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Z g PowerPoint PPT Presentation


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V ( z ), I ( z ). z. l – z. Z g. สายส่งที่มีค่าอิมพีแดนซ์ ประจำตัว Z 0 กับ . V L. Z L. V S. V g. l.  z = l. z = 0. ระบบสายส่ง. Z in ( z = l ). Z 0 ( z = 0). V ( z ) = V 0 + e +  z + V 0 – e – z , I ( z ) = [ V 0 + e +  z – V 0 – e – z ]/ Z 0.

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Z g

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Z g

V(z),I(z)

z

l z

Zg

Z0

VL

ZL

VS

Vg

l

z = l

z = 0

Zin(z = l)

Z0(z = 0)

V(z) = V0+e+ z + V0e z ,I(z) = [V0+ e+ z V0e z]/Z0

V(z) = VLcosh( z) + (ILZ0) sinh( z), I(z)= (VL/Z0) sinh( z) + ILcosh( z)

1


Z g

A

Z0

ZL

0

Zin

A

A

Z0

ZL

Zin

A

2


Z g

Z0

ZL

Zin

n/2

Z0

ZL

Zin

(2n-1)/4

n/2

Zin(z = n/2)= ZL

(2n1)/4

(Reflection coefficients)

(ZL= jXL)

V(z) = V0+e+ z + VV0+e z ,I(z) = [V0+ e+ z VV0+e z]/Z0

3


Z g

7.6 (Standing Wave)

|V(z)| = [V(z)V(z)*]1/2

|V(z)| = |V0+| [1 + |V|2 + 2|V| cos(2 z )]1/2

|I(z)| = [I(z)I(z)*]1/2

|I(z)| = |I0+|[1 + |V|2 2|V| cos(2 z )]1/2

  • |V(z)|() |I(z)|

4


Z g

()ZL=Z0 |V| = 0

()ZL = 0 |V| = 1

()ZL= |V| = +1

5


Z g

) |V(z)|maxlmax

2 z = 2 nn = 0, 1, 2, 3,

) |V(z)|minlmin

2 z = (2n+1)n =1, 0, 1, 2, 3,

|V(z)| = |V0+| [1 + |V|2 + 2|V| cos(2 z )]1/2

6


Z g

VSWR(Voltage Standing Wave Ratio)

VSWR

Loss(load)

Loss(dB) = 10log[1 |V|2]

7


Z g

8

Smith Chart and Reflection Diagrams

P.H.Smith .. 1939

(Reflection coefficient, V)

V = || exp(j) = r + ji

r = Re[] = || cos

i= Im[] = || sin

8


Z g

i

D

A = 1 + 0j = 10o

B = 1/3 + j/3 = 2/330o

C = 0 + j /3 = 1/390o

D = 1/2 +j3/2 = 1120o

E = 1/3 + j/3 = 2/3150o

F= 1/2 j3/2 = 1240o

G = j2/3 = 2/3270o

H= 3/2 j/2 = 1/3270o

C

B

E

A

r

H

G

F

9


Z g

10


Z g

zL = ZL/ Z0

(Normalized Load Impedance)

zL

zL = rL + jxL

rLxL

11


Z g

12


Z g

) (Fix Resistance Circle)

i

rL = 0

r

rL = 0.25

rL=

rL= 4

rL= 1

rL= 0.5

rL = 0.5

rL= 2

rL= 0

rL= 0.25

rL= 10

rL = 1

rL = 2

rL = 4

rL = 10

rL =

r =

13


Z g

) (Fix Reactance Circle)

i

xL = 0

xL = +1

xL = +0.75

xL = +1.5

xL = +0.5

xL = +2

xL = 0.3

xL = +4

xL = 0.5

xL = +0.3

xL= +10

xL = 0.75

xL =

xL = 0

r

1

xL= 10

xL = 1

xL = 0.3

xL = 4

xL = 1.5

xL = 0.5

xL = 2

xL = 2

xL = 0.75

xL = 1.5

xL = 1

xL = 4

xL= 10

xL =

(Fix Reactance Circle)

14


Z g

1.

0.5

2.

0.25

0.33

1.

0

5.

0

-0.25

-0.5

-2.

-1.

15


Z g

ZL = 100 j50Z0 = 50

zL= ZL/ Z0= 2 j

zL

rL = 2

xL = 1A

OA/OB 0.45OA26.6o

= 0.4526.6


Z g

zL = 2 j

ANGLE OF REFLECTION COEFICIENT IN DEGREES

= 26.6o

O

A

C = 26.6o

B

Reflection Coefficient

in term of V(E) or I

(RFL. COEFF., V(E) or I)

= 0.45

= 0.4526.6

D = 0.45

17


Z g

0.55

Z0100

0.8 j1.15

67o

0.55

18


Z g

(Line impedance)

ZLz = 0

z = l

V(l) = |V| e j( 2l)


Z g

V(l) = |V| e j( 2 l)

l

l 2 l4 l/

l/2

WTG

WTL

(Wavelengths Toward Generator)

(Wavelengths Toward Load)


Z g

50

ZL = 100 j50 0.1

zL = ZL /Z0 = 2 jA

OA

O AWTG = 0.287

WTG=0.2870.1

WTG =0.387

F F

0.6 j0.66Z0 (de-normalized)

Z(0.1) = Z0 z(0.1) = (50)(0.6 j0.66)

= 30 j 33


Z g

zL = 2 j

VSWR = 2.6

rL(0.1)= 0.6

O

0.1:

z(0.1) =

A

WTG = 0.287

0.6 j0.66

xL(0.1)= 0.66

+ 0.1

WTG =0.387

22


Z g

(VSWR)

= z( 2l = 2n) = rL + j0

VSWR rL

2nr

z( = 2n)rLVSWR

VSWR

VSWR

VSWR = 2.6


Z g

lminlmax

|V(z)|= |V0+| [1 + |V |2 + 2|V | cos(2l )]1/2

cos argumentg(2l ) = 0

(2l ) =

rL xL= 0r

r


Z g

zL = 2 jA

WTG 0.287VSWR

rxL = 0WTG0/4

lmax= (0.25 + 0.5) 0.287 = 0.463

lmin = 0.5 0.287= 0.213


Z g

/8

lmax= 0.5 0.287 + 0.25

zL = 2 j

0,

/2

VSWR = 2.6

O

/4

A

Toward generator

F

C = 26.6o

E = WTG 0.287

+ 0.1

lmin = 0.50.287

WTG = 0.387

3/8


Z g

zin(l )

l = /4


Z g

y = g + jb = Y / Y0 = Z0 Y = Z0( G + jB )

GB

g = Z0G b = Z0BY = y/Z0

Z0 = 50

ZL =25 + j50

V

VSWR

3.3


Z g

zL

WTG = 0.135

83o

1.7

A

WTG = 0.13583o

|V| = 0.62

V = 0.62 e j83 = 0.6283o

lmax = 0.25 0.135

A

E

A

rB

4.26

VSWR = 4.26

C

B

0.28

1.15

4.26

D

0.4

WTG 0.25B

lmax = 0.25 0.135 = 0.115

3.3

lmin = 0.5 0.135

0.62


Z g

WTG = 0.5C

lmin= 0.5 0.135 = 0.365

3.3A3.3

3.3 3= 0.3WTG = 0.435

WTGD

zin(3.3) = 0.28 j0.4

3.3

zin(3.3) = 50(0.28 j0.4) = 14 j20


Z g

3.3D(/4)E

yin(3.3) = 1.15 + j1.7

3.3

Yin(3.3) = yin(3.3)Y0 = yin(3.3)/Z0

= (1.15+j1.7)/50

= 0.023 + j0.034 S


Z g

50 ZLVSWR = 35 cm 20 cmZL

20 cm

= 40 cm

5 cm

5 cm/40 cm = 0.125

(lmaxlmin/4, /2)


Z g

OAVSWR = 3

WTG 0.25A0.125

A0.125B

B

VSWR C

zL= 0.6 + j0.8

ZL = 50(0.6 + j0.8)

= 30 + j40

B

C

O

A


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