Compact Reconfigurable HF-UHF Antennas

134 Pages·2005·5.67 MB·English

Form Approved
REPORT DOCUMENTATION PAGE
OMB NO. 0704-0188

Public Reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering
and maintaining the data needed, and completing and reviewing the collection of information. Send comment regarding this burden estimates or any other aspect of this collection of
information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for information Operations and Reports, 1215 Jefferson Davis Highway, Suite
1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188,) Washington, DC 20503.
1. AGENCY USE ONLY ( Leave Blank) 2. REPORT DATE June 7, 2004 3. REPORT TYPE AND DATES COVERED
Final , 01 June 1999 to 31 Dec., 2003

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Compact Reconfigurable HF-UHF antennas DAAD19-99-1-0197

6. AUTHOR(S)
Kamal Sarabandi

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
Radiation Laboratory, Department of Electrical Eng. and Computer Science REPORT NUMBER
The University of Michigan 991549
Ann Arbor, MI 48109-2122
9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING / MONITORING
AGENCY REPORT NUMBER
U. S. Army Research Office
P.O. Box 12211
39879.2-EL
Research Triangle Park, NC 27709-2211

11. SUPPLEMENTARY NOTES
The views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as an official
Department of the Army position, policy or decision, unless so designated by other documentation.

12 a. DISTRIBUTION / AVAILABILITY STATEMENT 12 b. DISTRIBUTION CODE

Approved for public release; distribution unlimited.

13. ABSTRACT (Maximum 200 words)

The development of a compact reconfigurable HF-UHF antenna is of great practical importance in mobile
military communications where low visibility and high mobility are required. Variations of monopole and di[pole
antennas in use today are narrowband and are prohibitively large and bulky at these frequencies. Broadband
antennas are not only large, but also suffer from jamming susceptibility and undesirable complex multiplexing
requirements. Development of efficient, small geometry, planar, and reconfigurable antennas is investigated.
Based on a resonating slot structure, small antennas that exhibit simultaneous bandselectivity and antijam
characteristics. So far very small antennas using novel topologies have been developed that areas as small as
(0.05λ)2 . Also efficient reconfigurability over a very wide range of frequency using electronic switches has
been demonstrated. Design of DC contact efficient MEMS switches and wideband designs are also being
considered.

14. SUBJECT TERMS 15. NUMBER OF PAGES

Small antennas, Planar reconfigurable

16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT
OR REPORT ON THIS PAGE OF ABSTRACT
UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL
NSN 7540-01-280-5500 Standard Form 298 (Rev.2-89)
Prescribed by ANSI Std. 239-18
298-102

GENERAL INSTRUCTIONS FOR COMPLETING SF 298

The Report Documentation Page (RDP) is used for announcing and cataloging reports. It is important
that this information be consistent with the rest of the report, particularly the cover and title page.
Instructions for filling in each block of the form follow. It is important to stay within the lines to meet
optical scanning requirements.
Block 1. Agency Use Only (Leave blank) Block 12a. Distribution/Availability Statement.
Denotes public availability or limitations. Cite any availability
Block 2. Report Date. Full publication date to the public. Enter additional limitations or special markings
including day, month, and year, if available (e.g. in all capitals (e.g. NORFORN, REL, ITAR).
1 Jan 88). Must cite at least year.
DOD - See DoDD 4230.25, “Distribution
Block 3. Type of Report and Dates Covered. Statements on Technical
State whether report is interim, final, etc. If Documents.”
applicable enter inclusive report dates (e.g. DOE - See authorities.
10 Jun 87 - 30 Jun 88). NASA - See Handbook NHB 2200.2.
NTIS - Leave blank.
Block 4. Title and Subtitle. A title is taken from the part of the
report that provides the most meaningful and complete information.
When a report is prepared in more than one volume, repeat the Block 12b. Distribution Code.
primary title, and volume number, and include subtitle for the
specific volume. On classified documents enter the title DOD - Leave Blank
classification in parentheses. DOE - Enter DOE distribution categories
from the Standard Distribution for
Block 5. Funding Numbers. To include contract and grant unclassified Scientific and Technical
numbers; may include program element number(s) project Reports
number(s), task number(s), and work unit number(s). Use the NASA - Leave Blank.
following labels: NTIS - Leave Blank.

C - Contract PR - Project Block 13. Abstract. Include a brief (Maximum
G - Grant TA - Task 200 words) factual summary of the most
PE - Program WU - Work Unit significant information contained in the report.
Element Accession No.
Block 14. Subject Terms. Keywords or phrases
Block 6. Author(s). Name(s) of person(s) responsible for writing identifying major subject in the report.
the report, performing the research, or credited with the content of
the report. If editor or compiler, this should follow Block 15. Number of Pages. Enter the total
the name(s). number of pages.

Block 7. Performing Organization Name(s) and Block 16. Price Code. Enter appropriate price
Address(es). Self-explanatory. code (NTIS only).

Block 8. Performing Organization Report Block 17. - 19. Security Classifications. Self-
Number. Enter the unique alphanumeric report number(s) explanatory. Enter U.S. Security Regulations (i.e.,
assigned by the organization performing the report. UNCLASSIFIED). If form contains classified
information, stamp classification on the top and
Block 9. Sponsoring/Monitoring Agency Name(s) bottom of the page.
and Address(es) Self-explanatory.
Block 20. Limitation of Abstract. This block must
Block 10. Sponsoring/Monitoring Agency be completed to assign a limitation to the
Report Number. (if known) abstract. Enter either UL (Unlimited) or SAR (same
as report). An entry in this block is necessary if
Block 11. Supplementary Notes. Enter the abstract is to be limited. If blank, the abstract
information not included elsewhere such as; prepared in is assumed to be unlimited.
cooperation with....; Trans. of...; To be published in.... When a
report is revised, include a statement whether the new report
supersedes or supplements the older report.

REPORT DOCUMENTATION PAGE (SF298)
(Continuation Sheet)
Compact Reconfigurable HF-UHF Antenna

In this interim report the details of our progress during the last fiscal year is presented by providing the papers
submitted for publications in archival journals and conferences and symposia. We submitted four journal papers
and 4 conference papers, which have been presented or will be presented in the next few months. Two students
are working on this project which are partially supported by the funds provided by this grant.

Journal Papers Submitted for Publications

1. R. Azadegan, K. Sarabandi, "High-Q double spiral miniaturized slot-line resonator filters," IEEE Trans.
Microwave Theory and Tech. May. 2004, pp 1548-1557.

2. N. Behdad, and K. Sarabandi, "A Multi resonant Single-Element Wideband Slot Antenna", IEEE Antennas
and Wireless Propagation Letters, Vol. 3, 2004, pp. 5-8.

3. R. Azadegan, K. Sarabandi, "Bandwidth enhancement of miniaturized slot antennas using folded,
complementary and self-complementary realizations," submitted to IEEE Trans. Antennas Propagat. (Jan
04).
4. R. Azadegan, and K. Sarabandi, “A novel approach for miniaturization of slot antennas” IEEE Trans.
Antennas Propagat., March. 2003, pp 421-429.

5. K. Sarabandi and R. Azadegan, “Design of an efficient miniaturized UHF planar antenna,” IEEE Trans.
Antennas Propagat., June. 2003, pp 1270-1276.

6. Peroulis, D., Pacheco, S. P., K. Sarabandi, and L. Katehi, “Electromechanical Considerations in Developing
Low-Voltage RF MEMS Switches ” IEEE Trans. Microwave Theory and Techniques., Jan. 2003, pp 259-
270.

7. Behdad, N., and K. Sarabandi, “Bandwidth Enhancement and Further Size Reduction of a Class of
Miniaturized Slot Antennas”, IEEE Transactions on Antennas and Propagation, vol. 52, no. 8, pp. 1928-
1935, August 2004.

8. Peroulis, D., K. Sarabandi, and L. Katehi, “Design of Reconfigurable Slot Antennas”, IEEE Transactions on
Antennas and Propagation, to appear in Feb. 2005 issue

9. Peroulis, D., S. P. Pacheco, K. Sarabandi, L.P. Katehi, “Electromechanical Considerations in Developing
Low-Voltage RF MEMS Switches”, IEEE Transactions on Microwave Theory and Techniques, Vol. 51, No. 1,
pp. 259-270, January 2003.

Conference Papers

1. N. Behdad and K. Sarabandi, “Miniaturized Slot Antennas with Enhanced Bandwidth,” Proc. IEEE
Antennas Propagation & URSI Symp. Columbus, OH, June 22-27, 2003.
2. N. Behdad and K. Sarabandi, “Slot antenna miniaturization using distributed inductive loading,” Proc. IEEE
Antennas Propagation & URSI Symp. Columbus, OH, June 22-27, 2003.
3. R. Azadegan, and. K. Sarabandi, “A compact printed folded dipole antenna for wireless applications,” IEEE
Antennas Propagat. Symp. Columbus, OH., June 2003, vol. 1, pp.
4. R. Azadegan, and K. Sarabandi, “Miniaturized Slot-line and Folded-Slot Band-pass Filters”, IEEE
International Microwave Symposium, Philadelphia, PA, June 2003, vol. pp. 1595-1598.
5. Peroulis, D., K. Sarabandi, and L.P.B. Katehi, “Low Contact-resistance Series MEMS Switches”,
Proceeding: IEEE International Microwave Symposium, Seattle, WA, June 2-7, 2002.
6. Peroulis, S. P. Pacheco, K. Sarabandi, and L.P.B. Katehi, “Alleviating the Adverse Effects of Residual
Stress in RF MEMS Switches”, Proceeding: 31st European Microwave Conference 2001, London, U.K.
September 24-28, 2001.
7. Peroulis, D., K. Sarabandi, and L.P.B. Katehi, “A Planar VHF Reconfigurable Slot Antenna”, Proceeding:
IEEE International Antennas and Propagation & URSI Symposium, Boston, MA, July 14-18, 2001.
8. Peroulis, D., S. Pacheco, K. Sarabandi, and L.P.B. Katehi, “Tunable Lumped Components with
Applications to Reconfigurable MEMS Filters”, Proceeding: IEEE Microwave Theory and Technical
Symposium, Phoenix, Arizona, May 2001.
9. Peroulis, D., K. Sarabandi, L.P.B. Katehi, and B. Perlman, “Planar Reconfigurable Slot Antenna for
Communications”, SPIE's 8th Annual International Symposium on Smart Structures and Materials, Newport
Beach, CA, March 2001.
10. Peroulis, D., S. Pacheco, K. Sarabandi, L.P.B. Katehi, “MEMS Devices for High Isolation Switching and
Tunable Filtering”, Proceeding: IEEE Microwave Theory and Technology Symposium(MMT-S), June 11-
16, 2000, Boston, MA (Digest Vol. 2, pp. 1217-1220).
11. Peroulis, D., S. Pacheco, K. Sarabandi, L.P.B. Katehi, “MEMS Devices for High Isolation Switching and
Tunable Filtering”, Proceeding: IEEE Microwave Theory and Technology Symposium(MMT-S), June 11-
16, 2000, Boston, MA (Digest Vol. 2, pp. 1217-1220).

Scientific Personal
R. Azadegan, N. Behdad, D. Peroulis.

Report of Invention
N.A

Scientific Progress and accomplishments
See attached papers

Technology Transfer
R. Azadegan and K. Sarabandi “Efficient Miniaturized Resonant Slot antennas” (patent pending)
D. Peroulis and K. Sarabandi, “Reconfigurable Slot Antennas for VHF/UHF Applications”, Disclosure
submitted to University of Michigan Intellectual Property Office, February 2002. File no. UM2269.

MASTER COPY: PLEASE KEEP THIS "MEMORANDUM OF TRANSMITTAL" BLANK FOR REPRODUCTION PURPOSES. WHEN
REPORTS ARE GENERATED UNDER THE ARO SPONSORSHIP, FORWARD A COMPLETED COPY OF THIS FORM WITH EACH
REPORT SHIPMENT TO THE ARO. THIS WILL ASSURE PROPER IDENTIFICATION. NOT TO BE USED FOR INTERIM
PROGRESS REPORTS; SEE PAGE 2 FOR INTERIM PROGRESS REPORT INSTRUCTIONS.

MEMORANDUM OF TRANSMITTAL

U.S. Army Research Office
ATTN: AMSRL-RO-BI (TR)
P.O. Box 12211
Research Triangle Park, NC 27709-2211

Reprint (Orig + 2 copies) Technical Report (Orig + 2 copies)

Manuscript (1 copy) Final Progress Report (Orig + 2 copies)

Related Materials, Abstracts, Theses (1 copy)

CONTRACT/GRANT NUMBER: DAAD19-99-1-0197

REPORT TITLE: Compact Reconfigurable HF-UHF Antenna

is forwarded for your information.

SUBMITTED FOR PUBLICATION TO (applicable only if report is manuscript):

Sincerely,
Kamal Sarabandi
1548 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.52,NO.5,MAY2004
Miniature High-Q Double-Spiral
Slot-Line Resonator Filters
RezaAzadegan,StudentMember,IEEE,andKamalSarabandi,Fellow, IEEE
Abstract—Anewclassoflowinsertion-lossminiaturizedfilters example, was made possible first by employing microstrip
usingslot-lineresonatorsisproposed.Miniaturizationisachieved stepped-impedance resonators (SIRs) [5], [6] and then by
byterminatingtheslotlinewithadouble-spiralinductivetermina-
using hairpin-line resonators [7]. A more compact hairpin
tionatbothends.Usingthisminiaturizedresonator,bothpositive
filterusingsplit-ringresonatorswithparallelcoupledlineswas
andnegativecouplingsmayberealized,andtherefore,bothstan-
dardcoupled-lineandcross-coupledquasi-ellipticfiltersarerealiz- later proposed [8]. This resonator is a capacitively end-loaded
able.Theunloaded oftheseslot-linefiltersisconsiderablyhigher hairpin resonator where the loading is implemented by dis-
thanthatofminiaturizedmicrostripfiltersofcomparabledimen- tributed coupled lines. The loaded hairpin resonator, together
sionsduetotheinherenthigher oftheslotline.Todemonstrate
with the SIR, resulted in an improved hairpin resonator [9].
thevalidityofthedesignproceduresandtheperformancecharac-
Incorporating dissimilar resonators in filter designs has also
teristics,twodifferenttypesoffilterswerefabricatedandtested.
Oneisafour-poleChebyshevfilterandtheotherisaquasi-elliptic beenreported[9].
filterwhere,ineachcase,thefull-wavesimulationsshowverygood Another form of resonator, which is similar to the above
agreementwithmeasurements. hairpin resonators, utilizes square open loops [10]. To further
IndexTerms—Microstripfilters,microwavefilters,miniaturized reduce size, the open-loop structure can be modified by intro-
filters,quasi-ellipticfilters,slot-linefilters. ducinganarrowcapacitivegapattheopenendoftheloop[11].
The same authors suggested an aperture coupled two-layer
filter design using the same type of resonator [12]. Using the
I. INTRODUCTION
two sides of the substrate provides additional miniaturization.
MOBILEwirelesssystemsofvariouskindshavebeenthe Inbothloadedopen-loopandloadedhairpinresonators,electric
drivingforcebehindsubstantialresearcheffortstoward and magnetic coupling can be implemented, which allows for
miniaturizingRFfrontends.High- lowinsertion-lossminia- the flexible design of many structures, such as quasi-elliptic
turizedfiltersareimportantrequirements.Afewapproachesin filters.
the literature address filter miniaturization, among which are Slotlinesandcoplanarwaveguides(CPWs)areotherimpor-
the use of lumped-element filters, high temperature supercon- tantconfigurationsfortherealization ofresonatorsandfilters.
ducting (HTS) filters, bulk acoustic-wave (BAW) filters, and In the early 1970s, slot transmission lines were shown to be
slow-wavedistributedresonatorfilters[1]–[4]. a practical configuration for the realization of microwave fil-
Lumped-elementfilterscanbemadeverysmallatlowerfre- ters and couplers [13], but more attention has been devoted to
quencies.Athigherfrequencies,however,theirextremelysmall CPWfilters[14]–[16].Alsoknownasuniplanarconfigurations,
size mayresultin highinsertion lossand possibly lowpower- slot and CPWs are fundamental to many microwave and mil-
handlingcapacity.Tocopewiththeinsertion-lossproblem,HTS limeter-waveintegratedcircuits[17],[18].WithregardtoCPW
filtershavebeenproposed.BAWfiltersalsohaveexceptionally filterminiaturization,theuseofquarter-wavetransmission-line
small size and quite good performance, but may be extremely resonators,e.g.,a CPWhairpinresonator[19],meandered
expensivetodevelopforanynewapplication.Thesetwoclasses superconductingCPWfilters[20],double-surfaceCPWfilters
offiltersarenotfurtherconsideredinthispaper,thesubjectof [21], and air-bridge capacitive loadings have been proposed.
whichistointroduceanewtypeofhigh- coiledslot-lineres- Additionally,theperiodicloadingofCPWlineshasbeensug-
onator with comparison to the microstrip. On the other hand, gestedtoconstructaslow-wavetransmissionlineandhasbeen
conventionaldistributedelementfiltersusingcoupledtransmis- usedinthefabricationofaminiaturelow-passfilter[22].
sion-line resonators exhibit superior performance, but are fre- Incontrast,theliteratureconcerningtheuseofslotlinesfor
quentlytoolarge. filterdesignandfilterminiaturizationisrathersparse[23].The
In order to reach a compromise between size and per- of slot-line resonators is higher than that of microstrip res-
formance, some compact architectures have been proposed. onatorsofsimilardimensionsduetothefactthatthestoreden-
The size reduction of ordinary microstrip line resonators, for ergyintheresonatorisconfinedwithinalargervolumeandthat
theelectriccurrentflowsoverawiderarea,whichtranslatesinto
lowerohmiclosses.Actually,slotlinesarecomparabletosus-
ManuscriptreceivedDecember1,2003.
The authors are with the Radiation Laboratory, Department of Electrical pendedsubstratestriplines,whichalsohavehigher thanmi-
Engineering and Computer Science, The University of Michigan at Ann crostripsduetothelargervolumeoccupiedbythestoredenergy.
Arbor,AnnArbor,MI48109-2122USA(e-mail:[email protected];
Inthispaper,newfilterarchitecturesbasedonaminiaturized
[email protected]).
DigitalObjectIdentifier10.1109/TMTT.2004.827044 slotlinewithdouble-spiralinductiveterminationsareproposed.
0018-9480/04$20.00©2004IEEE
AZADEGANANDSARABANDI:MINIATUREHIGH- DOUBLE-SPIRALSLOT-LINERESONATORFILTERS 1549
TABLE I
EFFECTOFTHESLOT-TO-STRIPWIDTH(s=w)ONTHEUNLOADEDQOF
THEMINIATURIZEDSLOT-LINERESONATOR
Fig.1. Proposedminiaturizedresonatorcapacitivelycoupledat400MHzwith
asymmetricendloadings.
Bothelectricandmagneticcouplingsareachievablebyappro-
priategeometriclayoutoftheminiaturizedresonators,enabling
quasi-ellipticfilterstobedesigned.
II. MINIATURIZEDSLOT-LINERESONATORTOPOLOGY
Fig. 2. Miniaturized slot-line resonator topology with different ratios of
Recently, the authors proposed a highly efficient miniatur-
slot-to-stripwidth(s=w).
izedslotantennausingaresonantslot-linegeometry[24].Com-
paring this slot antenna with its complementary printed strip
Usingtherelationship[1]
counterpart shows a considerable increase in the antenna effi-
ciencymainlyduetolowerohmiclosses[25].Thus,miniatur- (1)
ized slot-line resonators may be expected to exhibit higher
where isalineardimensionoftheresonator,and isacon-
thantheirmicrostripversions.
stant defined as a figure-of-merit, a better comparison can be
Fig. 1 shows the geometry of the miniaturized slot-line res-
madebetweenminiatureslot-lineandmicrostripresonators.For
onatorwithdouble-spiralinductiveterminations.Theverycom-
microstrip resonators, is defined as the substrate thickness,
pact inductive end loading is realized by coiled shorted slot
while for the slot resonators, represents the slot width. In-
lines, each with a length smaller than a quarter-wavelength.
voking(1),thefigure-of-meritconstant isfoundtobe
Thisresonatorexhibitsasuperiorminiaturizationfactorandis
fortheminiaturizedhairpinresonator[8],and for
capable of generating electric, magnetic, and mixed coupling
theslot-lineresonatorofFig.1.
mechanisms.
TheohmiclossoftheCPWlinesandslotlinesisdrastically
To assess the performance of the miniature slot-line res-
affectedbythewidthoftheslotor,equivalently,theimpedance
onators, a capacitively coupled miniaturized resonator, as
of the line [13]. At resonance, the electric current distribution
shown in Fig. 1, was fabricated on a 0.787-mm-thick Duroid
onthegroundplanearoundtheslothasahigherconcentration
substrate with a dielectric constant of and a loss
near the edges. By makingthe slotwider, the peak of the cur-
tangentof .1 Thesamesubstrateisusedforthe
rentattheedgesisreduced,andasmoothercurrentdistribution
restofthedesignspresentedinthispapertogivedirectcompar-
away from the slot edges is obtained. Lower current distribu-
isons. A low-permittivity substrate was used to minimize the
tionattheedgestranslatesintolowerohmiclosses.Inorderto
effects of dielectric loading on miniaturization. The resonator
obtainthe best , for a givenresonator, the width of the slot
of Fig. 1 is designed to operate at 400 MHz and fits within
linemaybeoptimized.TableIcomparestheunloaded ofthe
a rectangular area with dimensions . The
proposedminiaturizedresonatortopologywithanumberofdif-
unloaded canbefoundusingasingle-portimpedance/admit-
ferentslot-linewidths(seeFig.2).Inthisstudy,theoverallsize
tance measurement technique referred to as the critical-point
of the resonator is fixed while ( ), i.e., the ratio of the slot
method [26]. The unloaded of the miniaturized resonator
width( )totheadjacentmetallicstripwidth( ),isvariedasa
at 400 MHz was measured to be , which compares
parameter.Fortheproposedminiaturizeddouble-spiralslotres-
favorably with the of miniaturized hairpin resonators [8],
onator,thewidthofthemetallicstripsshouldbeapproximately
whilebeingaboutanorderofmagnitudesmallerinarea.
twicethewidthoftheadjacentslots( ).Fig.3shows
anoptimizedminiaturizedresonatorat2.45GHzwithapprox-
1RT/Duroid5880,Adv.CircuitMat.Div.,RogersCorporation,Chandler,AZ. imately the same size as the previous resonator relative to the
1550 IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.52,NO.5,MAY2004
Fig.3. Optimizedminiatureresonatorat2.45GHz.
wavelength,namely, .Theunloaded isfound
Fig. 4. Equivalent-circuit model of coupled miniaturized resonators
tobe .Acomparisonofthe ofthisresonatorwith
exhibiting: (a) electric coupling, (b) magnetic coupling, and (c) mixed
that of the scaled version of the resonator in Fig. 1 (shown in coupling.
TableIwith )exhibitsaconsiderableimprovement
duetotheeffectofslot-lineimpedanceonreducingtheohmic fect conductor, and therefore, the ohmic loss cannot be mod-
lossesoftheresonator.Thefigure-of-meritconstant forthe eled in this case. Obviously, the ground plane of the slot-line
optimizedminiatureresonatorwith( )at2.4GHzcan resonators under study is neither a perfect conductor, nor is it
be obtained from (1) as , which is four times higher extendedtoinfinity.Despitetheaforementioneddrawbacksof
thanthatofahalf-wavemicrostripresonator. theintegral-equationmethod,suchas[27],itcanpredictthefre-
Itisworthmentioningthat(1)indicatesthatthe ofagiven quencyresponseofthefiltersveryaccuratelywiththeexception
resonatorincreasesas .However,thereisalimitationonthe oftheinsertionloss.
maximum value of the linear dimension , which is inversely
proportional to frequency. Hence, if one compares resonators III. DIRECTCOUPLEDFOUR-POLEFILTER
having the maximum possible values of , one can define an
To demonstrate the versatility of the proposed miniaturized
available ,whichdecreasesbythesquarerootoffrequency.
resonatorstodesigndifferenttypesoffilters,webeginwiththe
Tomeasuretheradiationlossoftheresonator,itwasenclosed
designofdirectcoupledbandpassfilters.
inalargermetalliccavity,andits wasmeasuredtobe
.Therefore,the duetotheradiationlosscanbeobtained
A. CouplingStructures
from
For the case of capacitively coupled miniaturized slot res-
(2) onators, the resonators have a series equivalent circuit model.
Fig.4illustratestheequivalentcircuitoftwocoupledminiatur-
giving .Thisresultindicatesthatthe oftheres- ized resonators exhibiting electric, magnetic, and mixed cou-
onatorisdominatedbytheohmicanddielectriclosses. plings,allrealizedbyanimpedance( )inverter.
Here,onlymeasurementhasbeenusedtoidentifythequality In order to realize the desired values for the coupling co-
factoroftheproposedresonatorssinceanumericalestimateof efficients, there are differing coupling configurations. In each
fortheminiaturizedresonatorsdoesnotprovideveryaccurate of these configurations, the coupling coefficients may be ex-
results. For example, the finite-element method (FEM) would tractedusingthepole-splittingmethod[10]inconjunctionwith
requireenormousamountsofmemoryandextremelysmallcell full-wavesimulations[27].Giventhat and arethefrequen-
sizes due to the very large ratio of fine and coarse features of ciesatwhichthe reachesitspeakvalues,thecouplingco-
the structure. On the other hand, full-wave methods based on efficientscanbeobtainedfrom
integral equations [method of moments (MoM)] make use of
(3)
theGreen’sfunctionformultilayerstructuresofinfiniteextent.
Hence, ground planes and substrates of finite size cannot be
In the case of the pure electric or magnetic couplings whose
modeled efficiently. The equivalent magnetic-current method,
appropriatecircuitmodelsareshowninFig.4(a)and(b)
however,providesanumericallyefficientapproachforthesimu-
lationofslottedstructures.Inthisapproach,thetangentialelec-
electriccoupling
tric field overthe slot is replaced with an equivalent magnetic
current, while the field is assumed to vanish over the ground
magneticcoupling (4)
plane. This assumption implies thatthe ground plane is a per-
AZADEGANANDSARABANDI:MINIATUREHIGH- DOUBLE-SPIRALSLOT-LINERESONATORFILTERS 1551
Fig. 5. Extracted coupling coefficients for a back-to-back coupling
configurationAasafunctionofthehorizontalseparation(cid:1)xfortwodifferent
valuesofverticaloffsets(cid:1)y.
Fig. 6. Extracted coupling coefficients for configuration B (face-to-face
Note that, in the case of electric coupling, the capacitance arrangement)asafunctionofhorizontalseparation(cid:1)xfortwodifferentvalues
to ground of the impedance inverter is formed by the rel- ofverticaloffsets(cid:1)y.
atively wide ground-plane region of length between the
two resonators shown in Fig. 5. Since the inverter impedance
is , a larger gives a larger , and the in-
verter impedance becomes smaller. Note that the coupling co-
efficient is proportionalto inthe seriesrepresentation [28],
whichisconsistentwiththeloosercouplingrequirementas
and increase.Alsonotethat relatesonlytothe inverter
impedanceandisunrelatedtothemutualcapacitancebetween
the resonators.
Mixed coupling may also be represented by an impedance
invertor, as shown in Fig. 4(c). Since usually and
,thecouplingcoefficientforthemixedcouplingcan
besimplifiedas
(5)
Equation(5)indicatesthat,formixedcoupling,theelectricand
magneticcouplingareout-of-phaseandtendtocounteracteach
Fig. 7. Comparison between dominantly magnetic (configuration A) and
other.Examiningthemixedcouplingmoreclosely,itbecomes
dominantlyelectric(configurationB)forthesameoverallcouplingcoefficient.
clear that, at the frequency of , the two res- (Notethelocationsofzeros.)
onatorsinFig.4(c)becomedecoupled,andazerointhepass-
bandisintroduced.Fordominantelectriccouplingwhere
offsets( ).Fig.6showsaface-to-facecouplingarrangement
and its calculated coupling coefficients, henceforth referred to
asconfigurationB.
(6) Sincetheproposedresonatorsareverycompactandinclose
proximity to each other, the coupling mechanism is complex.
Likewise, when the magnetic coupling is dominant, the zero Theexternalcouplingtopologyalsohasasignificanteffecton
appearsbelowthepassband,i.e., . thenatureofthecouplings,andthus,eachcaseshouldbestudied
In order to design the first Chebyshev sample design, two separately. Fig. 7 shows the pole-splitting phenomenon in the
different coupling configurations are investigated. These con- responsesofthetwocouplingconfigurations.Thecoupling
figurations are identified according to the mutual orientation parameters for configuration A were set to mm and
ofthetworesonatorswithrespecttoeachother.Thefirstcou- , and for configuration B, to mm and
pling configuration, henceforthreferred to as configuration A, mmsoastoprovideapproximatelythesamecouplingvalue.
is one in which the resonators are positioned back-to-back, as The responsesshowninFig.7demonstratethatbothstruc-
showninFig.5.Thecouplingcoefficient( )iscalculatedfrom tures are coupled through a mixed-coupling mechanism since
(3) and is plotted as a function of the horizontal distance be- there is a zero in the transmission. The locations of the zeros,
tween the resonators ( ) for two different values of vertical however,aredifferent.ForconfigurationA, ,andthus,