a .Dt
• Compare your measured α to the value you calculated
before.
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Procedure-Part 1 (Measurements across
L) Measuring Rtot & RFGEN
• For your experimental α, calculate the total resistance Rtot in
the circuit using
R tot
a=
2L
• Calculate the function generator’s internal resistance using
RFGEN = Rtot - RS
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Procedure – Part 1 (Measurements across
L) Re-measuring RS & α
• Now knowing RFGEN, adjust RS so that Rtot=250Ω.
• Again measure the damping coefficient, α, and compare the
new measured value to your calculated value.
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Procedure-Part 2 (Measurements across
C) Circuit Setup
• Swap the positions of inductor and capacitor as shown in the
figure.
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Procedure-Part 2 (Measurements across
C) Underdamped Response
• Connect CH0 of the oscilloscope to measure the voltage across
the capacitor, being careful to avoid grounding errors.
• Continue to trigger the scope using the FGEN signal on CH1,
as before.
• In your laboratory notebook, sketch the waveform of the
voltage across the capacitor.
• If you were to perform the calculation for α using these data,
you would need to subtract from the peak heights the 1-volt
offset provided by the pulse from the function generator.
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Procedure-Part 2 (Measurements across
C) Critically Damped Response
• For the values of L and C used in this circuit, calculate the
value of total series resistance Rtot that gives critical damping.
• Change the resistance RS so that Rtot equals this value.
• Again observe the voltage drop across the capacitor and sketch
the resulting waveform in your laboratory notebook.
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Procedure-Part 2 (Measurements across
C) Overdamped Response
• Change RS so that Rtot is 10 times the value you calculated for
critical damping.
• Observe and record the capacitor voltage response.
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Lab 9-Student Tasks
• Students are required to solve the ‘Probing Further’ section,
given in the lab manual, in their laboratory notebooks.
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Preparations for Next Week
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References
• ECE 211 – Electrical Engineering Lab I. Latest Revised July
2010.
• Wikipedia
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ECE 211 - Electrical Engineering
Lab X
Pre-labs for ECE 211
Guneet Bedi
Created: 10/26/2012 Updated: 10/26/2012
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Introduction
• Uncertainty or some error in measurement is introduced by
assuming ideal meters in the measurement process and by the
use of the circuit components themselves.
• While a component is designed to have a particular value (its
"nominal" value), which is marked on the outside covering
(the "case" or "encapsulation"), random fluctuations in
materials and production processes will result in some range of
values for the manufactured devices.
• Thus, components are usually specified by a nominal value
and a range, called the tolerance, in which the actual value is
expected to lie.
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Fundamentals of Statistical AnalysisRandom Errors
• When the human errors and systematic errors associated with a
measurement procedure have been eliminated or brought under
control, there will still be some variability in the measurements
when they are repeated. These are called random errors.
• Random errors are characterized by irregularity, which may
appear to be a source of potential disagreement or confusion.
• The use of statistical analysis methods makes possible the
extraction of essential information.
• Two characteristics of the measurements are of special interest:
o The average/mean value of a series of measurements
o Measure of the degree of variability about the mean.
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Fundamentals of Statistical AnalysisAverage or Arithmetic Mean
• Consider a series of measurements: x1, x2, x3,..., xn of some
quantity.
• For each sample of n measurements one can calculate an
average or arithmetic mean value from
n
xav =
åx
j=1
n
j
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Fundamentals of Statistical AnalysisVariance & Standard Deviation
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• Variance can be calculated from
n
s =
2
å( x
j
- xav
j=1
)
2
n -1
• Variance is the mean-square deviation of each measurement from
the average value.
• Standard deviation, s is the square root of Variance.
• Standard Deviation is the root mean-square deviation of each
measurement from the average value.
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Fundamentals of Statistical AnalysisExample
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• Consider 6 measurements of a voltage source over a period of an
hour, repeated for 5 consecutive hours.
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Fundamentals of Statistical AnalysisExample (Observations)
• The most probable value that can be assigned to a measured
magnitude, on the basis of equally trustworthy direct
measurements, is the arithmetic mean.
• In any large number of measurements positive and negative
errors of the same magnitude are equally likely to occur.
• Small errors are much more likely to occur than large ones.
• All of the errors of measurement in a given series lie between
equal positive and negative limits.
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Lab Objective
• By the end of this lab, the student should:
o Know how to identify the tolerance of the resistors used in a
particular circuit.
o Understand what the specified nominal value and tolerance for
a component means statistically.
o Know how to apply statistical methods to obtain the best
estimate of the true value of a circuit component.
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Equipment Needed
• NI-ELVIS workstation
• Resistors
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Procedure
• Groups of resistors labeled GROUP A, GROUP B, GROUP C,
etc. will be passed in turn from lab team to lab team.
• For each group of resistors, measure the resistance of each
component using the NI-ELVIS digital multimeter.
• Make a table for each group, recording the resistances.
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Observation Table I-Individual Resistance
Record
Resistor
#
1
2
3
4
5
Total
Resistor
Gp A
(330Ω)
Resistor
Gp B
(1.5KΩ)
Resistor
Gp C
(3.9KΩ)
Resistor
Gp D
(5.1KΩ)
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Procedure contd…
• For the resistors in each group, calculate the mean, the
standard deviation, and the variance.
• Make a table showing these values for each of the groups
and the values determined by other lab teams.
• Find the average of the mean, variance and standard
deviation values obtained by all the lab teams.
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Observation Table II-Mean Record
Resistor
Gp #
Mean
(Team 1)
Mean
(Team 2)
Mean
(Team 3)
Mean
(Team 4)
Total
Average
A
B
C
D
(330Ω) (1.5KΩ) (3.9KΩ) (5.1KΩ)
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Observation Table III-Variance Record
Resistor
Gp #
Variance
(Team 1)
Variance
(Team 2)
Variance
(Team 3)
Variance
(Team 4)
Total
Average
A
(330Ω)
B
C
(1.5KΩ) (3.9KΩ)
D
(5.1KΩ)
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Observation Table IV-Standard Deviation
Record
Resistor Gp #
Standard Deviation
(Team 1)
Standard Deviation
(Team 2)
Standard Deviation
(Team 3)
Standard Deviation
(Team 4)
Total
Average
A
(330Ω)
B
(1.5KΩ)
C
(3.9KΩ)
D
(5.1KΩ)
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Questions
• Why do the values of mean, variance and standard deviation
obtained by other teams differ from what you obtained?
• Using the information from the tables, what would be the best
estimate of the resistance of each group? Why?
• How does the mean value of resistance obtained by your lab
team, compare to the nominal value of resistance marked on
the resistor’s body?
• How does the standard deviation obtained by your team
compare to the tolerance marked on the resistor case?
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Preparations for Next Week
• Review the material in your circuits textbook on voltage
dividers.
• Read and implement the procedure of Lab 11 (Design Lab).
• Before you come to lab, you should have completed your
circuit design i.e. the design procedure and resulting circuit.
• This is NOT a team exercise. Each individual will be required
to have a design completed in the notebook prior to coming to
lab class.
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References
• ECE 211 – Electrical Engineering Lab I. Latest Revised July
2010.
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ECE 211 - Electrical Engineering
Lab XI
Pre-labs for ECE 211
Guneet Bedi
Created: 11/02/2012 Updated: 11/02/2012
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Introduction
• In this lab you will design and build a circuit to meet certain
criteria.
• In calling for a circuit design, two fundamental questions must
be answered:
o "What function is the circuit to perform?", and
o "How well is the circuit expected to perform this function?".
• The detailed answers to these questions are usually called the
functional requirement and the specifications, respectively.
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Lab Objective
• The objective of this laboratory exercise is to introduce you to
the nature of the engineering design process, i.e., the process
of selecting combinations of components to perform a given
function with a given degree of precision.
• You will be designing a Voltage Regulator to maintain a
voltage of 7V across the load resistance RL for 1000Ω ≤ RL ≤
1500Ω.
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Specifications
• Voltage across RL(load resistor), VL=7V
• 1000Ω ≤ RL ≤1500Ω
• Supply Voltage, VS=10V
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Functional Requirements
• Use two resistors R1 and R2 between VS and RL in a Voltage
divider network.
• Select R1 and R2 to obtain no more than +5% variation about
7V as RL ranges from 1000Ω to 1500Ω.
• How would your design vary if the required VL specification of
7V+5% was modified to 7V±5%?
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Equipment Needed
•
•
•
•
•
NI-ELVIS workstation
R1=? (You specify)
R2=? (You specify)
1000Ω ≤ RL ≤ 1500Ω (I’ll specify)
Make sure that the values of R1 and R2 are standard resistors
(and not arbitrary resistors) as given in the table on the next
slide.
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Standard Resistor Values
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Procedure
• You Specify
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Lab 11-Student Tasks
• Students are required to submit a lab report on this experiment.
• Students MUST strictly adhere to the format as described in
the lab manual.
• For the ‘Questions’ section of the lab report, the students are
required to solve the problems given as a part of ‘Probing
Further’ section of this lab in the manual.
• Your report is due in TWO WEEKS from today.
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Preparations for Next Week
• Review the material in the textbook on RC and RL circuits.
• Before coming to the lab, determine theoretical time constants
of the circuits used in the lab.
• Be sure to account for the 150Ω output impedance of the
function generator in your calculations.
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References
• ECE 211 – Electrical Engineering Lab I. Latest Revised July
2010.
• http://ecee.colorado.edu/~mcclurel/resistorsandcaps.pdf
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ECE 211 - Electrical Engineering
Lab XII
Pre-labs for ECE 211
Guneet Bedi
Created: 11/29/2012 Updated: 11/29/2012
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THE END
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