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Modal analysis of dielectric loaded coaxial probe fed circular waveguide radiator

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HAL Id: hal-00722719

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Submitted on 3 Aug 2012

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Modal analysis of dielectric loaded coaxial probe fed circular waveguide radiator

S. Safavi-Naini, Hossein Ameri Mahabadi

To cite this version:

S. Safavi-Naini, Hossein Ameri Mahabadi. Modal analysis of dielectric loaded coaxial probe fed circular

waveguide radiator. Antennas and Propagation Society International Symposium, 1991. AP-S. Digest,

Jun 1991, United States. pp.1856-1859 vol.3. �hal-00722719�

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11 3.9

lodal Analysis of Dielectric Loaded Coaxial Probe Fed Circular Waveguide Radiator Safieddin Saf avi-Naini*and Hossein Ameri Department of Electrical Engineering,University of

Tehran,Iran

Tehran

Dielectric resonator antennas(DRA) have recently been proposed[l],[2]

as a simple efficient nonmetalic radiator,especially for microwave and millimeter wave range of frequencies.Various approximate and rigorous methods such as perturbational and variational approaches bs well as more elaborate mode matching techniques have been developed for analysing resonant characteristics and field distributions in nonradiating structures and particularly enclosed configurations/3].[O].DRA residing on an infinite p l a n e fed by a monopole has been treated by applying method of moments to coupled integral equations for equivalent surface currents on dielectric-air interfaces.The method uses free space Green's function which is obviously inappropriate for complex geometrics such as the one shown in Fig.1.In this paper an almost rigorous procedure for analysing DRA in cylindrical enclosures is presented.

Outline of the method: In many typical applications the diameter of the waveguide 2b, is chosen so that only dominant mode TE,, is propagating.

Diffraction at the open end propagation of the same mode with usually a small amplitude and excitation of a few higher evanescent modes.Therefore an appropriate starting point for analysis of the proximity of the impressed source(interior problem) is to 8osume that the dielectric loaded circular waveguide shorted at

one end is undergo

a partial reflection at the open end.Ref1ection coefficient 'I for 8

TEll wave incident onto the open end has already been derived [6].Based upon these assuuiptions,fields generatted by an infinitesimal r-directed electric current element located at r-(rO,O,r*) may now be evaluated.

To this end source and fields are expanded in terms of #-harmonics (sinp#,cosp#).Thus the analysis given below relates the p-th harmonic of the fields to the same harmonic of source.The fields generated by the p-th harmonic of the point source namely J cos(p#) constitute the p-th harmonic of the dyadic Green's functionTPfor electric fie1d.If we denote the solenoidal part of G by g then [7]:

will cause the back

field at the

semi-fnfinite(Fig.Zj, except for TE11 mode which may

--- ---

G(r,r ')=g(r,r')->;& F , p ) / k l ( I ) to find-git is noted that the fields throughout the structure immediate proximity of the source (Ir-z*lss) may be expanded in eigenmodes of the corresponding transverse section of the waveguide:

excluding terms of

E 4 { (B * exp [- jA (2- t ' )

I

+ B . exp[ j A (5-2' ) ] I

-7

n + n 2n

- n

2n -~1czcr

n + n 2n - n 2n 2n

-

H=I: { (B. expi- jA (0-2 ' ) ] - B - exp[jA (2-2 ' )

I) -; I

(3)

-

E-Z{(A-exp[-jR ( z - z ' ) ] + A . e x p [ j R ( z - z ' ) ] ) . ~ H=Z{(A-exp[-jR (z-z')]-A:exp[jR(z-z~)J)*~

E=I: D-exp(-jR z) *fr;;+y.-%exp(-jR l)-exp(jR z)-z H=C D. exp(- jR z )

-7, '5-

exp (- jR ?l 1) * exp(j% z ) *h,,

n + n 2n - n 2n (2C)

n * n 2n - n 2n n

n n

n n In

a

2 I

z>Sl (2d)

In

-

11

-

where -non zero only when (p=l,n=l) in this case: exp(j%l),G ,-) are the transverse electric and magnetic modal fields with radial % k x

" n e and azimuthal number " p " , 4 is the propagation constant for the same mode,and

3,

is the reflection In coefficient for T% .Figure 2 illustrates the case where the point source is located inside the dielectric.The fields due to a source in air,may be derived in a similar manner.However only the first case is treated here.Continuity of transverse fields at the interfaces z=*41 combined with following orthogonality relations:

provides us with expressions for Cn and Dn in terms of Jm and

a m

respectively.At the same time an infinite order matrix relation%hip between f m and E m a n d A, and A m c a n be established.Finally, invoking reciprocity between "true" pielas- (2b,2c)and m-th propagating mode in inhomogeneously filled part of the waveguide,the relationship between the modes'amplitudes in the close vicinity of the source is derived as:

where use has been made of the orthogonality relation [ 5 ] :

and e2,m 's are in

;-component of electric field of mp-mode.Substituting (4) centinuity relations mentioned earlier yields:

where

where

h=II

the sur ace integratrons are performed over the corresponding

6.y

and tnJ QS

(4)

waveguide cross section and the elements of column vectors a ,a defined ass

and g are

zz

m

2 t %sin fl s.sin[B (Jrl+z')]}.e

h nm In 2m

the infinite iinear system of equations (6) should be solved for unknowns A+ and then using (4J and continuity relations mentioned before other u-&owns

p

determined.To solve (6) the infinite systen ism trutcated by considering only a finite number of "N. modes in each region.Thus the matrices in ( 6 ) will have dimension NxN.The truncated system can easily be solved for A :

,C ,and D,,, will also be

it is interesting to note that t 'S and q 's can be calculated in closed form [I].Furthermore,the matrices' elements all their operations are independent of z'.Therefore all the numerical computations are performed once and then a finite analytical representation for Green's function is obtained which can be used to determine the field on the radiating aperture and input impedance for a known source distribution.

Numerical results and conc1usion:resonant frequency and radiation pattern of a circular waveguide radiator shown in Fig.1 have been analysed by the method presented here.The primary consideration in this special design has been the bandwidth.Experimenta1 results and theoretical predictions for two cases ( c =4,12) are show in Fig.3. AS it is evident from this comparison,the method has a reasonable accuracy.In both cases, a piecewise sinusoidal distribution for the probe current has been assumed.

In general a limited number of modes in both inhomogeneous and homogeneous regions provides us with sufficiently accurate results for many practical cases.More rigorous formulation of input impedance and extension to more complex structures are currently under investigation.

References:

[I] S.A.Long,et al.IEEE Trans.on antennas 6 propagat.,vol.AP-3l.No.3

[ Z ] AL.A.Xishk,etal.,1988 IEEE AP-S/RRSI,Proceedings,pp. 556-560.

[3] D. Xajfez,Dielectric Resonators,Artech House 1986.

[ a ] K.Zaki,etal.,IEEE Trans. on Microwave Theory 6 Technique, MTT-31

[ 5 ] R.E.Collin, Field Theory of Guided Waves, McGraw Hill ,1960.

[6] I.A.Weinstein,The Theory of Diffraction and The Factorization [?] P.H.Pathak,Trans. on Antennas 6 Propagat.,vol. Ap-31, N0.6,

. ,May 1983,pp. 406-412.

N0.12, Dec. 1983, pp.1039-1045.

Method, The Golem Press,l969.

pp.837-846, NOV. 1983.

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Zbr; 22 28 .?a= 7 2 63 i= 975 d- 9 0 I= 0.8 f= 7 . 2

RS 7 . 8 S r 9 1

a- 7 7 5 IC= 6 2

U

Fig.1

DRA

inside a cylindrical enclosure.

. . . . .- .. . . . .

F i g . 2 dielectric loaded semini- f i n i t e Circular Waveguide

Er:&

h12.6

STRT ~:o.dSSGHi CASH +‘:L.SfOGHZ STbp +12.499GHZ ____

0 0 0

-

x x x

Fig.3 Radiation pattern and return loss.

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