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`t
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0001
`
`

`

`LIE BABY 0F CONGRESB
`
`llifllfllilfiflfllml
`0 033 225 112 0
`
`IEEE
`
`TRANSACTIONS
`
`ON ANIENNAS
`
`AND
`
`PROPAGATION
`
`
`
`ZTE V. Fractus
`
`ZTE
`
`IPR2018-01461
`
`Exhibit 1014,0002
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0002
`
`

`

`~IEE.E TRAN SACTI 0 NS ON
`NTENNASAND
`PROPAGATION
`
`A pUBLICATION OF THE IEEE AHTl!NNAS AND PROPAGATION 80CIETY
`
`VOLUME 46
`
`NUMBER 4
`
`IETPAK
`
`(ISSN 0018-926X)
`
`APRIL 1998
`
`--PAPERS
`
`Physical Interpretation of the Phase Asymmetry of a Slant-Path Transmission Matrix . ........ ... . ... ... .. ... . . ... ..... . .
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N . .f. McEwan, Z. A. A. Rashid, and S. M. R. Jones
`A Wide-Band Single-Layer Patch Antenna .. . . .... . .... .. . .. ............. ........ .... .. ........ .. ........ .. .. N. Herscovici
`Multiport Network Model for CAD of Electromagnetically Coupled Microstrip Patch Antennas ............ ........ ... . .
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R. P. Parrikar and K. C. Gupta
`Simultaneous Time- and Frequency-Domain Extrapolation . .. .. ... . . ........ .. ..... .. ..... ... R. S. Adve and T. K. Sarkar
`Scattering from Structures Formed by Resonant Elements .... ... ....... ... .. .... . ....... ... . ... V. Veremey and R. Mittra
`Normalization and Interpretation of Radar Images ......................................................................... .
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. P. Skinner, B. M. Kent, R. C. Wittmann, D. L. Mensa, and D. J. Andersh
`Perfectly Matched Layer Mesh Terminations for Nodal-Based Finite-Element Methods in Electromagnetic Scattering . ..
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Tang, K. D. Paulsen, and S. A. Haider
`On the Behavior of the Sierpinski Multiband Fractal Antenna .. ... .. . .. ... ..... ....... . . .. . .. .. .. ... ... ... . . ........ .. .. . .
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Puente-Baliarda, J. Romeu, R. Pous, and A. Cardama
`On Modeling and Personal Dosimetry of Cellular Telephone Helical Antennas with the FDTD Code .................. .
`. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Lazzi and 0. P. Gandhi
`Study of Impedance and Radiation Properties of a Concentric Microstrip Triangular-Ring Antenna and Its Modeling
`Techniques Using FDTD Method ...................................................... I. S. Misra and S. K. Chowdhury
`Analysis of Stripline-Fed Slot-Coupled Patch Antennas with Vias for Parallel-Plate Mode Suppression .. . . .... . ..... .. .
`· ................................................................. A. Bhattacharyya, 0. Fordham, and Y. Liu
`Blindness Removal in Arrays of Rectangular Waveguides lMng Dielectrically Loaded Hard Walls .................... .
`· · · · ......................................................................... S. P. Skobelev and P.-S. Kildal
`iffracli n nnd Shooting and Bouncing Rays ................. .. S.-K. Jeng
`Neur- iehl 'cnttering by Physical Theory of'
`~ th d n! Moment. Solution for a Wire Attuched co nn Arbitrary Faceted Surface ......... I. Tekin and E. H. Newman
`orward- 'cmtering A nalyi;i s in n . ocuscd-Beam Sy ·1em .. . ............................ R. Shavit, T. Wells, and A. Cohen
`lllgh·Fn:quen y Arlalysis of nn Array o Linc Sources on a Truncated Ground Plane ................................... .
`A · · · · · · · · · · · · · ...•••.•...•..•........••..................•.••. F.
`11pofino, M. Albani, S. Maci, and R. Tiberio
`· · UTD Solution for the Scattering by a Wedge with Anisotropic Impedanc
`fle1 es: Skew Incidence Case ............. .
`'O · · · · · · · · · · · · · · · · · · · · ..................................................... G. Pelosi, G. Manara, and P. Nepa
`' h the Use of Cavity Modes as Basis Functions in the Full-Wave Analysis of Printed Antennas ....................... .
`· · · · · · · · · .. .... ... .. .. .. ... ... . , ..... . ... ... . . . . . . ... .. ........... .. . .. G. Vecchi, P. Pirinoli, and M. Orefice
`
`465
`471
`
`475
`484
`494
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`502
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`507
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`517
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`525
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`531
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`538
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`546
`551
`559
`563
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`570
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`579
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`589
`
`l.l:'T'tllR
`
`ll~c-Dom11 11 Spherical Near-Field Formulas in the Case Where the Radial Components of the Electromagnetic Field
`/\ C re Mca~11 reu ....... .. .. ..... ....... .... . ...... . .. .............. ... ..... .... ....... ......... ...... .. .. .... I. Chri.1·tic11M·e11
`Scat~n~Pllct l'll'A Suitable for Dual-1-<requency 900/1800-MHz Operation . .. . ........... . C. R. Rowell and R. D. Mwd1
`p1111i:r ng Iii a ~ielectric-Loadcd Nonplanar Slit-TM Case .. ..... ..... ...... .. .. ........... .1.-W. l'l.1 anti N.-fl. Myung
`1 t 11 1
`• ·~ lor Wide-Band Interference Suppression Using Eigen Approach ..... .. . . M. J. Mismar anti T. H. /.l'mail
`' I ~leme111 Approach to the Scattering from Inhomogeneous Dieleclric Bodies ........ G. Pelosi mul G. To.1·0
`
`, Bou
`1 111
`
`595
`596
`598
`600
`602
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0003
`
`

`

`·~ IEEE ANTENNAS AND PROPAGATION SOCIETY
`
`All members of the lEES are eligible for ntembcrship in the Antennas nnd Propugotion Society ond will rcceivo this l'RANSACTIONS upon pnyntent af the annuol Society membership
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`
`-
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0004
`
`

`

`IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
`
`465
`
`Physical Interpretation of the Phase Asymmetry
`of a Slant-Path Transmission Matrix
`
`Neil J. McEwan, Zainol A. Abdul Rashid, Student Member, IEEE, and Stephen M. R. Jones
`
`A/i.,·lrm:t-Thc phusc a y111mclr,v 111' u 20-G n:t. shmt-11nth 1r1ms-
`1ul!.i 11111 1111111'1 • durlni,: k · cl'l'nlN Is modrl d In l c1·m.~ uf I wo la)'llr.
`c nsL'lling of plutc- und nc di •·IYI, · -rys1111.~. Tlw rnicrnwnvc
`111·111mgutJnn d11h1 un· consl!llcnl wilh lhi! 111clc111·olo1tk11I rcpcn·ts
`th 11 lhc 1111111! form s 111• • usuully 11rt•domi1111nl ul higher 11Ull11dcs
`1111111 the ncl'tllc ronns.
`
`Index Termli-Electromagnetlc propagation.
`
`I. INTRODUCTION
`WITCHED polarization transmissions of a satellite beacon
`provide the opportunity to measure the full transmission
`marrix of the atmosphcril' slant-path. Al'l'llnlll' and properly
`calihralcd measurement of lhe matrix is importtinl in modeling
`the population~ or hydrometeors along. the p:ith. One dleet
`revealed by careful calibration is asymmetry of the matrix.
`Thi!- paper llisnlSSl'S an i111crcs1i11g physical interpretation of
`pha:,~ asymmetry recently observed in ice events using the
`Oly111pus 20-GIV. smcllitc hl'acon.
`u .. inµ 01ihogonal line;u hasis polarizations. a symmetric
`mntr 1 x is oh1oocrvcd when lhc path traverses citlwr an arbitrary
`medi11111 in which all particles lrnve the same pro,icctcd align-·
`ment or an arhilrnry pure phasc-shit'ling (los.~less) medium
`in which the s1u1is1ics 111' pal'lidc alignment remain rnnstanl
`along the path. Al u high frequency sud1 as 20 GH:t., pliasc
`asymmetry of the matrix should be detectable and this will
`indicate the presence of differently aligned rain-ice or ice-ice
`particle populations along the path or more complex mixtures.
`During ice events, the eigenpolarizations of the transmission
`matri · I roviu · a n1 •tulUr • of th · mean proje ·1c<.J orientnlion
`Ung! s 11 lhc ic' particl 'lo, whii.:h have u di fferent ch11ruc1 dstic
`bchav11 r fur n etll > nntl plat
`·1·ystuls. Any a ·yw motry of
`1111111 i (which on·esponds lo
`lh
`i • n1x>luriw tions h ·coming
`llipli ul is u mcusur · of th ~ ltomog'ncity of th
`urnowl111t
`lllcan alignm 111 along lh palh. This siruutiun cun h mod ·led
`(lhougl 1101 u11amhiguo11 ly) hy u rwn-luycr medium in whi ·h
`'U'.'h lay ' r has iLs own m 1m ori 111a1it111 dire ' Lion.
`iwo mosl ornmon 1yp ·s of i · partlcl s at high
`/ 11
`11
`Hud ·s ire n •tll ' · and plalc-typ' -ry. 1 I •• Knowlcdg of th
`0 :urrc,11 · • uml di 1ribuliun or ice pu;ii I s in
`It 111.ls Is not al>
`~~.\r~fa 'l11ry llS lhut uf' water pHrliciC-S. OWit1g lo Ill • di ffi ullies
`nC) 111,ca~u •m ·111 and th vuricty or pnrtic h.: 1yp 'S. Th ·re is
`Cl BC llCt nlly a c •pied lh Or"liCll l •x.planalit>n uf the ohs ·rv •d
`lllccut uio
`11·
`1· .
`.
`·louds and of their
`'
`ns 1:111l orms o u.:
`·rys1u!s 111
`
`M111n1~c1
`TI
`' 11'1 1 ·c 1vc<I Apl'l l I, lrJUf1; l'l!Vi~ull IJ~cc mhcr 2, 19'17,
`r 1·1
`'111
`na, lJnt
`l
`·1
`'11
`II
`"
`.
`lllC 11 1111 h CCl rll'ai Engineer-
`~ WI I
`' " ' " ' Ill"
`11: 11 'IJlll'illl ' 111 ii
`'I' ll
`>
`'
`ltuliliKI ll1 " 1 "' Brmlfor\l. Wt:s1 Ynrk~hl ~ •, Uffl IDP. 11 . K.
`l l!i It ' Ill l1k·nlil 1J1 S 00 18-926XI' ll )U2'14 l·ll,
`
`growth by deposition ol Watl'r Vilpor allll other prot.:t•sse1oo 111.
`Summarii'.inµ s1ullici. of il'l' nystals reprodul'ed in lahorntllrics.
`Mason 121 imlicatcd that lhl' principal !'actor rn111rulling the
`basil' nystal hahil i .~ the IL'mpcratun', bur lht' SL'l'llmlary growth
`foa1urcs arc dt•lennined hy thi: supersaturation. From several
`measurements made on real clouds, Srivastava [l] summarized
`the following pattern of ice crystal habit as a function of
`templ'ralurc: I l - 3 ° ( ·to -8 °C, needles: 2) -H " (' 111 - 25 "C,
`'.!O '' C. stellar dc11tlri1cs: 4)
`plates, ~l'l'lur slars: .\) -10 °C to
`less than
`20 "C, prisms; and 5) less than --· 30 °C, d11slcrs of
`hollow prisms. From the experimental and theoretical studies
`on ice crystal growth in supersaturated water vapor [3], [4), the
`mass growth rate (gram per secund) of ice crystal is enhanced
`in the temperature range between - 3 °C and - 21 °C and
`is maximum at -15 °C. Heymsfield [5] also found that ice(cid:173)
`particle concentrations at temperatures above -15 °C were
`2-4 orders of magnitude higher than at lower temperature.
`Since only gross shape can be resolved by microwave
`this JHIJll~r. we group all highly prohrlc J'orms
`in
`means,
`Cinduding rnh1111n~ and pri.~ms) as "net•dle:;'' and all highly
`nhlall~ for111s lin ·lulling sector st;lt's ;rnd ,·t ll:ir dendrites) as
`"ph1ll's." For propagalh>n anulysis. we expect the two main
`features to be a needle layer from -3 °C to -8 °C and a
`plate layer from -8 °C to -20 °C. It appears [2], [6] that
`"needles" would also appear at altitudes above the - 21 °C
`level and "plates" below the -3 °C level, but in much lower
`concentrations.
`Using a simplified ice model, we describe two methods of
`analysis that can reveal the existence of a 1wo-h1yercd ice
`medium along the path from the asymmetry of the transmission
`matrix.
`
`MODEi 1
`~1->'-<>: with a preferred
`f~ ..
`, v
`'
`f
`,
`' I ostalll' orces. Under
`1y_ II
`·/.Y . s fall in a horizontal plane
`l.I· ·
`aerodynamic l'o
`with their short axis vertical and needle-type crystals fall with
`their long axis horizontal [7], [8] . For needles in this state, it
`appears that only a small force would be needed to influence
`the azimuth of the long axis and it is reasonably certain that
`both wind shears and horizontal components of electrostatic
`fields can produce a high degree of systematic alignment of
`needle azimuths. The relative dominance of these forces is
`uncertain, as is also the extent to which a common needle
`azimuth exists over the large volume that affects a microwave
`link, even if a high degree of azimuth alignment exists locally.
`
`00 l 8-926X/98$ I 0.00 © l 998 IEEE
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0005
`
`

`

`ll:lEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
`
`531
`
`Study of Impedance and Radiation Properties of a
`Concentric Microstrip Triangular-Ring Antenna and
`Its Modeling Techniques Using FDTD Method
`
`Iti Saha Misra and S. K. Chowdhury, Senior Member, IEEE
`
`A/1.~trlll'I- A i:nnl'c11lrk mkruslrip h·iungulnr-rlng uutcnnn
`:. I rnl'lm't' using lhe l11g-1wriodk prlnl'i11I~ for lnere11sing the
`i11111cd1111t•1•
`l111ndwidth of the 111h'roslrl11 p11ld1
`1111h•111111
`ls
`1k~l·rihed. Th<' linilt•-dlITc1·c11t·c li11w-do11111i11 U'DTI)) method is
`ap11lled to analyze the 111·011oscd slrnt·tnn·. A s11cclal lt!chnique
`to 1111ull'I the slanted mctulllc boundurics ol' the lriilngulur ring
`ha~ been used In the g<'lll'ntl l•'DTU 1tlg11rllhm to avoid the
`s1:oin·nsc 111111roxlm11llon. The method l11111rovcs tht• 11ccur11cy of'
`1h•· original l'l>Tf> nlgurilhm wlllmul im·1'l~nsi11g the rnmpll'xity.
`Tiil' rndlnlion 1111lh!l'llS Ill diR'crt•nl rrcc1ue11l'il'S 11\'l'I' widl'·l11111d
`width are obtained experimentally.
`
`l11dex Terms-FDTD methods, microstrip antennas.
`
`I. INTRODUCTION
`
`A three-element concentric microstrip triangul:1r-ring an(cid:173)
`
`tenna (CMTRA) has been designed using a log-periodic
`principle and fabricated on a polytetra fiuroethylene (PTFE)
`substrate. The elements of the CMTRA are fed electromagnet(cid:173)
`ically by a 50-0 microstrip line. The impedance and radiation
`characteristics have been measured and compared with those
`of two single triangul:ir-ring antennas (STRA) having the
`largest and the s111ullcs1 element dimensions of the CMTRA.
`The impedance variation for the CMTRA has been measured
`at different feed locations. Results show that the bandwidth of
`the CMTRA is increased with respect to the STRA and the
`maximum bandwidth obtained for a particular feed location
`away from the center. The measured radiation characteristics at
`different feed location show its invariant nature. The measured
`impedance pattern for two feed locations are verified by FDTD
`method. This method is similar to the method described for
`cont: 111rk microsLrip ci rL·uh:tr· ring u111 •111111 ( M RA) in 111.
`A fl •c111I 1cchni 1uc 10 n10d •I the slum d mo1ulli · boumfari s
`'I' tht 1ri1111.,11tar ring hn. b en u. lld in 1he g n •rol Pl D
`UJ proicimutiOJl r2J. IJj, 'l'h
`ntgorilh111 I
`llV1lill Ill' llllli
`'II
`ll1't,hud im1 I'< vl!s the accuracy
`I' 1h ' origim1l l1D D nlgmi thm
`Williou1 in ·r~asing lh · cornpl xily.
`
`If. DESIGN OF THREE-ELEMENT CMTRA
`" ~e three-element CMTRA is shown in Fig. l(a). The width
`w and spacing "d" belween the elements are specified in
`M111111~ ri i
`•
`•
`'l'h,· u 1 11 received September 6, 1996; revised May 30, i997.
`ll11giih•c:11,11~" arc with the. De~rlmont of Elec1ronics nn~ Telecommunicntion
`Puh\iit
`/udnvpur University, CalouLLn, ?00 032 India.
`1
`irr lcm Ident ifier S 0018-926X(98)02680-5.
`
`(a)
`
`(b)
`
`(c)
`
`Fig. I. Geometry of (a) lhree-element CMTRA, (b) STRA investigation of
`the smallest element dimensions, and (c) STRA investigation of the largest
`element dimensions.
`
`this figure. First, the innermost element Was chosen with side
`a = 1.4 cm and width w = 0.2 cm. The spacing between the
`adjacent elements and their widths are then chosen maintaining
`the following relation:
`
`(I)
`
`where n is the suffix of the nth number of patch as indicated
`in Fig. l(a). The ring width and spacing decrease from the
`innermost element to the outermost element. Maintaining this
`relation the outermost ring has the sides a= 3.0 cm and width
`w = 0.128 cm. The STRA's investigated have the smallest
`
`0018--926X/98$10.00 © 1998 IEEE
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0006
`
`

`

`IBllB TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
`
`532
`
`y
`
`c
`
`o,o
`
`Fig. 2. Modeling of triangular ring in FDID domain.
`
`and the largest element dimensions of the CMTRA as given
`in Fig. l(b) and (c), respectively.
`
`III. ANALYSIS OF CMTRA AND SINGLE
`TRIANGULAR RING BY FDID METHOD
`
`In this investigation one CMTRA and two triangular rings
`having the largest and smallest element dimensions of the
`CMTRA are analyzed by FDTD method. These antennas are
`fed electromagnetically by a 50-fl microstrip line which was
`fabricated on PTFE substrate with dielectric constant 2.55
`and thickness 0.159 cm (Fig. l). The application of FDID
`method to these antennas are similar to those of CMCRA
`[I J. However, the modeling of the triangular-ring element
`is different. In the following sections, we will describe the
`modeling techniques of triangular ring in the FDID domain.
`
`A. Modeling of Larger Triangular Ring
`Fig. 2 shows the actual dimension of the triangular ring
`antenna in the X-Y plane of the FDTD domain. Since the
`ring is an equilateral triangle the angle between the X axis
`and slanting plane is 30°. All the slanting sides of this ring
`can be represented by the equation of a line as
`
`y=mx+C . ..
`
`(2)
`
`where rn = tan (}, (} =angle between the X axis and slanting
`plane.
`Putting the value of (} and any coordinate (x, y) passing
`through the line, the value of C can be found out.
`Now, if one can select the proper aspect ratio of each celJ in
`the FDTD domain, then the slanted plane wall can be modeled
`exactly, i.e., it is possible to locate the boundary nodes of the
`mesh exactly on the slanted planes [3]. In this particular case if
`we select !:i.x = 0.64 mm and, hence, y = !:i.x tan (} then for
`every space increment along X and Y direction the equation
`of the line will be well maintained.
`
`Impedance plot of largest triangular ring of Fig. l(c) at different feed
`Fig. 3.
`location-set l for center feed, set 2 for 0.35 cm off-center feed.
`
`Fig. 4.
`
`Impedance plot of smallest triangular ring of Fig. I (b) for center f~d.
`
`'ntc tangential eleclric field components I~.r und /;'11 und
`nonnul componenl of magnetic field IJ, were 11111dl' ,•4uul 10
`zero on the triangular-ring patch bounded by 1hc si)( fines.
`The POTD pammctcrs for this ring were: 6:1: = O IH 11
`1111•
`!:i.11 = 11.577 :J.J!:i.:c = o.:umtJ mm, aud !:J.z = 11.!i!J'.1.fi 111111j
`!:i.t = !:i.11/2Cu (eo = free-space velocity of li~·ht), u~~
`1 c
`Guassian half-width T = 18 ps. The distance Jw1wcct1
`source plane to microstrip antenna w11s :JU!:i.:r. and the 1i:~·l1':~i:
`plane wus set at a distance I !J!:i.:1: from lhc so11rc1~ l'l;Utll·
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0007
`
`

`

`MISRA AND CHOWDHURY: IMPEDANCE AND RADIATION PROPERTIES OF TRIANGULAR-RING ANTENNA
`
`533
`
`(a)
`
`(b)
`
`(a) and (b) Impedance plot of three-element CMTRA at different frequency band for center feed. (c) Impedance plot of three-element CMTRA
`Fig. 5.
`at <lilforent frequency bnnd for center feed.
`
`(c)
`
`50-n microstrip line width and the ring width were modeled
`as 12.::ly and 2Ax, respectively.
`
`8· Modeling of Small Triangular Ring
`Thl· ac1ual llimcnsions of 1he small lriungular ring is shown
`1
`11 1 I' · lfl ). The FDTD paramelers were A:i: = 1.0 mm. D.11 =
`ll.f,77 :1:,ei.:r "" O.!i77 :J.'i. 6z = O.ii2!Jli mm, Al = b. .>/'2011.
`ta -Wll I =
`11·
`· I h
`. 11
`•lrtd G·1u ·"
`I
`I<
`M '
`.
`I'
`1 ps.
`1cms1nr me Wit I l was
`• ss1a11
`~ ll _·~ 11 as 7 b.11, lhc reference plane was set at 11 dislancc
`•1 I ro1n lhc source plane.
`
`C. Modeling of Three-Element CMTRA
`
`The application of FDTD method is similar to the applica(cid:173)
`tion of single rings. The mesh size was considered such that it
`can model the actual dimensions of the CMTRA. The FDTD
`parameters were Ax = 0.4 mm, Ay = 0.230 94Az = 0.5296
`mm, At= Ay/2C0 , and Gaussian half-width= 20 ps.
`In all three cases Mur's first-order absorbing boundary
`condition had been applied at the end, side, and top walls
`[4]. The total and incident E field were stored at the ref(cid:173)
`erence plane. Frequency-dependent scattering parameter was
`
`•
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0008
`
`

`

`534
`
`IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 46, NO. 4, APRIL 1998
`
`TABLE I
`COMPARISON or 2 : I VSWR %BW or STRA AND CMTRA
`
`Antenna Feed location
`~ mallest CF
`STRA
`Largest
`STRA
`
`CF
`0.35 cm OCF
`0.60cmOCF
`
`MTRI\ CF
`
`Fre . Ran e in GHz
`5.950 • 6.180 ~ 0.230
`
`o/oBW
`3.790
`
`2.730. 2.770 = 0.040
`2.730. 2.755 = 0.025
`2.725. 2.735 = 0,010
`
`• 1-4540
`0.9110
`0.3660
`
`2.730. 2.790 = 0.060
`4.600. 4.710 = 0.110
`6.650 • 6.920 c 0.270
`
`2.1700
`2.3630
`3.9700
`
`0.35 cm OCF
`
`2.660 • 2. 730 = 0.070 .. 2.5900
`3.700. 3.830 = 0.130
`•3.4520
`6.340 • 6.620 = 0.280
`•4.3200
`
`0.60 cm OCF
`
`2.660 - 2.690 = 0.030
`2.720. 2.745 = 0.025
`3.690. 3.830 = 0.140
`6.400 • 6.600 - 0.200
`
`1.1200
`0.9149
`3.7200
`3.0760
`
`CF~ Center Feed, OCF =Off Center Feed,
`• = 2.2 : I VSWR, u = 2.4 : I VSWR
`
`Fig. 7. Mensured rndiation patterns for largest triangular-ring antennn at
`different feed locations.
`
`locations to observe the effect of feed location. The impedance
`pattern for the largest and smallest the single ring antennas
`are given in Figs. 3 and 4 and for the CMTRA are given
`in Figs. 5 and 6. The 2: 1 VSWR circles are shown in the
`corresponding figures.
`
`B. Bandwidth
`The computed 2: I VSWR bandwidth for single ring and
`clif~ ·r ·nt hand mu! feed locations ur gi\' · 11
`in
`MTRA 111
`I. Pr 1111 thb llll lc ii i · s n 1ha1 in ·1 nsc in bu11c.twidlll
`Tnl I
`i: obt 1in d for
`' MTRA 11:.
`·umpnrc<l to a sin •I • rin • and
`maximum 1. tal han<lwiulh Is obtt1in d 111 u recd lo ulion OJ S
`cm away from center for this particular CMTRA.
`
`(a) and (b) Impedance plot of three-element CMTRA at different
`Fig. 6.
`frequency band for 0.35-cm off-center feed.
`
`(b)
`
`computed following the procedure as described in [ l] and [5]
`and from this input impedance of the antennas were calculated.
`
`IV. MEASUREMENTS AND RESULTS
`
`A. Impedance Pattern
`The variation of input impedance for the two STRA and
`CMTRA were measured by HP 84108 network analyzer at
`different band of frequencies. For the large single ring and
`CMTRA impedance patterns are measured at different feed
`
`C. Radiation Patterns
`The rnclialion pall rmi for 'TRA u11d thre - •lc111 •nt ·~ • .rrr~A
`hnv b co 111cusuretl I or holh rp = !JO anti IP .==
`•
`(l" nlllfltl
`1• d n
`ov ·r th ent lr bunJwillLh or th nnt •nna nnd 1irc plo.tc~ ;11
`Figs. 7- Hl. .ompuri son of lh ' radiation pnll rn ol ;1 ·rng
`
`ZTE v. Fractus
`IPR2018-01461
`
`ZTE
`Exhibit 1014.0009
`
`

`

`MISRA AND CHOWDHURY: IMPEDANCE AND RADIATION PROPERTIES OF TRIANGULAR-RING ANTENNA
`
`535
`
`e
`
`(a)
`
`e
`
`w
`Fig. 8, Measured rndiution patterns for three-element CMTRA for center
`focd (a) at cp = oon plune and (b) ut 'f' = uo plane.
`
`ring and CMTRA shows that over the entire bandwidth the
`nature of the radiation pattern is qualitatively similar to that
`of the single ring operating at the fundamental mode. Again
`from Figs. 8-10 it is seen that radiation patterns for CMTRA
`remain unchanged with the change of feed location.
`
`V. NUMERICAL RESULTS
`The FDTD impedance patterns for the single rings and
`CMTRA arc computed for the center feed and for 0.35-cm
`off-center feed and are plotted in Figs. 3-6 with the measured
`patterns. From these figures it is seen that the computed
`patterns are in reasonable agreement with the experimental
`one. The difference between the computed data and the
`cx.perimental one may be due to the consideration of original
`FDTD algorithm for the 11lanted planes. A simple method of
`correcting this algorithm is described below [3].
`C\lnsidcr n rnctang11l11r ell