Active Passive Comp., license Sciencedownloads.hindawi.com/journals/apec/1994/035138.pdf · (far-zone field) andinserting electric andmagnetic currents in terms offields, we arrive

Active and Passive Elec. Comp., 1994, Vol. 17, pp. 157-161Reprints available directly from the publisherPhotocopying permitted by license only

1994 OPA (Overseas Publishers Association)Amsterdam B.V.

Published under license byGordon and Breach Science Publishers SA

Printed in Malaysia

VECTOR KIRCHHOFF ANALYSIS FOR THESTUDY OF RECTANGULAR MICROSTRIPANTENNAS IMMERSED IN A PLASMA

PREM BHUSHAN MITAL, FIETECentre for Applied Research in Electronics, Indian Institute of Technology, New Delhi-110 016,

INDIA

(Received April 23, 1994;" in final form May 11, 1994)

The radiation properties of a microstrip antenna immersed in an ionized medium have since beenstudied using potential function technique and linearized hydrodynamic theory. In the present paper,Vector Kirchhoff Analysis has been used for the study of rectangular microstrip antenna immersed ina plasma media. Expressions for radiated far fields have been obtained using this analysis. The analysisis mathematically precise and is used by reasonably approximating the actual aperture field distributions.The effect of ion sheath in the vicinity of a rectangular microstrip antenna is also discussed.

INTRODUCTION

It has been established that when an antenna is immersed in a plasma medium, anelectroacoustic wave is generated in addition to the usual electromagnetic wave.The fields are separated into em and plasma modes. The em mode is the usualelectromagnetic mode with an electric and magnetic field and gives a transverseem wave in the far zone of the antenna, whereas the plasma mode has an electricfield but no magnetic field. The electroacoustic wave becomes a longitudinal plasmawave in the far zone of the antenna.

The radiation properties of the antenna are modified in a plasma medium to agreat extent. ’4 The total radiation resistance of an antenna in a plasma consists ofthe sum of the radiation resistance due to electromagnetic (em) mode Re and theradiation resistance due to the plasma (P) mode Rp.

FORMULATION OF THE PROBLEM

A general solution of the field equations in terms of the sources distributed througha region v and from fields on the surfaces for a time-periodic field:

47rjto/xqJ + Jm Vtk-

+ 1 fs,+s:...+so [-j,.o x ) + ( x g) x v, + (.g)v,] d- (1)

157

158 P.B. MITAL

With Er, Hr denoting the components of scattered fields over the volume con-sidered and transforming the integrals, the expression can be reduced to:

E (V)1 fA [k2( H--)4’ + ( H--)’V(VO) + jwe( Er) VO] ds

47rjto

Finally, carrying through the reduction of the integrals for the Fraunhofer region(far-zone field) and inserting electric and magnetic currents in terms of fields, wearrive at

4rrR e-ikRRl Er- R1 (ff Hr) .ekm ds. (3)

where"

27rk to(/.e0)

Rl Unit vector from origin to the field point in the direction 0, $fi Outward unit vector normal to a surface.9 Vector from origin of the coordinate system to the element ds of the

aperture area.Er Electric field over the apertureHr Magnetic field over the apertureA Aperture Area.

Resultant far-zone fields are"

Electromagnetic mode:

-2jkEy47rr e-Jt’Ar.Fn(Afl0)[{k(eet) 1/2 cos0 cos

-2jkEy

+ jA sin:} F{k(eeff) 1/2 cos0 cos jA sin}] sinb. (4)

e-i’Ar.Fn(Afl0)[(k(eff) ’/2 cossc

+ jA cosO sin:} F{k(eff) 1/2 cos: jA cos0 sine}] cos4, (5)

Electroacoustics Mode:

2jEy(1 A2)oTrorA /3pe-iFn(/3p)[cos(/3p cos0 /3)1] (6)

VECTOR KIRCHHOFF ANALYSIS 159

Z::)0

o@

II

160 P.B. MITAL

where:

I xFn(x) -2hw sinc x to sin0 cosb sinc[xh sin0 sinb]O

ei sin0(1/2to cosb + h sinb)

sc kl[A cos0 (eff)/2]

ION SHEATH EFFECTS IN THE VICINITY OF RECTANGULARANTENNA

When a microstrip antenna is immersed in an ionized medium, electrons are dis-placed and move away from the patch conductor. This motion of electrons producesa polarization field due to election deficiency. An equilibrium condition is attainedforming a positive ion sheath adjacent to the patch conductor. The sheath shieldsthe medium from the effects of any charge on the antenna. Assuming an equivalentsharp boundary or sheath edge, the capacity of the antenna to this surface is Ce0A/d farads.

where A Area of patch conductor0 1/36r109 farads per meter

Thus, the charge Q on the antenna is Q e0A V/d or p Q/A 0 V/d.For a thin rectangular patch carrying a uniform charge ps C/m assuming negligiblemagnetic field, the z-directed electric field is given as

I"Ps tan_X |’o [.d(a2

ab ] -a<_x<_a

+ b2 + d2)1/2 -z b -< y -< b

Equating this field to the polarization field arising due to electron deficiency, valuesof sheath size for different values of V/N are obtained.

V"treo d(a + b + d2)1/2

Where V Antenna Potential in voltsN Number of electrons percubic meter.

From, this, the thickness d of the sheath is obtained for different values of V/N.

ACKNOWLEDGMENT

The author is indebted to Prof. B. Bhat and Prof. S.K. Koul, Centre for Applied Research in Electronicsfor providing research facilities.

VECTOR KIRCHHOFF ANALYSIS 161

REFERENCES

1. K.M. Chen, Interaction of a radiating source with a plasma. Proc. IEE. Oct. 1964 pp. 1668-1678.2. A.G. Derneryd, A theoretical investigation of the rectangular microstrip Antenna IEEE Trans.

vol. AP 26, July 78, pp. 532-535.3. R.K. Gupta, Plasma and its effect on Radiations from different types of Antennas I.E.T.E. Journal

vol. 8, No. 3, 1967, pp. 181-206.4. J.R. Wait, Radiation of Electromagnetic and electroacoustics waves in a plasma, part I. Applied

Sc. Res. 1965, pp. 413-432.

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Active Passive Comp., license Sciencedownloads.hindawi.com/journals/apec/1994/035138.pdf · (far-zone field) andinserting electric andmagnetic currents in terms offields, we arrive