Sheldon S. Sandler

The electromagnetic field of a vertical electric dipole in the presence of a three‐layered region

The electromagnetic field generated by a vertical electric dipole in the air over the surface of a two-layered region is determined for continuous-wave excitation. The region of interest consists of a conductor or dielectric with high permittivity, coated with an electrically thin layer of a dielectric under a half-space of air. Simple explicit formulas are derived for the field at all points in all three regions including the surface wave. Typical applications are to microstrip circuits and antennas, communication over the earth when this is coated with a layer of asphalt or cement, and communication over the sea or a lake when this is under a layer of ice.

The electromagnetic field of a vertical electric dipole over the Earth or sea

The analysis of King (1990) of the electromagnetic field of a vertical electric dipole over an imperfectly conducting half-space is applied to obtain the far field when the dipole is at a specified height d. The contributions by the space wave with its 1/r dependence and the lateral surface wave with its 1/r/sup 2/ dependence are separated and studied in detail when the dipole is over a wide range of media such as sea water, wet and dry Earth, lake water and dry sand. Graphs of the far-field patterns are shown. >

Electric fields and currents induced in organs of the human body when exposed to ELF and VLF electromagnetic fields

Formulas for the transverse components of the electric and magnetic fields of the traveling-wave currents of three different types of three-wire, three-phase high-voltage power lines and of a typical VLF transmitter are given. From them, exposure situations for the human body are chosen which permit the analytical determination of the total current induced in that body. With this, the fraction of the total axial current, the axial current density, and the axial electric field in each organ of the body are obtained at any desired cross section. The dimensions and conductivity of these organs must be known. The electric field so obtained is the average macroscopic field in which the cells in each organ are immersed when the whole body is exposed to a known incident field. It corresponds in vivo to the electric field used in vitro to expose cells in tissues.

Electromagnetic Resonances of a Straight Wire

With an interest in finding wires and distinguishing them from other electrically conducting objects, we have looked for an electromagnetic “fingerprint” in terms of resonances of a straight wire of length 2h and radius a. The resonances of the wire are formulated using the theory of the linear antenna, leading to an integral equation for the current on the wire. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current on the wire has non-zero solutions. By applying a variational technique we obtain approximate numerical solutions for the resonant frequencies and their widths. A table of the first five resonances is given for several ratios of wire half-length h to wire radius a. In a subsequent paper we propose to extend the method described here to deal with wires on an earth-air interface, for example as used to command the detonation of improvised explosive devices.

Response to remarks by J.R. Wait on the comments and reply to "The electromagnetic field of a vertical electric dipole over the Earth or sea"

In his remarks on the comments by Yokoyama (see ibid., vol.43, no.5, p.541-42, 1995) and the reply by King and Sandler (see ibid., vol.43, no.5, p.542-44, 1995) regarding our paper (see ibid., vol.42, no.3, p.382-9, 1994) J. R. Wait (see ibid., vol.44, no.2, p.271-72, 1996) makes a number of statements that require correction. These are considered in turn, but since they all center about the definition of the Sommerfeld numerical distance, this is introduced first. In a paper by Norton (1937), which is later quoted and applied by Wait, a formula is given for the generalized numerical distance for the height z and radial distance /spl rho/ due to a vertical dipole at the height d in the air (region 2, real wave number k/sub z/) over a conducting or dielectric region 1 (complex wave number k/sub 1/). It is important to emphasize that the purpose of this response is not to belittle the important pioneer work of Norton, Wait, and others. Interest a half century ago was in communication over the surface of the Earth and sea with (z+d)/sup 2//spl Lt//spl rho//sup 2/. In this range, their formulas are accurate. However, recent progress which eliminates the restriction (z+d)/sup 2//spl Lt//spl rho//sup 2/ or k/sub 2//spl rho//spl Gt/1 should not be ignored by blindly using restricted formulas where they do not apply.

Antennas with transmission-line interconnections

Arrays of cylindrical dipoles and monopoles are usually driven by means of interconnecting transmission lines, whereas analyses of such arrays are generally made in terms of currents or voltages with assigned relative amplitudes and phases at the individual input terminals. Moreover, it is commonly assumed that the distributions of current along all elements are the same and without phase variation. The properties of broadside and endfire arrays are treated with full consideration of interconnecting transmission lines and the effect of mutual coupling on the distributions of current. Driving-point admittances and field patterns of arrays of half-wave and full-wave elements are given. A novel broadside-endfire array is described.

The detection of dielectric spheres submerged in water

The basic theory is developed for the use of lateral electromagnetic waves to detect dielectric spheres submerged in fresh or salt water or human flesh. The source and receiver are, respectively, center-driven and center-loaded eccentrically insulated dipoles. A numerical example is computed to determine the magnitude of the scattered field that must be detected. >

The propagation of electromagnetic waves generated by a vertical electric dipole in the presence of two- and three-layered regions

The authors generalize the analysis of the vertical dipole in the presence of two layers to three layers. The electromagnetic field of a vertical dipole in the presence of a three-layered region has application to radio communication over asphalt- or cement-coated ground, as well as over Arctic ice or ice on a lake. The three-layer analysis provides the field generated by vertical elements in microstrip circuits and antennas. In combination with the field already available for the horizontal electric dipole, it provides the field of magnetic dipoles which are useful in the 10-100 Hz frequency range for detecting submerged submarines in the ocean and under Arctic ice.<<ETX>>

Electromagnetic Resonances of a Straight Wire on an Earth-Air Interface

Using a variational method, we recently determined an electromagnetic “signature” for characterizing a straight wire in free space. The signature consists of the first five resonant frequencies and their widths, more compactly expressed as the first five complex-valued resonant frequencies. Here we apply the variational method to the much more complicated case of determining the same signature for a straight wire or wire pair on a flat interface between a homogeneous earth and air. To calculate the resonances we obtain an integral equation for the current on a wire on the interface between two dielectric media. Complex-valued resonant frequencies are defined as those for which the homogeneous integral equation for the current in an equivalent thin strip on the interface has non-zero solutions. The variational method extracts good approximations to these complex-valued resonant frequencies, without having to solve the integral equation. A table of resonances is given for the case of a relative dielectric constant of the earth equal to 4 and for three values of the ratio of wire radius to wire half-length.

Effective area of satellite-borne antennas for radio astronomy

Abstract The problem of interpreting measurements on satellite-borne linear antennas is examined. Definitions of antenna parameters, such as effective area, are made in terms of physically observable quantities. Possible sources of error in applying conventional antenna formulae are pointed out. The short linear antenna is given as a specific example.