[email protected] electrical a.c...
TRANSCRIPT
1
انتكىهُجيً انجامؼت :انجامؼتأسم
انبصريتقسم ٌىذست انهيزر َاالنكترَوياث :انكهيتأسم
انبصريت فرع ٌىذست االنكترَوياث : أسم انقسم
صالح انذيه ػذوان طً : أسم انمحاضر
مذرس : انهقب انؼهمي
دكتُراي : انمؤٌم انؼهمي
انتكىهُجيً انجامؼت :مكان انؼمم
جمهورية الع اةةورة اللعلية العالةوة البحة العجلةةوز
القهرية العجلة إلشع ف معزةة
((انخطت انتذريسيت انسىُيت استمارة))
صالح انذيه ػذوان طً . د :انتذريسي اسم
[email protected] انبريذ االنكترَوي :
Electrical A.C Circuit اسم انمادة:
:لمقررا نفص
Study of the electrical A.C circuit &analysis انمادة أٌذاف :
In this section study all of theorem and all the type of A.C circuit
with series and parallel and the complex number with resistance,
capacitance ,inductors
انتفاصيم االساسيً
: نهمادة
INTRODUCTORY CIRCUIT ANALYSIS BY BOYLESTAD
: انكتب انمىٍجيت
Lessons In Electric Circuits, Volume II – AC By Tony R. Kuphaldt
: انمصادر انخارجيت
انثاوي المتحانا انمختبراث االمتحان انىٍائي األَل متحاناال انفصم انذراسي
50 50 15
15
10
10
األَل
انثاوي
: تقذيراث انفصم
: افيتإضمؼهُماث
2
األَل انفصم انذراسي – األسبُػيجذَل انذرَس
:تُقيغ انؼميذ: األستارتُقيغ
انىظريت انمادة ةيلانمادة انؼم انمالحظاث
عُسب
أل ا
Representation of A.C circuit
parameter, complex of voltage and
current
1
Complex impedance and admittance,
complex power
2
Series and parallel circuit 3
Phasor diagrams, solve question 4
Resonance, series ,resonant
frequency
5
Variation impedance, admittance
¤t against frequency
6
Quality factor & resonant voltage
rise, half power points and
bandwidth
7
Locus diagrams, impedance,
admittance and current locus
8
Variable inductance, variable
capacitance
9
Variable resistance, reactance
variation against frequency
10
Solution of AC- circuit 11
Superposition theory, Mesh
analysis,
12
Norton theorem, thevinon theory 13
Maximum power transfer theorem 14
15
16
3
انفصم انذراسي انثاوي – األسبُػيجذَل انذرَس
انىظريت انمادة ةيلانمادة انؼم انمالحظاث
عُسب
أل ا
Magnetically-coupled circuit, self
and mutual inductance coils
1
The Coupling coefficient ,polarity 2
Dot rule, analysis off magnetically 3
Coupled circuits 4
Two-port network(T.P.N.) 5
Forms of T.P.N, attenuation 6
Phase function, symmetrical &
unsymmetrical T.P.N.
7
ELECTIC FILTERS,LOW-
PASS FILTER&HIGH-PASS
FILTER
8
BAND-PASS FILTER&BAND-
STOP FILTER
9
PROTO-TYPE ,l,t ANDX
SECTION
10
M-derived T-section & M-
derived X-section
11
QUESTION & ANSWER 12
QUESTION & ANSWER 13
QUESTION & ANSWER 14
QUESTION & ANSWER 15
16
: تُقيغ انؼميذ: األستارتُقيغ
4
Representation of A.C circuit parameter, complex of
voltage and current
AC Circuits
w
im
R
im
wL
im
wC
m
N2
N1
(primary) (secondary)
iron
V2V1
5
Phasors
A phasor is a vector whose magnitude is the maximum value of a quantity (eg V or I) and which rotates counterclockwise in a 2-d plane with angular velocity w. Recall uniform circular motion:
The projections of r (on
the vertical y axis) execute
sinusoidal oscillation.
iL
tLm
wwcos
i C tC m w wcos
iR
tRm
wsin
x r t cosw
y r t sinw
V Ri tR R m wsin• R: V in phase with i
VQ
CtC m wsin• C: V lags i by 90
V Ldi
dttL
Lm wsin• L: V leads i by 90
w
x
y y
6
Phasors for L,C,R
i
wt
wV
R
i
wt
wVL
i
wt
w
VC
Suppose:
V Ri tR m sinw
VC
i tC m 1
wwcos
V Li tL m w wcos
t
iV
R
0
x ..,0r1
nr1
0 2 4 61
0
1
f( )x
x
x ..,0r1
nr1
0 2 4 61
0
1
f( )x
x
VC
x ..,0r1
nr1
0 2 4 61
0
1
f( )x
x
x ..,0r1
nr1
0 2 4 61
0
1
f( )x
x
0
i
i
0
x ..,0r1
nr1
0 2 4 61
0
1
f( )x
x
VL
x ..,0r1
nr1
0 2 4 61
0
11.01
1.01
f( )x
6.280 x
7
Complex impedance and admittance, complex
power
Series LCRAC Circuit
• Back to the original problem: the loop equation gives:
Here all unknowns, (im,) , must be found from the loop eqn; the initial conditions
have been taken care of by taking the emf to be: m sinwt.
• To solve this problem graphically, first write down expressions for the voltages across R,C, and L and then plot the appropriate phasor diagram.
LC
R
Ld Q
dt
Q
CR
dQ
dttm
2
2 wsin
• Assume a solution of the form: i i tm sin( )w
8
Phasors: LCR
• Assume:
From these equations, we can draw the phasor diagram to the right.
w
im
R
im
wL
im
wC
m
LC
R
• Given: w m tsin
This picture corresponds to a snapshot at t=0. The projections of these phasors along the vertical axis are the actual values of the voltages at the given time.
9
Phasors: LCR
• The phasor diagram has been relabeled in terms of the
reactances defined from:
w
im
R
m
imXC
imXL
LC
R
XC
C 1
wX LL w
The unknowns (im,) can now be solved for
graphically since the vector sum of the voltages
VL + VC + VR must sum to the driving emf .
10
Lecture 20, ACT 3
A driven RLC circuit is connected as shown.
For what frequencies w of the voltage source is the current through the resistor largest?
(a) w small (b) w large (c) w 1
LC
L
C
R
w
11
Conceptual Question
A driven RLC circuit is connected as shown.
For what frequencies w of the voltage source is the current through the resistor largest?
(a) w small (b) w large (c)
L
C
R
w 1
LC
w
• This is NOT a series RLC circuit. We cannot blindly apply our techniques for solving the circuit. We must think a little bit.• However, we can use the frequency dependence of the impedances (reactances) to answer this question.• The reactance of an inductor = XL = wL. • The reactance of a capacitor = XC = 1/(wC).• Therefore,
• in the low frequency limit, XL 0 and XC .
• Therefore, as w 0, the current will flow mostly through the inductor; the current through the capacitor approaches 0.
• in the high frequency limit, XL and XC 0 .
• Therefore, as w , the current will flow mostly through the capacitor, approaching a maximum imax = /R.
12
Series and parallel circuit
Resistive Elements
13
Impedance of the Resistor
14
Inductive Reactance
15
Capacitive Reactance
16
Series Configuration
17
Phasor diagrams, solve question
im
R
m
im(XL-XC)
im
R
m
imXC
imXL
XC
C 1
wX LL w
Z R X XL C 2 2
tan X X
R
L C
m m L Ci R X X2 2 2 2
i
R X X Zm
m
L C
m
2 2
18
Phasors:Tips
• This phasor diagram was drawn as a snapshot of time t=0 with the voltages being given as the projections along the y-axis.
im
R
m
imXC
imXL
y
x
imR
imXL
imXC
m
“Full Phasor Diagram”
From this diagram, we can also create a triangle which allows us to calculate the impedance Z:
X XL C
Z
R
“ Impedance Triangle”
• Sometimes, in working problems, it is easier to draw the diagram at a time when the current is along the x-axis (when i=0).
19
Phasors:LCR
We have found the general solution for the driven LCR circuit:
X LL w
XC
C 1
w
Z R X XL C 2 2
R
XL
XC
Z
tan X X
R
L C
iZ
mm
i Zm
the loop eqn
XL - XC
i i tm sin( )w
imR
imXL
imXC
m w
Phasors:LCR
We have found the general solution for the driven LCR circuit:
X LL w
XC
C 1
w
Z R X XL C 2 2
R
XL
XC
Z
tan X X
R
L C
iZ
mm
i Zm
the loop eqn
XL - XC
i i tm sin( )w
imR
imXL
imXC
m w
20
Lagging & Leading
The phase between the current and the driving emf depends on the relative magnitudes of the inductive and capacitive reactances.
R
XL
XC
Z
tan X X
R
L CiZ
mm
X LL w
XC
C 1
w
XL > XC
> 0current LAGS
applied voltage
R
XL
XC
Z
XL < XC
< 0current LEADS
applied voltage
XL = XC
= 0current
IN PHASEapplied voltage
R
XL
XC
Z
21
Conceptual Question
The series LCR circuit shown is driven by a generator with voltage = msinwt. The time dependence of the current i which flows in the circuit is shown in the plot.
How should w be changed to bring the current and driving voltage into phase?
(a) increase w (b) decrease w (c) impossible
• Which of the following phasors represents the current i at t=0?1B
1A
(a) (b) (c) ii
i
22
Resonance, series ,resonant frequency
Resonance
For fixed R,C,L the current im will be a maximum at the resonant frequency w0
which makes the impedance Z purely resistive.
the frequency at which this condition is obtained is given from:
• Note that this resonant frequency is identical to the natural frequency of the LC circuit by itself!
• At this frequency, the current and the driving voltage are in phase!
ie:
i
Z R X Xm
m m
L C
2 2
reaches a maximum when: X XL C
ww
oo
LC
1
woLC
1
tan
X X
R
L C 0
23
Resonance
The current in an LCR circuit depends on the values of the elements and on the driving frequency through the relation
i
Z R X Xm
m m
L C
2 2
iR R
mm m
1
1 2tancos
x ..,0.0r1
nr1
0 1 20
0.5
1
f( )x
g( )x
x
im
00
2wow
m
R0
R=Ro
R=2Ro
Suppose you plot the current versus w, the source voltage frequency, you would get:
24
25