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Air-filled square coaxial transmission line and its usein microwave filters

I. Llamas-Garro, M.J. Lancaster and P.S. Hall

Abstract: A suspended coaxial transmission line with an air propagation medium is presented. Thetransmission line is made only of metal, thereby avoiding dielectric and radiation losses. Short-circuit stubs suspend the centre conductor of the coaxial structure which is used in the design of twodual-mode narrowband microwave filters. Stacked layers of copper sheets are used to form thesquare coaxial transmission line, which has low loss and low dispersion.

1 Introduction

There is currently considerable interest in using micro-

machining technology in the implementation of microwaveand millimetre-wave passive circuits and numerous struc-tures have been presented in the literature. The objective isto have a micromachined structure which has lowpropagation loss and can be fabricated using currentlyavailable processes. The structures should also be able to beeasily integrated with other passive and active components.

Coaxial transmission lines are compact in size, andpresent low loss and low dispersion, making them a suitablestructure for the design of millimetre-wave circuits. Atmillimetre-wave frequencies the use of low loss and lowdispersion micromachined devices has mainly been targetedon the investigation of suspended microstrip lines [13]. Thethin centre conductor of the microstrip is usually suspended

by thin membranes. The layered coaxial structure proposedhere is more compact and has outstanding low losscharacteristics [4], compared with [13]. One of the fewstructures that exhibits lower loss is the rectangularwaveguide. However, at the frequencies of interest, this istoo large for micromachining processes and is alsounsuitable for many applications because of its size. Theair-filled coaxial cable has the advantages of small size andlow dispersion compared with the waveguide, and has anair propagation medium and high power characteristics. Anair-filled square coaxial transmission line can be optimisedto give a low attenuation constant by using a highlyconducting metal and by choosing an appropriate cross-section for the coaxial line.

The complete filter is shown in Fig. 1a. It is fabricatedfrom five conducting plates. Layer 3 is the middle layer andcontains the centre conductor of the square coaxial cable. Aplan view of this layer is shown separately in Fig. 1b, andconsists of an input feed line which is supported by quarter-wavelength stubs which are grounded. There is then acapacitive gap between the feed line and the resonator.

After the resonator there is another capacitive gap to theoutput transmission line. The design of the dual-mode filteris presented in Section 3 and details of the stub-suspended

transmission line can be found in [5]. The other layers inFig. 1a form the outer conductor, with layers 2 and 4providing the sidewalls and layers 1 and 5 forming the topand bottom of the coaxial cable.

In order to demonstrate these ideas, two suspended dual-mode narrowband filters having a 1% fractional bandwidth

a

b

layers

2 and 4

layers

1 and 5

alignment

holes

layer 3

connector

guide

d d

quarter-wavelength

stubs

capacitive gaps

air gaps

feeds

copper

resonator

Fig. 1 Layered coaxial filtera Five-layer coaxial assembly

b Top view of layer 3, showing the centre conductor of the coaxial

cable filter

The authors are with the Department of Electronic, Electrical and ComputerEngineering, School of Engineering, The University of Birmingham,Birmingham, B15 2TT, UK

E-mail: [email protected]

r IEE, 2005

IEE Proceedings online no. 20041159

doi:10.1049/ip-map:20041159

Paper first received 22nd March and in revised form 6th August 2004

IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 3, June 2005 155
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(FBW) centred at 9.1 and 29.75 GHz will be presented; theKa-band filter has potential application in a local areamultipoint distribution system.

2 Design of square-cross-section cables

To obtain a low-loss coaxial transmission line, for a givenoperating frequency range, the cross-sectional area of thecoaxial structure should be optimised. Figure. 2 shows anair-filled square coaxial transmission line. The appropriatechoice of cross-section to be used in a specific design is atrade-off between having a low attenuation constant for thetransmission line and predicting at what frequency thehigher modes will start to propagate. When higher modesare present, these lead to a dispersive transmission line, sofor most applications it is desired to propagate only a TEMmode. Information to calculate the presence of non-TEMmodes in square coaxial lines are given in [6].

The impedance of the square coaxial line in Fig. 2, can becalculated by [7]:

ZO 47:09ffiffiffiffier

p b w 0:2794b 0:7206w for b=wo2:5 1


p log10 0:9259 bw

for 2:5 b=w 4 2


p log10 0:914b

w

for b=w44 3

The attenuation constant due to conductor loss for thesquare coaxial line, can be calculated by [7]:

ac 47:09RsZoZO

1 bw

w0:2794b 0:7206w 2

for b=wo2:5 4

ac 59:37RsZoZO

1 bw

1

bfor 2:5 b=w 4 5

ac 59:96RsZoZO

1 bw

1

bfor b=w44 6

To choose the appropriate size for the cross-section of atransmission line, the following factors need to be taken intoaccount. A larger cross-sectional area for the line has thebenefit of having a low attenuation constant, as shown inFig. 3e. For the coaxial filters discussed in this paper, it isdesired to propagate only a TEM mode, which is thelowest-order mode in a coaxial line. We will design outtransmission line in such a way that the frequencies at whichthe higher-order modes begin to propagate is above thefilter operating frequency, which now limits the size of thecross-section.

Before moving on to the detailed discussion of the designit is interesting to compare the conductor losses of varioustypes of transmission line to justify our choice of a squarecoaxial cable. This comparison is shown in Fig. 3. Differenttransmission line cross-sections are considered in Fig. 3,these are the round coaxial (Fig. 3a), the square coaxial,(Fig. 3b), the microstrip (Fig. 3c) and the stripline (Fig. 3d).All transmission lines illustrated in Fig. 3 are air-filled andwe assume that there are no radiation losses, since it iscommon practice to have a completely shielded microstripor stripline. The cross-sectional area considered for themicrostrip and stripline were chosen to be approximatelythose that can be used in a practical transmission line. In

smaller areas coupling between adjacent microstrips canbecome very important. This is a little arbitrary but gives an

w b

Fig. 2 Air-filled square coaxial transmission line

round coaxial

square coaxial

microstrip (n=3)

stripline (n=1)

stripline (n=3)

microstrip (n=1)

0

0.5

1.5

2.5

1.0

2.0

5 10 20 3015 25

attenua

tionloss,

dB/m

area of the cross-section, mm2

b

a

round coaxial

area = b2

a

stripline

where n= 1,3area = b(2nb+ w)

d

b

b

w

square coaxial

area = b2

b

ewhere n= 1,3

microstrip

area = 2d(w+ 2nd)

c

w+ 2nd

nd

w

2b

w+ 2nb

nb

wb t

Fig. 3 Various different types of transmission linea Cross-section of a round coaxial cable

b Cross-section of a square coaxial cable

c Cross-section for a microstrip line

d Cross-section for a stripline transmission line

e Attenuation loss as a function of area for each transmission line

156 IEE Proc.-Microw. Antennas Propag., Vol. 152, No. 3, June 2005
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estimate for the comparison. The thickness of the centreconductor assumed for the microstrip and stripline is takento be 10mm, which is many skin depths at the comparisonfrequency of 29.5 GHz. The computed attenuation loss dueto the conductor, for 50O transmission lines, with differentcross-sectional areas is represented by the lines in Fig. 3e.Here we can see that the lowest attenuation is for the roundcoaxial cable, this is because it has a smooth surface-currentdistribution compared with the square coaxial cable, but thesquare cable is easier to fabricate using planar machinedlayers as discussed in this study. The formulas to calculatethe attenuation constant for the round coaxial cable can befound in [8], and the formulas to calculate the attenuationconstant for the microstrip and the stripline can be foundin [9].

For the Ka-band filter described in this paper, the 50Ofeed lines have a total area of 5.88 mm2. This gives anattenuation of approximately 1.5dB/m; the non-TEMmodes begin to propagate at approximately 44 GHz.Similarly, for the X-band filter, the 50O feed lines have atotal area of 81 mm2; this gives an attenuation ofapproximately 0.053 dB/m, and for this size the non-TEMmodes begin to propagate at approximately 14 GHz. Thesimulations to obtain the theoretical response of the filters

discussed in this paper were all performed using HFSS [10],and all simulated responses assumed perfect conductors toreduce the computation time.

3 Dual-mode filter design

The design procedure of the dual-mode filter follows aconventional filter design method, which starts with a low-pass prototype filter. The initial g values are then calculatedfrom these, a band-pass transformation can be applied andthe coupling coefficients between the modes of the resonator(kc), and the external quality factor (Qe) can be calculated.This general design procedure can be used regardless of the

physical shape of the filter, and is described in [11]. Thedual-mode filters were designed to have a narrowbandwidth and the following design issues were taken intoaccount. An increase in the number of resonators makes theinsertion loss increase for a given bandwidth, and it shouldalso be mentioned that as the bandwidth gets narrower, fora given filter topology, the filter insertion loss increases. Thedual-mode design presented is a compact, low loss wayto achieve this bandwidth inside an air-filled coaxial cable.The g values of the low-pass filter were chosen to have asmall pass-band ripple at the sacrifice of filter roll-offoutside the pass-band. The filters were designed to have a0.01dB band-pass ripple, and a 1% FBW at 9.1 and29.75GHz. Both have a Chebycheff response. The low-passprototype g values, the coupling between the two resonantmodes of the resonator, and the external quality factor aresummarised in Table 1.

The cross-shaped resonator is shown in Fig. 4; it supportsitself in the coaxial transmission line by using the two stubsthat fix it in the middle of the cable and keep it grounded to

the walls, as shown in Fig. 1. The coupling between the tworesonant modes of the resonator is controlled by modifyingthe dimensions A and B in Fig. 4.

The coupling coefficient between the resonant modes canbe calculated using a full-wave simulation of the wholestructure [10], by varying the dimensions A and B of theresonator. If the dual-mode resonator is simulated withparticular values ofA and B, the output from the simulationfor S12 would be similar to that in Fig. 5. The two peaks are

caused by the interaction of the two resonant modes. FromFig. 5, the coupling coefficient is given by [11]:

kij f2

2 f21f22 f21

7

where f1 and f2 are the frequencies of the two coupled peaks.By performing several separate simulations with differentvalues ofA and Bit is possible to produce the graphs shownin Fig. 6. These are for the Ka-band filter, for different

resonator dimensions, similar graphs can be obtained forthe X-band filter. Once this data has been produced it iseasy to read off a value of A and B to match with thecoupling coefficient kc in Table 1. The size of the capacitivegap (dimension din Fig. 1b), between the resonator and thefeed line needs to be adjusted to obtain the required externalQ, this is done in a similar way to the coupling coefficientsand is detailed in [11]. The dimensions of layer 3 for thefilters discussed in this paper are shown in Fig. 7. It shouldbe noted that there is a slight difference in the input andoutput of both filters; this is because the Ka-band filter isdesigned in such a way that a K connector can be mounteddirectly onto the structure.

A self-supported feed line was designed to provide input

and output connections to the dual-mode filter. The designconsists of a 50O transmission line supported by twoquarter wavelength stubs, as shown in Fig. 8a. The stubs are

Table 1: Design parameters for the dual-mode filters

Filter low-pass element gvalues

g1 0.4488 g20.4077 g31.1007

Qe and the coupling between modes

QeAE QeB 44.88 kc0.023

A

B

stubsdual mode resonator

Fig. 4 Plan of layer 3 of the filter in Fig. 1, showing just the dual-mode resonator

S21

f1

f2

f

mag

nitude,

dB

Fig. 5 S21 simulated response for the dual-mode resonator

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one-quarter wavelength long at the centre frequency of thefilters, since this will achieve a good open circuit at the pointwhere it supports the transmission line at the centre

frequency of the filter. Thus, they serve only as a mechanicalsupport for the centre conductor of the coaxial line; ofcourse this limits the usable bandwidth to some extent, ascan be appreciated in Fig. 8b. This Figure shows thesimulated response [10] for just the feed line structure for theKa-band filter. This bandwidth is more than adequate forthe narrowband filters studied. If wider bandwidths arerequired, a wideband coaxial transmission line using thesame stubs can be found in [5].

The square coaxial structure is made out of fiveplanar copper layers, which are machined, aligned andcompressed together to form the three-dimensional coaxialstructure. For this layered coaxial filter design, or for

any general stub supported multilayer coaxial circuit, layermisalignment should be considered in both the designand fabrication technique. Layer misalignment for thefilter presented in this paper is critical between layer 3 andlayers 2 and 4, because it can modify three characteristicsof the transmission line filter; the first one is the bandwidth,as misalignment can slightly modify the dimensionsof the resonator in the middle of the structure changingthe coupling between resonant modes. The second one isthe frequency shift of the mechanical supports, sincemodification of the effective lengths of the quarter-wavelength stubs will modify the usable bandwidth.The third one is the characteristic impedance of thecoaxial line, which can be changed by layer misalignments.

The assembly of the coaxial filters is shown in Fig. 1a.For the Ka-band filter, all layers are 0.7 mm thick,and the overall enclosed dimensions of the filter are

2.20.015

0.025

0.035

0.045

1.8 2.6 3.0 3.83.4

k12

B, mm

a

k12

A, mm

b

0.024

0.022

0.020

0.018

0.016

6.0 6.2 6.4 6.6 6.8 7.0 7.2

Fig. 6 Coupling coefficient for the Ka-band filtera When A is fixed to 6 mm

b When B is fixed to 3 mm

(0.7

3)

(0.1

0)

(6.1

3)

(2.9

0)

(0.9

0)

(0.5

0)

(0.5

0)

(3)

(2.80)

(1.23)

(9) (0.95)(3.75)

(3.75)

(8.15)

(9.50)

(20)

(3)

(1.85)

(1)

a

b

Fig. 7 Dimensions of layer 3All dimensions are in mm

a Ka-band filter

b X-band filter

a

good open

good short

quarter

wavelength

stub

50 input port

to filterfeed

b

26 27 28 29 30 31 32 33

0

10

20

30

40

50

60

70

S11,

dB

S21,

dB

frequency, GHz

f vs S21

f vs S11

0

0.1

0.2

0.3

0.4

0.5

Fig. 8 Feed of the dual-mode filtera Layout

b Response

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14mm 7.5 mm 2.1 mm. For the X-band filter, all layersare 2 mm thick, and the overall enclosed dimensions are40mm 25mm 6mm.

The X-band filter was produced by conventionalmachining, as the minimum dimension to mill was 1 mm.

However the Ka-band filter requires high precisionmachining, making conventional machining impossible touse since dimensions need to be kept within a few micronstolerance. The minimum dimensions were 0.2mm for thefilter and 0.1 mm for the K connector interface. The 0.1 mmvalue was carefully determined in order to obtain theappropriate external Q-value. For this particular filter, lasermachining was used which was able to provide the requiredsmall holes with an excellent accuracy. The filter plates wereclamped together for both filters. Other methods ofconstruction for integrated coaxial devices are metal-coatedthick resists, such as SU8 [3], or metal-coated reactive-ion-etched silicon wafers [12, 13].

The band-pass response of the dual-mode X-band filter isshown in Fig. 9 where a good agreement between theoryand experiment can be observed. The measured bandwidthincreased due to layer misalignment, which slightly changedthe coupling between the two modes.

The band-pass response of the dual-mode Ka-bandfilter is shown in Fig. 10 where a reasonable agreementbetween theory and experiment can be observed. Anincrease in the losses of this filter can be seen which isbelieved to be caused by the surface roughness of the copperplates, combined with a reduction in the quality ofthe copper, caused by the laser machining process. Weare currently investigating alternative of microfabricationtechniques [14] with the objective of finding a method

of microfabrication which can produce high qualityconductive layers out of which we can form the coaxialstructure. The return loss was degraded due to layermisalignment, which also changed the coupling betweenthe two modes, leading to an increase in the bandwidthof the filter. The transition from the connector to the circuitpresented a small mismatch, which was mainly causedby fabrication tolerances at the time of mountingthe connectors to the complete layered circuit. Never-theless, this new type of filter has been effectivelyimplemented.

4 Conclusions

Layered coaxial transmission line assembly presents apractical way of making low-loss microwave circuits, whichare compact in size. From this structure two dual-mode

narrowband filters were demonstrated. Microfabrication ormicromachining methods were devised to satisfy the designtolerances and layer finishing requirements to producequality air-filled coaxial devices for millimetre-wave opera-tion. Furthermore, millimetre-wave passive componentssuch as filters, antennas, coupling structures, delay lines andphase shifters can be easily matched and integrated usingthe multilayered low loss compact coaxial structure.

5 References

1 Blondy, P., Brown, A.R., Cros, D., and Rebeiz, G.M.: Low lossmicromachined filters for millimetre wave communication systems,IEEE Trans. Microw. Theory Tech., 1998, 46, (12), pp. 22832288

2 Brown, A.R., and Rebeiz, G.M.: A high performance integratedK-band diplexer, IEEE Trans. Microw. Theory Tech., 1999, 47, (8),pp. 14771481

3 Harriss, J.E., Pearson, L.W., Wang, X., Barron, C.H., and Pham,A.V.: Membrane-supported Ka band resonator employing organicmicromachined packaging, IEEE MTT-S Int. Microw. Symp. Dig.,2000, pp. 12251228

4 Llamas-Garro, I.: Micromachined microwave filters. PhD Thesis,University of Birmingham, UK, August 2003

5 Llamas-Garro, I., Lancaster, M.J., and Hall, P.S.: A low losswideband suspended coaxial transmission line, Microw. Opt. Technol.Lett., 2004, 43, pp. 9395

6 Gruner, L.: Higher order modes in square coaxial lines, IEEE Trans.Microw. Theory Tech., 1983, 31, (9), pp. 770772

7 Lau, K.H.: Loss calculations for rectangular coaxial lines, IEE Proc.H, Microw. Antennas Propag., 1998, 135, (3), pp. 207209

8 Rizzi, P.A.: Microwave engineering passive circuits (Prentice HallInc, 1988)

9 Pozar, D.M.: Microwave engineering (John Wiley and Sons Inc,

1998)10 Ansoft HFSS, http://www.ansoft.com11 Hong, J.-S., and Lancaster, M.J.: Microstrip filters for RF microwave

applications (John Wiley and Sons Inc, 2001)12 Shimizu, S., Kuribayashi, K., Ohno, M., Taniguchi, T., and Ueda, T.:

Low temperature reactive ion etching for bulk micromachining. Proc.IEEE Symp. on Emerging Technologies and Factory Automation,6-10 Nov 1994, pp. 4852

13 Marxer, C., and de Rooij, N.F.: Micro-opto-mechanical 2 2 switchfor single-mode fibers based on plasma-etched silicon mirror andelectrostatic actuation, J. Lightw. Technol., 1999, 17, (1), pp. 26

14 Llamas-Garro, I., Jiang, K., Jin, P., and Lancaster, M.J.: SU-8microfabrication for a Ka band filter. Proc. 4th Workshop on MEMSfor Millimeterwave Communications, LAAS-CNRS, Toulouse,France, 24 July 2003, pp. F55F58

8.4 8.8 9.2 9.6 10.0

10

20

30

40

0

frequency, GHz

magnitude,

dB

S11

measured

S21

simulatedS11 simulated

S21

measured

Fig. 9 Response of the dual-mode X-band filter

26 28 30 32 34

0

10

20

30

40

frequency, GHz

magnitude,

dB

S11

measured

S21

simulatedS11

simulated

S21

measured

Fig. 10 Response of the Ka-band filter

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