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oscillators in Lur’s form. In addition, experiments have been
conducted at both the baseband and radio frequency to verify
the validity of our design and the feasibility of the proposed
secure communication systems. The circuit implementation is
simple, and the communication quality is reliable. The system
is useful for those analog communications where high privacy
is required.
REFERENCES
1. K.M. Cuomo and A.V. Oppenheim, Circuit implementation of
synchronized chaos with applications to communications, Phys
Rev Lett 71 Ž1993., 65᎐68.
2. C.W. Wu and L.O. Chua, A simple way to synchronize chaotic
systems with applications to secure systems, Int J Bifurc Chaos 3
Ž1993., 1619᎐1627.
3. H. Dedieu, M.P. Kennedy, and M. Hasler, Chaos shift keying:
Modulation and demodulation of a chaotic carrier using selfsynchronizing Chua’s circuits, IEEE Trans Circuits Syst II 40
Ž1993., 634᎐642.
4. T.X. Wu and D.L. Jaggard, On chaotic electromagnetic wave
propagation, Microwave Opt Technol Lett 21 Ž1999., 448᎐451.
5. J. Peinke, J. Parisi, O.E. Rossler,
and R. Stoop, Encounter with
¨
chaos, Springer-Verlag, Berlin, Germany, 1992.
6. M. Vidyasagar, Nonlinear systems analysis, Prentice-Hall, Englewood Cliffs, NJ, 1993.
䊚 2000 John Wiley & Sons, Inc.
PLANAR SIR MICROWAVE BANDPASS
FILTER USING HIGH-PERMITTIVITY
CERAMICS
Cheng-Liang Huang,1 Pau-Yeou Yen,1 and Min-Hung Weng1
Department of Electrical Engineering
National Cheng Kung University
Tainan, Taiwan 70101, R.O.C.
1
Recei¨ ed 3 March 2000; re¨ ised 26 April 2000
Figure 4 Experiment at RF band; carrier at 462.5625 MHz, sine
wave of 4 kHz Žinformation.@voltage amplitude of 0.1 V. Ža. Spectrum of transmitted RF signal. Žb. Scope view of hŽy. versus hŽx.. Žc.
Original information Žtop. and recovered information Žbottom.
gation. The lagged synchronization is also illustrated in Figure 4Žc.. By comparing with the original signal, the recovered
signal is replicated, except that there is a time delay of about
30 ␮ s. Such a delay usually does not cause any harmful effect
in a general voice communication system.
3. CONCLUSIONS
In this letter, a secure communication system employing
chaotic synchronization has been systematically investigated.
Theoretical analysis has been developed based on the Rossler
¨
410
ABSTRACT: High-permitti¨ ity dielectric ceramic materials ha¨ e been
applied in the fabrication of a planar stepped-impedance resonator (SIR)
microwa¨ e bandpass filter. The input r output ports of the filter are
formed with transmission lines directly tapped to the resonators. The
admittance matrix for the equi¨ alent circuit of the filter has been deri¨ ed
and transformed to the scattering matrix to initially determine the required spec. Losses and other EM effects are taken into account to
further modify the actual dimension of the designed filter. The designed
structures are simulated using an IE3D simulator. Fabricated filters are
measured by an HP8510B network analyzer. Sample results of the filter
performances demonstrate responses in good agreement with the computer simulations. 䊚 2000 John Wiley & Sons, Inc. Microwave Opt
Technol Lett 26: 410᎐413, 2000.
Key words: stepped-impedance resonator; bandpass filter; high-permitti¨ ity ceramics
1. INTRODUCTION
As wireless communications are expanding worldwide in the
market, miniaturization for personal communication equipContract grant sponsor: National Science Council of the Republic of
China
Contract grant number: NSC-87-2218-E-006-061
Contract grant sponsor: Foundation of Jieh-Chen Chen Scholarship,
Tainan, Taiwan, R.O.C.
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000
ment has become one of the most fundamental requirements
in communication system technology. The filter is one of the
most important components in communication systems. Compact size is an essential requirement in many microwave filter
applications, such as cellular telephones. The high dielectric
constant of ceramic material provides filters will small resonator sizes, as well as high quality factor Ž Qs. Ceramic
material with a high Q-value Ž)10,000. and high dielectric
constant provides a means to create small coaxial structures
that could be coupled to form combline bandpass filters w1x.
However, further miniaturization becomes marginal, and integration is not provided for this filter. Planar filters, such as
parallel-coupled filters w2, 3x, interdigital filters w4, 5x, combline
filters w6, 7x, hairpin filters w8x, ring filters, and disk filters w9x,
provide good integration ability.
Filters using uniform impedance resonators ŽUIRs. have
been popularly used in microwave communication systems.
However, they suffer from poor harmonic suppression since
the center frequency of the second passband with ␭r2 or
␭r4 resonators is two or three times the fundamental frequency. Although capacitor-loaded UIRs can avoid this problem, their Q-factors are degraded due to the electric field
concentration in the capacitor-loaded section. The steppedimpedance resonator ŽSIR. was developed as a solution to
that problem. It exhibited the ability to shift the second
passband frequency and a higher Q-value than that of the
conventional capacitor-loaded UIR w10, 11x. A very small
dielectric bandpass filter was fabricated with the introduction
of the ceramic lamination technique w12x. Furthermore, a
miniaturized two-stage bandpass filter in a combline configuration was also reported using the same technique w13x. Since
all of the strip-line resonators and tapped lines were arranged
in the same layer, it could save an additional layer, and
simplify the manufacturing process owing to its simple structure. However, further miniaturization of the dimensions of
the filter was constrained to its low-permittivity substrate
material such as alumina. Although a multilayer structure
could effectively reduce the size, it needed a flexible process
w14x. By replacing the substrate material with high-permittivity dielectric ceramics, a smaller size can be obtained. In this
paper, high permittivity ceramics ŽCa, Ba. O᎐Li 2 O᎐
Sm 2 O 3 ᎐TiO 2 ŽCBLST. with ␧ r s 97 were applied in the
fabrication of a planar SIR bandpass filter. Analysis and
simulation of the filter were also reported. The frequency
response of the fabricated planar SIR filter was measured by
an HP85105B network analyzer.
Figure 1
filter
Configuration of the planar SIR microwave bandpass
Figure 2
Parallel-coupled strip lines
network. The matrix elements are given by
Y11 s Y22 s Y33 s Y44 s yj
Y12 s Y21 s Y34 s Y43 s yj
Y14 s Y41 s Y23 s Y32 s j
Y13 s Y31 s Y24 s Y42 s j
1
2
1
2
1
2
1
2
Ž Ye q Yo . cot ␪
Ž Ye y Yo . cot ␪
Ž Ye q Yo . csc ␪
Ž Ye y Yo . csc ␪
Ž1.
where Ye and Yo represent the admittances of the even mode
and the odd mode, respectively. ␪ is the electrical length of
the strip lines. If one side of the parallel-coupled strip lines
Žports 3 and 4. is grounded, the admittance matrix can be
simplified to the two-port matrix expressed as follows:
yj
Ys
yj
1
2
1
2
Ž Ye q Yo . cot ␪
yj
Ž Ye y Yo . cot ␪
yj
1
2
1
2
Ž Ye y Yo . cot ␪
. Ž2.
Ž Ye q Yo . cot ␪
When coupled strip lines are cascaded as shown in Figure
3, the coupled SIR configuration is formed. The admittance
2. ANALYSIS AND IMPLEMENTATION OF PLANAR SIR
BANDPASS FILTER
Figure 1 shows the configuration of the planar SIR microwave bandpass filter. The filter was made of two ␭r4coupled SIRs sandwiched by two high-permittivity CBLST
ceramic layers. The CBLST ceramics exhibit the dielectric
properties: ␧ r s 97, Q = f s 7300 at 7 GHz, and ␶ f ; q1.5
ppmr ⬚C. Two tapped lines were arranged in the same layer,
and were connected to each resonator to form the inputroutput ports. Ground planes were accomplished by metallizing
the top and bottom walls. With one end grounded and the
other end opened, it formed a resonator structure.
The transmission performance can be realized by obtaining the even- and odd-mode impedances of the parallel-coupled strip lines, as shown in Figure 2. The open-circuit
admittance matrix, then, can be derived for the four-port
Figure 3
lines
Coupled SIR configuration with cascaded coupled strip
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000
411
matrix of the proposed geometry can be expressed as follows:
Ye2 q Ye1 tan ␪ 1 cot ␪ 2
w Y1, 2 x 2=2 s j
1
cot ␪ 2 y K e tan ␪ 1
2
Ye2 q Ye1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K e tan ␪ 1
sj
q
y
1 Ye2 q Ye1 tan ␪ 1 cot ␪ 2 1
1
2 cot ␪ 2 y K e tan ␪ 1
Yo 2 q Yo1 tan ␪ 1 cot ␪ 2
Ye2 q Ye1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K o tan ␪ 1
cot ␪ 2 y K e tan ␪ 1
Yo 2 q Yo1 tan ␪ 1 cot ␪ 2
Ye2 q Ye1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K o tan ␪ 1
cot ␪ 2 y K e tan ␪ 1
1 Yo 2 q Yo1 tan ␪ 1 cot ␪ 2
1
1
qj
1
y1
2 cot ␪ 2 y K o tan ␪ 1
and
y
q
Yo 2 q Yo1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K o tan ␪ 1
Yo 2 q Yo1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K o tan ␪ 1
y1
1
Ž3.
and
yj
w Y3 x 2=2 s
yj
1 Ye3 q Yo 3
yj
tan ␪ 3
2
1 Ye3 y Yo 3
yj
tan ␪ 3
2
1 Ye3 y Yo 3
Y11 q Y12 s yj
tan ␪ 3
2
tan ␪ 3
Ytotal s Y1, 2 q Y3
1 Ye2 q Ye1 tan ␪ 1 cot ␪ 2 1
1
2 cot ␪ 2 y K e tan ␪ 1
qj
1 Yo2 q Yo1 tan ␪ 1 cot ␪ 2
2
yj
y
yj
cot ␪ 2 y K o tan ␪ 1
1 Ye3 q Yo 3
2
tan ␪ 3
1 Ye3 y Yo 3
2
tan ␪ 3
yj
yj
1
1
1
y1
y1
1
1 Ye3 y Yo 3
2
tan ␪ 3
1 Ye3 q Yo 3
2
Ye2
tan ␪ 3
qj
1
2
⭈
Ye2 q Ye1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K e tan ␪ 1
Ž7.
where Yei and Yoi represent the admittances of the even and
odd modes of the ith coupled strip lines, respectively. ␪ i is
the electrical length of the ith coupled striplines. K e s
Ye1rYe2 and K o s Yo1rYo 2 . The admittance for the entire
circuit then can be obtained as
sj
2
⭈
Ž4.
1 Ye3 q Yo 3
2
1
.
Ž5.
tan ␪ 3
where yY12 is the coupling between ports 1 and 2. The
admittance matrix of ports 1 or 2 to ground is denoted as
Y11 q Y12 . They can be further converted to a scattering
matrix to determine the parameters of the filter. The effects
of losses and discontinuities on the SIR structure were also
taken into account in practical filter design.
An SIR microwave ceramic bandpass filter centered at 890
MHz with a 3 dB bandwidth of 45 MHz was designed based
on the previously discussed method. Substrates were made of
CBLST dielectric material, which has a very high permittivity
of 97. The resultant dimensions of the filter were 0.8 mm =
0.6 mm = 0.1 mm. Figure 5 shows the computer simulation
result by using IE3D. The insertion loss and return loss of the
filter were y1.95 and y15 dB, respectively. Measurement of
the filter response was accomplished by using an HP8510B
network analyzer, and the result is illustrated in Figure 6. It
was observed that the insertion loss and return loss at a
center frequency of 1.015 GHz were y2.8132 and y7 dB,
respectively. A 3 dB bandwidth of 90 MHz was measured in
the experiment.
3. CONCLUSION
An equivalent ␲-network for the SIR bandpass filter is illustrated in Figure 4, which is useful in realizing the transmission characteristics, and can be expressed as
yY12 s j
1
2
⭈
Ye2 y Yo 2
tan ␪ 3
qj
1
2
yj
Figure 4
412
⭈
1
2
By using coupled strip-line theory and an admittance matrix,
a planar SIR microwave ceramic bandpass filter was designed
Yo 2 q Yo1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K o tan ␪ 1
⭈
Ye2 q Ye1 tan ␪ 1 cot ␪ 2
cot ␪ 2 y K e tan ␪ 1
Equivalent ␲-network of the SIR bandpass filter
Ž6.
Figure 5
Response of the SIR filter by IE3D simulation
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000
12. T. Ishizaki, M. Fujita, H. Kagata, T. Uwano, and H. Miyake, A
very small dielectric planar filter for portable telephones, IEEE
Trans Microwave Theory Tech 42 Ž1994., 2017᎐2022.
13. T. Ishizaki and T. Uwano, A stepped impedance comb-line filter
fabricated by using ceramic lamination technique, IEEE MTT-S
Dig 1994, WE1C-4, pp. 617᎐620.
14. C.-L. Huang and H.-S. Hsueh, Multilayer ceramic bandpass filter
at microwave frequency, Microwave Opt Technol Lett 24 Ž2000.,
258᎐260.
䊚 2000 John Wiley & Sons, Inc.
Figure 6
Measured frequency response of the SIR filter
and fabricated. The size of the filter can be further reduced
owing to the introduction of high-permittivity dielectrics
CBLST. The frequency response of the designed bandpass
filter was found to agree well with the simulation result. The
measured insertion loss of y2.8132 dB was higher than the
result Žy1.95 dB. from simulation since that CBLST exhibits
a Q = f value of 7300 at 7 GHz. It also expends the 3 dB
bandwidth. A 14% frequency shift was observed due to the
existence of a gap between the substrates. The pattern mismatch and the 90⬚ bend between resonators and inputroutput ports may also cause an error. With a cofiring process,
improvement of the filter response would be expected, although the measured result still agrees well with the simulation. The planar SIR filter using high-permittivity ceramics
can find many applications in today’s wireless communication
systems.
REFERENCES
1. C.-C. You, C.-L. Huang, and C.-C. Wei, Single-block ceramic
microwave bandpass filters, Microwave J 37 Ž1994., 24᎐35.
2. S.B. Cohn, Parallel-coupled transmission line resonator filters,
IRE Trans Microwave Theory Tech Ž1958., 223᎐231.
3. M. Makimoto and S. Yamashita, Bandpass filters using parallel
coupled stripline stepped impedance resonators, IEEE Trans
Microwave Theory Tech MTT-28 Ž1980., 1413᎐1417.
4. G.L. Matthaei, Interdigital band-pass filter, IEEE Trans Microwave Theory Tech MTT-10 Ž1962., 479᎐491.
5. S. Caspi and J. Adelman, Design of combline and interdigital
filter with tapped-line input, IEEE Trans Microwave Theory
Tech 36 Ž1988., 759᎐763.
6. G.L. Matthaei, Comb-line band-pass filter of narrow or moderate
bandwidth, IEEE Trans Microwave Theory Tech MTT-11 Ž1963.,
82᎐91.
7. J.A.G. Malherbe, Microwave transmission line, Artech House,
Norwood, MA, 1979.
8. U.H. Gysel, New theory and design for hairpin-line filters, IEEE
Trans Microwave Theory Tech MTT-22 Ž1974., 523᎐531.
9. J.S. Hong and M.J. Lancaster, Theory and experiment of novel
microstrip slow-wave open-loop resonator filters, IEEE Trans
Microwave Theory Tech 45 Ž1997..
10. M. Makimoto and S. Yamashita, Compact bandpass filters using
stepped impedance resonators, Proc IEEE 67 Ž1979., 16᎐19.
11. M. Makimoto and S. Yamashita, Bandpass filters using parallel
coupled stripline stepped impedance resonators, IEEE Trans
Microwave Theory Tech MTT-28 Ž1980., 1413᎐1417.
COMPARISON OF MOMENT-METHOD
SOLUTIONS FOR WIRE ANTENNAS
ATTACHED TO ARBITRARILY
SHAPED BODIES
1
J. M. Taboada,1 J. L. Rodrıguez,
and F. Obelleiro1
´
1
Departamento de Tecnoloxıas
´ das Communicacions
´
E.T.S.E. Telecomunicacion
´
Universidade de Vigo
36200 Vigo, Spain
Recei¨ ed 22 March 2000
ABSTRACT: A comparison of different testing procedures for subdomain moment-method formulations for arbitrarily shaped bodies, including attached wires, is presented here. It is shown that an accurate
e¨ aluation of the impedance matrix elements leads to important benefits
o¨ er the con¨ entional procedures. Otherwise, the use of an adapti¨ ely
generated meshᎏmore refined nearby the sourcesᎏis shown to reduce
the total number of unknowns, and therefore, the computational cost for
a fixed problem. 䊚 2000 John Wiley & Sons, Inc. Microwave Opt
Technol Lett 26: 413᎐419, 2000.
Key words: method of moments; attachments; Galerkin procedure;
adapti¨ e meshing
1. INTRODUCTION
The analysis of wire antennas mounted on complex conducting structures is addressed here. This problem requires a
good description of the electromagnetic behavior of the whole
body, including the coupling and junction effects between the
antennas and the supporting structure. For these kinds of
problems, the method of moments ŽMoM. w1x is the most
suitable tool due to its accuracy and versatility. By means of
this technique, an approximate induced current distribution
is obtained in the form of a series of known expansion Ž basis.
functions, usually defined over small portions of the body
surface Žsubdomain basis.. However, the high computational
cost of the MoM makes its application to electrically large
objects prohibitive due to the large number of expansion
terms required in order to accurately model the current
distribution.
Several subdomain MoM techniques have been developed
and applied to complex structures with connected wires. In
w2x and w3x, a point-matching w1x MoM approach considering
special functions for wire-to-surface junctions was presented.
In that work, the attachment points had to be located at the
Contract grant sponsor: E. N. Bazan
´
Contract grant sponsor: CICYTrFEDER
Contract grant number: Project Ref. 1FD97-0922
MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 26, No. 6, September 20 2000
413
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