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shown that the absolute directive gain pattern, for quarter-wave elements o n disc ground planes resting on Earth, variesby less than 1 dBi as the normalised ground plane radius isvaried from 0 to 8 wavenumbers.300

5 600 1-800 I

P -7001,4

normallsed groundscreen rodius Zna lh (wave number )1083131Fig. 3 Input reactance

O N = 4 A N = S + N = 1 6x N = 3 2 0 N = 8 4 V N=128

The radiation efliciency q is the rati o of the far-field radi -ated power to the available input power. The far-field radi-ation is confined to the air medium for an Earth conductivityu > 0. The radiation efficiency is a measure of the power lossin the Earth because the monopole element and radial wiresare assumed to have infinite conductivity. The radiation eff-ciency increases monotonically with increasing number of theradial wires (see Fig. 1) and with increasing length of themonopole element (not shown). The radiation efficiencyexhibits resonances with increasing wire length for a sparsenumber of radial wires.The input resistance and input reactance asymptoticallyapproach the values of disc ground plane as the gr oundscreendensity approaches infinity (i.e. as the number of radial wiresN + 00 as shown in Figs. 2 and 3). A unique characteristic ofradial-wire ground planes is the resonances in input imped-ance and radiation efficiency that occur for a sparse numberof radial wires provided that the Eart h is not of high conduc-tivity. These resonances occur apparently because the currentson the wires are not closely coupled, unlike the case for a highdensity of radial wires or the case of a disc ground plane. Amore detailed discussion of the electrical characteristics ofante nnas with electrically-small groun d planes in proximity t oEarth is given in Reference 12. Additional computer plots (forx = 15, 150, 1500 and zo/L = -lo- are given in Refer-ence 14.

2lst May 1992M. M. Weiner and S . Zamoscianyk (The MITRE Corporation,Bedford, MA 017300208, USA)G. J. Burke (Lawrence Livermore National Laboratory, Livermore, CA9545500808, USA)References

1 RICHMOND, J. H.: Monopole antenna on circular disk over flatEarth, IEEE Trans., 1985, AP-33, (6), pp. 633-6372 WEINF,R,. M.: Input impedance and gain of monopole elementswith disk ground planes on flat Earth. M90-92, The MITRE Cor-poration, Wford, MA, NTIS AD-A224284 (See also: Pro-ceedings, Progress in Electromagnetin Research SymposiumPIERS 1991, Cambridge, MA, July lst-5th, 1991, p. 691)3 BURKE, G. I., and FUGGIO, A. I.: Numerical electromagnetin code(NECFmethod of moments. Lawrence Livermore NationalLaboratory, Report UCID18834,19814 BURKE, G. J., and MILLER, E K.: Modeling antennas near to andpenetrating a lossy interface, EE E Trans., AP-32, pp. 1040-10495 BURKE, G. J.: Users guide supplement for NEC-3 for modelingburied wires. Lawrence Livermore National Laboratory, ReportUCID-19918,19836 BURKE, G. J.: Users guide monopoles on radial-wire groundplanes, Applied Computational Electronics Newsletter, 1983,1, (1)7 BURKE,. J.: Users guide supplement for NEC-GS. LawrenceLivermore National Laboratory, Report UCRL-MA-107572, 1991

8 WAIT, J. R., and POPE, w. A.: The characterization of a verticalantenna with a radial conductor ground system, Applied Scienti@cResearch, 1954,4, Sect. B, pp. 177-195 (The Hague)9 HILL, D. A., and WAIT,. R.: Calculated pattern of a verticalantenna with a finite radial-wire ground system, Radio Sci., 1973,8, (l), pp. 81-8610 RANSE, R. P., and R U W I.: Low angle radiation from verticallypolarized antennas over radially heterogeneous flat ground, RadioSci., 1975,10, pp. 1011-101811 BURKE,. I, , and MILLER, E.K.: Numerical modeling of monopoleson radial-wire ground screens. Proc. 1989 IEEE Antennas andPropagation Society Symp., 1, San Jose, CA, pp. 244-24712 WEINER,.M.: Performance of ground-based high-frequency recei-ving arrays with electrically-small ground planes. MTR-11277,The MITRE Corporation, Bedford, MA, 199113 WEINER,. M.: Validation of the numerical electromagnetics code(NEC) for antenna wire elements in proximity to Earth. MTR-11278, The MITRE Corporation, Bedford, MA, 199114 WEINER, M. M., and ZAMOSCIANYK,.: Radiation elliciency andinput impedance of monopole elements with radial-wire groundplanes in proximity to Earth. M91-104, The MITRE Corporation,Bedford, MA, 1991 (also available from National Technical Infor-mation Service as AD-A244578)

BANDWIDTH OF FM VIDEO SIGNALSF. V. C. Mendis

Indexing terms: Frequency modulation, Video, Subcarriermultiplexing, Optical transmissionAn experimental investigation has shown that the equationb = D + 4f. gives a better estimate of video FM bandwidththan [Le Carson bandwidth b= D + 2f. Accurate know-ledge of channel bandwidth is re&ed in FM subcarriermultiplexed video distribution systems as it affects the alloca-tion of interchannel spacing.

lntroduction: The bandwidth of a frequency modulated (FM )signal is often calculated using the Carson rule. This rule hasbeen derived in many ways [1-5] all using simi lar assump-tions. It may be written asb =D,, + 2f (1)

where D,, is the peak-to-peak frequency deviation and f, isthe frequency of the modulating signal, assumed to be sinus-oidal. If the modulating signal is nonsinusoidal, but is bandli-mited to a top frequency fo, the Carson rule is usuallyextended (forsaking mathematical rigour) to read

(2)=D,, + 2f0Anot her expression, often quoted in the literature [2, 31, givesthe bandwidth of an FM signal as

b =D,, + 4f (3)The Carson rule, eqn. 2, gives a better estimate of the FMbandwidth than eqn. 3 in the narrowband case whereD,, ef,where it is well known that b U 2f,. In wideband FM, D,, 9f , nd both equations give the same result, b = D,,.With the advent of F M subcarrier modulate d (SCM) broad-band optical fibre transport systems for multichannel videodistribution [6-91, where D,, is neither much smaller no rmuch greater than f,, accurate estimation of the signal band-width is required for the allocation of appropriate inter-channel frequency spacing. For the calculation of carrier andsignal-to-noise r atios also, an estimate of the FM signal band-width is required, and the Carson rule ha s been used hitherto[10-14].Experimental inuestigation o video FM bandwidth: To assessthe validity of using the Carson rule for F M video, we con-ducted an experiment where the bandwidth of an FM signal

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was measured when it was modulated with several dillerentvideo test signals. The peak-to-peak frequencq deblation D,,was increased in 1 . 6 M H z steps from 1.6 t o I h M H r and thebandwidth h (taken as the frequency spectral range withinwhich the power is greater than l':,, of the unmodulatedcarrier power). was measured on a 5pectrum analyser. The test

signals werc ohtained from a Rohde & Schwarz video testsignal generator (SPFZ) which provided PALIB video signalswith a nominal bandwidth of 5 M H z (i.e. 1; = 5 M H r ) . Theunmodulated carrier frequency was 75 M H r .Measurements were made for eight video test signals.shown 111 Fig 1 0 h The signals were chosen for their diver-

h Video standard level

c Red area

E CCIR-330

y CCIR-331Fig. 1 V i d m rest i iynuls (ohrarned f ro m (1 RohdP & Schwir:1552

h Colour barSPF.? t id< , , re,! u y n a l yenerilrorl

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sity in baseband spectral distribution so that the measure-ments covered a wide variety of video signals. The results areshown in Fig. 2 where the FM video bandwid th b is plottedagainst the peak-to-peak frequency deviation D,,. The uncer-tainty in the measurements is within (+ / - ) 1 MHz for testsignals, b, c, d , e, h and (+/-) 2MHz for the others. Thebandwidths calculated from eqn. 2 (Carson) and eqn. 3 ar ealso shown in Fig. 2 .

1 6 3 2 L 8 6 4 8 0 9 6 11 2 1 2 8 1 4 4 1 6 0peak-to-peak frequency deviation D ,MHr

Fig. 2 F M video bandwidth variation withfrequ ency deviationD i sc u ss i o n : It is observed from Fig. 2 that the bandwidths donot increase linearly with frequency deviation, but rather in awavy fashion (which can be explained). At very low deviations,the measured bandwidth approximates the Carson bandwidthbut as the deviation increases, the measured bandwidth curvesdiverge widely. At high deviations, some curves fall below t heCarson line whereas others go above the prediction of eqn. 3.It is clear, therefore, that the Carson rule is an insutticientestimate of FM bandwidth for video signals, and that eqn. 3 isa much better (safer) estimate of the upper bound. Eventhough the measurements were conducted on test videosignals, they were diverse enough to allow this conclusion tobe made for actual video signals. Also, there is no loss ofgenerality in using PA L signals for the measurements.Co n c l u s i o n : The equation b =D,, + 4f0, has been shown toyield a better estimate of FM bandwidth for video signalsthan does the Carson rule. Certain expressions quoted in theliterature [ll-141, which use the Carson rule, should beappropriately modified to give more accurate estimates for thevideo signal-to-noise ratio. The results should be useful tooperators and planners of all-optical (FTTH) or optical/coaxial (FTTC) cable television (CATV) systems employingFM-SCM for video distribution.A c k n o w l e d g m e n t : I wish to thank R. L. C. Wik (now at Singa-pore Airlines Limited), for helpful comments, and for carryingout some of the measurements.

;ramiP

19th June 1992F. V. C. Mendis (Department of Eiectrical Engineeriny, National Un i-versity of Singapore, 10 Kent Ridge Crescent, Singapore 0511.Singapore)ReferencesI CARSON, J. R .: Notes on the theory of modulation, Pro c . IRE,1922,lO. pp. 57-64 (Reprinted in: Proc . IEEE. , June 1963,51, pp.893-8962 LATHI, B. P.: Modern digital and analog communication systems(Holt-Saunders, 1983),Chap. 4. p. 2943 CARLSON, A. B.: Communication systems (McGraw-Hill, 1975),2nd edn., Chap. 6, p. 2364 TAUB, H., and SCHILLING, D. L.: Principles of communicationsystems (McGraw-Hill , 1986),2nd edn., Chap. 4, p. 1535 HA Y KI N , s. s.: An introduction to analog and digital communica-tions (John Wiley, 1989),Chap. 7, p. 336

ELECTR ONICS LETTERS 30th July 1992 Vol. 28 No. 16

6 OISHANSKY, R., LANZISERA, v. A., and HILL, P. M. : Subcarrier multi-plexed lightwave systems for broadband distribution,J. LightwaveTechnol., 1989, LT-7, pp. 1329-13427 WAY, w. I. : Subcarner multiplexed lightwave system design con-siderations for subscriber loop applications, J. LightwaveTechnol., 1989, LT-7, pp. 1806-18188 BICKERS, et ai.: The analog local loop: A growing revolution inoptical transmission, . Lightwave Technol., 1989, LT-7, pp, 1819-18249 DARCIE, 1. .: Subcarrier multiplexing for lightwave networks andvideo distr ibution systems, IEEE J . Sel. Areas Commun., 1990,SAC-E, pp. 1240-124810 LO, c. N. : A hybnd lightwave transmission system for subcarrier

multiplexed video and digital B-ISDN services in the local loop,J. Lightwave T echnol., 1989, LT-7, pp. 1839-184811 MENDIS, F. v. c., and ROSHER, P. A. : CNR requirements forsubcarrier-multiplexed multichannel video FM transmission inoptical fibre, Electron. Lett., 1989, 25, pp. 72-7412 SIACOS, C. A .: Satellite FM television bandwidth, Space Communi-cation and Broadcasting, 1984, 2, pp. 363-36913 CCIR Report 215-6, Vol. XjXI, art 2, Sec. 3.1, 1986, p. 2214 MENDIS,F. v. c . : Interpretationof signallnoise ratio expressions inFM video transmission, Electron. Lett., 1989, 25, pp. 67-69

OPTICAL LOW COHERENCEREFLECTOMETRY WIT H 1.9 pm SPATIALRESOLUTIONX. Clivaz, F. Marquis-Weible and R. P. Salatht

Indexing terms: Optical reflectometry, Interferometers, OpticalmeasurementAn optical low coherence reflectometer is presented whichuses an all-fibre Michelson interferometer with the fluores-cence light of a Ti: AI,O, crystal as a light source. Thebroad spectrum of the fluorescence allows a maximal spatialresolution of I.9pm to be reached, with a dynamic range of80 dB.

Optical low coherence reflectometry (OLCR) is an interferom-etry technique based on coherent crosscorrelation detection oflight reflected by a sample under test. This technique wasintroduced in 1987 [I , 23 to probe optical devices used intelecommunication, and is based on a Michelson interferome-ter with a CW light source characterised by a short coherencelength. Optical interfaces as well as light backscattered insidea sample can be detected with a spatial resolution inverselyproportional to the spectral width of the light source. Opticallow coherence interferometers have been presented by differ-ent authors, to characterise the position of weakly reflectingdefects in optical elements [3], or backscattering in single-mode optic al fibres [4]. The same technique has been appliedto measure optical distances inside the eye [SI, and to probethe diffused light inside an arterial wall [SI. It has recentlybeen introduced for noninvasive tomographic imaging in theretina and in coronary arteries, with a longitudinal resolutionof 17pm [7]. These devices are singlemode optical fibre inter-ferometers, using LEDs or SLDs as a source. The dynamics ofthe technique is directly related to the optical power launchedinto the interferometer. The spatial resolution is limited by thespectral width of the light source. With typical devices dis-cussed above, a dynamic range of 14 0dB has been reached,with a spatial resoluti on of 14p m [4]. In this Letter, wepresent the first results of reflectometry measurements, indi-cating a spatial resolution of 1.9 pm. They have been obt ainedusing the fluorescence light from a T i :A1,0, crystal.A schematic description of the all-fibre interferometer isgiven elsewhere [6]. Fluorescent light from the Ti : AI,O,crystal, excited by an argon laser, is emitted between 600 andIOOOnm. The spectrum exhibits an emission maximum at780 nm, and an FWH M of 180nm. 4.8 p W of this fluorescentlight is coupled into a low birefringence, singlemode optical

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