University of Birmingham
A Low-Loss Wideband Suspended Coaxial
Transmission Line
Llamas-Garro, I; Lancaster, Michael; Hall, Peter
DOI:
10.1002/mop.20386
Citation for published version (Harvard):
Llamas-Garro, I, Lancaster, M & Hall, P 2004, 'A Low-Loss Wideband Suspended Coaxial Transmission Line',
Microwave and Optical Technology Letters, vol. 43, no. 2, pp. 93-95. https://doi.org/10.1002/mop.20386
Link to publication on Research at Birmingham portal
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of the core and cladding are very similar” [6]. As observed from
Figure 3, this is only true for photonic-crystal fiber with small hole
diameters. The validity of this approach may therefore become
questionable for larger hole diameters.
More accurate results may be obtained by using numerical
differentiation to investigate the dispersion properties of photonic-
crystal fibers. Using values of n
1
obtained by the Sellmeier equa-
tion and corresponding values of n
2eff
(Fig. 3), the values of
propagation constant

are calculated for different wavelengths
using step-index fiber theory. The values of (

⌳) against (k⌳) are
modeled using a piecewise polynomial interpolation of order 3.
The normalized GVD in Eq. (3) is then obtained by differentiating
the interpolating polynomials. This procedure includes the effect
of dispersion in silica and does not need the addition of material
dispersion. Since no other approximations are used, the validity of
results obtained in this way is only limited by the degree of
accuracy to which the values of

have been computed.
Figure 5 shows the calculated results using the two different
approaches. The plots are given for the range of wavelength of
interest in current optical-fiber communication systems. Moreover,
outside this range of wavelength, the material (silica) dispersion
predominates over waveguide dispersion.
It may be observed that the normalized GVD calculated by both
procedures agree for small hole diameter, but not for larger holes.
This confirms the fact that the separation of normalized GVD into
the two components, as in Eq. (4), is only valid for a limited range
of hole diameters. The cause can be seen by examining the
variation of the refractive index of silica and that of the effective
refractive index with wavelength shown in Figure 3. For small hole
diameter, the variation of effective refractive index with wave-
length closely follows that of the refractive index of silica. How-
ever, for larger holes, the variation of effective index with wave-
length diverts from that of the refractive index of silica, thus
violating the principle upon which the separation is based [6].
CONCLUSION
Most of the reported research on photonic-crystal fibers uses a
nominal refractive index of silica, such as the “vector methods” in
[3, 7]. However, we note that in [7] material dispersion was
included by using an iterative algorithm and the standard Sellmeier
equation for calculating dispersion characteristics of a photonic-
crystal fiber.
In this paper, the separation of normalized GVD was shown to
be valid only for small hole diameters, in which case the variation
of the effective index closely follows that of the wavelength-
dependent refractive index of silica. It was further demonstrated
that, for a more accurate analysis encompassing a much wider
range of hole diameters, the wavelength-dependent refractive in-
dex of silica needs to be taken into account in all calculations.
REFERENCES
1. T.A. Birks, J.C. Knight, and P.St.J. Russel, Endlessly single-mode
photonic crystal fiber, Optics Lett 22 (1997), 961–963.
2. D. Mogilevtsev, T.A. Birks, and P.St.J. Russel, Group-velocity disper-
sion in photonic crystal fibers, Optics Lett 23 (1998), 1662–1664.
3. A. Ferrando, E. Silvestre, J.J. Miret, and P. Andres, Full-vector analysis
of a realistic photonic crystal fiber, Optics Lett 24 (1999), 276 –278.
4. R.K. Sinha and S.K. Varshney, Dispersion properties of photonic crys-
tal fibers, Microwave Opt Technol Lett 37 (2003), 129–132.
5. I.H. Malitson, Interspecimen comparison of the refractive index of
fused silica, J Optics Soc Am 55 (1965), 1205–1209.
6. D. Gloge, Dispersion in weakly guiding fibers, Appl Optics 10 (1971),
2442–2445.
7. D. Ouzonov, D. Homoelle, W. Zipfel, W.W. Webb, A.L. Gaeta, J.A.
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192 (2001), 219–223.
© 2004 Wiley Periodicals, Inc.
A LOW-LOSS WIDEBAND SUSPENDED
COAXIAL TRANSMISSION LINE
I. Llamas-Garro,
1
* M. J. Lancaster,
2
and P. S. Hall
2
1
Laboratory for Microsensors & Actuators
School of Electrical Engineering and Computer Science Seoul
National University
Kwanak P.O. Box 34
Seoul 151-600, South Korea
2
School of Electronic, Electrical and Computer Engineering
The University of Birmingham
B15-2TT, United Kingdom
Received 3 April 2004
ABSTRACT: This paper presents a transmission-line structure suitable
for micromachining technology. The structure is an air-filled square
coaxial cable, which is very low loss and has been designed in order to
utilise current manufacturing processes. This transmission line demon-
strates that such a structure can be designed to cover very wide band-
width. As the cable is air filled, the centre conductor needs to be sup-
ported and this is accomplished by attaching quarter-wavelength stubs
to the ground. The design method of such a cable is presented in detail and
the results of an X-band component are presented. © 2004 Wiley Periodi-
cals, Inc. Microwave Opt Technol Lett 43: 93–95, 2004; Published online
in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.
20386
Key words: coaxial transmission lines; microwave filters; millimetre
waves
1. INTRODUCTION
Today’s communications systems have a huge variety of carrier
frequencies where communications have traditionally been based
* I. Llamas-Garro’s current affiliation is Seoul National University, Seoul,
South Korea.
Figure 5 Total normalized GVD obtained by analytically evaluating the
sum of material and waveguide dispersion (dashed lines) and by numerical
differentiation (solid lines)
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 43, No. 2, October 20 2004 93
at frequencies around and below 2 GHz; however, it is now
common place to have systems based on many tens of gigahertz.
There are various types of technology for implementing these
systems and micromachined components are seen as a potential
candidate for low-cost, high-performance, receiver front ends. The
high precision of the micromachining is useful when the wave-
lengths become short. For all front-ends, the most important com-
ponent to consider is the basic transmission line or waveguide that
interconnects the various parts of the system and must be a
convenient structure for interface with other components as well as
having low loss. Several structures have been proposed over the
last few years, including a dielectric-filled coaxial line [1], sus-
pended coplanar line [2– 4], and air-filled microstrip [5, 6] or
inverted microstrip lines [7, 8].
Here, we propose a square coaxial cable for use with micro-
machining technology; such a cable is one of the lowest loss
structures for a given cross section. The proposed cable is air filled,
so that dielectric losses play no role in the attenuation. Addition-
ally, there is no radiation loss or cross coupling with other parts of
the circuit. A wideband transmission line is demonstrated at
around the X-band, but the intention is for the designs to be used
at much higher frequencies with construction out of laser ma-
chined metal [9], metal-coated thick resists such as SU8 [3, 6] or
metal-coated plasma-etched silicon wafers [10, 11]. One obvious
problem is that if the cable is air filled, how is the coaxial cable’s
centre conductor held up? This is achieved by quarter-wavelength
stubs which go from the centre conductor to the outer conductor at
appropriate intervals along the length of the cable. Of course, this
has a band-limiting effect, but the design described below maxi-
mises this bandwidth.
Figure 1 shows the construction of the cable. It is made of five
separate layers to allow for the micromachined construction pro-
cesses. The central layer, marked layer 3 in Figure 1, is the centre
conductor of the coaxial cable and the stubs can be seen connect-
ing this to the outer ground, which is on the same level. Layers 2
and 4 are the ground layers, with layers 1 and 5 forming the top
and bottom ground of the square coaxial structure, respectively.
Once these five layers are bonded together, a fully enclosed self-
suspended coaxial structure is formed.
The coaxial cable can be designed for wideband use. The best
way to do this and include the effects of the stubs is to use a
conventional filter-design technique, thus making the filter band-
width as wide as possible. This gives precise control over the
ripple and bandwidth of the coaxial cable. A simple Chebycheff
response is chosen. In order to minimise loss, it is important to
have a large cable cross section; however, there comes a point
where nonTEM modes begin to propagate [12, 13], and this
therefore limits the size. The particular filter demonstrated in this
paper has a centre frequency of 9 GHz with a 0.01-dB passband
ripple, and a 70% fractional bandwidth. The frequency at which
the nonTEM modes occur is 13 GHz. Although this particular
cable is at the X-band, a filter using these ideas has been produced
at 29.75 GHz for local-area multipoint distribution systems [9].
2. WIDEBAND TRANSMISSION LINE DESIGN
A general quarter-wavelength stub-supported transmission-line fil-
ter can be designed starting with a low-pass prototype filter. A
band-pass transformation can then be applied to obtain the band-
pass filter, which is implemented physically as shorted quarter-
wavelength stubs connected by quarter-wavelength transmission
lines. The design formulas and the general procedure to calculate
the impedance required for the different transmission line sections
are described in [14]. Table 1 contains all the resulting impedances
involved in the design and the low-pass prototype g values used.
The centre frequency for the design is 9 GHz, with a 70% frac-
tional bandwidth, having four poles with 0.01-dB passband ripple,
and a Chebycheff response.
Figure 1 Assembly of the self-supported coaxial transmission line.
[Color figure can be viewed in the online issue, which is available at
www.interscience.wiley.com.]
TABLE 1 Design Parameters for the Suspended Coaxial
Transmission Line
Low-Pass Prototype g Values
g
1
⫽ 0.7128, g
2
⫽ 1.2003, g
3
⫽ 1.3212, g
4
⫽ 0.6476, g
5
⫽ 1.1007
Characteristic Impedances of the Shunt Stubs
Z
1
⫽ 99.179 Z
2
⫽ 50.241 Z
3
⫽ 50.24 Z
4
⫽ 99.174
Characteristic Impedances of the Connecting Lines
Z
12
⫽ 45.879 Z
23
⫽ 44.167 Z
34
⫽ 45.88
Figure 2 Suspended coaxial transmission line supported by stubs: (a)
center conductor only and the dimensions of layer 3; (b) cross section of
the different impedance coaxial transmission-line sections. [Color figure
can be viewed in the online issue, which is available at www.
interscience.wiley.com.]
94 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 43, No. 2, October 20 2004
The different impedances needed for the suspended coaxial
transmission line can be achieved by varying the size of the centre
conductor [15]; here, the size of the outer conductor is fixed. The
centre conductor of the resulting suspended coaxial transmission
line is shown in Figure 2(a), with the cross-sections of the 50⍀ line
and the stubs shown in Figure 2(b). The input and output of the
suspended transmission line, as shown in Figure 1, consist of 50⍀
sections of transmission line.
For the coaxial assembly shown in Figure 1, layer 3 is 1-mm thick,
and layers 2 and 4 are 2.25-mm thick. The complete device has an
enclosed overall dimension of 45 ⫻ 20 ⫻ 5.5 mm. The five layers
were clamped together for the experimental results given as follows.
3. RESULTS
The response of the suspended coaxial transmission line is shown
in Figure 3; good agreement between theory and experiment is
obtained. The transmission line was designed to work up to 13
GHz in a TEM mode; beyond this frequency, higher modes prop-
agate through the structure, thus leading to a dispersive coaxial
line. The suspended coaxial transmission line presented has low-
loss transmission, and a usable frequency range from 5 to 13 GHz.
The simulations were done according to [16]. The deviation of S
11
from the simulations at the higher frequencies is probably due to a
slight layer misalignment.
4. CONCLUSION
The layered air-filled coaxial cable discussed in this paper is a
compact transmission line suitable for manufacture using micro-
machining technologies. The cable has been successfully demon-
strated at the X-band, showing a low-loss wideband cable made
out of five conducting layers. It is important to note that the
structure allows the possibility of integrating other 3D structures
made out of planar machined layers, such as filters, coupling
structures, phase shifters, antennas, and delay lines.
REFERENCES
1. J.A. Bishop, M.M. Hashemi, K. Kiziloglu, L. Larson, N. Dagli, and U.
Mishra, Monolithic coaxial transmission lines for mm-wave ICs, High
speed semiconductor devices and circuits, Proc IEEE/Cornell Conf
Adv Concepts, Ithaca, NY, 1991, pp. 252–260.
2. K.J. Herrick, T.A. Schwartz, and L.P.B. Katehi, Si-micromachined
coplanar waveguides for use in high-frequency circuits, IEEE Trans
Microwave Theory Tech 46 (1998), 762–768.
3. W.Y. Liu, D.P. Steenson and M.B. Steer, Membrane-supported CPW
with mounted active devices, IEEE Microwave Wireless Compon Lett
11 (2001), 167–169.
4. J.-H. Park, C.-W. Baek, S. Jung, H.-T. Kim, Y. Kwon, and Y.-K. Kim,
Novel micromachined coplanar waveguide transmission lines for ap-
plication in millimetre-wave circuits Jpn J Appl Phys 39 (2000),
7120 –7124.
5. P. Blondy, A.R. Brown, D. Cross and G.M. Rebeiz, Low-loss micro-
machined filters for millimetre-wave telecommunication systems,
IEEE MTT-S Dig, Baltimore, MD (1998), 1181–1184.
6. J.E. Harriss, L.W. Pearson, X. Wang, C.H. Barron, and A.V. Pham,
Membrane-supported Ka band resonator employing organic microma-
chined packaging, IEEE MTT-S Dig, Boston, MA (2000), 1225–1228.
7. H. Henri, S. Gonzague, V. Matthieu, C. Alain, and D. Gilles, Ultra
low-loss transmission lines on low resistivity silicon substrate, IEEE
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and H. Yabuki, Packaging using microelectromechanical technologies
and planar components, IEEE Trans Microwave Theory Tech 49
(2001), 2099 –2104.
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rication for a Ka band filter, 4
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mun, Toulouse, France, 2003, pp. F55–F58.
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temperature reactive ion etching for bulk micromachining, IEEE Symp
Emerging Technologies and Factory Automation, 1994, pp. 48 –52.
11. C. Marxer, N.F. de Rooij, Micro-opto-mechanical 2 ⫻ 2 switch for
single-mode fibers based on plasma-etched silicon mirror and electro-
static actuation. J Lightwave Tech 17 (1999), 2– 6.
12. L. Gruner, Higher order modes in square coaxial lines, IEEE Trans
Microwave Theory Tech 31 (1983), 770 –772.
13. L. Gruner, Higher order modes in rectangular coaxial waveguides,
IEEE Trans Microwave Theory Tech MTT-15 (1967), 483– 485.
14. J.-S. Hong and M.J. Lancaster, Microstrip filters for RF/Microwave
applications, Wiley, New York, 2001.
15. T.-S. Chen, Determination of the capacitance, inductance, and char-
acteristic impedance of rectangular lines, IRE Trans Microwave The-
ory Tech 8 (1960), 510–519.
16. Ansoft HFSS. http://www.ansoft.com.
© 2004 Wiley Periodicals, Inc.
DUAL-FREQUENCY-SELECTIVE
SURFACES FOR NEAR-INFRARED
BANDPASS FILTERS
S. Govindaswamy,
1
J. East,
1
F. Terry,
1
E. Topsakal,
2
J. L. Volakis,
3
and G. I. Haddad
1
1
Solid State Electronics Laboratory
Electrical Engineering and Computer Science Department
University of Michigan
Ann Arbor, MI 48109
2
Department of Electrical and Computer Engineering
Mississippi State University
Mississippi State, MS 39762
3
Radiation Laboratory
Electrical Engineering and Computer Science Department
University of Michigan
Ann Arbor, MI 48109
Received 8 April 2004
ABSTRACT: A bandpass filter resonating at ⬃1.4
m and based on a
dual-frequency-selective surface design is fabricated and characterized
on a silicon substrate. The filter consists of square apertures arranged
J.L. Volakis is also a Professor and the Director of ElectroScience Laboratory,
Electrical Engineering Department, The Ohio State University, Columbus, OH
43212. E. Topsakal was formerly with the University of Michigan.
Figure 3 Response of the suspended coaxial transmission line. [Color
figure can be viewed in the online issue, which is available at www.
interscience.wiley.com.]
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 43, No. 2, October 20 2004 95
![Figure 1 Assembly of the self-supported coaxial transmission line. [Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]](/figures/figure-1-assembly-of-the-self-supported-coaxial-transmission-3krtdpzr.webp)
![Figure 2 Suspended coaxial transmission line supported by stubs: (a) center conductor only and the dimensions of layer 3; (b) cross section of the different impedance coaxial transmission-line sections. [Color figure can be viewed in the online issue, which is available at www. interscience.wiley.com.]](/figures/figure-2-suspended-coaxial-transmission-line-supported-by-33nt2lgj.webp)
![Figure 3 Response of the suspended coaxial transmission line. [Color figure can be viewed in the online issue, which is available at www. interscience.wiley.com.]](/figures/figure-3-response-of-the-suspended-coaxial-transmission-line-1bbjhs5w.webp)