Char of Quad Ridged Coaxial Waveguide for Dual Band Horn Appln

7/27/2019 Char of Quad Ridged Coaxial Waveguide for Dual Band Horn Appln

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Character is t ics of qu ad-r idg ed coax ial w avegu idesfo r dual-band horn applicationsH Z.ZhangG.L. James, FlEE

Indexing te rms. Quad-ridged waveguides, Broadband diplexers, Dual-band horn, Ritz-Galerkin method

Abstract: Circular coaxial quad-ridgedwaveguides find application in the design ofbroadband diplexers for the dielectrically loaded,ultrawide, dual-band horn. The three basicstructures, where the four ridges are placedsymmetrically on the inner conductor, on theouter conductor or on both conductors of thecoaxial waveguide, are analysed using a modifiedRitz-Galerkin method. To find the optimumconfiguration, the cutoff wavenumbers of the firsttwo (effective) dominant modes for each of thesestructures, from whilsh we deduce the bandwidthcharacteristics, are ciilculated and compared. Theaim is to obtain the preferred coaxial ridgedstructure in terms of broad bandwidth and easeof fabrication.

1 IntroductionA dielectric cone-loaded, hybrid-mode feed horn hasbeen developed recently for broadband applications [11.Analysis using the mode-matching method has shownthat the bandwidth of this feed horn is extremelybroad, and that it can be excited by using a coaxialwaveguide for dual-band applications [I], as shown inFig. 1. However, the limited bandwidth of the excitingcoaxial waveguide inhibits the full potential of the hornto be realised.

exciting coaxial horn 7ir

band

Fig. 1 Duul-band, dielectric cone-loaded feed horn and launchingWaveguide sectionTo exploit the broad dual-band capability of thishorn more fully, we propose the coaxial quad-ridgedwaveguide structure as the basis for a widebanddiplexer. The concept 'behind this diplexer is to excite

the TE, mode only over a very wideband quad-ridged0 EE, 1998IEE Proceedings online no. 195'81777Paper first received 11 h July and in revised form 11h November 1997The authors are wth CSIROTelecommmcations and Industrial Physics,PO Box 76,Eppmg,NSW 2121, Australia

coaxial waveguide of appropriate dimensions. Then theoutput of the diplexer can be directly coupled to theinput of the horn, by a gradual transformation of thecoaxial waveguide section from the quad-ridged geome-try at the diplexer to a conventional coaxial waveguideat the horn, as shown in Fig. 1.

In this paper, we propose three basic configurations:the coaxial waveguides with four ridges placed symmet-rically on the inner conductor, on the outer conductoror on both conductors, as shown in Fig. 2a, b and c,respectively. We also analyse the cutoff and bandwidthcharacteristics of these structures with the intention ofdeveloping the capability of analysing the performanceof an entire system comprising the dielectric cone-loaded horn connected to a coaxial ridged waveguidediplexing section.To seek the optimum configuration, the cutoff and

bandwidth characteristics of the three waveguide struc-tures under consideration need to be analysed andcompared. There are a number of methods availablefor analysing the similar circular ridged waveguidestructures, such as the radial mode-matching method[2 ] , magnetic field integral equation method [3], gener-alised spectral domain method [4], frequency domainTLM method [5 ]and finite-element method [6, 71. Con-sidering the computing efficiency, in particular, the easeof connecting to the software (developed earlier fordesigning the dielectrically loaded horn using the mode-matching method) for analysing the entire system(comprising a dielectric cone-loaded horn and a coaxialridged waveguide diplexer), we chose a modified Ritz-Galerkin method [8, 91 for analysing the proposedstructure. This method, in principle, is a mode-match-ing with reduced matrix size [lo]. The program devel-oped using this method can be easily interfaced withthe existing software using the mode-matching method[l]. Hence, all the subsequent results are obtained usingthe modified Ritz-Galerkin and validated using thefinite-element method [7].2 FormulationA coaxial waveguide with four ridges symmetricallyplaced on the inner and outer conductors (hereaftercalled inner and outer ridged waveguides) are shown inFig. 2a and b , respectively. The coaxial waveguide withfour symmetrically placed double ridges (hereaftercalled double ridged waveguide) is shown in Fig. 2c .When the height of th e outer ridges reduces to zero (c= d in Fig. 2 4 , the double ridged structure becomes theinner ridged structure of Fig. 2a . Similarly, when theheight of the inner ridges reduces to zero (a= b) , the

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double ridged structure becomes the outer ridged struc-ture. Therefore, the double ridged structure is a genericone and the formulation given for this structureincludes all the configurations of interest.

metal ridged structure

circular waveaufor higher banda bY*

Xridged structure

C dFig.2 Three proposed circular coaxial ridged waveguidesThe coaxial waveguide with four double ridges is

symmetric with respect to the x and y axes (seeFig. 2c), and hence, only one quarter of the structureneeds to be considered. This quarter of the structurecan be divided into three regions I, I1 and 111, as shownin Fig. 2d . The Hertzian potential for the TE modescan then be described as [2, 8, 91

P

where fL/, ( kP ) = JA+ (ka)Y&J ( k P )- Jn7r/, ( k P ) Y A / , ( k a )I I U

IIbf ( 2 m - 1 ) ( 'P) 1(2m-1) ( k ~ )f ( z m - 1 ) ('P) == Y(zm-1 ) ('P)f;,,@P) = J ;T / p (")Y,T/, ( kP )- J,T/,(b)Y;,/, ( W

J and Y are Bessel functions of the first and secondkind, respectively, and k is the transverse wavenumberwith respect to the z axis. A, B and C are amplitudecoefficients.The expressions for the E-fields at the interfacesbetween the various regions are assumed as follows:

Jt 2 ( 4 ) D ~ I os -($ - a )43where D' and D" are the amplitude coefficients of theaperture fields.

Using the Ritz-Galerkin technique [8], modified forthis circular cross-section application, the followingmatrix equation is obtained:

at p = c9 =O

where

M .

with

The eigenvalues can be obtained by finding the roots ofDetlH(k)l = 0 (see [8] for details).3 Numerical resultsThe cutoff and bandwidth characteristics of the threecoaxial ridged waveguide structures were calculatedusing eqn. 2. Fig. 3 shows the variation of the normal-ised cutoff wavelength of the dominant TE ll mode as afunction of the angle a (defined in Fig. 2 4 for all threecoaxial ridged structures. It is seen that the cutoffwavelength of these three structures increases and thendecreases with the increase in the width (2a) of theridge. We note that the inner ridged structure has the

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longest cutoff wavelength, whereas the cutoff wave-length of the double ridged structure is longer than thatof the outer ridged structure. We also note that the cut-off wavelengths of all the three coaxial ridged struc-tures are significantly longer than those (dcll/d= 4.078)of the coaxial waveguide without ridges.

(VI

5 10 15 20 25 30 35 40aFig.3 Variation of the normalised cutoff wavelength (Ac,,/d) r thethree coaxial ridged waveguide structures as a functio n o cr(degreefaid = 113(i) (c - b)/d = 1/12, (ii) double ridged waveguide, (iii) inner ridged waveguide,(iv) (e - b) /d = 116, (v) outer ridged waveguide

(iii) (ii)

5 10 15 20 25 30 35 40a

Fig.4 Variation of the bandwidth (Acll/Ac31)or the three coaxial ridgedwaveguide structures as a functi on of a(de gree )aid = 113(i) (c - b)/d = 1/12,(ii)ouble ridged waveguide, (iii) inner ridged waveguide,(iv) (c - b)/d = 116, (v) outer ridged waveguideFig. 4 shows that the bandwidth of these three struc-

tures (defined as the ratio of the cutoff wavelengths ofthe first two propagating modes of interest; in this casethe TE,, and TE,, modes) also increases and thendecreases with the increase in the width ( 2 4 of theridge. In comparison to the cutoff wavelength of theTE ll mode (Fig. 3), the change of bandwidth with thevariation of the ridge width a is more significant. Themaximum bandwidth of the inner ridged structure iswhere a = 15" while the bandwidth of the remainingstructures reaches a maximum when a = 20". Thebandwidth of the double ridged structure is comparablewith that of the inner ridged waveguide, whereas thebandwidth of the outer ridged structure is narrower.Fig. 4 also shows that the bandwidth of all the threecoaxial ridged structures are significantly broader thanthose (Acll/Ac312.702) of the coaxial waveguide with-out ridges.

To show the influence of the radius ( a ) of the innerconductor on the cutoff and bandwidth characteristics.

these quantities are plotted in Figs. 5 and 6 as afunction of inner-to-outer conductor ratio ald. In Fig. 5we see that the cutoff wavelength of the inner ridgedstructure is significantly longer than those of the othertwo structures. This is because this structure attracts ahigh intensive field to its outer conductor and thusfully uses the dimension of this conductor. Similarly,we found the cutoff wavelength of the double ridgedstructure to be longer than that for the outer ridgedstructure. For the inner ridged structure, the smallerthe inner conductor, the longer the cutoff wavelength.

t5 116 113 1 2 213 516

d dFig.5ratio d dInner ridged structure: = 60", c = d, (c h)/d = 1/12Outer ridged structure: p = So", a = b, ( c b)/d = 1/12Double ridged structure: 9,= 50" , b - a = d ~ e, (c - b)/d= 1/12x inner ridged waveguide0 0 outer ridged waveguideAA double ridged waveguide

Variution o the normalised cutosf wavelength as U function o

3i16 113 112 213 516

aidFig.6Inner ridged structure: p = 60", c = d, (c - b)/d = 1/12Outer ridged structure: 'p = 50", a = b, (c - b)/d= 1/12Double ridged structure: 'p = SO", b ~ U = d ~ e, (c - b)/d = 1/12x inner ridged waveguideAA double ridged waveguide

Variation of th e bandwidth (AclI/Ac3,)s a function o ratio d d

outer ridged waveguide

Fig. 6 indicates that the bandwidths of the threestructures are comparable when the ratio ald is in therange 5/12 to 11/12. The Figure also shows that thebandwidth within this range decreases with increasedratio uld. However, when aid is smaller than about 5112, the bandwidth of the outer ridged struc ture appearssignificantly shorter than those of other two structures.In contrast, the bandwidth of the inner ridged structureincreases continuously with reduced a/ d ratio. The

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maximum bandwidth of the double ridged structureappears at ald = 113.Figs. 7 and 8 show the variation of cutoff andbandwidth of the structures as a function of the gap (e- b)/d along the radial direction. Both Figures showthat the cutoff wavelength and bandwidth increasewhen the gap decreases. Figs. 7 and 8 also indicate thatthe cutoff and bandwidth characteristics of the innerridged structure are better than those of the other twostructures.

2 1 " " " " ' " "2/24 4124 6/24 8/24 10124 12/24 14/24Vartution of the normalised cutoff wavelength us a function of(c-b) ldFig.7ratio (c - b)/dInner ndged structure' 9 = 60", c = d, aid = 113Outer ridged structure 'p = So", a = 6 , aid = 113Double ridged structure 'p = 50", b ~ a = d - c, aid = 113xx inner ridged waveguide- ut a r idged waveguideAA double ridged w aveguide

5Ll

2 5 -m4 -

3 -

2/24 4124 6/24 8/24 10124 12\24 14/24Vuriation ofthe bandwidth (AcTlll/Ac3,)s a junction of ratio (c -c-b)idFi .8

Inner ridged structure 'p = 60", c = d, ald = 1/ 3Outer ridged structure 'p = 50", a = b, aid = 113Double ridged structure. m = 50", b ~ a = d - e, aid = 113xx inner ridged wavegutdeAA double ridged waveguide

blqd

outer ridged waveguide

The computational results obtained using the modi-fied Ritz-Galerkin method have been verified using thefinite-element method [7]. As shown in Table 1, theagreement of the results obtained using these two meth-ods is excellent.4 Conc lus ionThe numerical results obtained using the modifiedRitz-Galerkin method show that the cutoff and

Table 1: Comparison of normalised cutoff wavelengthfor ridged coax ia l waveguide obtained using tw o differ-ent methods

a/d 113 5/12 113 112Dimensions (p=45" ) b/d 7/12 7/12 113 112

c/d 9/12 9/12 213 213Ritz-Ga ler kin 3.539 3.639 4.276 5.443Finite elemen t [71 3.545 3.646 4.277 5.450

bandwidth characteristics of a coaxial waveguide canbe made significantly longer and broader with theinclusion of ridges. (As a check, results obtained usingthe modified Ritz-Galerkin method have shownexcellent agreement with those obtained using thefinite-element method.) The improvement of the cutoffand bandwidth characteristics increases with the reducein the gap between the ridges (or between ridge andinner or outer conductor) along the radial direction.

The cutoff and bandwidth characteristics of thewaveguide with four ridges placed symmetrically on theinner conductor are better than those of the structureswith ridges placed on the outer conductor and on bothconductors. The inner ridged structure with 30O-wideridges (2a)and infinite small inner conductor has thebroadest bandwidth. Moreover, this structure is themost easily machined and excited for the requiredmode.

The results presented here are to form the basis of awideband diplexer for coupling the incomingloutgoingsignals from a dielectrically loaded, ultrawide dual-band horn. Currently, we are extending the analysispresented here with the software (developed earlier fordesigning the dielectrically loaded horn using the mode-matching method) for analysing and designing theentire system, comprising a dielectric cone-loaded hornand the diplexer described above.512

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5

6

78

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ReferencesCLARK, P R , and JAMES, G L 'Ultra-wideband hybrid-mode feeds', Elect ron Let t , 1995, 31, (23), pp 1968-1969DEYGEN, M I 'Denvation of cutoff' conditions in a circularridged waveguide contaming a dielectric rod', Radzo Eng Elec-tron Phys , 1977, (2), pp 120-122SUN, W , and BALANIS, C.A.. 'Analysis and design of quadru-ple-ridged waveguides', ZEEE Tvans Microw Theory Tec h , 1994,42, (12), pp 2201-2207OMAR, A S , JOSTINGMEIER, A , RIECKMANN, C , andLUTGERT,S 'Application of the GSD technique to the analy-sis of slot-coupled waveguides', IEE E Trans Microw TheoryT e c h , 1994, 42, ( I l ) , pp 2139-2148HUANG, J , VAHLDIECK, , and JIN, H 'Computer-aideddesign of circular ridged waleguide evanscent-mode bandpass fil-ters using the FDTLM method' IEEE MTT-S SymposiumDigest, 1993, pp 4594 62DILLON, B M , and GIBSON, A A P 'Triply-ndged circularwaveguide', J Electromagn Waves Appl 1995, 9, (1/2), pp 145-156'HP85180A High frequency structure simulator user's manual'(Hewlett Packard, May 1992)MONTGOMERY, J P 'On the complete eigenvalue solution ofridged waveguide', IEE E Truns Microw Theory Tec h , 1971, 19,ZHANG, H 2 , BEARD, G E , MOHAN, A S , and BEL-CHOR , W R 'Rectangular waveguide with two symmetricallyplaced double L-septa', Elect ron Let t , 1993, 29, (22), pp 1956-1957

(6) , pp 547-555

10 ZHANG, H Z 'Waveguides with two symmetrically placed dou-ble L-septa for processing of dielectric sheet materials' PhD the-sis, University of Technology, Sydney, 1995, pp 115-120

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Char of Quad Ridged Coaxial Waveguide for Dual Band Horn Appln