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AEL 104/21/23
Power divider
( Arbitrary Termination Impedance,
Arbitrary Power Division )
2004-21566
유지호
AEL 204/21/23
• Necessity of the power divider
• Problems of conventional power dividers
• Size reduction technique
• Arbitrary termination Impedance technique
• Arbitrary power division technique
• Conclusion
Contents
AEL 304/21/23
Necessity of the power divider
power combining
in phase or out of phase
AEL 404/21/23
1.Large size at UHF or VHF band.
2.Designed to match 50 Ohm termination. ( Additional matching networks are necessary. - Increase system size )
3.Symmetry -> Only equal power division ratio.
Problems of conventional power dividers
AEL 504/21/23
Size reduction technique (1) –> MTT-Trans (1991)
A-A’ : symmetrical axis
ring hybrid’ scattering matrix
25.1
0...........
...........
)1(2
2
)1(2
22
)1(2
)1(
31422112
41321122
22
211
221
22
211
141
22
211
22
21
11
SSSS
SSSS
YYjY
YS
YYjY
YS
YYjY
YYjS
Isolation
122
21 YY
12
3212
4121
2,... YYThus
SS
SS
3
2....
3
1... 21 YandYTherefore
AEL 604/21/23
Size reduction technique (1) –> MTT-Trans (1991)
A-A’ : symmetrical axis
ring hybrid’ scattering matrix
6
7
1. Find S-parameter
2. Isolation : S31=S42=0 at f=f0
3. 3dB output power division
-> |S21|=|S41| & |S12|=|S32|
Then, obtain 4
3
21
Y
YYY
AEL 704/21/23
Size reduction technique (1) –> MTT-Trans (1991)
3dB power division & good matching
AEL 804/21/23
Size reduction technique (2) –> MTT-S (1989)
BUT -> 1. series L : high resistive losses 2. Same termination
impedances
AEL 904/21/23
Size reduction technique (3) –> MTT-Trans (1994)
Reduce series L
1 : Input
2 : +90 output
4 : -90 output
3 : isolation
1 : Input
2 : +90 output
4 : -90 output
3 : isolation
series L : 3개 series L : 1개
AEL 1004/21/23
Size reduction technique (3) –> MTT-Trans (1994)
Remove series L
(1980 )
But limited to equal-power split-ring hybrid
AEL 1104/21/23
Arbitrary termination impedances (1) –> MTT-Trans (1999)
Excitation at port 2 (V)
(1)Transmission line Eq
node 1&2, node 3&1
(2)node Eq
node 1, node 2, node 2&GND, nod 2&3
(3)3dB power division
(4)
So determine optimum load
)(
2
baacb
avxbxc
RRRZZ
RRRR
(1) ~ (4) Then,
cbav RRR
4
cb
AEL 1204/21/23
Arbitrary termination impedances (1) –> MTT-Trans (1999)
Power division & isolation
matching
AEL 1304/21/23
Arbitrary power division & termination impedances (2) –> MTT-Trans (1997)
Lossless -> 12
41
2
31
2
21
2
11 SSSS
3 port isolation & 1 port matched ->
12
41
2
21 SS
S31=0 & excitation for port 1 & put
wave ratio = b1 : b2 = S21 : S41
Under the assumption S31=0, the characteristic
admittances Y1, Y4 determined
441
022
21
22
4
022
21
21
1
)(
)(
Ybb
bknY
Ybb
bmnY
AEL 1404/21/23
Arbitrary power division & termination impedances (2) –> MTT-Trans (1997)
excitation for port 3
The dummy arms Y2 and Y3 makes port 2&4 isolation
If isolation is not ideal -> small power flows forward to port 3
For these two waves to be isolated from port 1, two conditions must be satisfied.
1. The two waves must have a phase shift of 180degree against each other,
->
2. The wave ratio must be b2 : b1 as shown left.
Reciprocal 하므로
4
3.......4 32
022
21
22
3
022
21
22
2
)(
)(
Ybb
bkpY
Ybb
bmpY
m=n=p=k & b1:b2=1:1 => conventional ring hybrid
AEL 1504/21/23
Arbitrary power division & termination impedances (2) –> MTT-Trans (1997)
Simulation Result Port 1 : n=1 -> 50 Ohm
Port 2 : m=1.1 -> 45.45 Ohm
Port 3 : p=0.7 -> 71.429 Ohm
Port 4 : k=0.8 -> 62.5 Ohm
Power spilt ratio : 2dB ( 20log(b1/b2) =2dB )
Power division
Isolation matching
S21=-2.124dB , S41=-4.124dB
S43=-2.124dB , S23=-4.124dB
S31=-158..656dB , S42=-160.656dB
AEL 1604/21/23
Conclusion
• Power divider’s size may be reduce ( less than quarter wave line,
& lumped element ) • We can remove matching network with
Arbitrary termination Impedance & Arbitrary power division power divider.
-> realize small size system
AEL 1704/21/23
References
• Three-Port 3-dB Power Divider Terminated by Different Impedances and Its Application to MMIC’s , IEEE MTT Trans. 1999
• Arbitrary Termination Impedances, Arbitrary Power Division, and Small-Sized Ring Hybrids, IEEE MTT Trans. 1997
• Miniaturized 3-dB ring hybrid terminated by arbitrary impedances, IEEE MTT Trans. 1994
• Design of new hybrid-ring, directional coupler using λ/8 or λ/6 sections, IEEE MTT Trans. 1991
• 180° lumped element hybrid, IEEE MTT-S.1989