Bài giảng Electric circuit theory - Chapter IX: Sinusoid and Phasors - Nguyễn Công Phương
Phasor Relationships for Circuit Elements (6 e1 = 10sin10t V; j = 4sin(10t + 30o) A; e2 = 6sin(10t + 60o) V; L = 1 H; R1 = 1 Ω; R2 = 5 Ω; C = 0.01 F
Bạn đang xem nội dung tài liệu Bài giảng Electric circuit theory - Chapter IX: Sinusoid and Phasors - Nguyễn Công Phương, để tải tài liệu về máy bạn click vào nút DOWNLOAD ở trên
Nguyễn Công Phương
Electric Circuit Theory
Sinusoid & Phasors
Contents
I. Basic Elements Of Electrical Circuits
II. Basic Laws
III. Electrical Circuit Analysis
IV. Circuit Theorems
V. Active Circuits
VI. Capacitor And Inductor
VII. First Order Circuits
VIII.Second Order Circuits
IX. Sinusoid and Phasors
X. Sinusoidal Steady State Analysis
XI. AC Power Analysis
XII. Three-phase Circuits
XIII.Magnetically Coupled Circuits
XIV.Frequency Response
XV. The Laplace Transform
XVI.Two-port Networks
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 2
Sinusoid & Phasors
1. Sinusoids
2. Complex Numbers
3. Phasors
4. Phasor Relationships for Circuit Elements
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 3
Sinusoids
vt( ) Vm sin( t )
v(t)
2 Vm
T 2π
π
0
1 ωt
f
T
–Vm
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 4
Complex Numbers (1)
zxjyr rej ;1 j
Imaginary axes
y
rxy22;tan 1
x y
r
xrcos ; yr sin
Real axes
x Re(zy ); Im( z ) 0 x
zxjyr rej r(cos j sin )
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 5
Ex. 1 Complex Numbers (2)
34jr ? Imaginary axes
j
rxy22
rab2234 22 5 y
11oy 4 yr sin
tan tan 53.1 y
x 3 tan1
x 1
o
345j 53.1 0 xr cos x
Real axes
Ex. 2
10 60o xjy ?
x 10cos60o 5
y 10sin 60o 8.66
10 60o 5j 8.66
Mạch xoay chiều - sites.google.com/site/ncpdhbkhn 6
Complex Numbers (3)
zxjyz; 11 x jyr 11 12222; zxjyr 2
zz12 ()() xx 12jy 1 y 2
zz12 ()() xx 12jy 1 y 2
zz12 rr 12 12
zr11
12
zr22
11
zr
zr /2
zxjyr* re j
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 7
Ex. 3 Complex Numbers (4)
3456jj(3 5)jj (4 6) 8 2
34(56)jj(3 5)jj [4 ( 6)] 2 10
oo
345j 30o 34[(5cos30)(5sin30)]34(4.332.50)jjjj
1.33 j 6.50
(3jj 4)(5 6) 35jjjj 453 6 4 6
15jj 20 18 ( 1)24 39j 2
o o oo
5 53.1 7.81 50.2 (5 7.81) 53.1 50.2
39.1 2.9o
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 8
Ex. 4 Complex Numbers (5)
34 j 3456jj35 jjjj 453 6 4 6 15 jj 20 18 24
56 j 5656jj 5(6)22 j 25 ( 1)36
938 j 938j
0.15 j 0.62
61 61 61
5 53.1o 5
53.1oo ( 50.2 ) 0.64 103.3o
7.81 50.2o 7.81
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 9
Ex. 5 Complex Numbers (6)
o
345j 30o 7.33 j 6.50 7.33 j 6.50 9.80 41.6
o
(4jj 5)(6 7)* (4jj 5)(6 7)* 59.00 100.7o 59.00 100.7
0.17 51.1o
5 30oo (5cos30 )jj (5sin 30 o ) 4.33 2.50
o
345j 30o (3jj 4) (4.33 2.50) 7.33 j 6.50 0.41 25.6
(4j 5)(6jjj 7)* (4 5)(6 7)
45j 4522 tan1 (5/ 4) 6.40 51.3o
67j 6722 tan1 (6 / 7) 9.22 49.4o
o o o
(4jj 5)(6 7) 6.40 51.3 9.22 49.4 59.00 100.7
7.33j 6.50 7.3322 6.50 tan1 (6.50 / 7.33) 9.80 41.6o
Mạch xoay chiều - sites.google.com/site/ncpdhbkhn 10
Sinusoid & Phasors
1. Sinusoids
2. Complex Numbers
3. Phasors
4. Phasor Relationships for Circuit Elements
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 11
Phasors (1) 2sint + 4sin(t+30o)
xt() 2sin t X 2 0o 4sin(t+30o)
yt() 4sin( t 30)o Y 4 30o 2sint
xt() yt () XY 0
X 2 02o
Y 4 30o 3.46j 2
XY2 (3.46 jj 2) 5.46 2 5.82 20o
xt( ) yt ( ) 5.82sin( t 20o )
xt() Xmm sin( t ) X X
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 12
Phasors (2)
Ex.
4sin(20t 40o ) 4 40o
6sin(314t 120o ) 6 120o
5cos(100t 20o ) 5sin(100t 110o ) 5 110o
o
12 30o 12sin(t 30 )
o
24 60o 24sin(t 60 )
34 j 5 53.1o 5sin(t 53.1o )
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 13
Phasor Relationships for Circuit Elements (1)
i R I R
+ v – + V –
iIsin( t )
m vRIsin( t )
vRi m
V RIm
v(t) VIR
I Im
V
Im
0 i(t)
ωt I
Re
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn0 14
Phasor Relationships for Circuit Elements (2)
i L I jωL
+ v – + V –
iIm sin( t )
o
di vLItm sin( 90 ) VIjL
vL
dt
i(t)
v(t) Im
V
0
φ ωt I
Re
900
0
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 15
Phasor Relationships for Circuit Elements (3)
1
i C I
jC
+ v – + V –
vVm sin( t )
o
dv iCVtm sin( 90 ) IVjC
iC
dt 1
900 VI
v(t) jC
i(t) Im
ωt I
φ 0 V
Re
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn0 16
Phasor Relationships for Circuit Elements (4)
i L C
i R di i 1
vRi vL vidt
dt C
+ v – + v – + v –
1
I R I jωL
i jC 1
VI R VI jL VI
+ V – + – jC
V + v –
V Im Im
Im V
I
V
I I
Re Re Re
0 0 0
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 17
Phasor Relationships for Circuit Elements (5)
Ex. 1 10sin5t V20Ω 6H 0.02F
20 20 – +
6H jL jj56 30
1110
j10
0.02 F jC j50.02 j
10 0o 1
20 j30
o j0.1
10sin5t 10 0 – +
+ – + –
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 18
Phasor Relationships for Circuit Elements (6)
Ex. 2
L
+
+ R R
e = 10sin10t V; j = 4sin(10t + 30o) A; 1 2
–
1 –
e = 6sin(10t + 60o)V; L = 1 H; R = 1 Ω;
2 1 C
e1 j e2
R2 = 5 Ω; C = 0.01 F.
Sinusoid & Phasors - sites.google.com/site/ncpdhbkhn 19
Các file đính kèm theo tài liệu này:
- bai_giang_electric_circuit_theory_chapter_ix_sinusoid_and_ph.pdf