Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE CROSS POLARIZATION OF MILLIMETER WAVE BACK SCATTERED FROM SPHERICAL
DUST PARTICLES IN STORMS Mrs. Swastika
Ph.D. Research Scholar, Dept. of Faculty of Science (Electronics), Magadh University, Bodh Gaya
Abstract:- In the present work deals with the cross polarization of millimeter wave back scattered for spherical dust particles in storms. It is found that the cross-polarization has significantly affected by the orientation of the dust particles present in the atmosphere. The Cross-polarization value improves as frequency increases with different values of visibility.
It is also observed that, the cross-polarization reduces as visibility increases. According to reality as visibility increases density of particle decreases in atmosphere. The change in loss with frequency as visibility varies indicates that cross-polarization results loss which improves with increasing value of visibility.
1. INTRODUCTION
Due to use of satellite communication, the propagation of millimeter wave through atmosphere has become important. Propagation of millimeter wave is affected by the precipitations available in the atmosphere scattering, cross-polarization, absorption, refraction and reflection becomes a reason for the changes amplitude and phase of a signal to a wide range.
Here, attempt has been confined to investigate for cross-polarization while the wave propagation takes place in the atmosphere during dust and sand storms. So, It developed equations to evaluate the extent of cross-polarization. The equations developed which is used to calculate the cross-polarization degree by considering different atmospheric parameters. Details of the entire investigation are given here.
2. THEORETICAL CONSIDERATION
Cross-polarization indicates to the polarization change that an electromagnetic wave follows as a field of reflection, propagation, diffraction or scattering etc. Polarization of different wave can be explained as of two orthogonal components which is polarized linearly in time phase for linear polarization; and in case of elliptical polarization it is out of time phase.
The cross-polarization, D, developed for dipole which is randomly oriented (Figure 1) is given as
Figure 1: Randomly oriented dipole
The reflected and incident field can be related as for the transmission of arbitrary polarization
(1)
Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE reflection coefficients are axx, ayy, axy and ayx.
E
1x,E
y1 are incident electric field vector along x and y axis andE
xr ,E
yr are reflected electric field vector along axes x and y. so in case of circular reference system the matrix equation may be expressed as mode of(2)
Where subscripts 2 and 1 indicate right hand and left hand circular polarization respectively. E1, E2 are two orthogonally polarized electric field will be in the plane perpendicular in the direction of propagation. Because of reciprocity of antenna here output for two circular polarizations is given by
(3) and
Combining equations (1), (2) and (3) one gets
(4) and therefore, here overall echo power is given by
(5) And the depolarized power is given by
(6)
The cross polarization, D, it is the ratio of depolarized power to the overall echo power [30]
and hence
(7)
Since the radar cross section is proportional to square of the field strength one can write
Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE 2
21
k C |
21|
(8)
If the change in phase is same for both the polarization after reflection then axx = ayy
equation (8) modifies to And
(9) Combining equations (6), (7), and (9) results into
(10) Here dipole is isolated considering an angle β with x-axis, so
(11)(a) (11)(b)
(11)(c) Here cross section of radar σxy is mentioned by
(12)
Where, Here cross-polarization
(13) Where σxy = σCos2β, Sn2β = orientation of dipole,
(14) and σ = σ11 + σ22 + σ12 + σ21. Here, σ11 +σ22 indicates the radar cross-section of a target for mono static scatter and σ12, σ21 denote the radar cross-section of the target for bi static scatter and k = 4r2.
Further, the radar cross-section, σ (d), for a dipole is given by
(15)
Where a is dust particle’s radius and Єc is of dust particle’s complex dielectric constant.
To find the number of diploes in unit volume of storm, one has ascertained the particle’s number in it. The total volume of particles in unit volume of storm is suggested by Ghobrial [1] as
Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE Volume of particles per unit volume of storm
(16)
Where V is the visibility, in km, and γ = constant = 1.07. If spherical dust particles are assumed then the number of particles per unit volume of storm can be given by
(17)
Since two particles together form a dipole, the number of dipoles per unit volume of storm is
(18) The cross-polarization, therefore because of N/2 dipoles is to be find out as
(19)
Now putting the value of σ (d), one gets the value of cross-polarization as, loss due to cross- polarization
(20) 3. LOSS DUE TO CROSS-POLARIZATION
The loss Ld due to cross-polarization can be given as
(21)
Where
P
r1 is the power obtained in free space and Pr the power obtained in the medium after cross-polarization of wave (depolarized power). If E1 is free space incident field and E2the received field after cross-polarization, then for cross-polarization angle, ξ is given by (22)
and loss due to cross-polarization can be obtained as
Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE The value of ξ can be obtained from the expression
ξ = arc tan (A
xtan
1)
1 (24)Where Ax is cross-polarization factor for medium along x-axis
9.43 109 1
r 1 x
V and 1 the angle between incident field and horizontal vector.
From equation (24),
(25) Combining equations (23) and (25), one gets cross-polarization loss Ld, as
d 9
2
r 1 1
r
L 1
9.43 10 1
cos arc tan tan
V
1
x
(26)
Where ϕ is the phase shift, in rad. /m; 1 the grazing angle, in rad., and λ the wavelength, in m.
4. DISCUSSION OF RESULTS
To study the nature of variation of cross-polarization with various parameters, several calculations were made using equation (20). The typical parameters used in the calculations were a = 0.0001m, r = 100 m, γ = 1.07, Єr = 5.2, = 40-100GHz. The data obtained from these calculations are summarized in Figure 2 - Figure 4. Further, to obtain the nature of variation of cross-polarization loss with frequency and visibility, a number of calculations were made using equations (26). The data thus obtained are summarized in Figure (5) and Figure (6).
From theoretical computations it is obtained that:-
1. Cross-polarization improves with increasing value of incident beam orientation and attain its maximum value at 45°. Later on, cross-polarization reduces with increasing incident beam orientation. It has similarities similar to the one observed experimentally by Cox, Arnold and Hoffman [4] for ice and rain at 19 GHz and 28 GHz.
2. The level of cross-polarization is observed that increasing with decreasing visibility.
This is results the fact that decreasing visibility enhances the dust particles density in the path resulting into high value of cross-polarization.
3. With increasing value of frequency and decreasing visibility, the value of cross- polarization increases. This is related with previously done experimental observations of researchers. When the frequency is raised the value of cross- polarization for ice and rain is raised.
4. When the visibility increases and frequency decreases then cross-polarization loss decreases.
Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE
Figure 2: Variation of cross-polarization with orientation for different visibilities
Figure 3: Variation of cross-polarization with frequency for different visibilities.
Vol. 02, Issue 06,June2017 Available Online: www.ajeee.co.in/index.php/AJEEE
Figure 4: Variation of cross-polarization with visibility for different frequencies.
Figure 5: Variation of loss (dB) with frequency for different visibilities.
REFERENCES
1. S. I. Ghobrial and S. M. Sharief, Microwave Attenuation and cross polarization in Dust Storm, IEEE Transaction on Antennas and Propagation, Vol. AP 35, No. 4, p.421, 1987.
2. John G. Griffith, Radio wave Propagation and Antenna, PIH, U.K., 1987.
3. N. J. McEwen and S. O. Bashir, Microwave Propagation in Sand and Dust Storms, The Theoretical Basis of Particle Alignment, IC, PA Norwich, p.40, 1933.
4. D. C. Cox, H. W. Arnold and H. H. Hoffman, Depolarization of 19 and 28 GHz Earth Space Signals by Ice Particles, Radio Science, Vol. 13, p.511, 1978.
5. D. C. Cox, et al., Depolarization of Radio waves by Atmospheric Hydrometers in Earth Space Paths, Radio Science, Vol. 16, p.781, 1981.
