Department of Electronic EngineeringNational Taipei University of Technology

•• ( )

• ( )

• ( )

••

Department of Electronic Engineering, NTUT2/41

(I)

•

Department of Electronic Engineering, NTUT

( ) sinmv t V tω=

Vm

t (sec)

T

v(t)

−Vm

2

πω

πω

3

2

πω

2πω

5

2

πω

6

2

πω

0

T

ω

: Vm(volt)

: T (sec)

: f (Hz, cycle/sec)

: (rad/sec)2 fω π=

3/41

(II)

• ( ) ( )sinmv t V tω φ= +

ω

: Vm(volt)

: T (sec)

: f (Hz, cycle/sec)

: (rad/sec)2 fω π=

φ: (rad)檔案中找不到關聯識別碼 rId12 的圖像部分。

Vm

t (sec)

v(t)

−Vm

2

πω

πω

3

2

πω

2πω

5

2

πω

6

2

πω

0

T

φ

1t

Department of Electronic Engineering, NTUT4/41

( )

• vR = iR( ) ( )

• ,

•

R, L, C = + ( ) ( / )

L

div L

dt= 1 t

Cv idtC −∞

= ∫

Department of Electronic Engineering, NTUT5/41

1

• RL i(t)i f (t)

,

KVL+−

L

Ri(t)

( ) ( )cos Vs mv t V tω=

( ) ( ) cosm

di tL Ri t V t

dtω+ =

( ) cos + sinfi t A t B tω ω=

( ) ( ) cosm

di tL Ri t V t

dtω+ =

mRA LB Vω+ = 0LA RBω− + =

( ) ( )sin cos cos sin cosmL A t B t R A t B t V tω ω ω ω ω ω ω− + + + =

, 2 2 2mLV

BR L

ωω

=+2 2 2

mRVA

R Lω=

+( )fi t

( ) ( ) ( )12 2 2 2 2 2 2 2 2

cos sin cos tan cos AR

m m mf m

RV LV V Li t t t t I t

R L R L R L

ω ωω ω ω ω φω ω ω

− = + = − = + + + +

2 2 2

mm

VI

R Lω=

+1tan

L

R

ωφ −= −

( ) ( ) ( )f ni t i t i t= +( ) 1RtL

ni t Ae−=

( )sv t

Department of Electronic Engineering, NTUT6/41

2

• RLC v(t) i(t)

KVL

+−

+

−

5

3R = Ω 5 HL = ( )i t

( )v t1

F25

C =( )sv t

( ) 17cos3sv t t=

( ) ( ) ( ) ( )2

2

1 sd v t dv t v tRv t

dt L dt LC LC+ + =

( ) ( ) ( )2

25 85cos3

d v t dv tRv t t

dt L dt+ + =

( ) ( ) ( ) ( )20cos3 +5sin 3 =5 17 cos 3 2.9 5 17 cos 3 166 Vv t t t t t= − − = −

( ) ( ) ( ) ( ) ( ) ( ) ( )1 1 3 17 3 1760sin 3 15cos3 cos 3 1.33 cos 3 76 A

25 25 5 5

dv t dv ti t C t t t t

dt dt= = = + = − = −

,

( ) 1 2cos3 sin3v t A t A t= +

( ) ( )1 2 1 24 cos3 4 sin 3 85cos3A A t A A t t− + + − − =

1 24 85A A− + = 1 24 0A A− − = 1 20A = −

2 5A =

Department of Electronic Engineering, NTUT7/41

(Complex Number)

•

θa

b

A a jb= +

Re

b

Im

| |A

+A a jb=jA A e Aθ θ= = ∠

[ ]Re cosa A A θ= =

[ ]Im sinb A A θ= =

2 2A a b= + 1tanb

aθ −=

1j = −1 1 1A a jb= + 2 2 2A a jb= +

( ) ( ) ( ) ( )1 2 1 1 2 2 1 2 1 2+A A a jb a jb a a j b b= + + + = + + +

( ) ( ) ( ) ( )1 2 1 1 2 2 1 2 1 2A A a jb a jb a a j b b− = + − + = − + −

• +A a jb= A a jb∗ = −

•

( )( )( ) ( )

21 2 1 1 2 2 1 2 1 2 2 1 1 2

1 2 1 2 1 2 2 1

A A a jb a jb a a ja b ja b j b ba a b b j a b a b

= + + = + + += − + +　　　

( ) ( ) ( )1 2 1 1 2 2 1 2 1 2A A A A A Aθ θ θ θ= ∠ ∠ = ∠ +

•( )( )( )( )

1 1 2 21 1 1 1 2 1 2 1 2 1 22 2 2 2

2 2 2 2 2 2 2 2 2 2 2

a jb a jbA a jb a a b b b a a bj

A a jb a jb a jb a b a b

+ −+ + −= = = ++ + − + +

( )111 2

2 2

AA

A Aθ θ= ∠ −

Department of Electronic Engineering, NTUT8/41

(a+jb) (I)

•

(a) A = 4 + j3

,

A

(b) A = –4 + j3

A θ∠

2 24 3 5A = + = 1 3= tan 36.9

4θ − =

5 36.9A = ∠

1 13 3= tan 180 tan 180 36.9 143.1

4 4θ − − = − = − = −

　 　

( )2 24 3 5A = − + =

5 143.1A = ∠

(a)

4

θ = −tan134

| |A =5

Re

3

j

o

o

A

A

jA

9.365

9.3643tan

534

34

1

22

∠=⇒

==⇒

=+=⇒

+=

−θ

Re

j

θ = −180° 3

41tan

−4

| |A =53

( )

oo

oo

A

A

jA

1.14351.143

9.3618043

tan

534

34

1

22

∠=⇒=−=−=⇒

=+−=⇒

+−=

−θ

(b)

Department of Electronic Engineering, NTUT9/41

(a+jb) (II)

(c) A = –4 –j3

( )

o

oo

oo

A

A

jA

9.365

9.361.323

9.3636043tan

534

34

1

22

−∠=⇒

−==

−=−=⇒

=−+=⇒

−=

−θ

j

| |A =5

Re

−3

4

θ = −360° 3

41tan

−3

Re

j

−4

| |A = 5( ) ( )

o

oo

oo

A

A

jA

1.1435

1.1439.216

9.3618043tan

534

34

1

22

−∠=⇒

−==

+=−−=⇒

=−+−=⇒

−−=

−θ

θ = −180° + 3

41tan

A θ∠

( ) ( )2 24 3 5A = − + − =

1 13 3 = tan 180 tan

4 4

180 36.9 216.9 143.1

θ − −− = − −

= + = = −

　

　

5 143.1A = ∠ −

(d) A = 4 –j3

( )224 3 5A = + − =

1 13 3 = tan =360 tan

4 4

323.1 36.9

θ − −− −

= = −

　

5 36.9A = ∠ −

(c)

(d)

Department of Electronic Engineering, NTUT10/41

(I)

•

•

• RL (Complex excitation)(Real excitation)

i(t)

KVL:

cos sinj tm m mV e V t jV tω ω ω= +

cos Re

sin Im

j tm m

j tm m

V t V e

V t V e

ω

ω

ω

ω

=

=

1j t

mv V eω= ( ) [ ]1cos Reg mv t V t vω= =

+−

L

Ri(t)cosmV tω

11+ j t

m

diL Ri V e

dtω=

1j ti Ae ω=

( ) j t j tmj L R Ae V eω ωω + =

-1tan

2 2 2

Lj

m m RV VA e

R j L R L

ω

ω ω−

= =+ +

1tan

1 2 2 2

Lj t

RmVi e

R L

ωω

ω

− − =

+

i1 i(t)

⇒⇒⇒⇒

Department of Electronic Engineering, NTUT11/41

(II)

6 RL

i(t) i1 ( vg(t) v1 )

i1 v1 i f (t)= Re[i1] vg = Re[v1]

1tan

1 2 2 2

Lj t

RmVi e

R L

ωω

ω

− − =

+

( ) [ ]1tan

11 2 2 2 2 2 2

Re Re cos tanL

j tRm mV V L

i t i e tRR L R L

ωω ωωω ω

− − − = = = −

+ +

[ ]11 1Re Re

diL Ri v

dt

+ =

[ ]( ) [ ]( )1 1Re Re cosm

dL i R i V t

dtω+ = ( ) ( ) [ ]1Refi t i t i= =

Department of Electronic Engineering, NTUT12/41

• 11 :

• ?

KVL: 11+ j t

m

diL Ri V e

dtω= 1

j ti Ae ω=

( ) j t j tmj L R Ae V eω ωω + =

-1tan

2 2 2

Lj

m m RV VA e

R j L R L

ω

ω ω−

= =+ +

1tan

1 2 2 2

Lj t

RmVi e

R L

ωω

ω

− − =

+

A

” ”

” ”

j te ω

j te ω

jω

j te ω

1 jω

Department of Electronic Engineering, NTUT13/41

(I)

• (Euler’s formula)

(Phasor)

• rms

• ”−”

( ) ( )cos Re Rej j t j tm mv t V t V e e Veθ ω ωω θ = + = =

jm mV V e Vθ θ= = ∠

2j m

rms rms

VV V e Vθ θ θ= = ∠ = ∠

jm mV e Vθ θ= = ∠V j

m mV V e Vθ θ= = ∠

j te ω

j te ω

1:

Department of Electronic Engineering, NTUT14/41

(II)

I

R

+

=

−V RI

i

R

+

=

−v Ri

I

+

−

i

L

+

−

div L

dt= V j LIω= j Lω

+

−V

1I j CV V I

j Cω

ω= ⇒ =

1

j CωC

+

−v

dvi C

dt=

R R

L j Lω

C1

j Cω

( )

( )

2:

Department of Electronic Engineering, NTUT15/41

(III)

+−

L

Ri(t)cosmV tω +− RI0mV V= ∠

j Lω

j LI R Vω + =1

2 2 2

0tan

Lm mV VV L

IR j L R j L RR

ωω ω ω

−∠= = = ∠ −+ + +

( )1 1tan tan

1

2 2 2 2 2 2 2 2 2Re Re cos tan

L Lj j t

j tR Rm m mV V V Li t e e e t

RR L R L R L

ω ωωω ωω

ω ω ω

− − − − − = = = −

+ + +

2:1:

, !

3:!

!

Department of Electronic Engineering, NTUT16/41

R L C

I

R

+

=

−V RI

(a)

i

R

+

=

−v Ri

t

v i,vi

(b)

i

L

+

−

I

+

−(a) (b)

div L

dt= V j LIω= j Lω

vi

t

v i,

v

i

t

v i,

Department of Electronic Engineering, NTUT

C

+

−v

+

−

I

1

j Cω

dvi C

dt=

(a) (b)

1V I

j Cω=

17/41

(I)

Z (Impedance)

( ) ( )1cosmv t V tω φ= +

( ) ( )2cosmi t I tω φ= + 2mI I φ= ∠

1mV V φ= ∠

( ) ( )1 2= m

m

VVZ Z R jX

I Iθ φ φ= = ∠ ∠ − = + Ω

(a)

+

−

+

−V

I

(b) ( )

( )v t

( )i t

[ ]ImX Z=

[ ]ReR Z=

(Reactance)

(Resistance)

Z ω

ω

( )Z jω( )R R ω=

( )X X ω=

θR

XZ R jX= +

Re

Im2 2Z R X= +

1tanX

Rθ −=

cosR Z θ=

sinX Z θ=

Department of Electronic Engineering, NTUT18/41

(II)

•

• (Admittance)

• Z Y Y

Y = G + jB G = Re[Y] B = Im[Y]

(Susceptance) Y G B

R

VZ R

I= =

LX Lω=L L

VZ jX j L

Iω= = =

1CX

Cω= − 1

C C

VZ jX j

I Cω= = = −

1Y

Z=

( ) ( ) 2 2 2 2

1 1=

R jX R XY j G jB

Z R jX R jX R jX R X R X

−= = = − = ++ + − + +

Department of Electronic Engineering, NTUT19/41

• (a) RL (b)

KVL:

+−

L

Ri( )cos VmV tω

(a)

+− R

j Lω

I0mV ∠

(b)

0L mZ I RI V+ = ∠ ( ) 0mj L R I Vω + = ∠

( ) 1

2 2 2cos tanmV L

i t tRR L

ωωω

− = − +

1

2 2 2

0tanm mV V L

IR j L RR L

ωω ω

−∠ = = ∠ − + +

Z j L Rω= + 0mVVI

Z R j Lω∠= =

+

Department of Electronic Engineering, NTUT20/41

3

• (a) v(t) i(t) 1. (a) (b)

2. (c)

3. (c)

10 0V = ∠ 2 rad secω =

( )Z 2 L j L jω= = Ω ( )11 CZ j j

Cω= − = − Ω

1 1.5 2Z j= + ( )( )2

1 10.5 0.5

1 1

jZ j

j

−= = −

− +

( ) ( )0.283sin 2 81.9 Vv t t= −

1 2

10 0 10 04 36.9

2.5 36.9TI Z Z

∠ ∠= = = ∠ −+ ∠

( )1 4 36.92.83 8.1 A

1 1 2 45TI I

j

∠ −= = = ∠− ∠ −

( ) ( ) ( )2.83sin 2 8.1 Ai t t= +

+−

+

−( )10sin2 Vt

1.5 Ω 1 H

0.5 F 1 Ω( )Ti t ( )i t

( )v t

(a)

+−

+

−10 0∠ 1 Ω

2 j Ω

1 j− Ω

1.5 Ω

TII

V

(b)

+−

+

−

TI

10 0∠ V

1Z

2Z

(c)

,

,

,

( ) ( )2

1 2

0.5 0.510 0 10 0

1.5 2 0.5 0.5

Z jV

Z Z j j

−= × ∠ = × ∠+ + + −

0.283 81.9 V= ∠ −

Department of Electronic Engineering, NTUT21/41

4

• (a) i(t)

1. (a) (b)

a KCL:

+−

a

12

18F

+

−v1

i t( )

4Ω( )10cos4 At v1

(a)

+−

a

12

−j2 Ω

+

−V1

I

4Ω( )10 0 A∠ V1

(b)

( )1 1

21

48

C

jZ j j

Cω= − = − = − Ω

4rad secω =10 0I = ∠

1 1

12 10 02

V VI

j

−+ = ∠

− ( )1 1 10 0I j+ = ∠ ( )10 0

7.07 45 A1 1

Ij

∠= = ∠ −+

( ) ( )( )7.07cos 4 45 Ai t t= −

, ,

Department of Electronic Engineering, NTUT22/41

(Phasor Diagram)

• (Vector)

•

Vg= VR + VL + VC

(b) VR , VL , VC

V|VL| |VC|

+−

Vg

R

+ −VR + −VL+

−VC

1j Cω

j Lω

VL VC+

VR

(a) RLC I

(a) RLC

0I I= ∠

I I I

(b)

VR

VL

VC

(a)

VL

VC (c) VR + VL + VC = Vg

Department of Electronic Engineering, NTUT23/41

Department of Electronic Engineering, NTUT24/41

5 −

• (a) i(t)

1. (a) (b)

2. V V + 3000I

KVL:

4.

3. KCL:

(a)

+−

+−

1 k

2Ω

2 kΩ1

F5

µ( )3000 Vi t

( ) ( )3000 v t i t+

2 kΩ

1 F

5µ

( ) ( )4cos5000 Vsv t t=

( )sv t

I V

+−

+−

1 k

2Ω 3000V I+

3000I

4 0sV = ∠ ( )21 2 k

5j− Ω ( )2 1 kj− Ω

(b)

( ) ( )( ) ( )( )4 3000

01 2 2 1 103103 1 2 1032 5

V V V I

jj

− ++ + =−−

( )4

1103

2

VI

−=

324 10 53.1 A=24 53.1 mAI − °= × ∠ ∠

( ) ( )24cos 5000 53.1 mAi t t °= +

Department of Electronic Engineering, NTUT25/41

( )i t ( )v t

6 −

• (a) i1(t) i2(t)

1. ω = 2 rad/s : (b)

(b)

+− 1I 2I

3 Ω 2 j Ω 1 Ω

1 j Ω

2 j− Ω1 Ω18 0sV = ∠

2.

( ) 1 24 2 18 0j I I °+ − = ∠

( )1 22 1 0I j I− + − =

2 2 0 AI °= ∠1 4.47 26.6 AI °= ∠ −

3.

( )2 2sin 2 Ai t t=

( ) ( )1 4.47sin 2 26.6 Ai t t °= −

Department of Electronic Engineering, NTUT26/41

+−

3 Ω

(a)

1 H 1 Ω

1 Ω

( ) ( )18sin 2 Vsv t t=

( )sv t ( )1i t

1H

21

F4

( )2i t

7 −

• (a)

1. (b) I i(t) I = I1 + I2

2. I1 I2 (c) (d)

3. (c)

+−

+−

5 Ω

(a)

4 Ω1 H( )i t

1F

20( )1sv t

( ) ( )1 20sin 2 Vsv t t= ( ) ( )2 10sin 2 Vsv t t=

( )2sv t

+−

+−

5 Ω 4 Ω2 j Ω

20 0∠

10 j− Ω10 0∠

I

(b)

+−

5 Ω 4 Ω2 j Ω

20 0∠

10 j− Ω

1I

(c)

+−

5 Ω 4 Ω2 j Ω

10 j− Ω10 0∠

2I

(d)

( ) ( )1

10 4 2 10 4 25 5 10

10 4 2 4 8

j j j jZ

j j j

− + − += + = + = Ω

− + + −

11

20 0 20 02 0 A

10I

Z

° °°∠ ∠= = = ∠

Department of Electronic Engineering, NTUT27/41

7 − ( )

3. (d)

:

4. I

( )2

10 54 2 4 2 4 2 8

5 10

jZ j j j

j

−= + + = + + − =

− +−

5 Ω 4 Ω2 j Ω

10 j− Ω10 0∠

2I

(d)

3I

( )3

10 0 50 A

8 4I

∠= = ∠

( )2 3

10 2 1 5153.4 A

5 10 2 2

j jI I

j

− − += − = = ∠−

( )1 2

2 12 0 1 0.5 1.12 26.6 A

2

jI I I j

− += + = ∠ + = + = ∠

( ) ( ) ( )1.12sin 2 26.6 Ai t t= +

Department of Electronic Engineering, NTUT28/41

•Zth

( ) Zth

: V Z Ioc th sc=

a

b

a

b

Zth

Eth Voc= +−

a

b

a

b

IN Isc= Zth

Department of Electronic Engineering, NTUT29/41

8 −

• (a) a-b

1. Voc

a

b

+−

4 Ω 10 j Ω

6 Ω

I

4 j− Ω

(a)

( )6 0 V∠

a

b

+−

4 Ω 10 j Ω

4 j− Ω

(b)

( )6 0 V∠

+

−

ocV

a

b

4 Ω 10 j Ω

4 j− Ω

(c)

thZ

46 0 3 3 4.24 45 V

4 4oc

jV j

j° °−= × ∠ = − = ∠ −

−

2. Zth

( )4 410 2 8 8.246 75.96

4 4th

jZ j j

j°−

= + = + Ω = ∠ Ω−

4.24 45 4.24 450.375 90 A

2 8 6 11.3 45I

j

° °°

°

∠ − ∠ −= = = ∠ −+ + ∠

3. a

b

+−

2 8 j+ Ω

6 Ω

I

4.24 45 V°∠ −

Department of Electronic Engineering, NTUT30/41

9 −

• (a) a-b I

1. Voc Zth

2. 6Ω

a

b

+−

4 Ω 10 j Ω

6 Ω

I

4 j− Ω

(a)

( )6 0 V∠

4.24 450.515 120.96 A

8.246 75.96oc

th

VI

Z

°°

°

∠ −= = = ∠ −∠

( )2 80.515 120.96 0.375 90 A

2 8 6

jI

j° °+= ∠ − = ∠ −

+ +

b

a

2 8 j+ Ω 6 Ω

I

0.515 120.96 A°∠ −

Department of Electronic Engineering, NTUT31/41

(AC Steady-State Power) (I)

• ( ) ( ) ( ) ( ) ( )1 1cos cosm mp t v t i t V t I tω φ ω φ= ⋅ = + × +

( ) ( ) ( )1 20 0cos cos

T T

m mt tW p t dt V t I t dtω φ ω φ

= == = + × +∫ ∫

( ) ( )1 2 1 2

0

1 1 1sin 2 cos cos

2 2 2

T

m m m m

t

V I t t V I Tω φ φ φ φ θω =

= − + + + − =

( )1 2

1 1cos cos cos cos cos

2 2 2 2m m

m m m m rms rms

V IWP V I V I V I S

Tφ φ θ θ θ θ= = − = = = =

( ) ( )1 2 1 20

1cos 2 cos

2

T

m mtV I t dtω φ φ φ φ

== + + + − ∫

(((( ))))

Peak RMS ( )

cosθ : Power Factor (PF)

( )1 2θ φ φ= −( )

S:

+

−v(t)

i(t)

Department of Electronic Engineering, NTUT32/41

(II)

V I ( )

(a)

( )( )

1 1

2 2

V

Arms

rms

V V V

I I I

φ φφ φ

= ∠ = ∠ = ∠ = ∠

1cos cos

2 m mP VI V Iθ θ= =

cosR

Zθ = ( ) 2cos

RP VI Z I I I R

Zθ

= = =

I+

−V

Z

+

−v(t)

i(t)

j

θ

(a)

Z R jX Z θ= + = ∠

Z

[ ]Re Z R=

[ ]Im Z X=θ Z

Department of Electronic Engineering, NTUT33/41

10

• (a)

(a)

+−

( )i t 10 Ω

0.5 H( )sv t

( ) ( )40sin 2 Vsv t t=

+

−

10 Ω

10 j Ω( )400 V

2sV = ∠

(b)

I

400 V

2V °= ∠

( )( )10 20 0.5 10 10Z R j L j jω= + = + = +

10 2 45 , 45θ° °= ∠ Ω =

( )40 2 02 45 A

10 2 45I

°°

°

∠= = ∠ −∠

( )40cos 2 cos45 40W

2rms rmsP V I θ ° = = =

Department of Electronic Engineering, NTUT34/41

(Complex Power)

• S = P + jQ S VA P WQ VAR

(a)

QS

θP

j

QS

θPj

(b)

cosP S θ=( ):

sinQ S θ=( ):

:( )cosθ:sinθ

( ) ( )rms rmsrms

V VVI I

Z Z Z

φ φ θ φ θθ

∠= = = ∠ − = ∠ −∠

0θ >

0θ <( ) ( )rms rmsI I Iφ θ θ φ∗ = ∠ − − = ∠ −

rms rmsS S V I VIθ θ ∗= ∠ = ∠ =

( )rms rms rms rmsVI V I V I Sφ θ φ θ θ∗ = ∠ ⋅ ∠ − = ∠ = ∠

ReP VI∗ = ImQ VI∗ = S VI∗=

Department of Electronic Engineering, NTUT35/41

R L C

• R θ = 0°

=

• ( )

θ +90° – 90°

( )

( )

cos0 1PF = =2

2 rmsrms rms rms

VP S V I I R

R= = = =

( )cos 90 0PF = ± =

j Lω 1j

Cω−

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R

Z

j

θ

−XC

(a)

90 0θ− < <

CZ R jX= − 0 90θ< <

LZ R jX= +

I

Vθ

(b)

RC RL

jXL

Z

R

θ

(c)

I

Vθ

(d)

cosθ θ RC RL( )

I V

I V

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11

•

(1).

(2).

(3).

(4).

(5).

(6).

(7).

10 15Z °= ∠ Ω 50 0V °= ∠

50 05 15 A

10 15

VI

Z

°°

°

∠= = = ∠ −∠

5 15 AI ∗ °= ∠

( )( )50 0 5 15 250 15S VI∗ ° ° °= = ∠ ∠ = ∠

( )250 VAS S= =

15θ °=

cos15 0.966PF °= =

( )cos 250cos15 241.5 WP S θ °= = =

( )sin 250sin15 64.7 VARQ S θ °= = =

Department of Electronic Engineering, NTUT38/41

• ZL Zth θL = –θth

ZL ()

•

Ia

b

+−

( Eth )

2 22 2

max 2 4th th

L L L th thth th

E EP I R I R R

R R

= = = =

( )L thZ Z=

L thθ θ= − L thZ Z∗=

thE

th th thZ Z θ= ∠

L L LZ Z θ= ∠

Department of Electronic Engineering, NTUT39/41

12

•W

( )( )500 0 2000 90/ / 485.07 14.04 470.58 117.68

500 2000th LZ R X jj

° °°

∠ ∠= = = ∠ = +

+

470.58 117.68L L CZ R jX j= − = − Ω

2 2

max

1207.65W

4 4 470.58th

th

EP

R= = =

×

a

b

RL= ?

X = ?XL= 2kΩ

R = 05. kΩ

RMS+−120 0thE = ∠

Department of Electronic Engineering, NTUT40/41

•

•

Department of Electronic Engineering, NTUT

j te ω

j te ω

jωj te ω

jω

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