AEL 104/22/23

Power divider

( Arbitrary Termination Impedance,

Arbitrary Power Division )

2004-21566

유지호

AEL 204/22/23

• Necessity of the power divider

• Problems of conventional power dividers

• Size reduction technique

• Arbitrary termination Impedance technique

• Arbitrary power division technique

• Conclusion

Contents

AEL 304/22/23

Necessity of the power divider

power combining

in phase or out of phase

AEL 404/22/23

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 504/22/23

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 604/22/23

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 704/22/23

Size reduction technique (1) –> MTT-Trans (1991)

3dB power division & good matching

AEL 804/22/23

Size reduction technique (2) –> MTT-S (1989)

BUT -> 1. series L : high resistive losses 2. Same termination

impedances

AEL 904/22/23

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 1004/22/23

Size reduction technique (3) –> MTT-Trans (1994)

Remove series L

(1980 )

But limited to equal-power split-ring hybrid

AEL 1104/22/23

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 1204/22/23

Arbitrary termination impedances (1) –> MTT-Trans (1999)

Power division & isolation

matching

AEL 1304/22/23

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 1404/22/23

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 1504/22/23

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 1604/22/23

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 1704/22/23

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