The interaction of sinusoidal oscillation and sinusoidal ...
01 Sinusoidal Waveforms
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Purdue University ECET 207 AC Electronic Circuit Analysis
ECET 207 AC Electric Circuit Analysis
Class 3, lab. 3, cr. 4.Prereq: ECET 157, MA 151 or 154
AC circuits including the j operator, phasors, reactanceand impedance are studied. Circuit laws, networktheorems, and the fundamental concepts of Fourieranalysis are applied and used in the study of topics suchas passive filters, IC filters, amplifiers, resonant circuits,single phase and three phase circuits, and elementarymagnetic circuits.
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Purdue University ECET 207 AC Electronic Circuit Analysis
Texts
u J. Michael Jacob, Advance AC Electronics ,Delmar/Thomson
u J. Michael Jacob, ECET 207 AC ElectronicsCircuit Analysis Study Guide & Lab Manual ,
Learning Systems
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Purdue University ECET 207 AC Electronic Circuit Analysis
Syllabusu It is a contract.
Read it! Use it!u General Information #8: Professional conduct
u General Information #9: Cheating
u Attendance
u HW, Quizzes, Labs
u Grading Policy
u Standards: HW and Lab Reports
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Purdue University ECET 207 AC Electronic Circuit Analysis
Calendar
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Purdue University ECET 207 AC Electronic Circuit Analysis
u Homework due BEGINNING of class WWW
See course web site
u Lab syllabus in lab
u No ECET 207 parts kit, ECET 107 &157 needed.
uFlash drive, or diskette, or career account accessneeded for lab this week.
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Purdue University ECET 207 AC Electronic Circuit Analysis
Role
Nick name
Initial beside your name, under todays date
Attendance policy!
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Purdue University ECET 207 AC Electronic Circuit Analysis
Web Sitehttp://www2.tech.purdue.edu/eet/courses/eet207/
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Purdue University ECET 207 AC Electronic Circuit Analysis
Other handouts
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Waves
u Alternating Currentu sinewave terms
u average valueu effective value (RMS)
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Purdue University ECET 207 AC Electronic Circuit Analysis
Alternating Current
u many waveforms ( waveshapes )u sineu
squareu triangleu pulseu exponential
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Purdue University ECET 207 AC Electronic Circuit Analysis
AC means
volts
time
Sinusoidal
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Purdue University ECET 207 AC Electronic Circuit Analysis
Why Sine Waves?
u Most easily and commonly generated
u RLC do not alter the shape
uAll other shapes can be made bycombining sine waves
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Purdue University ECET 207 AC Electronic Circuit Analysis
Period of a Sine Wave
volts
time
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Purdue University ECET 207 AC Electronic Circuit Analysis
Period of a Sine Wave
time
period
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Purdue University ECET 207 AC Electronic Circuit Analysis
Period of a Sine Wave
time
period = T
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Purdue University ECET 207 AC Electronic Circuit Analysis
Period of a Sine Wave
time
period
Unit of measure = _________
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Purdue University ECET 207 AC Electronic Circuit Analysis
Period of a Sine Wave
time
period
Unit of measure = seconds
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Wave Terms
u periodu frequency
u angular velocityu general equationu phase relationship
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Purdue University ECET 207 AC Electronic Circuit Analysis
Frequency of a Sine Wave
u cycles per second
u unit of measure: Hertz = Hz
u f = 1/T
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Wave Terms
u periodu frequency
u angular velocityu general equationu phase relationship
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle ( instead of time for x axis)
u degreesu 360 o/cycle
u radianangle whose arc distance = 1 radius2 rad/cycle
? o/rad360 o/cycle x 1 cycle /2 rad = 57.3 o/rad
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle (instead of time on the x axis)
volts
angle
360 o
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle (instead of time on the x axis)
volts
angle
180 o
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle (instead of time on the x axis)
volts
angle
90 o
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle (instead of time on the x axis)
volts
angle
270 o
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle (instead of time on the x axis)
volts
angle
____rad ____rad ____rad ____rad
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angle (instead of time on the x axis)
volts
angle
2 rad3/2 rad rad/2 rad
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angular Velocity (instead of frequency)
units ?
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angular Velocity (instead of frequency)
units
rad /sec
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angular Velocity (instead of frequency)
units
rad /sec
=t
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angular Velocity (instead of frequency)
units
rad /sec
= =t T
2
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Purdue University ECET 207 AC Electronic Circuit Analysis
Angular Velocity (instead of frequency)
units
rad /sec
= = =t T
f 2
2
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Wave Terms
u periodu frequency
u angular velocityu general equationu phase relationship
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Purdue University ECET 207 AC Electronic Circuit Analysis
General Equation of a Sine Wave
A peak sin
A imum A peak m=max = angle
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Purdue University ECET 207 AC Electronic Circuit Analysis
General Equation of a Sine Wave
A peak sin
A imum A peak m=max = angle
= t = t
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Purdue University ECET 207 AC Electronic Circuit Analysis
General Equation of a Sine Wave
A peak sin
A imum A peak m=max = angle
= t = t A t peak sin( )
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Purdue University ECET 207 AC Electronic Circuit Analysis
Solution a.
v V = 152
At t =3msec, calculate v(3msec).
v(t) 168Vsin(377t)=
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Purdue University ECET 207 AC Electronic Circuit Analysis
Example b.
At what time does v(t) = 100V ?
v t V t ( ) sin( )= 168 377
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Purdue University ECET 207 AC Electronic Circuit Analysis
Solution b. continued
t milli= 1 69. sec
At what time does v(t) = 100V ?
v t V t ( ) sin( )= 168 377
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Wave Terms
u periodu frequency
u angular velocityu general equationu phase relationship
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Purdue University ECET 207 AC Electronic Circuit Analysis
Phase Relationship : positive = leading
time
volts
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Purdue University ECET 207 AC Electronic Circuit Analysis
Phase Relationship : positive = leading
time
volts
t
360 o
T
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Purdue University ECET 207 AC Electronic Circuit Analysis
Phase Relationship : positive = leading
time
volts
t
360 o
T
t T f =
=
360360
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Purdue University ECET 207 AC Electronic Circuit Analysis
Phase Relationship : negative = lagging
360T
t
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Purdue University ECET 207 AC Electronic Circuit Analysis
Complete General Equation
v t A t pk ( ) sin( )=
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Purdue University ECET 207 AC Electronic Circuit Analysis
Complete General Equation
v t A t pk ( ) sin( )=
radians
degrees
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Purdue University ECET 207 AC Electronic Circuit Analysis
Example c.
At t = 3msec, calculate v(3msec).
v t V t ( ) sin( )= + 168 377 50
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Purdue University ECET 207 AC Electronic Circuit Analysis
Example c.
At t = 3msec, calculate v(3msec).
v t V t ( ) sin( )= + 168 377 50
v m V ( sec) .3 152 5=
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Waves
u Alternating Currentu sinewave termsu
average valueu effective value (rms)
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Purdue University ECET 207 AC Electronic Circuit Analysis
Average ValueVave = Vdc
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Purdue University ECET 207 AC Electronic Circuit Analysis
Average ValueVave = Vdc
Vave = area under the curve / length
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Purdue University ECET 207 AC Electronic Circuit Analysis
Average ValueVave = Vdc
Vave = area under the curve / length
( ) ( )V h l L L
h l ave
L
= = 10
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Purdue University ECET 207 AC Electronic Circuit Analysis
Average ValueVave = Vdc
Vave = area under the curve / length
( )( )V
h l L L h l ave
L
=
= 1
0
V A d Aave half wave peak peak _
sin( ) = = 1 2
0
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Purdue University ECET 207 AC Electronic Circuit Analysis
Average ValueVave = Vdc
Vave = area under the curve / length
( )( )V
h l L L h l ave
L
=
= 1
0
V A d Aave half wave peak peak _ sin( ) = = 1 20
V ave full wave _ = 0
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Waves
u Alternating Currentu sinewave termsu
average valueu effective value (rms)
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Purdue University ECET 207 AC Electronic Circuit Analysis
Effective Value
u Indicated on a meter
uAlso called rms (root mean squared)
u The amplitude of a signal which will deliver
the same power as a numerically equal dc .
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Purdue University ECET 207 AC Electronic Circuit Analysis
DerivationLook it up !
v T A d rms pk T
= 1
20 ( sin )
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Purdue University ECET 207 AC Electronic Circuit Analysis
DerivationLook it up !
v T A d rms pk T
= 1
20 ( sin )
= V
pk
2
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Purdue University ECET 207 AC Electronic Circuit Analysis
Sine Waves
u Alternating Currentu sinewave termsu
average valueu effective value (rms)
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Purdue University ECET 207 AC Electronic Circuit Analysis
MATLAB demo
Plot two cycles of a sine wave with:
V p = 170 V p f = 60 Hz T = 16.7 ms 2 T = 33.4 ms
v = V p sin(2 f t )
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Purdue University ECET 207 AC Electronic Circuit Analysis
MATLAB demo