S-PARAMETERS Scattering Matrix
1
i
V V2i
01
Z
O
02
Z
1
r
Input T.L L1=0 Onput T.L L2=0
1 1
V =V +V V2=V V2i + 2r
1 01
a
Z
=
2 01
a
Z
=
2 01
b
Z
=
a1a2
11 12
b =S a +S a
21 22
b =S a +S a
2
I
1
I I1
Trang 21 11 12 1
=
π
Trang 3L1 L2
t1’ t1 t2 t2’
2 1
S =S e− β S22'=S e22 −j2 βL2
↑ ↑
t1’,t2’ t1,t2
.( 1 2)
S =S e− β + S12'=S e12 −j .( 1 2) β L L+
Ma tran
Z
Z(in)=Z+1 1
(1)
Z
Γ
Z(in)=Z+1 1
t1 t2
( ) 0
( ) 0
in
in
−
Γ =
+
=
( ) ( )
1 1
in in
Z Z
− +
=
1 1
1 1
z z
+ − + +
z
z+
=
11
S
Trang 411 22
z (Tính đối xứng) =
z+2
S =S
1
I I2
1
V
Z
2
V
t1 t2
V1 = a1 + b1 V2 = a2 + b2
Tổng
I1 = a1 - b1 I2 = a2 - b2
∴ = −
@ Port 2 a2=0
b a b
2 0
≡S21
Biết
1
z = y
Trang 5zin
1 = Zin
y+1
0
0
1 -1
1
y+1
Γ
1+ y+1 2 + y
b1 b2
a2 + b2 = a1+ b1
∴
v1v2
y
Tải phù hợp trên Port a2 0∴ =
b2 a1 b1
b1 a1 a1
2 + y 2 + y 2 + y 2 + y
S21
a1 a2
S11 S22 b1b2
S12
Trang 62 1
Taùi Port 1 coõng suaỏt vaứo a
2 1
coõng suaỏt ra b
coõng suaỏt vaứo thửùc a - b
∴
Mạch đối ngẫu
S =S
(
S =S
)
or or
b = a
laứ ma traọn ủụn
S
⇒
= ∂ =
∑ *
i.s i.r
Porti
≠
=0 khi s r
2port i=1,2 s,r=1&2
11 11 21 21
S = r= S S +S S =
2
21 1 11
11 11 21 21
S= r= S S +S S =
Trang 712 1 22
12 21 22 11
11 11 21 21
S= r= S S +S S =
11 j 12 j 21 j 22 j 0
e
S e ϑ × S e− ϑ + S e ϑ ×S e− ϑ =
12 21 11 22
.( ) ( )
e ϑ ϑ + e ϑ ϑ +
12 21(đảo)
ϑ =ϑ
12 11 22
(2 ) ( )
e ϑ = −e ϑ ϑ +
12 11 22
12 11 22
π
11, 11& 22
S ϑ ϑ
Trang 80
L
L
L
Z Z
Z Z
−
Γ =
a b
L
a b
1 11 1 12 2 11 1 12 .2 L
b =S a S a+ =S a S b+ Γ
2 21 1 22 2 21 1 22 .2 L
b =S a S a+ =S a S b+ Γ
1
11
1
S
a
=
;
2 21
1
S
a
=
2 21 1 22 2
21
S
Γ
chuyển vế
2 22 2 21 1
Γ
21'(1 22 )L 21
S −S Γ =S 21 21
22
'
S S
S
21
22
L
L
S
S
(Chia 2 vế cho
1
a
)
21 12
11 11
22
'
S S
S S
S
Γ
Trang 912 21
22 22
11
'
S S
S
Γ
12
12
11
'
S
S
S
=
11 11
S InputV S W R
S
+
=
−
(dB)=
=
2 1
10 2 10 11 1
b = −
1
in
o
+ + Γ
Trang 102 2 2
b =ρB VB+ρ ρA B +ρA ρB Vo+
2
B Vo A B A B
1
B Vo
b
A B
ρ
ρ ρ
=
−
1 1
b B a
ρ = ∴ =a1 ρb1B
1
Vo
a
A B
ρ ρ
∴ =
−