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`IPR2018-01461
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`Exhibit 1015.0003
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`

`

`.t1lUi''· MICROWAVE
`''''""'11'' AND 013 1 ICAL
`TECHNOLOGY
`1 S: I IERS
`
`VOLUME 11 I NUMBER 2
`
`FEBRUARY 5 1996
`
`EDITOR
`Kai Chang
`Texas A&M University
`College Station
`Texas
`
`EDITORIAL BOARD
`
`K. K. Agarwal, E-Systeme, USA
`J. Archer, CSIRO, Australia
`I. J. Bahl, ITT, USA
`P. Bamardl, University of Rome, Italy
`K. B. BhHln, NASA Lewis Research Center, USA
`K. J. Button, MIT National Magnet Laba, USA
`H. J. C•ulfteld, Alabama A & M University, USA
`J. Chroatowekl, National Research Council,
`Canada
`R. A. Cryan, University of Norlhumbrla, UI<
`A. A. de B•llH, CETUC-PUC, Brazil
`U. Efron, Hughes Research Labs, USA
`M. Ettenbarg, David Sarnoff Research Center,
`USA
`H. R.Fett•nn•n,UCLA, USA
`L. Figueroa, Boeing Co., USA
`T. K. Flnd•kly, Hoechst Celanese Corp., USA
`T. T. Fong, Hughea Aircraft Co., USA
`N. N. ,omln, Moscow Technical University, Rua.
`ala
`V. ,ou1d H1nn1, CNET PAB I STS, France
`P. II. G1lllon, ENST, France
`,, Q.rdlol, ~cole Polytechnlque Federal, Switzer(cid:173)
`land
`H. Ghlfourl·lhlru, University of Birmingham,
`England
`J. Goel, TRW, USA
`P. '· Qoldemlth, Cornell Unlveralty, USA
`K. c, Gupt1, University of Coloredo, USA
`G. I. H1dd1d, Unlverelty ol Michigan, USA
`R. c. H1n11n, Con1ullant, USA
`A. H1rdy, Tel Aviv Untverally, Israel
`P. A. Htrozfeld, Drexel University, USA
`W. J, R. Ho1fer, Unlveralty of Victoria, Canada
`M. Horna, University of Sevilla, Spain
`
`H. C. Huang, Shanghai Science Technology Uni·
`varsity, Chine
`C. Jackeon, TRW, USA
`R. J1nHn, Industrial Microwave and RF Tech-
`niques Inc , Germany
`S. K1w1k1ml, Tohoku Unlverelty, Japan
`M. A. K•rlm, University of Dayton, USA
`E. L. Kollb1rg, Chalmers University of Technol-
`ogy, Sweden
`J. A. Kono, MIT, USA
`V. Konlthl, Unlden Corporation, Japan
`S. K. Koul, Indian lnalllute of Technology, India
`H. J. Kuno, Hughes Aircraft Co., USA
`c. H. Ln, University of Maryland, USA
`J. N. Lee, Naval Research Labs, USA
`R. Q. L11, NASA Lewis Research Center, USA
`8, W. L11, University of Illinois, USA
`T. LI, Bell Telephone Labs, USA
`C. Lin, Bell Communloallon Research, USA
`J. C. Lin, University ol llllnola, USA
`W. Lin, Chengdu Institute ol Radio Engineering,
`China
`
`H. Ling, University ol Texas, USA
`I. V. Llndell, Helslnkl University of Technology,
`Hel1lnkl, Finland
`V. T. Lo, University of llllnole, USA
`J. M. McMahon, Naval Research Labs, USA
`K. A. Mlch1l1kl, Texas A & M University, USA
`T. Mldford, Hughes Aircraft Co., USA
`J. W. Mink, North Carolina State University, USA
`V. Naito, Tokyo lnslllute of Technology, Japan
`R. Nevel•, Texas A & M University, USA
`A. I. No1tch, National Academy Science, Ukraine
`
`J. OJed1·CHt1ned1, lnslltuto Nallonel de As·
`lrons1ca, Mexico
`K. Petermen, Technical University, Berlin, Ger-
`many
`J. Re, KAIST, l<orea
`
`A. RoNn, David Sarnoff Research Center, USA
`o. S1lmer, Unlversltd des Sciences el Tech-
`nlquea de Lllle-Flanders-Artols, France
`F. K. Schwering, US Army CECOM, USA
`A. K. Sharm1, TRW, USA
`L. C. Shen, University ol Houston, USA
`D. W. Smith, British Telecom Research Labs,
`England
`
`B. E. Splelm1n, Washington University In St.
`Louis, USA
`C. Sun, California Polylechnlc State University,
`USA
`
`H. F. T1ylor, Texas A 4 M University, USA
`C. s. THI, University of Calilornla at lrvlne. USA
`H. Q. THrng, Texas Instruments, USA
`
`J, B. Y. T1ul, Wrlght-Pallerson AFB, USA
`
`O. W1C11, Fujitsu Labs, Japan
`
`R. W. Wing, Academia Slnlce, China
`A. O. Wllll•mean, University ol Auckland, New
`Zealand
`J. c. Wlll11, Georgia Technology Research Insti(cid:173)
`tute, USA
`J. Wu, Nattonal Taiwan University, Taiwan
`E. Y1mHhlt1, University of Electro·Communlca-
`llons, Japan
`
`S. K. Via, Optech, USA
`H. W. Yen, Hughes Research Labs, USA
`F. T. S. Vu, Pennsylvania State University, USA
`
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`

`THE RESONANT FREQUENCY OF
`RECTANGULAR MICROSTRIP ANTENNA
`ELEMENTS WITH VARIOUS SUBSTRATE
`THICKNESSES
`
`. •• , 1
`
`Mehmet Kara
`Weapons Systems Division
`Aeronautical & Maritime Research l 111 iolnt1Jry
`Defence Science and Technology 01nan1:;n1ton
`P.O Box 1500
`Salisbury SA 5108, Australia
`
`KEY TERMS
`Resonant frequency, va1'io11s subs/rate, patch antenna, microstrip
`
`ABSTRACT
`Formulas based on transmission-line, cavity, and magnetic-wall models
`10 detemtine the resonant frequencies of a rectangular microstrip antenna
`element have been studied and their validity assessed. Their variations
`were experimentally verified by analyzing a sel of newly designed antenna
`elements with substrates satisfying the crileria h ~ 0.0815A11 for 2.22 ~
`e, ~ 10.2, where A0 is the free-~pace wavelength, h /he lhickness, and e,
`/he relative permittivity of /he dielectric substrate. © 1996 John Wiley &
`Sons, Inc.
`
`1. INTRODUCTION
`The resonant frequency of microstrip antenna elements must
`be determined accurately, as they have narrow bandwidth
`and can only operate effectively in the vicinity of the reso(cid:173)
`nant frequency.
`Factors for determining the frequency at which resonance
`occurs include
`
`(a) The voltage standing-wave ratio (VSWR), referred to
`the input terminals of the antenna, is at a minimum.
`This corresponds to a minimum in the magnitude of
`the reflection coefficient.
`(b) The input impedance, referred to the input terminals,
`is real (Z;n = R; 11 ), which means the input impedance
`has no reactive part. Generally, this point is very close
`to the frequency where the resistance reaches a maxi(cid:173)
`mum. Therefore the resonant frequency may also be
`defined as the point at which the resistance reaches a
`maximum, independent of the value of reactance.
`
`This article is primarily concerned with antenna elements
`that are matched to their transmission-line feeds. In this case,
`the frequency at which the input impedance is real is equal to
`the frequency at which the VSWR is at a minimum.
`Several methods have been proposed and used to deter(cid:173)
`mine performance properties of microstrip antenna elements
`(l-17]. These methods have different levels of complexity,
`require vastly different computational efforts, and can gener(cid:173)
`ally be divided into two groups: simple analytical methods
`and rigorous numerical methods. Simple analytical methods
`can give a good intuitive explanation of antenna radiation
`in rigorous
`properties. Exact mathematical formulations
`methods involve extensive numerical procedures, resulting in
`~·01md-off errors, and may also need final experimental ad(cid:173)
`justments to the theoretical results. They are also time con(cid:173)
`~uming and not easily included in a computer-aided-design
`sy·.r · ni. Basically, there is no clear-cut rule as to which one of
`th •:c is Ille bes! to use; the first guideline would be the
`thil kll •ss of the substrate.
`
`Based on this observation, simplified analytical methods
`are used in this work. Formulas based on transmission-line,
`cavity, and magnetic-wall models to determine the resonant
`frequencies of a rectangular microstrip antenna element have
`been investigated. Their respective regions of validity in the(cid:173)
`ory and applicability for a given antenna element have also
`hccn established. For the above-specified range of substrates,
`a transmission line model has been verified and successfully
`u~d to calculate the resonant frequencies of rectangular
`nikrostrip antenna elements without involving complicated,
`time-consuming, and difficult numerical methods. These re(cid:173)
`sult~ are then compared with specified' design frequencies.
`
`2. ANALYSIS
`The configuration of a probe-fed rectangular microstrip an(cid:173)
`tenna element is shown in Figure 1. The transmission-line
`[1-4], the cavity [5-10], and the magnetic-wall models [11]
`have been used for calculating the resonant frequencies, and
`there have been variations compared with measurements.
`The basic formulas for computing the resonant frequen(cid:173)
`cies are given in the following sections.
`
`2.1. Formulas Based on the Transmission-Line Model. To cal(cid:173)
`culate the resonant frequency of a rectangular microstrip
`antenna element, the antenna is regarded as two parallel
`radiating slots [3] with dimensions W and h having constant
`field aperture distributions and separated by the element
`length l of approximately half the wavelength in the dielec(cid:173)
`tric.
`In reality the electric field at the open end of the patch is
`distorted by an abrupt termination at the edges, resulting in
`fringing electric fields. This fringing effect is incorporated
`into the formula for the resonant frequency.
`A formula for the resonant frequencies of rectangular
`antenna elements with thin substrates was given by Bahl [2]
`and Derneryd [4] as
`
`f, = 2(l + idW)-./-s.-(W~) '
`
`(1)
`
`where c0 is the velocity of electromagnetic waves in free
`space and e.(W) is the effective dielectric constant, which is
`obtained from [18]
`
`&,.-1
`&,.+1
`e.(W) = -2- + 2.../1 + lOh/W;
`
`(2)
`
`DIELECTRIC
`SUBSTRATE
`
`GROUND PLANE
`
`Figure 1 Configuration of a rectangular microstrip antenna cle(cid:173)
`ment with dimensional parameters
`
`MICROWAVE AND OPTICAL TECHNOLOGY LETTERS I Vol. 11, No. 2, February 51996
`
`•
`
`55
`
`ZTE v. Fractus
`IPR2018-01461
`
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`Exhibit 1015.0005
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`

`

`TABLE 2 The 0.9-GHz Cavity Resonator
`
`Dimensions
`
`Measured
`FDTD
`
`a (cm)
`
`21.9075
`22.0000
`
`b (cm)
`
`8.89
`9.00
`
`c (cm)
`
`22.065
`22.000
`
`Type
`
`Derivation
`
`Q
`
`Resonant Frequency
`
`Empty Cavity
`Empty Cavity
`Tunable Cavity
`Tunable Covity
`
`Analytical
`Numerical
`Measured
`Numerical
`
`23,171
`23,174
`N/A
`20,229
`
`963.58 MHz
`967.50 MHz (error < 0.5%)
`N/A
`900.20 MHz
`
`TABLE 3 The 1.4-GHz Cavity Resonator
`
`Dimensions
`
`Measured
`FDTD
`
`a (cm)
`
`13.081
`13.000
`
`b (cm)
`
`8.859
`9.000
`
`c (cm)
`
`15.113
`15.250
`
`Type
`
`Derivation
`
`Q
`
`Resonant Frequency
`
`Empty Cavity
`Empty Cavity
`Tunable Cavity
`Tunable Cuvity
`
`Analytical
`Numerical
`Measured
`NumericHI
`
`22,982
`22,992
`N/A
`20,698
`
`1.5152 GHz
`1.5185 GHz (error < 0.3%)
`1.48170Hz
`1.464 GHz (errnr < 1.2%)
`
`ImFERENCES
`l. K. A. Zaki and C. Chen, "Loss Mechanism in Dielectric-Loaded
`Resonators," IEEE Tra11s. Micl'owave The01y Tech., Vol. MIT-33,
`Dec. 1985, pp. 144!H452.
`2. J. Krupka, "t>mpertics nl Sluclilcd Cylindrical Oun~i-Tl:i011 n1 ·mode
`Dkh:c 1ric R 'M111>11nrs," 11'. hl:' frmrs. Mic:rowm11· llt<Cmy Tech., Vol.
`MTI-36, April 1988, pp. 774-779.
`3. J. E. Leburic and D. Kajfez, "Analysis of Dielectric Resonator
`C~vltic~ using the Finite Jntcgrnilon Technique," IEEE 1iw1s.
`Mkro1v111.1c Tl11101y Tech., Vol. MTI-37, Nov. 19H9, pp. 1740- 1748.
`4. A. Navarro, M . .I. Nunez, und E. M11rtin, "Finite Difference Time
`Domain FFT Method Applied to Axially Symmetrical Electromag(cid:173)
`netic Resonant Devices," IEE Proc. Pt. H, Vol. 137, No. 3, June
`IWU. Pl» 193- 1%.
`5, 1 •. Wung, B. 0 . Gnu, und C. D. Deng, "Accuru1c Stud of
`()-h1c1or o f Rc<;i>nator by u Finite-Difference Tim ··I omain
`Method," IEEE 1i'1111.\'. Micmwari11 Thcwy Ti.:d1., Vol. MTT-43, .July
`1995, pp. 1524-1529.
`6. R. r. Harrington, Time-Harmonic Elec:tmmag11etic Fiel<ls,
`McGraw-Hill, Inc., New York, 1%1.
`
`Rcceioe<l 8-18-95
`
`Microwuvc and Opticul Technology Letters, 11 /2, 64-66
`© 1996 John Wiley & Sons, Inc.
`CCC 0895-2477 /96
`
`To compute the resonant frequencies, the FDTD method
`was used. The cavities were excited by a sine wave with a
`Gaussian envelope. Using the Foutier transform, the timc(cid:173)
`domain data were transformed to the frequency domain. The
`resonant frequencies were discerned as dislinctivc peaks that
`corresponded lo the var.ious modes present in the cavity.
`Once the resonant frequencies were fo und, the cavity was
`excited with a continuous sinusoidal wave at that resonant
`frequency, and the method previously described was used to
`obtain the Q factor.
`T he Q factors and resonant frequencies computed with
`Lhc FDTD algorithm are shown in Tables 2 and 3 for the 0.9
`and 1.4-GHz re&onators, respectively. For bolh empty cavi(cid:173)
`ties, the numerical results are compared with analytical val(cid:173)
`ues, nod lhc agreement is less th an ·1 % for both the Q and
`resonant frequency. For the tunable cavi1y at 0.9 GHz, the
`numerical values are shown in Table 2, but no anulyt ical or
`measured results were available. For the tunable cavity at I .4
`GHz, measurnments of the resonant frequency were avail(cid:173)
`able, and the FDTD vulue is within 1.2% error of the
`measurements. The measured resonant frequency wns ob(cid:173)
`tained from the scattering parameters measured with a net(cid:173)
`work analyzer. The numerical results for the Q of the tunable
`cavities in both Tables 2 and 3 show the right trends, because
`the Q decreases from that of the empty cavity, as would be
`expected due to the additional loss of the tuning disk and
`truss.
`
`IV. CONCLUSIONS
`A technique for computiag the quality factor of complex
`resonators was demonstrated. The advantages of this ap(cid:173)
`pmiu;h are that lhc FDTD method can be employed to model
`resonators of arhitrary shape that contain di ·lectric and
`metallic materials such as tuning disks, and the results are
`obtained directly from the time-domain fields through time
`averaging. A similar approach can be used to account for
`dielectric losses.
`
`EXPERIMENTAL INVESTIGATIONS ON
`THE IMPEDANCE AND RADIATION
`PROPERTIES OF A THREE-ELEMENT
`CONCENTRIC MICROSTRIP
`SQUARE-RING ANTENNA
`
`I. Saha Misra and S. K. Chowdhury
`Department of Electronics & Telecommunication Engineering
`Jadavpur University
`Calcutta 700 032, India
`
`KEY TERMS
`Concentric micros/rip square ring a11te11110, impec/011ce and mdiation
`/iamlwidth, feed location
`
`ABSTRACT
`Exp11d111e11wl i1111estiga1lm1 011 mr 11/ectm111ug11etirnlly c:m1pli:d concimtric
`111ic:ms11ip .vq1wra-ri11g 0111i:111w (CMSl?A) h11s h1:en p1'l!sl!llled. Our pn:1ii(cid:173)
`ous work 1111 cu11L·e11llil' micmstri111111111t101~1i11g t'l!SO/lrtlor.i rcllullfotl llwl
`the impedance nm/ mdiotion bandwulth can In• imprmwd c1111.1·ida1·ubly.
`A ilwee-a/emallf CM SRA has heen rh·signed 111u/ Its 11111as11nu/ i111pe.d1111ce
`n111/ rtuliatlu11 p111t11ms h111ie b11t•11 compurrul with thast~ Clf a single
`sq11.m··dt1J: 11ntt?111111 /111l'i11>1 a 1//111e111 fr111 equal 10 tlw lntgd t el11m1•111 of
`the Cfl'ISI I. The cffi'<'l t>f t'lw11n1· offc1·d luct11!011 /in~· alro bee11 11mlied.
`Result~· show 1ha1 the Iota/ percem bandwidth (BW) for tire co11cen1ric
`micro ·tri{J square ri11g antenna is larger with respect to the si11gfe-ri11g
`Ull/CllllO, Cl/Id this efl~c/ is /JCty 1111/C/I pl'Olllille/I/ a/ ll pal'tic11Jar fectl
`location. © 1996 Joh11 Wiley & Sons, /11c.
`
`INTRODUCTION
`One of the most important aspects of any anlcnrw is its
`handwidth. The main drawback of microstrip antennas (MA)
`is their narrow bandwidth. 111e bandwidth of an antenna can
`fn ·r ·aslng 1hc . 111»
`he n ·reused proportiunatcl ell her h
`s1rn1c 1hickncss or hy rcuucing the dicl c ·1ric
`·1111s111n1 f ll
`I lmv ·v ·1'. th· lncrcns · in s11hsrrnw th ckncs_~ is g • 11 ·rnll
`ll111ltcll hy exci1111ion nl Nurfucc wnvc~, :ind 1l11: rc al'· praclir;t l
`
`66
`
`MICROWAVE AND OPTICAL TECHNOLOGY LEITERS I Vol. 11, No 2, February 5 1996
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1015.0006
`
`

`

`limitations in decreasing the value of the dielectric constant.
`Thus, the BW obtained from conventional MA is not suffi(cid:173)
`cient for many purposes. Another important aspect of MA is
`a variety of feeding techniques that can be applied to them.
`Electromagnetic coupling is an attractive one, due to its
`multilayered structure, which allows the antenna to be inte(cid:173)
`grated with its feed circuitry [2]. Another reason for electro(cid:173)
`magnetic coupling is that it has been used in configurations
`that significantly enhance the BW of a patch antenna [3].
`Our previous works on electromagnetically coupled con(cid:173)
`centric microstrip ring antennas [4, 5) show that these struc(cid:173)
`tures give wide bandwidth. The present article deals with a
`concentric microstrip square-ring antenna (CMSRA) contain(cid:173)
`ing three elements. The variation of input impedance at
`different bands of frequencies have been measured by an HP
`
`84108 network analyzer and compared with those of an
`electromagnetically coupled microstrip single square-ring an(cid:173)
`tenna. The variation of input impedance has also been mca-
`
`frequency step 0 OJ GHz
`
`- o- Center lead
`-·- •-·- 0 4 5 cm owoy (rom can/er
`- -o- - Corner feed
`
`r"'centerfeed'
`I
`I
`,
`0 ·4!Jcm
`
`'<Corner feed
`,
`
`Figure 1 Electromagnetically fed concentric square-ring antenna
`showing different feed positions
`
`Figure 3
`locutions
`
`Impedance plot of single-ring antenm1 al different feed
`
`1-- - - Cl
`
`.•
`
`-
`
`--J
`
`Figure 2
`
`(u) Three-element concentric microstrip square-ring antenna (b) single square-ring antenna
`
`(b)
`
`·1 ABLE 1 Comparison of Percent BW Between Single Square-Ring and Concentric Square-Ring Antennas
`
`Single Square Ring
`
`Concentric Squure Ring
`
`Feed location
`
`Center feed
`
`0.45 cm away
`fro1n center
`
`Coiner feed
`
`Frequency range
`in GHz
`
`2.7 - 2.74 = 0.04
`
`2.698 - 2.76 = 0.068
`
`2.638 - 2.692 = 0.054
`
`2.805 - 2.852 - 0.047
`
`% Bandwidth
`
`1.47
`
`2.49
`
`2.02
`
`1.66
`
`Frequency range
`in GHz.
`
`2.655 - 2.685 = 0.03
`5.31-5.435=0.125
`6.55 - 6.85 = 0.30
`
`2.654 - 2.694 = 0.04
`6.64 - 7.5 = 0.86
`
`2.612 - 2.65 = 0.038
`2.74 - 2.773 = 0.033
`6.74 - 7.2 = 0.46
`7.33 - 7.53 = 0.20
`
`% Bandwidth
`
`1.12
`2.32
`4.47
`
`1.49
`12.16
`
`l.44
`1.19
`6.6
`2.69
`
`MICROWAVE AND OPTICAL TECHNOLOGj LETIERS I Vol 11, No 2, February 5 1996
`
`67
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1015.0007
`
`

`

`sured at three different feed locations (Figure 1). These
`measurements indicate that the I : 2 VSWR bandwidth ob(cid:173)
`tainable by this structure is about 14%.
`
`DESIGN OF THREE-ELEMENT CMSRA
`The three-element CMSRA is shown in Figure 2(a). We have
`first chosen the innermost square-ring antenna with side
`a = 1.0 cm and width w = 0.2 cm. The spacing between the
`adjacent elements and their widths are then chosen, main-
`
`ffequenq .rep DD I GHz
`--o- · Center feed
`-· .. •-·- 0 A5 cm away from cettle:
`• -o- ~ Cornor feed
`
`{
`/
`·I
`
`-
`
`/ /
`I
`I
`fa,, .
`
`/
`
`(a)
`
`frequency step D 05 GHz
`
`-·-·-·- 045cm away from center
`
`--:--~~~---=
`
`,,
`
`taining the following relation:
`
`T ~ d,, + 1 = w,,+ 1
`w,,
`d,,
`
`= 1.15,
`
`as indicated in Figure 2(a),
`
`where the suffix n represents the nth patch number.
`The ring widths and spacings increase from the innermost
`element to the outermost element. Maintaining this re lation,
`the outermost sq uare ring has side " = 2.42 cm and width
`w = 0.267 cm. The single-element square-ring antenn a invcs(cid:173)
`l!gaLed hus an identical dimension (Figure 2(b)]. The three(cid:173)
`elemcnt CMSRA and single-element square-ring have been
`fabricated on PTFE substrate having dielectric constant e, =
`2.55 and thickness 0.159 cm. Both of them are fed clectro(cid:173)
`magneticully by a 50-0 microstrip line fabricated on a sub(cid:173)
`stra te wit h identical dielectric constant and other properties.
`
`EXPERIMENTAL RESULTS
`The measured input impedance loci for the single square ring
`and conoentric ring h;wc been plOtted in ·Figures 3 and 4,
`respectively. The I : 2 VSWR circle has also been drawn on
`the corresponding Figures. T he compared 'I ; 2 VSWR BW
`for the single square ring and concentric ring at different
`feed .l ocat io n~ is given in Table l. From this tnble, it is seen
`lhat U1e total I : 2 VSWR BW is increased for the three·
`clement CMSRA as compared to that of the single ring. This
`effect is prominent at the feed loca tion 0.45 cm away from
`the center [Figure 4(b)].
`
`RADIATION PATTERN
`The rndiation patterns for the single square-ring and three(cid:173)
`clemcnt CMSRA have been measured for different feed
`locutions and arc plotted in Figure 5 and 6, respectively,
`covering the entire bandwidth of the untcnnu. CompUJ·ison of
`the rndia lion pnttcrn of a single ring and CMSRA (Figure 5
`nnd 6) shows that over the cntin.: ba ndwidth Lhe nature of the
`rntllution pattern is quali tatively si milar to that uf the single
`ring operating ut tb fundament al mode. Again from Figure 6
`it is seen that radiation patterns for MSRA remain un(cid:173)
`changed with the change of feed location.
`
`CONCLUSION
`From the above investigations it may be said that the concen(cid:173)
`Lric mlcrostr ip square-ring antenna has a mul tiple band effect
`with increase In total percent bandwidth with respect Lo the
`single square ring having the large L physical dimension of
`the CMSRA. Chungi ng thu location of the feed the total
`percen t bandwidth
`increases considcrnbly, and with the
`
`(b)
`
`Figure 4
`Im pedunce plot of concentric squurc-ring 1101ennu (a) for
`lower band of frequ encies, (b) for higher band of freq ue ncies for the
`feed 0.45 cm away from center
`
`Figure 5 E-plunc radiation pattern of single square-ring antenna al
`different feed locations
`
`68
`
`MICROWAVE AND OPTICAL TECHNOLOGY LETIERS I Vol 11, No 2, February 5 1996
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1015.0008
`
`

`

`-•- 2.65 GHz
`---- 6.75 GHz
`
`GHz
`
`-•- 2·65 GH1
`- - 6 6 GHz
`---- 6.9 GH1
`-·- 7.3 GHz
`
`-•-2·62 GHz
`- -6.84GHz
`---- 7.12 GHz
`-·-7.4 GHz
`
`(a)
`
`(b)
`
`(c)
`
`Figure 6 E-plane radiation pattern of concentric square ring an(cid:173)
`tenna (a) for center feed (b) for the feed 0.45 cm away from center
`and (c) for corner feed
`
`changed feed location radiation patterns of the CMSRA
`remain unaltered. The most attractive feature of this struc(cid:173)
`ture is the increase of impedance and radiation bandwidth
`without losing the microstrip antenna's advantage of small
`size.
`
`ACKNOWLEDGMENT
`The authors would like to thank CSIR, Government of India
`tor financial assistance for this research.
`
`RlWERENCES
`1 G. _Kuma1 m11t K. C'. Ciupta, "Brnad-Band Micrustrip Antennas
`~sing i\dtlitional Rcsonutors c iap-Coupkll tu the Radi;l!ing
`Edges," /l:/:'f-.' Tram·. A11t1'1111US l'mpt1}{11t .. Vol. i\l'-.U. Dec. 1'184,
`pp, 1375-1379.
`2· fl. lldcntcpc, "Modelling uml I sign ol' F.lcc1rnmag11cticallv Cou-
`1•il•d Micms1rip P111d1 A111..:1111.1s aml i\n1cnna Am1ys,". IEEE
`i''"'''""' l'm11aga1. M<1J:11ww. Vol. :n. h:h. 1•1•15, pp. JI JX.
`'· M. 1'1m1r 11ml S, M. 1nlu, "Rigorn11~ Anulysis oJ' a Mir1ostrip
`
`3
`
`·
`
`Feed Patch Antennas," IEEE Trans. Antennas Propagat., Vol.
`AP-35, Dec. 1987, pp. 1343-1350.
`4, I. Saha Misra and S. K. Chowdhury, "Experiments on
`the
`Impedance and Rudlation Properties of Concentric Microstrfp
`Ring Rcsonalur," Elcct1r111 L.r.11., VoL 16, March 1095, pp-421-422.
`5. I. Saha Misra and S. K. Chowdhury, "Oe.~fgn of Concentric
`Microstrip Ring Antennas," IEEE Ante1111a Propagat. Magazine, to
`be published.
`
`Rccei11ed 9-15-95
`
`Microwave and Optical Technology Letters, 11 /2, 66- 6Y
`© 1996 John Wiley & Sons, Inc,
`CCC 0895-2477 /96
`
`RADIATION BEHAVIOR OF PLANAR
`DOUBLE-LAYER DIELECTRIC
`WAVEGUIDES COMBINED WITH A
`FINITE METAL-STRIP GRATING
`
`Victor I. Kallnlchev
`Rad o Engineering D partment
`Moscow Power En l11•eilng Institute (Technical University)
`14 Krasnokazarmennaya, Moscow 111250, Russia
`
`KEY TERMS
`Metal-~·1rip grating, dott/J/e-layer dielectric wuuegttide, ~wj'ace mode, leaky
`mode, radiation
`
`ABSTRACT
`The radialimt and scal/ering cliaracterfrlic.I' of double-layer planar die/e,·(cid:173)
`lric 11111tmg11itl11.1· inl~graled witlr a mc111l-s1rip gmting 11re 111111/ywd usi11g a
`two-tllmenl'itmal 111otli:l 111ul a 1wnvw--itrip c111re111 apprrp;imation. Some
`11umerica/ data co11cemi11g I/re highly direclional a111e1111a applications uj
`these structures in the millimeter-wcwe mnge are pres11111ed. © 1996 Jol111
`Wiley & Sons, Inc.
`
`1. INTRODUCTION
`Research performed during the last Revernl years showed that
`radiating structures based on a dielectric waveguide inte(cid:173)
`grated with a metul-strip grating are very promising as low(cid:173)
`cosl, low-profile, and easy-to-fabricate microwave and mil(cid:173)
`limeter-wave printed antennas [I , 2]. The most commonly
`used geometry of such antennas is based on a single-layer
`grounded dielectric slab or u dielectric-inset waveguide [3-5].
`In this work, the subject of investigation is u radiating
`structure formed by a double-layer planar dielectric wave(cid:173)
`guide combined with a finite metal-strip grating [Figures l(a)
`and l(b)]. The lower layer may be either an auxiliary dielec(cid:173)
`tric substrate ( e 2 > 1) or an air gap ( e 2 = 1). It is assumed
`here that the upper layer guides a slow surface wave; that is,
`we suggest that e 1 > c 2.
`The goal of the work is to develop an effective approach
`to the analysi of such double-layer structures and ro obtain
`some data concerning their radiation and scattering charac(cid:173)
`teristics in millimeter-wave range. In particular, it would be
`interesting to compare the radiation behavior depending upon
`whether the grating is located on the bottom or top surface of
`the upper guideway layer. Moreover, there is a further aspect
`of interest to us. As was established by Jackson and Oliner,
`the higher-order below-cutoff modes (leaky modes) existing
`
`MICROWAVE AND OPTICAL TECHNOLOGY LETIERS I Vol. 11, No 2, February 5 1996
`
`•
`
`69
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1015.0009
`
`