Admittance Loading Of Dielectric Loaded Inclined Slots In The Narrow Wall Of A H-Plane Tee Junction

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1 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) Admittance Loading Of Dielectric Loaded Inclined Slots In The Narrow Wall Of A H-Plane Tee Junction G. Srivalli Department of Electronics & Communications, Stanley College of Engineering and Technology for women,abids, Hyderad 5,INDIA srivalligundala@gmail.com Dr. Srinivasa Ba V S S N Department of Electronics & Communications, Stanley College of Engineering and Technology for women,abids, Hyderad 5,INDIA vssnsba@gmail.com Abstract : Slotted waveguide antennas find applications in microwave communication and radar systems requiring narrow beam or shaped beam patterns because of its compactness. They are particularly useful in airborne, space craft applications where light weight and small scan volumes are important. Array of such slots are used to improve the directivity. Such slots are analysed by several researchers. However analysis on dielectric loaded slot coupled H-plane tee junctions is not considered. It is therefore of interest to investigate dielectric loaded H-plane tee junctions in order to control admittance loading, coupling and VSWR. The analysis involves plane wave spectrum approach and expression for the admittance is derived from the knowledge of self-reaction and discontinuity in modal current. The simulated results on normalised conductance, susceptance, coupling and VSWR as a function of frequency are presented in figures to. The data presented in this paper is extremely useful for the design of small and large arrays of H-plane Tee junction radiators. Key Words: Slot coupled waveguide junctions, Waveguide slots, Dielectric loading, Slot arrays, Selfreaction, Discontinuity in modal current, Admittance parameter, coupling, VSWR.. INTRODUCTION It is evident from the open literature [-8] that the overall admittance characteristics of waveguide junction radiators can be controlled by introducing dielectric loading. In this work, it is of interest to present detailed studies on the variation of equivalent network parameter, coupling and VSWR when different dielectric sls are present. In a waveguide Tee junction, slot between the feed waveguide and coupled waveguide, couples the power. This result in the coupling of internal field into the space, such a slot forms a radiating element. The coupled arm is fed with a rectangular slot which can be either longitudinal or inclined. The slots can be cut either in the broad wall or in the narrow wall of a rectangular waveguide. Slots like inclined slots, centered and displaced longitudinal slots in the narrow wall of a rectangular waveguide or inclined slots and displaced slots in the broad wall will only radiate. The amount of power coupled by slot in a H-plane tee junction depends on the slot dimensions, slot orientation and its position, dimensions of internal narrow and broad walls of feed and coupled waveguides, wall thickness, orientation of feed waveguide, and frequency. When the coupling slot is loaded with dielectric, the designer will have an additional parameter namely slot dielectric loading to control normalized conductance, susceptance, coupling and VSWR. In order to include the effect of the dielectric loading over the slot Bailey [7] and Christen [8] have modified theoretical models for waveguide slots in free space. However, the works of these researchers are confined to the cases of inhomogeneous dielectric or plasma layer over the slot. Design and performance methodology of flush-mounted waveguide slotted array in one of the broad walls when dielectric sl is placed over the slot in the array aperture is reported Sharp et al. [9]. In fact this type of antenna can also operate when the dielectric is placed within each Page 974

2 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) guide. The theory presented involving empirical design method is found to be approximate. Galejs [] has computed the admittance of a waveguide or a cavity backed slot which radiates into a homogeneous isotropic plasma or a thick dielectric layer [>]. The formulation is found to be highly involved and is not applicle to thin dielectric layers. As a result the waveguide boundary is found to be simplified to a large extent in the admittance calculations. In most of the works on the slot radiators in the narrow wall of a rectangular waveguide junction, the data on the effect of dielectric loading of the slot on the admittance characteristics is not considered. But the dielectric loading has a definite effect on the admittance parameter. In view of this, in the present work, some investigations are made to consolidate the effect of dielectric loading of the inclined slot in the narrow wall of a rectangular waveguide on the admittance parameter. It is of interest to present detailed studies on the variation of equivalent network parameter, coupling and VSWR when different dielectric sls are present. Here the main objective is to bring out the effect of dielectric on the admittance loading. This data is useful for the design of array of such slots. For array designers, dielectric loading would serve as an additional parameter for the design of junction coupled slot arrays. The slots considered in the present case are extremely useful for high power applications. In the present work, the analysis is carried out to obtain variation of slot conductance and susceptance as a function of frequency for the resonant slot length. Plane wave spectrum approach has been used for the analysis. The concepts of Rumsey [4] and Marcuvitz and Schwinger [] is made in use to simplify the formulations in electromagnetic theory for the slots of present interest. The results are found to be more accurate as no assumptions on the thickness of the slots are made. The results are valid for both thin and thick slots.the slots which are entirely in the narrow wall having resonant length for a given inclination are only considered in order to make them suitle for planar arrays. The computed data on the variation of normalized conductance and susceptance as a function of frequency for higher slot inclinations with different dielectric loadings in the feed and coupled guides are presented.. FORMULATION The slot coupled H-plane tee junction of present interest is shown in Fig.. The geometry and co-ordinate system for the slot is also shown. The electric field in the aperture plane of the slot is replaced by an equivalent magnetic current I dm. Fig. Inclined slot in the narrow wall of a rectangular waveguide Tee junction The Expression for self-reaction is of the form Here H. M () dv H is the magnetic field, M <r, r> fc = is the equivalent magnetic current in the slot, v is the coupled volume, some part of which is in guide and the remaining part in guide. <r, r> fc = <r, r> f + <r, r> c where <r, r> f and <r, r> c are the self-reactions guide and coupled guide respectively. The electric field distribution E in feed in the aperture plane of the slot is related to the equivalent magnetic current M by the relation. M = E U n () where U n is the unit vector normal to the aperture plane. The field distribution in the slot is assumed to be sinusoidal and is given by E = x U E max.(sin K ).A.δ( B ) Page 975

3 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) a W L where A = (L - z ) a x W B =y y - b for and - L z Here K =, is the wavelength, E max is the maximum electric field in the slot, L is the length and W is the width of the slot. Since the magnetic current is distributed over the surface, the volume integral appearing in the expression of selfreaction () is reduced to a surface integral. Taking the effect of image in the wall y=b into account, the expression for the self-reaction takes the form, < r,r > f = s H. M (3) ds Simplifying the ove expression for self-reaction in guide and considering the dielectric loading into effect the equation takes the following form, m n K b a and mn = here K r = r, r the dielectric constant of dielectric in the feed guide. In the ove expression, summation is taken for all combinations of m and n excluding m=, n= and m=, n=. The modified expression for self-reaction in guide considering the effect of dielectric loading is obtained as r, r c = SinF m mn K L M Sin Cos F CosN X m n F is <r,r> f = m n j m n o C.D Cos [(/)E ] Cos F [Sin F /F ] I (I SinH -CosH +J )-.5(+J ) (4) Where C = D = K Kr r mn E = 4Emax mn m n F = n F =bgw S D G = I = Cos H J = e mn L I = H = K r L L mn ma nb Here K = L = F = E m W nw a K M = K n F = N = X = K r r r m b L sd m j n m Cos b n b L 4 j mn n a (5) Page 976

4 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) K r = r, r is the dielectric constant in the coupled or secondary guide.. EXPRESSION FOR DISCONTINUITY IN MODAL CURRENT The expression for the discontinuity in modal current I dm given by [] is modified taking the dielectric loaded slot in the narrow wall into account and is expressed as I dm = E max K r A B CosC CosD (6) Where A = K r SinW X WY fc Sin B = C = r L D = K r L X = Y = r Sin r Sin Sin θ is the slot inclination angle of the slot and r K r b. EXPRESSION FOR ADMITTANCE LOADING From the knowledge of self-reaction and discontinuity in modal current, admittance parameter is evaluated from the following expression Y r = I dm. I r, r dm fc (7) The corresponding normalized admittance is obtained from y nr = Yr Y r = g nr + jb nr (8) Where Y is the characteristic admittance of guide, g nr is normalized conductance and b nr is normalized susceptance..3 EVALUATION OF COUPLING AND VSWR It has been possible to represent the slot radiator of the present interest by its equivalent circuit which consists of a shunt admittance parameter. As described by [] a transmission matrix of the shunt admittance parameter can be written in the following form ynr / y / nr C C C C y = y nr nr / / With the matched termination at port (ii) no reflec tions take place from the termination i.e. C = The reflection coefficient can be written as where y Ln = + y nr = y y Using the concept of power balance conditions, the relative power coupled to the free space is given by P r = Lnr Lnr (9) p p p p 4g = nr where X = g n bn X where P +, P -,P + -,P are the incident and reflected powers of ports and respectively at the plane of centre of slot seen from guide. The coupling in db is given by p rdb = log P r The corresponding VSWR is obtained Page 977

5 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) VSWR = 3. RESULTS AND CONCLUSIONS () Using the expressions (-), computations are made to obtain the resonant length of dielectric loaded inclined slot in the narrow wall of a rectangular waveguide for various relative permittivity values and using the corresponding resonant length and the same expressions, normalized admittance is numerically computed.. From the computed results, variations of normalised conductance and susceptance as a function of frequency AT resonant slot lengths, for dielectric constants of, 3 & 4 and slot width of. cm for slot inclinations of 6 are presented in fig. to 3. Normalised conductance Normalised susceptance Frequency(GHz) Fig GUIDE Eps =. & GUIDE Eps=. GUIDE Eps =. & GUIDE Eps=. GUIDE Eps =. & GUIDE Eps=. GUIDE Eps =. & GUIDE Eps= Fig & 3. Variation of Normalised Conductance and Normalised Susceptance with frequency for a dielectric loaded H-Plane Tee Junction, Slot width=. cm and slot inclination =6 o Normalised conductance Normalised susceptance Fig 4 GUIDE Eps=. & GUIDE Eps=3 GUIDE Eps=3 & GUIDE Eps= Fig 5 GUIDE Eps=. & GUIDE Eps=3 GUIDE Eps=3 & GUIDE Eps=. Fig 4 & 5. Variation of Normalised Conductance and Normalised Susceptance with frequency for a dielectric loaded H-Plane Tee Junction. width=. cm and slot inclination =6 o Slot -. Fig 3 Page 978

6 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) Normalised conductance GUIDE Eps =. & GUIDE Eps=4 GUIDE Eps =4 & GUIDE Eps=. Coupling (db) GUIDE Eps =. & GUIDE Eps=. GUIDE Eps =. & GUIDE Eps=. Normalised susceptance GUIDE Eps =. & GUIDE Eps=4 GUIDE Eps =4 & GUIDE Eps= VSWR GUIDE Eps =. & GUIDE Eps=. GUIDE Eps =. & GUIDE Eps= Fig 6 Fig 7 Fig Fig 6 8 Fig 9 Fig 6 & 7. Variation of Normalised Conductance and Normalised Susceptance with frequency Fig 8 & 9. Variation of Coupling and VSWR with for a dielectric loaded H-Plane Tee Junction frequency for a dielectric loaded H-Plane Tee Junction. Slot width=. cm and slot inclination =6 o Page 979

7 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) Coupling (db) GUIDE Eps=. & GUIDE Eps=3 GUIDE Eps=3 & GUIDE Eps=. Coupling (db) GUIDE Eps =. & GUIDE Eps=4 GUIDE Eps =4 & GUIDE Eps=..8.6 GUIDE Eps=. & GUIDE Eps=3 GUIDE Eps=3 & GUIDE Eps=..6 GUIDE Eps =. & GUIDE Eps=4 GUIDE Eps =4 & GUIDE Eps=. VSWR.4. VSWR.4. Fig Fig Fig &. Variation of Coupling and VSWR with frequency for a dielectric loaded H-Plane Tee Junction. Slot width=. cm and slot inclination =6 o Fig Fig Fig & 3. Variation of VSWR with frequency for a dielectric loaded H-Plane Tee Junction. Slot width=. cm and slot inclination =6 o From the investigations carried out in this work, it is found that the admittance parameters can be controlled when feed guide is loaded with dielectric compared to that of coupled guide loaded with dielectric. The coupling power is Page 98

8 Communication Technology, Vol 4, Issue, November- 5 ISSN (Online) ISSN (Print) increased and VSWR is found to be nearly unity with primary dielectric loaded guides. It is evident from the results that dielectric loading has considerle effect on the variation of admittance parameter and can be used as an additional parameter for the design of slot coupled H-plane Tee junction arrays. REFERENCES [] Cheng - Geng Jan,; Powen Hsu(99) : Moment method Analysis of Side wall inclined slots in Rectangular Waveguide IEEE Antennas & Propagat., Vol. AP-39, No., pp [] Collin, R.E. and Zucker,P.J.(968). Antenna theory,vol, Mc Graw-Hill, Newyork. [3] Das, B.N.; K K Joshi (98) :Impedance of a radiating slot in the ground plane of a microstripline. IEEE Trans. on Antennas & Propogat.,Vol. AP-3, no.5, pp [4] as, B.N.; J. Ramakrishna ; B. K. Sarap (984) : Resonant conductance of Inclined slots in the Narrow wall of a Rectangular Wave guide. IEEE Trans. on Antennas & Propogat.,Vol. AP-3, no.7, pp [5] Elliot, R.S. ; Kurtz, L.A. (978): The design of small slot Arrays. IEEE Trans. on Antennas & Propagat., Vol. AP-6, No., pp [6] Elliot, R. S.(98). Antenna Theory and Design, Prentice - Hall Inc., [7].Harrington, R.F.(96).Time-Harmonic Electromagnetic Fields, McGraw-Hill, Newyork. [] Powen Hsu.; Chen, S. H.(989): Admittance and Resonant length of Inclined slots in the Narrow wall of a Rectangular Waveguide. IEEE Trans. on Antennas & Propagat., Vol AP-37, No., pp [3] Rumsey V.H.(954) The reaction concept in electromagnetic theory. Phys. Rev., Vol. 94, No. 6, pp [4] Silver, S. (995). Microwave Antenna theory and design,, Dover publication Inc., New York. [5] Stevenson A F (948): Theory of Slots in Rectangular Waveguides.J. appl. Phys. Vol. 9, pp [6] Watson, W. H. (946) : Resonant Slots. Proc. IEE., vol. 93 (III A), pp [7] M.C. Bailey, Design of dielectric - covered resonant slots in a rectangular waveguide, IEEE Trans. on Antennas & Propagat., Vol AP-5, No.5, pp , Sept [8] R.E. Christen, Investigations of the interaction between a longitudinal slot and a plasma, Antenna l. Ohio State Research foundation Dept 46-4, June 5, 966 [9] E. D. Sharp, EMT Jones, An Antenna Array of Longitudinally - slotted Dielectric - loaded waveguide, IRE Trans. on Antennas & Propagat., pp , March. 96. [] J. Galejs, Admittance of a waveguide radiating into stratified plasma, IEEE Trans on Antennas & Propagat., pp. 64- [8] Jasik, H. Ed.(96). Antenna Engineering Handbook, Mc Graw Hill, New York [9] Keshavamurthy, T.L. ; Butler, C.M.(98) : Characteristic of a slotted parallel -plate waveguide filled with a truncated dielectric. IEEE Trans. on Antennas & Propagat., Vol. AP-9, No., pp. -7 [] N. Marcuvitz, N. ; Schwinger, J.(95) : On the representation of electric and magnetic fields produced by the currents and discontinuities in waveguides. J. Appl. Phys., Vol., No. 6, pp [] Oliner AA (957) : The Impedance Properties of Narrow - Radiating Slots in the Broad face of Rectangular Waveguide. Part I & II. IEEE Trans. on Antennas & Propagat., Vol. AP-5, No. pp Page 98