Mirrored Coupling Structures for Microwave Signal Splitting and Combining

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1

Abstract This paper discussed a method of creating

multi-port couplers by mirroring conventional coupler structures, such as 90o hybrids, Saleh power dividers, Wilkinson couplers and so on. These created structures maintain some very useful features of the original structures, for example, stable phase shifting between ports, equal power dividing, port isolation... Theoretical analysis method of these structures was discussed for S-parameter derivation. Example structures: a 4-way coupler by mirroring 90o hybrid couplers, an 8-way coupler by mirroring Saleh power dividing couplers, were built and tested according to the method discussed. Good match was found between theoretical analysis and measurements.

Index Terms multi-way, couplers, mirrored structures

I. INTRODUCTION ouplers are import components for many microwave systems. That is why lots of efforts were put on finding

new coupler structures by researchers in the past few decades. Many interesting couplers were designed to meet different system requirements, for example Wilkinson couplers [1], 90o Quadrature couplers [2], Rat-race couplers [3], Lange couplers [4] and Saleh's multi-way dividers [5]... Till today, researchers continued on searching for couplers with different properties: couplers with ultra-wide bandwidth [6], couplers working at multi-bands[7], couplers with un-equal dividing ratio[8] and more. However, most of these designs are some kind of re-structuring the conventional couplers. It is not easy to find new coupler structures, especially those couplers with multi-ports, equal power division and stable phase shifting. Such couplers possibly will become attractive for power amplifier designs [9] and antenna array designs [10] where lots of stringent requirements arise from real applications. In this paper, we discussed a method of creating a new group of coupler structures: by mirroring conventional coupling structures, such as quadrature couplers, Wilkinson couplers, Rat-race couplers and so on, we can get some new coupling structures, which, by careful design, can maintain useful features of the original structures.

Manuscript received May, 2013. This work was supported by SERC. JiJun Yao is with Institute for Infocomm Research, A*STAR, Fusionopolis,

Singapore. (email: [email protected]); Shi Bo is with Institute for Infocomm Research, A*STAR, Fusionopolis,

Singapore. (email: [email protected]);

In the theory part of the paper, we presented the idea and method of mirroring conventional couplers. Then a general theoretical S parameter analysis method was suggested for such coupler analysis. To validate the method, we derived the S parameters of a 6-port coupler by mirroring the conventional 90o quadrature couplers, which is compared with ADS (Advanced Design System, CAD software by Agilent) simulation results. The theoretical analysis and simulation results match very well. More mirrored structures were discussed in the end of this section. Interesting multi-port couplers were found and presented.

In order to validate our design theory, we designed and

fabricated a 4-way coupler (by mirroring 90o quadrature couplers) and an 8-way coupler (by mirroring Saleh's 4-way couplers[5]) according to the theory discussed. Tested results showed that these couplers maintained useful features of the original couplers, such as equal power division, stable phase shifting between output ports and good isolation between ports.

With the method of mirroring, we created a new group of

coupling structures. These couplers could be useful in many microwave applications. Especially when we design high power multi-way power combining amplifiers working at high frequencies, mirrored couplers have many advantages compared with conventional designs: it can provide more splitting / combining ways, lower insertion loss, more compact size, easier power transistor position arrangements and more.

II. DESIGN THEORY

Fig. 1. (a) original coupler structures with a transmission line between 2 selected ports, and a passive network connecting these 2 ports with all other ports; (b) using the transmission line as mirror edge, new structure with more input/ output ports can be created. where Pn represents port n#

Figure 1 (a) showed a general passive coupling structure.

Between 2 selected ports (port 1 and port 2 in this case), there is a transmission line connecting them, and a passive network

Mirrored Coupling Structures for Microwave Signal Splitting and Combining

Jijun Yao, Member, IEEE, Shi Bo

C

(a)

P N+2

P1

passive network

P2

P3

P4

PN

P1

passive network

P2

P3

P4

PN

passive network

PN+1

P2N-2

(b)


2

connecting these 2 ports with the rest ports. Using the indicated connecting line as the mirror edge, we can create a new structure as shown in figure 1(b). Assuming that the original coupler structure has following properties: with port 1 as input port, power can be equally split between M ports (M < N-1), there are stable phase shifting between these M ports, and the rest L ports (L = N-M-1) are isolated from port 1. Then with careful design of the passive network, we possibly can get a mirrored structure which maintains many characteristics of the original structure: when using port 1 as input ports, power can be equally split between the M ports and the corresponding mirrored M ports, stable phase shifting can be obtained between them, port 1 will be isolated with the L ports and their mirrors.

Certainly it is very hard to prove whether this statement is

correct or wrong in the general case. However many conventional structures were used to obtain their corresponding mirrored structures and it is found that these mirrored structures do can have similar performances as the original structures. Following is one such case by mirroring the conventional quadrature coupler.

In figure 2, a quadrature coupler is used for mirrored

structure building. In figure 2 (a), the transmission line between the input port P1 and isolation port P2 is used as the mirror edge; and in figure 2 (b), the transmission line between input port P1 and one output port P3 is used as mirror edge. According to the assumption, for the structure of fig. 2(a), it is expected that port P1 and P2 remain isolated and input power will be equally divided between port P3 to P6; for the mirrored structure of fig. 2(b), it is expected that input power equally divided between port P3, P4, P6, and input port P1 will be isolated with port P2 and P5. Theoretical S parameter analysis of figure 2(a) and 2(b) showed that these expectations can be met.

Fig. 2. (a) mirrored structures with a transmission line between 2 selected ports, and a passive network connecting these 2 ports with all other ports; (b) using the transmission line as mirror edge, new structure with more input/ output ports can be created, *note: all impedance used are normalized impedance, and all lines are 90o in length unless otherwise stated

In figure 3, the S parameter analysis method of the mirrored

quadrature coupler shown in fig. 3 (a) was presented. To analyze the S parameters of port 1 (such as S11 , S12 , S13 ...), the coupler can be divided to 2 symmetrical parts. Because any

power injection at port 1 will be divided equally to these 2 parts, the impedance of port 1' and the characteristic impedance of the mirrored edge line will be doubled (as shown in figure 3 (b), voltage remains the same, and current is divided by 2); Using the S parameter deriving method discussed in a previous work[11], it is easy to obtain the S parameters (S11' , S12' , S13' ...) of the divided part as shown in fig. 3 (c); the port 1 S parameters of the mirrored structure can then be obtained with following equations:

S11 = S11'; S12 = S12'; S13 = S15 = S13' / 2 ; S14 = S16 = S14' / 2 ; ...(1)

Fig. 3. S parameter analysis for mirrored quadrature couplers (a) original mirrored structure for S parameter analysis, (b) symmetric cutting of a structure to explain the doubled characteristic impedance after cutting, where voltage remain the same and current halved; (c), symmetric cut parts of the proposed coupler for port 1 S parameter analysis, where all characteristic impedance along the cutting edge doubled, including the port impedance; (d) normal even / odd mode analysis of port 3 parameters, open and short connection applied along the cutting edge as shown in the figure

For an ideal quadrature coupler, S11 = S12 = 0 at the center

frequency; to obtain the same performances for the mirrored structure in figure 2 (a), following design equations are obtained from the derived S parameters:

1 3

32 2

3

21

Z Z

ZZZ

...(2)

With above design equations, the port 1 S parameters at the center frequency can be obtained:

11 12

313 15 2

3

14 16 23

0

2(1 )1

2(1 )

S SZS S

Z

S SZ

i ...(3)

To complete the theoretical S parameter analysis, it is needed to obtain the S parameters of port 3 to port 6 (Sii , Sij , i,j = 3,4,5,6). Typical even / odd analysis method can be used as shown in figure 3 (d). With designed equations (2), the rest S parameters can be obtained:

(a)

P1

P2

P3

P4

P5

P6

Z2' Z2'

Z2'Z2'

Z1' Z3'Z3'

mirror edge P1 , 2 Z p

P2 , 2Z p

P3 , Z p

P4 , Z p

2Z1Z3 Z2

Z2split to 2 symmetric parts

(c)

(b)

Vleft Vright

Ileft Iright

symmetric cutting of a line structure

P1

P3

P5 Z2'

Z2'Z1' Z3'Z3

'

even/ odd mode analysis of port 3 S parameters cutting edge

(d)

P2 P1

P3 P4

P5

P6

(a)

P1 input

P2 isolation

P3 out 1#

P4 out 2# P1

P2

P3

P4

P5

P6

(b) Original quadrature coupler

mirror edge

mirror edge Z1 Z1

Z2

Z2

Z2' Z2'

Z2' Z2'

Z1' Z3'Z3'

Z1" Z1"

Z1" Z1"

Z2" Z3"Z3"


3

23

23

23

34 23

335 36 2

3

1 , 3, 4,5,62(1 )

12(1 )

(1 )

ii iZS

ZZSZ

ZS SZ

i

...(4)

One typical solution based on equation (2), (3) and (4) is the 4-way equal power splitting design with Z1 = Z2 = Z3 = 1 (normalized impedance), and consequently we have |S13| = |S14| = |S15| = |S16| = 0.5; Simulation results of this design is shown in figure 4 (the simulation is performed with Agilent's ADS software). It is observed that the mirrored structure maintains all the features of the original coupler: matching port, total isolation between the input port P1 and the isolation port P2, equal power distribution between output ports, stable phase shifting between output ports (90o or 0o).

One thing need to mention is the return losses of port 3 to 6

are not 0 in designs when Z1 1. Reflection happens at these ports. But based on previous experiences, it is possible to obtain very small reflection at all ports by optimizing the network parameters with solutions given by equation 2.

Figure 2(b) shows the other possible mirrored structure of the quadrature coupler. Based on the assumption, it should be possible to obtain a coupler with port 1 isolated from port 2 and 5 and injection power of port 1 equally divided between port 3, 4 and 6. Using the port 1 S parameter analysis method discussed, following design equations can be obtained to satisfy S11 = S12 = S15 =0:

1 3

32 2

3

21

Z Z

ZZZ

...(5)

With above design equations, following S parameters were derived:

11 12 15

214 16 3

13 3

0

(1 ) / 2

S S S

S S ZS Z

i

...(6)

And S parameters relating to port 2, 4 ,5 ,6: 23

2323

25 23

23 3

24 23

23 3

26 23

1 , 2, 4,5,62(1 )

12(1 )

(1 )2(1 )

(3 )2(1 )

ii iZS

ZZSZ

Z ZSZ

Z ZSZ

i

i

...(7)

With S parameter expressions in (3), the 3-way equal power division design can be obtained : Z1 = Z3 = 1/ 3 , Z2 = 1; for this design, |S13| = |S14| = |S16| = 1/ 3 . ADS simulation of this structure is shown in figure 5. It should be noted that the return losses of port 2,4,5 and 6 are not 0. It is, however, not difficult

to obtain 3-way equal power dividing design with all ports nicely matched (Sii < -20dB) by some optimize. Suggested optimize values for the couplers are Z1 =0.62, Z3 = 0.74, Z2 = 1.17.

0.6 0.8 1.0 1.2 1.40.4 1.6

-40

-30

-20

-10

-50

0

frequency

S11

, S33

and

S12

(dB

)

0.6 0.8 1.0 1.2 1.40.4 1.6

-11

-10

-9

-8

-7

-12

-6

freqeuncy

S13

, S

14

(dB

)

Fig. 4. S parameter simulation results of the 4-way equal dividing structure shown in figure 2(a), the structure has Z1 = Z2 = Z3 = 1, simulated with Agilent ADS

0.6 0.8 1.0 1.2 1.40.4 1.6

-40

-30

-20

-10

-50

0

frequency

S11

, S22

and

S12

(dB

)

0.6 0.8 1.0 1.2 1.40.4 1.6

-11

-10

-9

-8

-7

-6

-5

-12

-4

freqeuncy

S13

, S

14, S

16 (d

B)

Fig. 5. S parameter simulation results of the 3-way equal dividing structure shown in figure 2(b), the structure has Z1 = Z3 = 1/ 3 , Z2 = 1, simulated with Agilent ADS

More interesting mirrored structures can be obtained using

the discussed mirror method. Figure 6 shows several example structures: the 3-way coupler by mirroring the Wilkinson coupler; the 3-way coupler by mirroring the rat-race coupler; the 4-way coupler by mirroring the 3-section branch-line coupler, this coupler has increased bandwidth compared with structure in fig 2(a); it seems that we can increase the mirrored

S12

S22 S11

S13

S14 & S16

S11

S12 S33

S13 S14


4

structures' working bandwidth like the conventional branch-line couplers; and the 8-way coupler by mirroring the 4-way Saleh coupler.

Fig. 6. interesting mirrored structures; (a) the 3-way coupler by mirroring the Wilkinson coupler, (b) the 3-way coupler by mirroring the rat-race coupler, (c) the 4-way coupler by mirroring the 3-section branch-line coupler, (d) the 8-way coupler by mirroring the 4-way Saleh coupler; *note: all lines are 90o in length unless otherwise stated

III. REALIZATION AND TESTS Based on the developed theory, some real structures were

built to test their performances. 2 structures were chosen: the 4-way coupler shown in figure 2(a) and the 8-way coupler shown in figure 6(d). And the commonly used RO4003C 32mil 1/4 oz laminate was selected for these coupler design and fabrication.

Fig. 7. mirrored couplers optimized for maximizing working bandwidth (a) the mirrored quadrature coupler structure; (b) mirrored Saleh coupler structure, and where Pn represents port n#

With the values given by equation (2) and the values in

figure 5(b), the 4-way couplers and 8-way couplers as shown in figure 7 can be designed. In order to obtain the largest bandwidth centered at 6.1GHz, so that these couplers can be directly used for high power satellite SSPAs (Solid State Power Amplifier), these 2 structures were optimized with the error functions (EF) given by equation 8 (searching for minimum of the error functions). The key parameters of these 2 designs are listed in table 1.

2 26 62

12 11 3| | | | || | 0.5 |ii i

f i iEF S S S

...(8a) 2 210 10

212 1

1 3| | | | || | 0.355 |ii i

f i iEF S S S

...(8b) where equation 8a is for the 4-way coupler in figure 7(a); and

equation 8(b) is for the 8-way coupler in figure 7(b); f represents the frequencies to be optimized; and the optimization was performed from 5.8GHz to 6.4GHz.

The simulated and measured performances of these 2

couplers are shown in figure 8 and figure 9.

5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.85.0 7.0

-8.0

-7.5

-7.0

-6.5

-6.0

-8.5

-5.5

frequency (GHz)

pow

er d

ivis

ion

ratio

(dB

)

measured S13 ------ simulated S13 measured S14 simulated S14

(a) simulated & measured power dividing ratio S13 & S14

5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.85.0 7.0

-30

-25

-20

-15

-10

-35

-5

frequency (GHz)

retu

rn lo

ss &

isol

atio

n (d

B)

measured S12 ------ simulated S12 measured S11 simulated S11

measured S33 simulated S33 (b) simulated & measured return loss S11 & S33, isolation S12

(a) (b)

Z1

Z2

Z3

Z01

Z02

Z1 Z3 Z2 Z4

Z1

Z5 Z6 Z5

Z01

Z02 Z03

P1 P2

P3 P4

P5 P6

P1

P4 P5 P6 P3

P8 P9 P10 P7

TABLE I-B KEY PARAMETERS OF THE MIRRORED STRUCTURE OF FIGURE 7(B) AFTER

OPTIMIZATION Impedance(Ohm) Width (mm) Length (mm)

Z1 48 1.9 8 Z2 73 0.94 4.5 Z3 Z4 Z5 Z6

54 60.5 35

29.5

1.6 1.3 3.1 3.9

8.9 4.3 6.7 7

Z01 Z02

43 48

2.3 1.9

4.9 4

TABLE I-A KEY PARAMETERS OF THE MIRRORED STRUCTURE OF FIGURE 7(A) AFTER

OPTIMIZATION Impedance(Ohm) Width (mm) Length (mm)

Z1 48.5 1.9 6.6 Z2 32.6 3.4 5.0 Z3 27.4 4.3 6.6 Z01 Z02

36.5 36.5

2.9 2.9

8 5.4

80 106 84.5

80 106 46

P1

P3

P2

P4

70

59 59 70 70

96 , 270o96 , 270o P1

P4 P3 P2 P5 P6

P3 and P5 are isolate ports from port 1

28.5

30 27 27 36

46 38

P3

P4

P5

P6

P1 P2

(a) (b)

(c)

66 P1

P2

P7

P8

P9

P10

78

78

66

49

59

49

51

53

51

P3

P4

P5

P6

(d)

P2


5

5.2 5.4 5.6 5.8 6.0 6.2 6.4 6.6 6.85.0 7.0

0

20

40

60

80

-20

100

frequency (GHz)

phas

e di

ffere

nces

(deg

.)

* * * measured deg(S14/S13) ------ simulated deg(S14/S13) measured deg(S16/S13) simulated deg(S65/S13)

measured deg(S15/S13) simulated deg(S15/S13) (c) simulated & measured phase differences, deg(S14/S13) , deg(S15/S13) and

deg(S16/S13) Fig. 8. Simulated and measured results of the mirrored quadrature coupler

The mirrored couplers have many useful features and can be used in many circuit applications, especially for power splitting and combining. The 4-way mirrored quadrature coupler was then used as an example to demonstrate the advantages of these couplers. In figure 10 (a), the 4-way mirrored quadrature coupler was tested with the back to back configuration. The cables connecting the splitting and combining couplers are 12cm long semi-rigid cables with 90o bending SMA adaptors. The tested insertion loss for these cables is 0.6dB from 5.6GHz to 6.6GHz. Then the coupler was used to build a 4-way power combining amplifier as shown in figure 10(b). The amplifier used 4 separate 2W C-band high power amplifiers. Each 2W amplifier has 30.5 +/- 0.5 dB gain working from 5.6GHz to 6.6GHz, and 32.3 dBm of P1dB @ 6.1GHz .

5.9 6.45.4 6.8

-14

-12

-10

-8

-16

-6

frequency (GHz)

pow

er d

ivis

ion

ratio

(dB

)

measured S13 ------ simulated S13 measured S14 simulated S14 measured S15 . . . . . simulated S13 * * * measured S16 simulated S14

(a) simulated & measured power dividing ratio S13, S14, S15 & S16

5.9 6.45.4 6.8

-40

-30

-20

-10

-50

0

frequency (GHz)

retu

rn lo

ss &

isol

atio

n (d

B)

measured S11 ------ simulated S13 measured S33 simulated S14 * * * measured S44 simulated S14 measured S12 . . . . . simulated S12

(b) simulated & measured return loss S11, S33 & S44 , isolation S12

5.9 6.45.4 6.8

-100

0

100

-200

200

frequency (GHz)

phas

e di

ffere

nces

(deg

.)

* * * measured deg(S14/S13) ------ simulated deg(S14/S13) measured deg(S16/S13) simulated deg(S65/S13)

measured deg(S15/S13) simulated deg(S15/S13) (c) simulated & measured phase differences, deg(S14/S13) , deg(S15/S13) and

deg(S16/S13) Fig. 9. Simulated and measured results of the mirrored Saleh coupler

(a) back-back connection of the 4-way mirrored quadrature coupler

(b) 4-way power combining using the designed coupler

Fig. 10. Back-back configurations of the designed 4-way mirrored quadrature coupler, and high power

5.8 6.0 6.2 6.4 6.6 6.85.6 7.0

-30

-20

-10

-40

0

-5

-4

-3

-2

-6

-1

frequency (GHz)

retu

rn lo

ss (d

B)

insertion loss (dB)

(a) measured results of the back-back connection of the 4-way mirrored

quadrature coupler

input port

isolate port

high power load

high power PA

isolate port term.

S11

S21


6

5.8 6.0 6.2 6.4 6.6 6.85.6 7.0

-20

-10

0

-30

10

20

25

30

15

35

frequency (GHz)

retu

rn lo

ss (d

B)

small signal gain (dB)

(b) measured return loss and small signal gain of constructed high power

amplifier with the 4-way mirrored quadrature coupler

Fig.11, measured results of the back-back connected 4-way coupler and high power amplifier constructed with it

From the tested results shown in fig.11 (a), it is obtained that the insertion loss of the single 4-way mirrored coupler varies between 0.5dB to 0.7dB from 5.6GHz to 6.4GHz (back-back insertion loss cable loss, then divided by 2), which is a little bit higher than that of the traditional 4-way waveguide coupler built with 3 2-way waveguide couplers, but with a much lower fabrication costs. And the size of the mirrored coupler is only about 10% ~20% of the traditional 4-way microstrip couplers built with the cascade method. Hence, the mirrored couplers can provide very good performances with much smaller size and lower costs. The amplifiers shown in fig. 10(b) and its test results shown in fig. 11(b) further prove above statement. The new 3-dimensional arrangement of the combining power amplifiers helped in reducing the final size. Such arrangement improves thermal design of the PA as well. And the gain obtained varies at 29.8 + / - 0.6dB from 5.6GHz to 6.6GHz. The power test also shows 37.5dBm P1dB output @ 6.1GHz. All these results show that the new mirrored couplers are very suitable for low cost multi-way power splitting and combining applications.

IV. CONCLUSION In this paper, a passive structure mirroring method was

proposed. With the method, it suggests that new coupling structures could be obtained by mirroring passive structures; and the most important is these mirrored structures can maintain useful features of the original structures, such as equal power splitting, stable phase shifting between output ports, good port matching and isolation and more.

To validate the proposed method, the quadrature coupler was

used as examples; the design equations and S parameter expressions for 2 mirroring structures were derived: the 4-way mirrored coupler and the 3-way mirrored coupler. More interesting mirrored structures were discussed in the theory section. It is possible to find more useful couplers with the proposed method.

A 4-way mirrored quadrature coupler and a 8-way mirrored

Saleh coupler were designed and tested. Measurement results match well with theory. The mirrored couplers can be useful in many circuit applications and have many advantages. A high

power 4-way power combining amplifier was used to demonstrate these advantages in multi-way power splitting and combining. Testing results showed that the coupler can provide very good performances, which is comparable to the waveguide designs, at much lower costs, and has much smaller size and better thermal design options. More applications can be found for these mirrored couplers where signal splitting / combining is needed. Antenna array could be another interesting application.

ACKNOWLEDGMENT This work is supported by SERC fund.

REFERENCES [1] Ernest Wilkinson, An N-way high power divider, IRE Trans. on MTT,

1960, Vol, 8, Jan. , pp. 116118. [2] Reed J., " A method of analysis of symmetrical four-port networks," IRE

Trans. on MTT, 1956, Vol, 4, Issue 4. , pp. 246252. [3] Luzzatto G., "A general 180-degree hybrid ring" IEEE Trans. on

broadcasting., 1968, Vol.BC-14, issue 1, pp 41-43. [4] Lange J., "Interdigitated strip-line quadrature hybrid ", Microwave

symposium 1969 G-MTT international, 1969, pp 10-13 [5] Saleh A.A.M., Planar multiport quadrature-like power dividers /

combiners, IEEE Trans. on MTT., 1981, Vol.29, No.4, pp 332-337. [6] Abbosh A.M; Bialkowski M.E., " Design of compact directional couplers

for UWB applications" IEEE Trans. on MTT., 2007, Vol.55, No.2, pp 189-194.

[7] Duran-Sindreu, etc., " Planar multi-band microwave components based on the generalized composite right/ left handed transmission line concept" IEEE Trans. on MTT., 2010, Vol.58, No.12, pp 3882-3891.

[8] Ki Tae Kim etc., " Reconfigurable power divider and combiner with variable power ratio" Microwave symposium digist 2004 IEEE MTT-S., 2004, Vol.1, pp 57-60.

[9] Eroglu A., " N-way planar high-power combiner design for RF power amplifiers" Science, Measurement & Technology, IET., 2008, Vol.2, No.2, pp 61-67

[10] Taeksoo Ji; etc., " Ku-band antenna array feed distribution network with ferroelectric phase shifters on silicon" IEEE Trans. On MTT., 2006, Vol.54, No.3, pp 1131-1138

[11] Yao J.J.; etc., " Non-standard Hybrid and Crossover Design with Branch-line Structures" IEEE Trans. on.MTT, Dec. 2010, Vol.58, No.12, pp 3801-3808

J.J. Yao received his B.S. and M.S. degrees in 1996 and 1999 respectively from Huazhong University of Science & Technology, Wuhan, P.R. China; and PhD in 2009 from National University of Singapore. He worked on RF circuit design for 4 years in Huawei Technologies, Shanghai and Shenzen, P.R. China; and 3 years in ST Electronics, Satcomm and Sensor Systems, as an assistant principle engineer on PA designs. He currently is with Institute for Infocomm Research, A*STAR, Singapore. His main research interests include Terahertz circuits, microwave passive circuits and power amplifiers. Shi Bo

gain

return loss

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Mirrored Coupling Structures for Microwave Signal Splitting and Combining