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AIR/ ICE/ WATER P POLARIZATION

I V d = ern

-0.6 0.00 o m 0 10 015 0.m 0.a o m

TIME (MICROSEMNOS)

Fig. 6 . Reflected pulse response for d = 8 m, for E parallel to plane of incidence.

I I I 000 0.05 0 IO 0 15 0 2 0 0 25 C

TIME (MICROSECONDS)

Fig. 7. Reflected pulse response for d = 6 m, for E parallel to plane of incidence.

between snow and wet earth to result in a high reflection coeffi- cient there. This is true for parallel as well as normal polarization. The results are shown in Fig. 7 for a constant depth of d = 8 m. Further results are given in 181. However, as in Case I for parallel polarization, the reflection coefficient has a positive peak at 48”, which gives an average q of 1.21 for snow. Thus the Brewster angle effect enables us to estimate an average dielectric constant, which would have been difficult to get otherwise.

CONCLUSIONS The three examples considered in the previous section clearly

illustrate that incidence at oblique angles provides more informa- tion in remote probing than at normal incidence. For an incident pulse at some angles of incidence at parallel polarization the power from the second interface exceeds the primary reflection from the first interface. This enables one to probe deeper with the same source than at normal incidence and also an average dielectric constant could be obtained by noting the angle at which the reflection coefficient becomes positive. No such effects were observed at normal polarization. This is to be expected as the characteristic impedance at normal polarization, Z, = q sec 8, increases as B increases while the characteristic impedance Z,, for parallel polarization, decreases with 8.

The theoretical analysis also shows the need to take into account the frequency dependence of the complex dielectric constant in pulse propagation studies.

REFERENCES

[l] R. W. ,P, King and C. W . ,Harrison, “Th: transmission of electro- magnetlc waves and pulses Into the earth, J . Appl. Phys., vol. 39,

[2] J. A. Fuller and J. R. Wait, “Electromagnetic pulse transmission in p. 4444. 1968.

(Commun,), vol. AP;20, pp.,53?533, July 1972. homogeneous dispersive rock,” IEEE Trans. Antennas Propagar

[3] J. R. Walt, “Trans~ent excltatlon of the earth by a true source of current,” PFOC. IE€E, vol. 59, p. 1287-1288, Aug. 1971.

[4] K. Sivaprasad and K. C. Stotz, “Reflection of electromagnetic pulses from multilayered media,” IEEE Trans. Geosci. Electron., vol. GE-11.

[5] D. H. Lam, “Finite difference methods for transient signal propagation pp. 161-164, July 1973.

in stratified dispersive media,” Electroscience Laboratory, Ohio State Univ., Columbus, Tech. Rep. 3892-1, Grant NSG-3005, Jan. 1975.

161 L. Rabiner and C. Rader. Diaifal Sianul Processino. New York: IEEE, pp. 294-304.

I -

[7J A. Von Hippel, Dielectric Materials and Applications. New York:

[SI N. N. Susungi, “Electromagnetic pulse reflection from stratified Wiley, 1954.

dispersive media,” Master’s thesis, Dep. Elec. Eng., Univ. of N. H. , Durham, 1974.

A Note on Painted Reflecting Surfaces

T. S . CHU AKD R. A. SEMPLAK

Abstract-The microwave depolarization arising in the process of oblique reflection from a painted surface has been found insensitive to the dielectric constant of the paint and is not negligible for higher microwaye frequencies if the polarization requirement is very stringent; the calculated cross polarization of a 19-GHz example agrees with the measured result. The approximate reflection coefficients also suggest lenient tolerance for the uniformity of the paint layer on reflector antennas of large FID ratio.

The authors are w t h Bell Laboratorles, Crawford Hill Laboratory, Manuscript received.April 4, 1975; revised July 15. 1975.

Holmdel, N.J. 07733.

100 ~EEE TRAUSACXIONS ON ANTENNAS AND PROPAGATION, JANUARY 1976

A thin layer of paint is often applied to a microwave reflecting surface for protection from oxidation or for thermal stability. This communication will treat the depolarization of oblique reflection from the paint. In particular, we found it is often unnecessary to determine precisely the dielectric constant of the paint for estimating the depolarization. An implication on the tolerance required of the paint uniformity will also be discussed.

The reflecting surface under the paint will be assumed to have a surface impedance Z, such as that of copper. Following pro- cedures employed by Ram0 et al. [l ], the apparent wave impedance at the painted surface is given by

Z' = z, Z, + jZ, tan (kl& cos 0,) Z, + jZ, tan (kl&cos 0,)

where k is the free space phase constant, I the thickness of the paint, E the dielectric constant of the paint,

.the angle between the surface normal and the propagation direction inside the layer of paint, Bi the angle of incidence, and 2, is related to the free space impedance Zo by

2, = -= cos e,, for E in plane of incidence L O

JE ZO 4 8

Z, = sec e,, for E normal to plane of incidence.

Since Z, = 0.01 Id& ~ 4 5 " a, where f is the frequency in gigahertz, in most practical cases

ZJZ, << kl& cos 0, << 1 (2)

(1) then becomes Zll ' = jZokl cos2 0, (3a)

ZL' = jZokl. (3b)

Now the reflection coefficient at oblique incidence on a painted surface will be

jkl cos2 e, - COS Bi 'I' = jkl cos2 e, + COS Oi

jkl - sec Bi = jkl + sec Oi '

These two reflection coefficients have the same unity amplitude' but a differential phase shift

When the dielectric constant of the paint is fairly high and the direction of incidence is not close to grazing, COS 0, is aP- proximately unity. Then

A d 2 2kI sin Bi tan ei (6)

which indicates the insensitivity of the depolarization to the dielectric constant of the paint. Let us consider a numerical

MIRROR WITH LACQUER PAINT OFFSET

PARABOLOID 3

OFFSET PARABOLOID I

T D L * - NOTE : *=SLANT DIMENSION

ALONG HORN AXIS 1- DIMENSION-METER

OFFSET f PARABOLOID

SCALE k- 1.0 -4

2

Fig. 1. Top view of layout for near-field transmission experiment.

0 45O POLARIZATION

I I I I I 19.0 19.5

FREQ. GHr

4 5 O POLARIZATION

I I I I

19.0 19.5 20.0 FREQ. GHz

Fig. 2. (a) Transmission between reflectors 2 and 3 via flat mirror with lacquer paint. (b) Transmission between reflectors 2 and 3 via flat mirror with silver paint.

example at 19 GHz. Here Bi = 45", 1 = O . O 4 m m , and the polarization is oriented at 45" from the plane of incidence. Then Ad = 0.023 rad leads to a cross polarization of -39 dB. Thus the depolarization of the paint is not negligible for higher microwave frequencies if the polarization requirement is very stringent or if a number of reflections are involved. On the other hand, the depolarization is expected to be small when the direc- tion of incidence is close to the normal or when the incident polarization is almost parallel or perpendicular to the plane of incidence.

The paint-induced cross polarization has been confirmed in a recent 19 GHz experiment on near-field transmission behveen two offset paraboloidal reflectors of 0.76 m diameter with strongly tapered (- 22 dB) illuminations. The offset reflectors and the dual mode feed horns shown in Fig. 1 have been de- scribed elsewhere [2]. Polarization grids are installed at the feed apertures to purify the polarization. A flat copper-clad silvered mirror of 0.76 x 1.07 m with a lacquer paint of about 0.04 mm thickness is also shown in Fig. 1. The dielectric constant of the lacquer paint is of the order 10 but not precisely known. In the

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case of vertical and horizontal polarizations, the received cross polarization relative to the copolarization for the transmission between reflectors 2 and 3 is essentially the same (< - 40 dB) as that between reflectors 1 and 3 without the mirror. However, for the polarization oriented 45" from the vertical, the received cross polarization for the transmission between reflectors 2 and 3 via the mirror becomes significantly higher as shown in Fig. 2(a), whereas that between reflectors 1 and 3 remains the same as for vertical and horizontal polarizations. This higher measured cross polarization (- 36 dB) agrees with the kombination of the calculated paint cross polarization (-39 dB) and the back- ground cross polarization (- - 41 dB) without the mirror. After a layer of conductive silver paint is applied to the mirror, the received cross polarization between reflectors 2 and 3 is reduced to that of Fig. 2(b). The oscillations in Fig. 2 result from the imperfect impedance matching of the dual mode horns. Better measuring accuracy is needed for a more precise comparison between measured and calculated values. .

For reflector antennas of large F/D ratio, cos 0, and COS,^, are close to unity. Then the reflection coefficients of (4) will have approximately the same phase shift as in the absence of the paint. The above observation suggests that lenient tolerances on the evenness of the paint covering such reflector antennas can be tolerated provided that the condition in (2) is satisfied.

REFERENCES [ I ] S. Ramo et a/., Fields and Waces in Communication Electronics. New

[Z] M. J . G??s and R. A. Semplak, "Some far field studies of an offset York: Wiley, p. 365.

launcher, Bell S y t . Tech. J . , vol. 54, pp. 1319-1340, Sepr. 1975.

On the Radiation Pattern of a Multibearn Antenna HOWARD H. S. LUH

Abstruct-The optimum radiation of a lens antenna with an array feed of 34 elements is desired, which will exhibit maximum gain in a number (k) of specified directions and nulls in other 0 ' ) specified direc- tions. This optimum is not derived; however, a condition for the optimum is shown to be some superposition of just (k + j ) individual radiation patterns where each individual pattern is obtained by a separate ex- citation set of all :M feed elemens such that the gain is maximized in each of the (k + j ) directions. (The feed array excitation set for each of the (k + j ) maximum gain individual patterns is derived.) Thus the number of unknown feed excitation coefficients is reduced from M to (k t j ) .

Antennas with two-dimensional variable pattern control are attractive for satellite communications. One realization of such an antenna is the lens with multiple.feeds shown schematically in Fig. 1 . In some applications, it is desired to communicate with discrete earth stations in the presence of earth jammers. The jamming environment requires that the satellite antenna gain be maximized in desired directions and minimized in the directions of jammers. Dion and Ricardi [l ] suggest that antenna pattern control be executed by properly varying the excitation coeficients of the horns in the feed array. This is accomplished by means of a variable power divider network. For example, in

The author is with the Aeronutronic-Ford Corporation, Western Manuscript received May 11. 1975; revised August 15, 1975.

Development Laboratories, Palo Alto, CA 94303.

f - AND AMPLITUDE CONTROL PHASE l o " OR 180'1

the case of the Dion-Ricardi antenna, the proper excitations must be determined and applied to a 19 feed horn array. This communication will show that the number of unknown variables can be reduced when the total number of jammers and earth stations is less than the number of feed horns.

Let Si(@, a real function, be the electric field intensity of the ith beam produced by the ith feed horn, where 0 is the direc- tional vector. Then the electric field intensity of the shaped radiation pattern is

where cli, a real number, is the excitation of the ith horn and M is the number of horns. The above equation is realistic when the mutual coupling between feed horns is negligible. This is the case for sufficiently large horns. If one defines the column vectors G and A as

~ ( 0 ) = (gl(e),gz(0),. . .,grim (2) and

A = (a13a2,. . -9%) (3)

then (1) can be rewritten as

<A,G(Q)) E ( @ = , . (4) x' ( A , A )

Now let Oi, i = 1,. . ,k, be the directions of the desired signals and si, i = k + 1 , . a , k + j , be the directions of the jammers, where M > k + j . The desired A is such that

is maximum with the constraints

We shall prove that the solution (the desired A ) is in the space 9 spanned by (k + j ) vectors

G(B,),. * .,G(Qk+j) i.e.

A E Y [G(Ql), . ' .,G(Bk+,)].

In other words, there are only (k + j ) variables to be deter- mined instead of 1M variables.