New Method for Calculating Pulse Radiation from an ... - IEEE Xplore

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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 39, NO. 1, FEBRUARY 1997

New Method for Calculating Pulse Radiation from an AntennaWith a Reflector Oleg V. Mikheev, Stanislav A. Podosenov, Member, IEEE, Konstantin Y. Sakharov, Alexander A. Sokolov, Member, IEEE, Yanis G. Svekis, Member, IEEE, and Vladimir A. Turkin

Abstract—A simple method for calculating the pulse radiation of an antenna with a reflector is proposed both in the near and far zones. The method is based on a substitution of the radiation field from a parabolic mirror by the radiation field from an exciting Vantenna reflected from the mirror. An experimental investigation of the system radiation field and a comparison with the theoretical resuts have been performed.

I. INTRODUCTION

T

HE PROBLEM of a directed radiation of short electromagnetic pulses is of importance for solving the applied problems of electromagnetic compatibility. The theory of pulse radiation of a reflex antenna with small angular divergence has first been proposed in papers by Baum and Farr [1]–[4]. In [2] a formula has been obtained to calculate the electric field intensity on the reflector axis at the distance from it at the instant .

(1) , where is an input impedance of the Here V-antenna irradiating the parabolic reflector, is the velocity of light, is a wave impedance of vacuum. The antenna is excited by an arbitrary time-dependent voltage pulse from the V-antenna. The excitation point of the V-antenna is located at the reflector focus with a focal length . The distance between the antenna ends is equal to the mirror diameter . The formula contains a term with a derivative of the generator voltage at the instant of the signal arrival at the point of observation with respect to the time , related to the radiation from the reflector, and the term with a difference of two voltages corresponding to the radiation from the exciting antenna. The field intensity decreases in inverse proportion to the distance from the emitter. The analysis of (1) shows that the term with a derivative in the near zone does not reflect the problem essence. As we shall show below, while applying a step signal to the input, the amplitude of the signal being emitted by the mirror is independent of the distance and constant in magnitude at any finite distance from the mirror. There changes only a pulse Manuscript received May 7, 1996; revised November 15, 1996. The authors are with the All-Russian Research Institute for Optophysical Measurements, Moscow 119361, Russia. Publisher Item Identifier S 0018-9375(97)01782-1.

duration which decreases in inverse proportion to the square distance from the mirror. Starting from the aforesaid, we introduce a definition of the near zone for pulsed fields. The distance from the source for which the duration of the emitted pulse from a step signal is equal to the front duration from a quasistep one is called a boundary distance of the near zone . is evident. At the distances The physical meaning of from the source less than the quasistep pulse does not vary in magnitude. Beyond the boundary of the near zone the amplitude will be diminished due to adding the fronts from the pulses of opposite polarity. As will be shown below, this critical distance is determined by the formula (1a) where is a quasistep pulse front duration. From the formula it follows that, as the front duration vanishes, the boundary between the zones tends to infinity. For example, for . In paper [5] the pulse radiation from a parabolic antenna with a reflector has been investigated experimentally. However, as distinct from (1), the calculated relation presented in the paper for determining the electric field intensity at the observation point is independent of the output voltage value but depends on the value of the current in the reflector. The absence of a formula for the antenna input impedance does not allow absolute values of fields to be calculated. Therefore paper [5] is appropriate for determining only time-dependences of emitted pulses and their relative amplitudes. II. METHOD FOR CALCULATING THE RADIATION FIELD OF AN ANTENNA WITH A REFLECTOR The present paper gives a new method of calculating the radiation field of an antenna with a reflector. Consider the essence of the method. The mirror image method is used in the antenna theory to calculate the radiation field of sources located over a perfectly conducted plane. This method lies in the total field from a source over the conducted plane being a sum of the source radiation field in a free space and the radiation field from its mirror image. Apply the mirror image method not to a flat surface but to a parabolic mirror, having reflected a V-antenna from it. Since an excitation point of the V-antenna is located at the parabolic

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MIKHEEV et al.: NEW METHOD FOR CALCULATING PULSE RADIATION

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Fig. 1. Modes of a V-antenna with a reflector.

by a direct calculation of the electromagnetic field tensor comprising both the electric and magnetic fields [10], [11]. Fig. 2 depicts symmetric sections of the antenna with a break formed by intersection of two rectilinear sections. The beginning of the rectilinear section is at a distance , measured along the wire, the end is at a distance and the break is at a distance from the antenna excitation point. and magnetic fields The contributions to the electric from the selected parts of the antenna are determined by the expressions obtained in [8]

Fig. 2. Geometry of symmetric parts with a facture.

reflector focus, the excitation point image in the mirror will be virtual and lies at infinity beyond the mirror. The ends of the exciting antenna and its mirror image will coincide with each other and lie on the mirror generatrix. The distance between the ends is equal to the mirror diameter. Thus, instead of the V-antenna-reflector system we obtained two V-antennae with different expansion angles. Thereby, the antenna expansion angle will vanish for the antenna replacing the reflector. A superposition of the fields from these antenna gives the sought-for field (Fig. 1). In [6]–[8] a theory of nonstationary radiation from traveling wave wire antenna has been elaborated. Apply the results of the theory to the calculation of our antenna. From [9] it follows that it will have a very narrow directional pattern. On the basis of [8] it is easy to calculate the field at an arbitrary point of space for any instant, any wire shape, and any time-dependence of the exciting voltage pulse. The basic formulae of the theory proved most easily obtainable

(2)

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Fig. 3. Coordinates of the points of measuring the electric field.

(3) From formula (3) we shall find the electric field of an antenna with a reflector having replaced the parabolic mirror by the V-antenna “reflected” from it (Fig. 1). The fact that the signal in the “reflected” antenna propagates with the velocity more than that of light is unimportant, i.e., the signal velocity in it is a phase one which may take any value. Outside the antenna the signal propagation velocity coincides with that of light in vacuo. The total electric field is represented as , where corresponds to the a sum of the fields exciting antenna field and —to the reflector field. The field we present in the form from the exciting antenna

the reflector. Then in the phase expressions for the currents we allow for the signal, reflected from the antenna reflector, falling on the focal plane of the mirror, with a delay by the value from the initial excitation instant. From (4) we obtain a value of the field from the exciting antenna on the mirror axis. From the problem symmetry it follows that one field component will be nonzero. For it we find

(5) where is a distance from the antenna ends to the point and the of observation, is an angle between the vector mirror axis, is a slope of the exciting antenna (Fig. 1). on the mirror axis at an We represent the total field arbitrary distance from the focus in the form

(6) (4) is an excitation current, is an exciting antenna where arm length (Fig. 1). Suppose that the current is not reflected from the antenna ends. The field from the reflector can be obtained similarly taking account of the limiting transition , where is an angle between the generatrices of the antenna “reflected” from

For a parabolic mirror the formula is valid (7) , where In the far zone is a distance from the reflector expansion plane to the point of observation. From the analysis of (6) it follows that the field from the exciting antenna falls in inverse proportion


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to the distance, and the field reflected from the mirror is proportional to the difference of two voltages phase shifted. While exciting the antenna by a step voltage, the amplitude of the field reflected from the mirror remains unchanged along the mirror axis, with the pulse duration decreasing as the distance increases. From (6) it follows that the pulse duration, depending on the distance from the mirror expansion plane to the point of observation, can be representented in the form (8) The same result can be obtained from paper [3] as well. In the far zone, according to (1a), the pulse transforms into a rectangular one with the duration (9) From (9) and the definition of the near zone we find (1a). For the signal of an arbitrary form in the far zone we find

Using the result of [8], we find the expression for the field in meridional plane (14) where (15) Apply (11)–(15) for our case, namely, when the field observation point lies at an infinitely large distance from the imaginary source (the distance from the mirror to the to the observation point is finite and may take any value). Thus, we should like to investigate the field at a finite distance from the mirror axis. The solution to the problem to be sought reduces to finding the limits of (13)–(15) at . , and the angle is It’s evident that conventionally introduced instead of , with being valid. Introduce designations (16)

(10) which coincides (to within the choice of the origin of a time scale) with the result [2] obtained by another method and applicable, from our viewpoint, only away from the emitter, i.e., at . (Note that in the expressions for phases of formulae (10) and (1) there are different values displaced in phase by . This means that we measured the time from the instant of switching on the generator, and the authors of paper [2] did it from the instant of the signal arrival at the point of observation). In the near zone a differentiation of the signal does not occur, and instead of (10) one should use (6) applicable both near and away from the mirror as well. In [8] an expression has been found for the radiation pattern of a V-antenna in the equatorial and meridional planes when the field observation point lies at a finite distance from the antenna excitation point and the antenna arms are infinite. In particular, in the equatorial plane, an expression has been found for an infinite V-antenna, with the expansion angle , to be in the form (11) where is an equatorial angle being measured from the antenna plane, is a distance from the excitation point to the observation one. As applied to our case, (11) is representable in the form (12) where (13)

Equalities (16) are evident from the geometry, with and being displacements from the mirror axis along the corresponding coordinate axes setting the points at which we should like to find the field. Having calculated the limits, we find (17) (18) Equation (17) gives the distribution for the field on the equatorial plane shifted, relative to the mirror axis away from the antenna plane, by the value . Assuming , we obtain the contribution to the field on the mirror axis, which corresponds to the first term in the second square brackets of (6). The noncoincidence of signs is natural, as the components and are opposite in sign. Since we are interested in a change of the leading edge, we do not take account of the signal from the antenna ends arriving at the observation point with a delay and being determined by the second term in the section square brackets of (6). If one assumes , then we obtain the value of the field at the point , which is twice less than that on the axis. Equation (18) gives the distribution of the field in the meridional plane coinciding with the antenna plane. For we obtain the field on the axis, which is in agreement with (6). However, for , i.e., for (18) diverges. The reason for divergence is that (18) makes a contribution from an infinite V-antenna to the field, and the equality corresponds to the field on one of the antenna arms. Since in theory the antenna is asummed to be infinitely thin, then the field on it tends to infinity. Really, the observation point under consideration lies on not the antenna arm, but outside it, namely, on the line being a continuation of the arm. From geometrical consideration it follows that for finding the field in this case it is necessary to take also into account the field from the antenna end, which arrives in this case simultaneously with

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Fig. 4. Comparison of the experimental results with the calculated ones at points 1 through 10,

calculated,

measured.

the field from the exciation point but due to (6) is of opposite sign. One may show that the field from the antenna end has the form (19) which on adding to (18) gives (20) Thus, the divergence vanishes with regard to the field of the nearest end. The method being proposed allows one to calculate the field inside the central spot taking into account the arrival of the signal from the ends of the exciting and “reflected” antennae. Omitting simple but rather cumbersome transformations, we present the general expression for fnding the -component of the toal electric field for the points having arbitrary coordinates (Fig. 3)

(21)

we obtain the formula for the In particular, for field on the antenna axis reducing to (6).


Fig. 4. (Continued.)

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Comparison of the experimental results with the calculated ones at points 1 through 10,

III. COMPARISON OF THEORY WITH EXPERIMENT An objective of the experimental investigation was to verify (21). The research set comprised emitting and measuring systems.The emitting one was shaped as a parabolic reflector with the diameter 0.9 m and ratio shaped as a parabolic reflector with the diameter 0.9 m and ratio . The V-antenna with served as an irradiation for it. The exciting generator produced at the input of the Vantenna step pulse with the amplitude 9.9 V, risetime 80 ps and duration 50 ns. The measuring unit consisted of a wideband digital oscillograph with the risetime 30 ps and a striplinelike transducer, with the theory of the latter being presented in [12], [13]. The transducer had a transient response risetime 75 ps, its duration 4.7 ns, conversion ratio 0.67 (mV/(V/m)), and overall dimensions 500 60 8 mm. To determine a dependence of the -field intensity distribution inside the central spot, the measurements were performed at the points located on the geometrical axis of the reflector at different distances from the expansion surface and at the points shifted from the reflector axis. Fig. 3 presents ten points at which the field measurements have been performed. Points 1, 4, 7 lay on the antenna axis at the distances of and from the expansion surface. Points 2, 5, 8 and 3, 6, 9 lay at the corresponding distances from the expansion surface but were shifted along the axes or by the value . Point 10 had coordinates . Fig. 4 presents the results measured and calculated by (21) at selected points, where are experimental values, are calculated ones. As seen from the figures, the experimental results are in good agreement with the theoretical ones. A noticeable discrepancy between theory and experiment in Fig. 4 was due to the pulse decay along the transducer of field away from the exciting antenna. As increases, the effect diminishes.

calculated,

measured.

The measured duration of pulses coincides with the duration calculated by (8) to within the measurement error. The presence of bursts on the ends of pulses on the experimental curves and their absence on the corresponding calculated ones is related to matching the V-antenna with the reflector. Theoretically, such an agreement has been assumed. The performed measurements were related mainly to the near zone where Baum and Farr’s formula (1) is not valid. In the far zone (1) is in agreement with the experimental data. IV. CONCLUSION The proposed calculation method permits one to determine, to sufficient accuracy, the radiation field of an anternna with a reflector at any distance from the reflector. The use of the method being proposed allows one to find simply the solution to the problems whose calculation by other known methods requires considerable efforts. As distinct to [2] and [5], the field measurements were performed not over a conducting surface but in a free space, which permits the elaborated equipment to be used for measuring the field of real emitters. REFERENCES [1] E. G. Farr and C. E. Baum, “Impulse radiating antennas,” Int. Symp. Electromag. Environ. Consequenes, Book of Abstracts. Bordeaux, France, May 30–June 4, 1994. [2] E. G. Farr, C. E. Baum, and C. J. Buchenauer, “Impulse radiating antennas,” Ultra Wideband/Short-Pulse Electromagnetics 2. New York: Plenum, 1995, Pt. II, pp. 159–170. [3] E. G. Farr and C. E. Baum, “The radiation pattern of reflector impulse radiating antennas: Early-time response,” Sensor and Simulation Note 358, June 1993. [4] E. G. Farr and G. D. Sower, “Design principles of half impulse radiating antennas,” Sensor and Simulation Note 390, Dec. 1995.

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[5] Hao-Ming Shen, “Experimental study of electromagnetic missiles,” Microwave Particle Beam Sources Propagat., vol. 873, pp. 338–346, 1988. [6] S. A. Podosenov and A. A. Sokolov, “Calculations for nonstationary wire emitters in the electromagnetic compatibility problems,” Metrologiya, no. 1, pp. 17–25, 1994 (in Russian). , “Nonstationary radiation of a V-antenna and a linear source,” [7] Metrologiya, no. 1, pp. 26–35, 1994 (in Russian). [8] S. A. Podosenov, Y. G. Svekis, and A. A. Sokolov, “Transient radiation of traveling waves by wire antennas,” IEEE Trans. Electromag. Compat., vol. 37, pp. 367–383, Aug. 1995. [9] C. E. Baum and E. G. Farr, “Impulse radiating antennas,”Ultra Wideband/Short-Pulse Electromagnetics, H. L. Bertoni et al., Eds. New York: Plenum, 1993, pp. 139–147. [10] L. D. Landau and E. M. Lifshitz, Field Theory. Moscow, Russia: Nauka, 1973 (in Russian). [11] J. A. Stratton, Electromagnetic Theory. New York: McGraw-Hill, 1941. [12] S. A. Podosenov and A. A. Sokolov, “Linear two-wire transmission line coupling to an external electromagnetic field, Part I: Theory,” IEEE Trans. Electromag. Compat., vol. 37, pp. 559–566. Nov. 1995. [13] S. A. Podosenov, K. Y. Sakharov, Y. G. Svekis, and A. A. Sokolov, “Linear two-wire transmission line coupling to an external electromagnetic field, part II: Specific cases, experiment,” IEEE Trans. Electromag. Compat., vol. 37, pp. 566–574, Nov. 1995.

Oleg V. Mikheev graduated in 1992 from the Moscow Engineering Physical Institute and specialized in electrophysical plants. Since 1992, he has been working at the laboratory for electromagnetic compatibility in the All-Russian Research Institute of Optophysical Measurements, State Standards of Russia (VNIIOFI). Presently, he is working in the field of short EM-pulse radiation and measurement.

Stanislav A. Podosenov, for a photograph and biography, see p. 10 of this TRANSACTIONS.

Konstantin Y. Sakharov graduated in 1981 from the Moscow Engineering Physical Institute and specialized in electrophysical plants. He received the Ph.D. degree in measurement and generation of the pulse EM-field in 1987. Since 1980, he has been working at the laboratory for electromagnetic compatibility in VNIIOFI. Presently, he is working in the field of EM-pulses radiation and measurement.

Alexander A. Sokolov, for a photograph and biography, see p. 10 of this TRANSACTIONS.

Yanis G. Svekis graduated in 1985 from the Moscow Engineering Physical Institute and specialized in electrophysical plants. Since 1985, he has been working at laboratory for electromagnetic compatibility in VNIIOFI. Presently, he is working on problems of short EMpulse radiation and measurement and elaborating EM-field sensors of radio-frequency range.

Vladimir A. Turkin graduated in 1989 from the Moscow Engineering Physical Institute and specialized in electrophysical plants. Since 1988, he has been working at VNIIOFI. Presently, he is working in the field of short EMpulse radiation and measurement.