New Design of Directional Coupler Based on Ridge-waveguide

Chengfang Fu

1

, Bo Zhao

1

1

Faculty of Electronic Information Engineering, Huaiyin Institute of Teconology, Huaian, China

Keywords: Ridge Waveguide, Directional Coupler, Coupling, Chebyshev Function.

Abstract: Ridge waveguide devices are used extensively in microwave system because with the same section size,

ridge waveguides have relatively wider single-mode bandwidth than rectangular waveguides. A new method

for designing a directional coupler whose main and vice-waveguide are both ridge waveguide is presented,

mean while, Chebyshev function is used as distribution function. The designing of the coupler is simulated

by HFSS.

1 INTRODUCTION

A number of scholars have been systematically

studied the design of directional couplers, especially,

the main and vice-waveguides of the directional

coupler are rectangular waveguide. But main and

vice-waveguides are ridge waveguide is relatively

rare. The boundary conditions of ridge waveguide

are more complex, it is quite difficult to analytic

solution to the field of the ridge waveguide, which

limits the study and applications of the ridge

waveguide. Ridge waveguide is divided into the

ridge area and the slot area by W. J. Getsinger, and

the transverse electric field is matched to deduce the

analytical expression to descript the ridge

waveguide, which laid the foundation to study ridge

waveguide[Getsinger, 1962].

The Chebyshev function has been proposed as a

distribution function by scholars in the study of

microwave devices, which can improve the device

performance. Therefore, the pore size distribution of

the holes is on the Chebyshev function, a directional

coupler device of the center frequency of 3GHz, the

coupling of -40dB is designed using the small hole

coupling theory. HFSS simulations show that such a

design in a wide frequency range, the coupling is

relatively flat.

2 MAIN BODY

2.1Calculation of

±

v

A

[Miller, 1954]

The main and vice-waveguides of the multi-hole

directional coupler are in the fundamental mode of

the waveguide. Coupling holes are relatively

symmetrical distribution to the centerline, not only

the locations of each pair of symmetrical holes

symmetry, but also the shape and size of them are

symmetry. The main waveguide excites the

fundamental positive and anti-wave through those

coupling holes in the vice waveguide, respectively,

whose relative intensity are

±

0

a

，

±

1

a

…

±

n

a

,

where the superscript

±

are the positive and reverse

wave, respectively, the subscript are the coupling

hole number, the total number of coupling holes is

12 += nN

.

Figure 1: Multihole directional coupler.

The voltage of the positive and reverse wave

which are excited by the modes of the main

waveguide m in the vice waveguide[Wang

Wenxiang, 2003].

d

2

d

n

d

k

d

1

S

k

S

n

S

1

S

2

S

2

S

1

S

k

S

n

0

112 2

0

1

2 cos 2 cos

2 cos 2 cos

2cos

v

kk nn

n

kk

k

Aa

aa

aa

aa

θθ

θθ

θ

±±

±±± ±

±± ±±

±±±

=

=+

++

+++

=+

∑

L

L

(1

)

Where

⎪

⎭

⎪

⎬

⎫

=

=

∑

=

±

n

k

kk

kvmk

Sd

d

1

2

2/)(

ββθ

m

(2)

2.2Determination of S

In multihole coupling the space between the

coupling holes

k

S

are equal and the space is

S

,

which is the pitch coupling, so

kSd

k

2=

(3)

±

±

=

ϕθ

k

k

2

(4)

where

2/)( S

vm

ββϕ

m=

±

(5)

When

πθ

kk

i=

+

，

),2,1,0( L=

k

i

, when, all

the positive waves are overlaying, while when

πθ

)2/1( +=

−

kk

i

，

),2,1,0( L=

k

i

, all the

reverse wave are to offset each other(

0

a

is

excepted). Therefore, according to the above

conclusions, selecting the appropriate value

k

i

, the

hole spacing

S

can be got.

2.3Calculation of the Single-hole

Coupling Coefficient

In order to improve the performance of the

directional coupler, the coupling strength of the

coupling region is set to change according to some

certain laws. To this end, the hole spacing is fixed

unchanged, leaving the pore size changes according

to certain rules, that is the different aperture holes

are arranged so that the coupling strength of the

coupling region to meet a certain distribution. We

use the Chebyshev distribution law to arrange the

pore size of the hole [Levy, 1959, Jiang P Y, 2004].

For the equal spacing ranging and the unequal

intensity distribution, there are the following

equations.

±

±

±

±

±

±

=== aaaaaa

nn

δδδ

,,,

1100

L

(6)

While (1) changes into

∑

=

±±

±

+=

n

k

kv

kaA

1

0

)2cos(2

ϕδδ

(7)

First Chebyshev function is defined as

)arccoscos()( xnxT

n

=

)1( ≤x

(8)

When

−

=

ϕ

cosx

, so

1≤x

,and

∑

=

−

−

+=

n

k

kkv

xTxTaA

1

200

)(2)(

δδ

(9)

The reverse incentives

−

v

A

are limited not

exceed a certain maximum value within a certain

range, so the result is

)(

2

txTKA

nv

=

−

(10)

According to experience, t is set as 1.5, then

equal the functions (9) and (10), making the

corresponding coefficient equal, then

n

δ

δ

δ

L,,

10

can be obtained when the number holes is N

))2cos(2/(10

1

0

20/

∑

=

±+

+=

n

k

k

C

ka

ϕδδ

(11)

where C is the coupling coefficient of the directional

coupler (dB). From the coefficient

n

δ

δ

δ

L,,

10

,

the coupling coefficient of the single hole can be

calculated.

2.4Calculation of the Single-hole Radius

According to the field expressions of the ridge

waveguide[Getsinger, 1962] and small hole coupling

xarccos=

−

ϕ

theory[Bethe, 1944, Collin, 1966], the relative

amplitude of the waves of the vice-waveguide:

kkk

aaa

,2,1

m=

±

(12)

where

1

1

1

1

3

1, 0

2

2

2

1

cos / 2

sin

sin

cos / 2

2

sin sinh cos

sinh

2

3

cos / 2

sin

sin

cos / 2

2

sin sinh cos

sinh

c

c

c

c

n

n

n

kkee

s

c

c

c

c

n

n

n

dks

kx

bkl

ks

nynd

x

nlb b

j

arKR

p

dks

kx

bkl

ks

nynd

x

nlb b

ππ

γ

πγ

ω

ε

ππ

γ

πγ

∞

=

∞

=

⎧⎫

⎡⎤

+

⎪

⎢⎥

⎪

⎢⎥

×

⎪

⎢⎥

⎪

⎢⎥

⎪⎣ ⎦

=−

⎨

⎡⎤

⎪

⎢⎥

⎪

⎢⎥

⎪

⎢⎥

⎪

+

⎢⎥

⎪

⎣⎦

⎩

∑

∑

⎪

⎪

⎪

⎪

⎪

⎬

⎪

⎪

⎪

⎪

⎪

⎭

(13)

2

22

1

1

1

2

3

2

2, 0

1

cos / 2

sin

sin

cos / 2

2

sin sinh cos

sinh

cos / 2

sin

sin

cos / 2

2

4

sin sinh cos

()

sinh

3

c

c

c

z

c

n

n

n

c

c

c

c

n

kkmm

n

n

s

dks

kx

bkl

k

k

ks

nynd

x

nlb b

dks

kx

bkl

ks

ny

nd

j

x

arRK

nlb b

p

η

ππ

γ

πγ

π

π

ω

γ

μ

πγ

∞

=

∞

=

⎧

⎡⎤

⎪

⎢⎥

⎪

⎢⎥

×

⎪

⎢⎥

+

⎪

⎢⎥

⎪⎣ ⎦

⎨

⎡⎤

⎢⎥

⎢⎥

⎢⎥

+

⎢⎥

=−

⎣⎦

∑

∑

2

2

22

1

1

1

1

2

2

1

1

cos / 2

cos sin /

2

cosh cos

sin sinh

cos sin /

2

cosh cos

sin sinh

c

c

cc

n

n

cnn

cc

n

n

cnn

k

ks

k

dkx k ndb

ny

x

bkl n l b

dkx k ndb

ny

x

bkl n l b

η

π

π

γ

πγ γ

π

π

γ

πγ γ

∞

=

∞

=

⎧

⎫

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎬

⎪

⎪⎪

⎪

⎪⎪

⎪

⎪⎪

⎪⎪

⎪⎪

⎨

⎩⎭

⎧⎫

×

⎪⎪

⎪⎪

⎪⎪

⎡⎤

⎪⎪

−− ×

⎨⎬

⎢⎥

⎣⎦

⎪⎪

⎪⎪

⎡⎤

⎪⎪

−

⎢⎥

⎪⎪

⎣⎦

⎩⎭

∑

∑

⎫

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪⎪

⎪⎪

⎬

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎪⎪

⎩⎭

(14)

where

s

p

is the normalized power coefficient.

mmee

RKRK ,,,

are the factor and the thickness of

the macro-hole factor[Sporleder, 1979].

11

, yx

are

the locations of the holes in the main waveguide,

22

, yx

are the position of the vice-waveguide. From

(12) and the single-hole coupling coefficient from

above calculation, the aperture of the hole can be

obtained.

3DESIGN EXAMPLES

3.1Design of an Example

The example directional coupler is set at the center

frequency of 3GHz, the coupling is -40dB, so the

standard single-ridge waveguide is chosen, the

single-mode operating frequency range of the

waveguide is 2.0 ~ 4.8GHz. The design directional

coupler structure is as follows (Unit: inch)

Figure 2:The structure and dimension of the directional

coupler.

3.2Simulation Results

Figure 3:Coupling of the directional coupler versus the

frequency.

It can be seen from the above simulation results

figure that the coupling curve is relatively flat in

broad frequency range, so our design method is

feasible.

4CONCLUSIONS

It can be seen that when the coupling hole is two

rows, each row is set as 15 holes, the radius of the

center hole is 0.216 " in our example design. If the

coupling is stronger, the aperture and the number of

holes are need to increase. When the aperture is

increased, then the aperture is too large, the small

hole coupling theory is no longer reasonable. If the

number of holes is increased, not only the

fabrication becomes more difficult, but also the

coupler length will increase. Therefore, the design

method of the directional coupler whose main and

vice-waveguides are ridge waveguide based on the

small hole coupling theory is feasible only for the

case of weak coupling.

REFERENCES

1.

Getsinger W J,1962.Ridged waveguide field

description and application to directional couplers.

IRE Trans. Microwave Theory Tech., 1(MTT-10) ,

pp.41-50.

2.

Miller S E.,1954. Coupled wave theory and waveguide

applications. BSTJ, pp.661-719.

3.

Wang Wenxiang, Gong Yubin, Yu Guofen, et al.2003.

Mode discrimination based on mode-selective

coupling. IEEE Trans. on MTT,51(1), pp.55-63.

4.

Levy R, 1959. A guide to the practical application of

Chebyshev functions to the design of microwave

components. The Institution of Electrical Engineers

Monogragh, 6(337E) , pp.193-199.

5.

Jiang P Y,2004. The optimal design of the broadband

mode discriminators. B. S. thesis. University of

Electronic Sience and Technology of China.

6.

Bethe H A, 1944. Theory of diffraction by small holes.

Physics Review, 66, pp. 163-182.

7.

Collin R E, 1966. Foundations for Microwave

Engineering. McGraw-Hill, New York, 2

nd

edition.

8.

Sporleder F, Unger H G,1979. Waveguide tapers

transitions and couplers. Peter Peregrinus Ltd. London,

1

st

edition.