射頻電子 - [第四章] 散射參數網路
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Transcript of 射頻電子 - [第四章] 散射參數網路
Department of Electronic EngineeringNational Taipei University of Technology
•••• (Power waves)
• (Traveling waves) −
Department of Electronic Engineering, NTUT2/25
(Traveling Waves)
( ) ( ) ( ) j x j xV x V x V x Ae Beβ β+ − −= + = +
( ) ( ) ( ) ( ) ( )0 0
V x V xI x I x I x
Z Z
+ −+ −= − = −
( ) ( )( )
V xx
V x
−
+Γ =
•
•
• (Normalized traveling waves)
( ) ( )0
V xa x
Z
+
=
( ) ( )0
V xb x
Z
−
=
( ) ( ) 2
2
0
V xa x
Z
+ =
( ) ( )( )
210log 10log
20log
aP a x
a x
=
=( ) ( ) ( ) ( ) ( )0
0
1 1
2 2b x v x i x V x Z I x
Z= − = −
( ) ( ) ( ) ( ) ( )0
0
1 1
2 2a x v x i x V x Z I x
Z= + = +
( ) ( ) ( ) ( )0
V xv x a x b x
Z= + =
( ) ( ) ( ) ( )0i x a x b x Z I x= − =
( ) ( ) ( )b x x a x= Γ
slide 16, 30
3/25 Department of Electronic Engineering, NTUT
Two-portNetwork
( )2 2a l
( )2 2b l
( )2 2a x
( )2 2b x
( )1 1a l
( )1 1b l
( )1 1a x
( )1 1b x1oZ 2oZ
Input port Output port
Port 1
1 1x = l
Port 22 2x = l
• Port 1 ( )
• Port 2 ( )
( )1 1a l ( )1 1b l1 1x = l
( )2 2a l ( )2 2b l2 2x = l
Incident wave Reflected wave
• (Scattering Matrix)
( ) ( ) ( )1 1 11 1 1 12 2 2b S a S a= +l l l
( ) ( ) ( )2 2 21 1 1 22 2 2b S a S a= +l l l
( )( )
( )( )
1 1 1 111 12
2 2 2 221 22
b aS S
b aS S
=
l l
l l
xx
4/25 Department of Electronic Engineering, NTUT
( )( ) ( )2 2
1 111
1 1 0a
bS
a=
=l
l
lInput reflection coefficient with output properly terminated
( )( ) ( )1 1
2 222
2 2 0a
bS
a=
=l
l
lOutput reflection coefficient with input properly terminated
Forward transmission coefficient with output properly terminated
( )( ) ( )1 1
1 112
2 2 0a
bS
a=
=l
l
lReverse transmission coefficient with output properly terminated
(measured with port 2 properly terminated)
(measured with port 2 properly terminated)
(measured with port 1 properly terminated)
(measured with port 1 properly terminated)
( )( ) ( )2 2
2 221
1 1 0a
bS
a=
=l
l
l
5/25 Department of Electronic Engineering, NTUT
( )( ) ( )2 2
1 111
1 1 0a
bS
a=
=l
l
l
• Return Loss (RL)
( )( ) ( )2 2
2 221
1 1 0a
bS
a=
=l
l
l
( )( )
21 12 1
11 21 1 1
b
a
b PS
a P= =
l
l( )21
11 111
10log 10 log 20 log (dB)b
a
PS S
P
= =
11Return Loss (RL) 10 log 20 log (dB)in
reft
PS
P
= = −
( , )
( )( )
22 22 2
21 21 1 1
b
a
b PS
a P= =
l
l( )22
21 211
10log 10 log 20 log (dB)b
a
PS S
P
= =
21Insertion Loss (IL) 10 log 20 log (dB)transmit
receive
PS
P
= = −
( , )• Insertion Loss (IL)
|S11| −12 dB12 dB
6/25 Department of Electronic Engineering, NTUT
S11
Two-portNetwork
( )2 2 0a =l
( )2 2b l
( )1 1a l
( )1 1b l
1oZ 2oZ
Port 1
1 1x = l
Port 2
2 2x = l
2 2oZ Z=+
−1E
1 1oZ Z=
( )( ) ( )2 2
1 111
1 1 0a
bS
a=
=l
l
lOUTZ
• Z2=Zo2 (i.e. Zo1=Zo2)50Ω
( )2 2 0a =l
( )( ) ( )2 2
1 111
1 1 0a
bS
a=
=l
l
l( ) ( ) ( )1 1 11 1 1 12 2 2b S a S a= +l l l
0
port 2 ( )2 2 0a =l
7/25 Department of Electronic Engineering, NTUT
•Zoi (i=1 ton) n port
[ ] [ ][ ]b S a=
n-portNetwork
1oZ
Port 1Port 1'
1TZ
( )1 1a l
( )1 1b l
2oZ
Port 2Port 2'
( )2 2a l
( )2 2b l
onZ
Port nPort n'
( )n na l
( )n nb l
[ ]
11 12 1
21 22 2
1 2
n
n
n n nn
S S S
S S S
S
S S S
⋅ ⋅ ⋅ ⋅ = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
8/25 Department of Electronic Engineering, NTUT
•
•
(i=1 for port 1 and i=2 for port 2)
( )0iP+ ( )0iP−
+
1oZ 2oZ
Port 1
1 1x = l
Port 2
2 2x = l
Port 1'
1 0x =
( )1 1I x
Port 2'
2 0x =
2l1l
−
( )1 1V x
( )2 2I x
+
−
( )2 2V x( )0iP+
( )0iP−
( )0iP+
( )0iP−
11 12
21 22
S S
S S
( )( )
( )( )
1 1 1 111 12
2 2 2 221 22
b aS S
b aS S
=
l l
l l
( )0iP+ ( )0iP−
( )a x
( )b x
9/25 Department of Electronic Engineering, NTUT
( ) ( ) 210 0
2i iP a+ =
( ) ( ) ( ) ( ) ( ) ( )2
22
,
01 1 10 Re 0 0 0 0
2 2 2i
i i i i i rmsoi
VP V I b b
Z
−∗− − − = ⋅ = = =
• ith port (x1=0, x2=0)
•
( ) ( )0i i iP P+ += l
( ) ( )0i i iP P− −= l
( ) ( )2 21 10
2 2i i ia a x=
( ) ( )2 21 10
2 2i i ib b x=
( ) ( ) 210 0
2i iP b− =
• ith port (x1=0, x2=0)
( ) ( ) ( ) ( ) ( ) ( )2
22
,
01 1 10 Re 0 0 0 0
2 2 2i
i i i i i rmsoi
VP V I a a
Z
+∗+ + + = ⋅ = = =
( ) ( )0
V xa x
Z
+
=
( ) ( )0
V xb x
Z
−
=
10/25 Department of Electronic Engineering, NTUT
( ) ( )2 2 20 0oV Z I= −
( ) ( ) ( ) ( ) ( )2 2 2 2 2 2 2 2
2 2
1 10 0 0 0 0 0
2 2o o o
o o
a V Z I Z I Z IZ Z
= + = − + =
Two-portNetwork
+
1oZPort 1
1 1x = l
Port 2
2 2x = l
Port 1'
1 0x =
( )1 0I
Port 2'
2 0x =
−
( )1 0V
( )2 0I
+
−( )2 2V l
2oZ
( )1 1I l ( )2 2I l
( )1 1V l
+
−
( )2 2a x
( )2 2b x
( )1 1a x
( )1 1b x
+
−
( )2 0V
+
−1E
1 1oZ Z=
2 2oZ Z=
• x2=0
( ) ( )1 1 1 10 0oV E Z I= −
( ) ( ) ( ) 11 1 1 1
1 1
10 0 0
2 2o
o o
Ea V Z I
Z Z= + = ( )
22 1
11
04 o
Ea
Z=• x1=0
Vpp
matched
• E1 (available power) x1=0 (Z1=Zo1 )
( ) ( )2
2 11 1
1
10 0
2 8AVSo
EP P a
Z+= = = ( ) ( )2 2
1 1 1
1 10
2 2a a= l
matched
11/25 Department of Electronic Engineering, NTUT
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )2 2 21 1 1 1 1 1 21 1 1 1 1 1 1 1 1 1
1 1
0 0 0 01 10 0 0 0 0 0 0
2 8 8o o
o o oo o
V Z I V Z Ia V Z I V Z V I Z I
Z Z
∗
∗ ∗+ + = = + + +
( ) ( ) ( ) ( ) ( ) ( ) ( )2 2 221 1 1 1 1 1 1 1 1 1
1
1 10 0 0 0 0 0 0
2 8 o o oo
b V Z I V Z I V Z IZ
∗ ∗ = − − +
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2
1 1 1 1 1 1 1 1 1 1 1
1 1 1 10 0 0 0 0 0 0 0 0 Re 0 0
2 2 4 2P P P a b I V I V I V+ − ∗ ∗ ∗ = − = − = + =
• Z1 Zo1
• port 1' ( port 1 )
( ) ( )2
1 1
10 0
2 AVSb P P= − ( ) ( )2
1 1 1 1
1
2 AVSb P P= −l l• port 1 ( port 1')
( ) ( ) ( ) 2
1 1 1 1
10 0
2AVSP P P b= = −l
• ZT1=Zo1 0 ZT1≠Zo1
port 1
( )( )
( )
( )
2 2
2
2 1 1 1 111 2
1 1 0
AVS
AVSa
b P PS
Pa=
−= =
l
l l
l
( ) ( ) ( )2
1 1 1 110 1AVSP P P S= = −lor
12/25 Department of Electronic Engineering, NTUT
(Power Waves) (I)
•
• (Z0)Rs
s sV E Z I= −
LZ
+
−sE
sZV
I
+
−
sourceimpedance
loadimpedance
Department of Electronic Engineering, NTUT
L s
L s
Z Z
Z Z
∗−Γ =+
• ( )*L sZ Z= Γ = 0
slide 46
13/25
(Power Waves) (II)
( )1
2p s
s
a V Z IR
= + ( )1
2p s
s
b V Z IR
∗= −
LZ
+
−sE
sZ pa
pb
V
I
+
−
sp s L s
p s L ss
VZb V Z I Z ZI
Va V Z I Z ZZI
∗∗ ∗−− −Γ = = = =
+ ++p pa bΓ =
• (Normalized power waves)
0pb =L sZ Z ∗=
• (Available power)
( )1
2p s
s
a V Z IR
= + s sV E Z I= −
( )1
2 2s
p s s s
s s
Ea E Z I Z I
R R= − + =
22
4s
ps
Ea
R=
22 2
,
1
2 8s
AVS p p rmss
EP a a
R= = =
• ( )
2
21 1Re Re
2 2s
L L Ls L
EP I Z Z
Z Z= =
+
2
,max
1
8s
L AVSs
EP P
R= =
14/25 Department of Electronic Engineering, NTUT
( )( ) ( )( ) 2 2 *1 1 1 1 1Re
2 2 8 8 2L p p s s s ss s
P a b V Z I V Z I V Z I V Z I V IR R
∗∗ ∗ ∗= − = + + − − − =
2 2 21 1 1
2 2 2L p p AVS pP a b P b= − = −
21
2 p AVS Lb P P= −
= ( – )
•
= ( – )
15/25 Department of Electronic Engineering, NTUT
− (Traveling Waves)
0
0
ss
s
Z Z
Z Z
−Γ =+
0
0
LL
L
Z Z
Z Z
−Γ =+
1 11 1 12 2b S a S a= +
2 21 1 22 2b S a S a= +
Transistor[S]
2a
2b
1a
1b
Port 1 Port 2
+
−sE
sZ
outΓ
LZ
inΓ
sΓ LΓ
•[S] Z0
sΓ LΓ
?
+
−sE
sZ
sΓ
LZ
LΓ
Transistor[S]
1b
1a 2a
2b
16/25 Department of Electronic Engineering, NTUT
1
1in
b
aΓ =
2 2La b= Γ
2 21 1 22 2Lb S a S b= + Γ 21 12
221 L
S ab
S=
− Γ
• inΓ[ ]SLΓ
1 12 2111
1 221L
inL
b S SS
a S
ΓΓ = = +− Γ
12 211 11 1 12 2 11 1 1
221L
LL
S Sb S a S b S a a
S
Γ= + Γ = +− Γ
a1 b1
1 11 1 12 2b S a S a= + a1 b1 = a2
a2 = b2
Transistor[S]
2a
2b
1a
1b+
−sE
sZ
outΓ
LZ
inΓ
sΓ LΓ
1 11 1 12 2b S a S a= +2 21 1 22 2b S a S a= +
inΓ
17/25 Department of Electronic Engineering, NTUT
2
2 0s
out
E
b
a =
Γ =
1 1sa b= Γ
1 11 1 12 2sb S b S a= Γ + 12 21
111 s
S ab
S=
− Γ12 21
2 21 1 22 2 2 22 2111
ss
s
S Sb S b S a a S a
S
Γ= Γ + = +− Γ
12 21222
2 1101
s
sout
sE
S SbS
a S=
ΓΓ = = +− Γ
• outΓ[ ]S
sΓ
Transistor[S]
2a
2b
1a
1b+
−sE
sZ
outΓ
LZ
inΓ
sΓ LΓ
1 11 1 12 2b S a S a= +2 21 1 22 2b S a S a= +
outΓ
outΓ inΓ2 21 1 22 2b S a S a= +and
18/25 Department of Electronic Engineering, NTUT
+
−sE
sZ
sΓ
1a
1b
•
inΓ
+
−1V
1I
• 1 1s sa a b= + Γ
inΓ outΓ
Pin
1 1inb a= Γ
1 1 1s s s s ina a b a a= + Γ = + Γ Γ 1 1s
s in
aa =
− Γ Γ
( )2
2 2 2 2 2
1 1 1 2
11 1 1 11
2 2 2 2 1in
in in s
s in
P a b a a− Γ
= − = − Γ =− Γ Γ
•2 2
2 2 2
2 2 22 2
1 11 1 1 1
2 2 2 11 1in s
s sAVS in s s s
ss s
P P a a a∗
∗
Γ =Γ
− Γ − Γ= = = =
− Γ− Γ − Γ
( )( )2 222
2 2
1 111
2 1 1
s ininin s AVS AVS s
s in s in
P a P P M− Γ − Γ− Γ
= = =− Γ Γ − Γ Γ
• Ms (source mismatch factor) (mismatch loss)
inΓ s os
o so
E Za
Z ZZ=
+
19/25 Department of Electronic Engineering, NTUT
LZ
LΓ
outΓ
+
−thE
outZ 2a
2b
+
−LV
LI
LZ
LΓ
outΓ
( )2 2 2 2
2 2 2
1 1 11
2 2 2L LP b a b= − = − Γ
• ZL
22
2
11
2 1L
L th
out L
P b− Γ
=− Γ Γ
• ( source)
2
2
1 1
2 1L outAVN L th
out
P P b∗Γ =Γ= =
− Γ
( )( )2 2
2
1 1
1
L out
L AVN AVN L
out L
P P P M− Γ − Γ
= =− Γ Γ
• ML (load mismatch factor) (mismatch loss)
( source)outΓ
2 2La b= Γ
20/25 Department of Electronic Engineering, NTUT
Transistor[S]+
−sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interfaceML
• (power gain) Lp
in
PG
P=
• (transducer power gain) LT p s
AVS
PG G M
P= =
• (available power gain) AVN TA
AVS L
P GG
P M= =
p TG G>
A TG G>
• p T AG G G= =
21/25 Department of Electronic Engineering, NTUT
Gp (Operating Power Gain)
( )( )
2 2
2
2 2
1
11
21
12
LL
pin
in
bPG
P a
− Γ= =
− Γ
21 12
221 L
S ab
S=
− Γ
22
212 2
22
11
1 1L
p
in L
G SS
− Γ=
− Γ − Γ
• The Operating Power GainGp
where
Transistor[S]+
−sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interfaceML
slide 17
22/25 Department of Electronic Engineering, NTUT
GT (Transducer Power Gain)
• The Transducer Power GainGT
in inL LT p p s
AVS in AVS AVS
P PP PG G G M
P P P P= = = =
2 2 2 22 2
21 212 2 2 2
22 11
1 1 1 1
1 1 1 1s L s L
T
s in L s out L
G S SS S
− Γ − Γ − Γ − Γ= =
− Γ Γ − Γ − Γ − Γ Γ
( )( )2 2
2
1 1
1
s in
s
s in
M− Γ − Γ
=− Γ Γ
where
Transistor[S]+
−sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interfaceML
slide 19
23/25 Department of Electronic Engineering, NTUT
GA (Available Power Gain)
• The Available Power GainGA
AVN AVN AVNL TA T
AVS AVS L L L
P P PP GG G
P P P P M= = = =
22
212 2
11
1 1
1 1s
A
s out
G SS
− Γ=
− Γ − Γ
Transistor[S]+
−sE
sZ
LZ
PAVNPAVS PLPin
Ms
interface interfaceML
( )( )2 2
2
1 1
1
L out
L
out L
M− Γ − Γ
=− Γ Γ
where
slide 20
24/25 Department of Electronic Engineering, NTUT
•
(1) ( )
(2) (power waves, [Sp])
(3) (traveling waves, [S])
Re 2L L LP V I ∗=
• ( )
22 2
,
1
2 8s
AVS p p rmss
EP a a
R= = =
2 2 21 1 1
2 2 2L p p AVS pP a b P b= − = −
•
L p inP G P= L T AVSP G P=
• (defined with traveling waves, circuitries areseparately measured in aZo system):
25/25 Department of Electronic Engineering, NTUT