Arthur D. Yaghjian

An overview of near-field antenna measurements

After a brief history of near-field antenna measurements with and without probe correction, the theory of near-field antenna measurements is outlined beginning with ideal probes scanning on arbitrary surfaces and ending with arbitrary probes scanning on planar, cylindrical, and spherical surfaces. Probe correction is introduced for all three measurement geometries as a slight modification to the ideal probe expressions. Sampling theorems are applied to determine the required data-point spacing, and efficient computational methods along with their computer run times are discussed. The major sources of experimental error defining the accuracy of typical planar near-field measurement facilities are reviewed, and present limitations of planar, cylindrical, and spherical near-field scanning are identified.

Approximate formulas for the far field and gain of open-ended rectangular waveguide

Approximate formulas are derived for the far field and gain of standard, open-ended, rectangular waveguide probes operating within their recommended usable bandwidth. (Such probes are commonly used in making near-field antenna measurements.) The derivation assumes first-order azimuthal dependence for the fields, and an E -plan pattern given by the traditional Stratton-Chu integration of the transverse electric ( TE_{10} ) mode. The H -plane pattern is estimated by two different methods. The first method uses a purely E -field integration across the end of the waveguide. The second, more accurate method approximates the fringe currents at the shorter edges of the guide by isotropically radiating line sources. The amplitude of the line sources is determined by equating the total power radiated into free space to the net input power to the waveguide. Comparisons with measurements indicate that for X -band and larger waveguide probes, both methods predict on-axis gain to about 0.2 dB accuracy. The second method predicts far-field power patterns to about 2 dB accuracy in the region 90deg off boresight and with rapidly increasing accuracy toward boresight.

Multiwavelength three-dimensional scattering with dual-surface integral equations

We apply dual-surface integral equations, which have the same form as, and yet eliminate, the spurious solutions from conventional electric- and magnetic-field integral equations, to determine the scattering from multi-wavelength, three-dimensional perfect conductors. We determine accuracy by increasing the patch density and by comparisons with a high-frequency solution, a finite-difference time-domain solution, and measurements. Surface currents and scattered far fields computed with the dual-surface magnetic-field equation are displayed for perfectly conducting cubes 3 and 15 wavelengths on a side. Condition numbers and the number of iterations for convergence of the conjugate gradient method are shown to be linearly related to the electrical size of the scatterer. The logarithmic relationship between the number of iterations and the inverse of the residual error is also confirmed. For large scatterers the number of computer operations increases as the fifth power of electrical size; however, on massively parallel computers the run time increases only as the third power of the electrical size.

Sampling criteria for resonant antennas and scatterers

From a knowledge of the characteristic constant of an antenna or scatterer, simple expressions are found for the modal bandlimits and near‐field sample spacing in planar, cylindrical and spherical coordinates required to reconstruct the fields everywhere outside the antenna or scatterer (except possibly within a small fraction of a wavelength from discontinuities in the surface of the antenna or scatterer). For resonant antennas and scatterers the modal bandwidths can be much larger and the required sample spacings much smaller than for nonresonant antennas and scatterers. The modal bandwidths also determine upper bounds on the gain and effective area of antennas, and on the total and bistatic scattering cross sections of scatterers. The maximum possible radius of the significant reactive fields of an antenna or scatterer is shown to equal the radius of the maximum possible effective area of an antenna, or the radius of the maximum possible total scattering cross section of a scatterer. For resonant anten...

Shadow boundary incremental length diffraction coefficients for perfectly conducting smooth, convex surfaces

General expressions are obtained for incremental length diffraction coefficients (ILDCs) that can be integrated along the shadow boundaries of perfectly conducting surfaces to correct for the fields radiated by the “shadow boundary current” missing from the physical optics (PO) current approximation. As an initial step in obtaining these shadow boundary ILDCs, uniform high-frequency approximations are derived for the scattered and PO far fields of perfectly conducting circular cylinders illuminated by normally and obliquely incident plane waves. Subtracting the approximate PO far fields from the approximate scattered far fields and separating the resulting fields into contributions from the top and bottom of the cylinder leads to a uniform high-frequency approximation for the fields radiated by the shadow boundary current at a single shadow boundary of the cylinder. The shadow boundary ILDCs are then determined by substituting these high-frequency approximations for the shadow boundary fields into the general formulas derived in previous papers for obtaining three-dimensional ILDCs from the two-dimensional far fields of cylindrical scatterers. Comparisons with the exact eigenfunction solution for plane wave scattering by a sphere show that the integration of the ILDC fields around the shadow boundary of the sphere significantly enhances the accuracy of the PO far fields, especially for large bistatic scattering angles. Finally, the shadow boundary ILDCs are modified to increase their accuracy when they are applied to surfaces with more rapidly varying radii of curvature.

Time‐domain far fields

The behavior of classical time‐domain electromagnetic far fields is investigated with emphasis placed on those characteristics that are unique to the time domain. Necessary conditions are derived for the time‐domain far fields to decay slower than 1/r and for the energy in a far‐field pulse to decay slower than 1/r2. Time‐domain near fields are expressed in terms of integrals over the time‐domain far‐field pattern. Analyticity with respect to angular variation of the time‐domain far‐field pattern is determined, and restrictions are derived on the time dependence of the electromagnetic far fields.

Electromagnetic and Acoustic Field Equations

This chapter contains sections titled: Time-Domain Electromagnetic Field Equations Time-Domain Acoustic Field Equations Frequency-Domain Electromagnetic Field Equations Frequency-Domain Acoustic Field Equations Equations for Lossy Media ]]>

Appendix D: Validation of the PlaneWave Spectrum Representation

This chapter contains sections titled: D.1 Evaluation of the Spectrum for ( k x , k y ) ?????? (0,0) D.2 Evaluation of the Spectrum for ( k x , k y ) = (0,0)

Appendix B: Proofs of Theorems 2I and 2II

This chapter contains sections titled: B.1 Proof of Theorem 2-I B.2 Proof of Theorem 2-II

Theorems on Time-Domain Far Fields

The far-field characteristics of classical electromagnetic fields satisfying Maxwell’s equations have been investigated quite thoroughly for sources radiating at a single frequency, that is, for frequency-domain or time-harmonic fields [1]. For example, frequency-domain far fields radiated by integrable sources in a volume of finite extent decay as 1/r or faster as the distance r to the far field approaches infinity. In addition, these far fields are entire analytic functions of their angular variables θ and o. Using a plane-wave decomposition, frequency-domain near fields can be expressed as an integral of the far-field pattern and its analytic continuation to complex angles of observation [2],[3].