Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Power Dividers and Directional Couplers
S. R. [email protected]
Department of Electrical & Electronics EngineeringBITS Pilani, Hyderbad Campus
May 7, 2015
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Outline
1 Power Dividers and Couplers
2 Three-Port Networks
3 Four-Port Networks
4 A Few Other Power Dividers
5 Problems
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Outline
1 Power Dividers and Couplers
2 Three-Port Networks
3 Four-Port Networks
4 A Few Other Power Dividers
5 Problems
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Power Dividers and Combiners
DividerP1
P1 = P2 + P3P2
P3P3=(1-αP1)
P2 = αP1
Combiner
Both the above shown devices are loss-less. Do you know why? Do they have to beloss-less always?
What happens if the above devices are reciprocal?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Power Dividers and Combiners
DividerP1
P1 = P2 + P3P2
P3P3=(1-αP1)
P2 = αP1
Combiner
Both the above shown devices are loss-less. Do you know why? Do they have to beloss-less always?
What happens if the above devices are reciprocal?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Power Dividers and Combiners
DividerP1
P1 = P2 + P3P2
P3P3=(1-αP1)
P2 = αP1
Combiner
Both the above shown devices are loss-less. Do you know why? Do they have to beloss-less always?
What happens if the above devices are reciprocal?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
A Few Types of Dividers or Combiners
4
Z0
2Z0
2Z0
Z0
λ
Z0
Z0 Z0
Z0/ 2
Z0/ 2
Z0
Z0 Z0
12
3
12
3
Now, let’s discuss the differences between the above shown power dividers/couplers ..
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
A Few Types of Dividers or Combiners
4
Z0
2Z0
2Z0
Z0
λ
Z0
Z0 Z0
Z0/ 2
Z0/ 2
Z0
Z0 Z0
12
3
12
3
Now, let’s discuss the differences between the above shown power dividers/couplers ..
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
3-port Networks
If all ports are matched, then Sii = 0, and if the network is reciprocal, [S] reduces to
[S] =
0 S12 S13S12 0 S23S13 S23 0
.
If the network is also loss-less,
|S12|2 + |S13|2 = 1
|S12|2 + |S23|2 = 1
|S13|2 + |S23|2 = 1
S∗13S23 = 0
S∗23S12 = 0
S∗12S13 = 0.
All the above equations can’t be satisfied simultaneously. So, three-port networks can-not be simultaneously loss-less, reciprocal, and matched at all ports. 4-port networksdo not have such kind of restriction.
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Let’s Revisit the Previous Slide ...
4
Z0
2Z0
2Z0
Z0
λ
Z0
Z0 Z0
Z0/ 2
Z0/ 2
Z0
Z0 Z0
12
3
12
3
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
4-port Networks
The scattering matrix of a reciprocal four-port network matched at all ports has thefollowing form:
[S] =
0 S12 S13 S14
S12 0 S23 S24S13 S23 0 S34S14 S24 S34 0
If the network is loss-less too, then, it can be shown that
S∗13S23 + S∗14S24 = 0
S∗14S13 + S∗24S23 = 0
S∗12S23 + S∗14S34 = 0
S∗14S12 + S∗34S23 = 0
S∗12S24 + S∗13S34 = 0
S∗12S13 + S∗24S34 = 0
|S12|2 + |S13|2 + |S14|2 = 1
|S12|2 + |S23|2 + |S24|2 = 1
|S13|2 + |S23|2 + |S34|2 = 1
|S14|2 + |S24|2 + |S34|2 = 1
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
4-port Networks ... Cont’d
{S∗24(S∗13S23 + S∗14S24
)= 0
S∗13 (S∗14S13 + S∗24S23) = 0
=⇒ S∗14
(|S13|2 − |S24|2
)= 0{
S12 (S∗12S23 + S∗14S34) = 0S34(S∗14S12 + S∗34S23
)= 0
=⇒ S23
(|S12|2 − |S34|2
)= 0
If S14 = 0 and S23 = 0,
|S12|2 + |S13|2 = 1
|S12|2 + |S24|2 = 1
|S13|2 + |S34|2 = 1
|S24|2 + |S34|2 = 1,
which imply that |S13| = |S24| and |S12| = |S34|.
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Directional Couplers
1 2
4 3
Input
Isolated
Through
Coupled
Coupling = C = 10 logP1
P3
Directivity = D = 10 logP3
P4
Isolation = I = 10 logP1
P4
Insertion loss = L = 10 logP1
P2
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Directional Couplers
1 2
4 3
Input
Isolated
Through
Coupled
Coupling = C = 10 logP1
P3
Directivity = D = 10 logP3
P4
Isolation = I = 10 logP1
P4
Insertion loss = L = 10 logP1
P2
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Outline
1 Power Dividers and Couplers
2 Three-Port Networks
3 Four-Port Networks
4 A Few Other Power Dividers
5 Problems
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
T-Junction Power Dividers
T-Junction Power Dividers
The above shown power dividers ... Are they lossy or loss-less?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
T-Junction Power Dividers
T-Junction Power Dividers
The above shown power dividers ... Are they lossy or loss-less?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
T-Junction Power Dividers
Loss-less T-Junction Power Dividers ... EquivalentCircuit
Yin
jBV0Z0
Z1
Z2
+
–
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
T-Junction Power Dividers
Lossy T-Junction Power Divider
Zin
Port 1
Port 3
Port 2
Z0/3
V1Z0
Z0
Z0
P2
P3
P1
+
–V Z+
–
Z0/3
Z0/3
V 2+
–
V3
+
–
Z =4Z0
3
V = V12Z0/3
Z0/3 + 2Z0/3=
23
V1
V2 = V3 = VZ0
Z0 + Z0/3=
34
V =V1
2
So, it is a 6 dB power divider ... What happens to the rest of the power? And what isthe corresponding scattering matrix [S]?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
T-Junction Power Dividers
Lossy T-Junction Power Divider
Zin
Port 1
Port 3
Port 2
Z0/3
V1Z0
Z0
Z0
P2
P3
P1
+
–V Z+
–
Z0/3
Z0/3
V 2+
–
V3
+
–
Z =4Z0
3
V = V12Z0/3
Z0/3 + 2Z0/3=
23
V1
V2 = V3 = VZ0
Z0 + Z0/3=
34
V =V1
2
So, it is a 6 dB power divider ... What happens to the rest of the power? And what isthe corresponding scattering matrix [S]?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
T-Junction Power Dividers
Lossy T-Junction Power Divider
Zin
Port 1
Port 3
Port 2
Z0/3
V1Z0
Z0
Z0
P2
P3
P1
+
–V Z+
–
Z0/3
Z0/3
V 2+
–
V3
+
–
Z =4Z0
3
V = V12Z0/3
Z0/3 + 2Z0/3=
23
V1
V2 = V3 = VZ0
Z0 + Z0/3=
34
V =V1
2
So, it is a 6 dB power divider ... What happens to the rest of the power? And what isthe corresponding scattering matrix [S]?
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider
4
Z0
2Z0
2Z0
Z0
λZ0
Z0
2Z0
Z0
2Z 0
2Z0
λ/4
λ/4
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider ... Exploiting Symmetry
4
Z02Z0
2Z0
Z0
λPEC/PMC
2Z 0
Z0
2Z0
Z0
2Z 0
2Z0
λ/4
λ/4
2Z 0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider ... Even Mode Analysis
2Z 0
Z0
2Z0
Z0
2Z 0
2Z0
λ/4
λ/4
2Z 0
2Z 0
Z0
2Z 0
λ/4 V0
+
V1
+e
V0
+
V0
+
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider ... Even Mode Analysis
Zein =
(√2Z0
)2
2Z0= Z0
Ve1 = −j
√2V0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider ... Odd Mode Analysis
2Z 0
Z0
2Z0
Z0
2Z 0
2Z0
λ/4
λ/4
2Z 0
2Z 0
Z0
Z0
2Z 0
λ/4V0
+
-V0
+
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider ... Odd Mode Analysis
2Z 0
Z0
2Z0
Z0
2Z 0
2Z0
λ/4
λ/4
2Z 0
2Z 0
Z0Z0
2Z 0
λ/4
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Power Divider ... Odd Mode Analysis
Zoin = Z0
Vo1 = 0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
Combining Even & Odd Mode Analyses ...
Z 0
Z0
2Z0
Z0
2Z 0
2Z0
λ/4
λ/4 V0 +V0
+
V0 -V0
+
-j√2V0
+
S22 = S33 = 0
S12 = S21 = S31 = S13 =−j√
2V0
2V0=−j√
2S23 = S32 = 0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
What About S11?
/4
/41
1
1
Port 3
Port 2
2
Zin
2
1
1
1
Port 3
Port 2
2
Zin
2
2
Port 1
Port 1
S11 = 0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
What About S11?
1
1
1
Port 3
Port 2
2
Zin
2
1
1
1
Port 3
Port 2
2
Zin
2
2
Port 1
Port 1
λ/4
λ/4
S11 = 0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
What About S11?
1
1
1
Port 3
Port 2
2
Zin
2
1
1
1
Port 3
Port 2
2
Zin
2
2
Port 1
Port 1
λ/4
λ/4
S11 = 0
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
So, S Paramters of a Wilkinson Power Divider are ...
0.5 f0 f0 1.5 f0–40
–30
–20dB
–10
0
|Sij|
|S12||S23|
|S11|
4
Z0
2Z0
2Z0
Z0
λ
13
2
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
The Wilkinson Unequal Power Divider ***
1
2
3
Z0Z03
Z02
R2 = Z0K
R3 = Z0/K
R
P3
P2= K2
Z03 = Z0
√1 + K2
K3
Z02 = Z0
√K (1 + K2)
R = Z0
(K +
1K
)
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
The Wilkinson Power Divider
N−way, Equal-split Wilkinson Power Divider ***
Z0 N
Z0 N
Z0 NZ0
Z0
Z0
Z0
Z0Z0
Z0
Z0
Z0
Z0 N
.
.
.
λ/4
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Outline
1 Power Dividers and Couplers
2 Three-Port Networks
3 Four-Port Networks
4 A Few Other Power Dividers
5 Problems
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
90◦ (Quadrature) Hybrid Coupler
Z0
Z0 Z0
Z0/ 2
Z0/ 2
Z0
Z0 Z0
1
4
(Input)
(Isolated)
(Output)
(Output)
2
3
4λ
4λ
[S] =−1√
2
0 j 1 0j 0 0 11 0 0 j0 1 j 0
................
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
90◦ (Quadrature) Hybrid Coupler
Z0
Z0 Z0
Z0/ 2
Z0/ 2
Z0
Z0 Z0
1
4
(Input)
(Isolated)
(Output)
(Output)
2
3
4λ
4λ
[S] =−1√
2
0 j 1 0j 0 0 11 0 0 j0 1 j 0
................
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
Quadrature Hybrid Coupler - Normalized Form
4 3
1 2A1 = 1
B3B4
B1 B2
1
1 1
1
11 1
1
1
1/ 2
1/ 2
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
Even Mode Analysis
1 2
4 3
+1/2
+1/21 1
1
1 1 1
11
1/ 2
1/ 2
Line of symmetryI = 0V = max
+1/2
+1/2
Te
1 1
1
1
1
1
1
1
1/ 2
1/ 2
Open-circuited stubs(2 separate 2-ports)
Γe
[A BC D
]e=
[1 0j 1
] [0 j/
√2
j/√
2 0
] [1 0j 1
]=
1√2
[−1 j
j −1
]
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
Even Mode Analysis ... Cont’d
Γe =A + B− C−DA + B + C + D
=−1 + j− j + 1−1 + j + j− 1
×√
2√2= 0
Te =2
A + B + C + D=
2−1 + j + j− 1
×√
2 =−1√
2(1 + j)
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
Odd Mode Analysis
1 2
4 3
–1/2
+1/21 1
1
1 1 1
11
1/ 2
1/ 2
Line of antisymmetryV = 0I = max
–1/2
+1/2
To
1 1
1
1
1
1
1
1
11
1/ 2
1/ 2
Short-circuited stubs(2 separate 2-ports)
Γo
[A BC D
]o=
[1 0−j 1
] [0 j/
√2
j/√
2 0
] [1 0−j 1
]=
1√2
[1 jj 1
]
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
Odd Mode Analysis ... Cont’d
Γo =A + B− C−DA + B + C + D
= 0
To =2
A + B + C + D=
1√2(1− j)
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
Now, you calculate Sij values from the obtained Γe, Te, Γo, and Tovalues ...
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
90◦ Hybrid Coupler
S Paramters of a Quadrature Hybrid
0.5 f0 f0 1.5 f0–40
–30
–20
–10
0
4
Z0
Z0 Z0
Z0/ 2
Z0/ 2
Z0
Z0 Z0
1
4
(Input)
(Isolated)
(Output)
(Output)
2
3
λ
4λ |Sij|
|S12|
|S13|
|S11|
|S14|
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Rat-race Coupler
2
4
3
1
2Z0
Z0
Z0
Z0
Z0(Σ)
(Δ)
λ/4
λ/4
λ/4
3λ/4
[S] =−1√
2
0 j 1 0j 0 0 11 0 0 j0 1 j 0
................
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Rat-race Coupler
2
4
3
1
2Z0
Z0
Z0
Z0
Z0(Σ)
(Δ)
λ/4
λ/4
λ/4
3λ/4 [S] =−1√
2
0 j 1 0j 0 0 11 0 0 j0 1 j 0
................
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Even Mode Analysis
4
1 22
1
3
+1/2
+1/21
1
O.C.
O.C.
O.C.
Te
√2√2
+1/2
Γe
λ/4
3λ/8√2λ/8
[A BC D
]e=
[1 0
j/√
2 1
] [0 j
j/2 0
] [1 0
−j/√
2 1
]=
[1/√
2 jj −1/
√2
]
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Even Mode Analysis ... Cont’d
Γe =A + B− C−DA + B + C + D
=−j√
2
Te =2
A + B + C + D=−j√
2
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Odd Mode Analysis
4
1 22
1
3
+1/2
–1/21
1
S.C.
S.C.
S.C.
To
√2√2
+1/2
Γe
λ/4
3λ/8√2λ/8
[A BC D
]e=
[1 0
−j/√
2 1
] [0 j
j/2 0
] [1 0
j/√
2 1
]=
[−1/√
2 jj 1/
√2
]
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Odd Mode Analysis ... Cont’d
Γo =A + B− C−DA + B + C + D
=j√2
To =2
A + B + C + D=−j√
2
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
Now, you calculate Sij values from the obtained Γe, Te, Γo, and Tovalues ...
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
180◦ Rat-race or Ring Hybrid Coupler
S Paramters of a Rat-race Coupler
0.5 f0 f0 1.5 f0–40
–30
–20
–10
0
dB
2
4
3
1
2Z0
Z0
Z0
Z0
Z0
|Sij|
|S12|
|S13|
|S11|
(Σ)
(Δ)
λ/4
λ/4
λ/4
3λ/4
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Outline
1 Power Dividers and Couplers
2 Three-Port Networks
3 Four-Port Networks
4 A Few Other Power Dividers
5 Problems
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Bethe Hole Directional coupler
a3
4
2
(Isolated)
(Through)
1(Input)
3(Coupled)
2(Through)
4 (Isolated)
1S b
b
y
x
z
(Coupled)
(Input)
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Multi-Hole Couplers
4 3
1 2
g /4
0° –90°
(Isolated)
(Out of phase) (In phase)
(Input)
(Coupled)
(Through)
d
B0A
B F
A A
F0A
n = 0
B1A F1A
n = 1
B2A F2A
n = 2
B3A F3A
. . .
BNA FN A
n = N
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Coupled Line Couplers
1
3 4
2
Coupled Isolated
ThroughInput
Z0e, Z0o
I3Z0 Z0
+V3 +V4
I4
I1Z0 Z0
+V1 +V2
I2
2V0
1 2
43
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Multisection Coupled Line Couplers
V3 V4
V1 V2
C1 C2 CN – 1 CN
Coupled Isolated
Input Through
. . .
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Lange Couplers
4
1
W
Isolated
Input
2
3
Coupled
Through
Z0
S
Z0 Z0
Z0
/4
2
Through
Input
4
1 3
Coupled
Isolated
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Tapered Coupled Line Hybrid
Differenceinput
Output
Suminput
Output
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Magic T
4
2
1
3
(Σ)
(Δ)
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
Power Dividers and Couplers Three-Port Networks Four-Port Networks A Few Other Power Dividers Problems
Outline
1 Power Dividers and Couplers
2 Three-Port Networks
3 Four-Port Networks
4 A Few Other Power Dividers
5 Problems
Course Outline RF & Microwave Engineering, Dept. of EEE, BITS Hyderabad
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