Radiation is the fundamental physical property of electromagnetic fields from which everything else follows. The goal of the book is to explain why and where radiation occurs from simple perfect-electric conducting objects as exemplified by wire antennas and scatterers. Numerous examples to illustrate how radiation occurs and its relationship with the behavior of the current and charge on such objects are presented. The numerical results are primarily derived using two well-known and well-validated computer models, TWTD (Thin-Wire Time Domain, described in Appendix A) and NEC (Numerical Electromagnetics Code, described in Appendix B) with which the author has been long associated.

Several different methods for determining why and where radiation originates from a perfect electric conductor are examined. While electromagnetic (EM) radiation is caused by acceleration of electric charge, this fact is rarely mentioned in engineering texts. In spite of that, computing the radiation patterns of complex, perfect-electric conductors (PEC) has been long-established and validated using Maxwell's equations (ME). Although charge acceleration is not explicitly included for PEC objects in ME, they obviously contain this effect implicitly in far-field computations based on them. Typical physics texts do discuss charge acceleration as the basis of EM radiation, but in terms of free charge in space, rather than in connection with, for example, how a physical antenna operates.

The goal of this book is to demonstrate the relationship between charge acceleration and how PEC objects behave when excited by localized sources as antennas or by incident waves as scatterers. Various analytical and numerical techniques developed by the author address the question "Where and in what amount is the power (frequency domain) or energy (time domain) emitted by PEC objects for various representative geometries?" A method called FARS (Far field Analysis of Radiation Sources) is demonstrated to provide an answer to this question in both the frequency and time domains. It follows that also answered is where the charge acceleration that produces radiation occurs. FARS also applies to specified currents such as the sinusoidal current filament, long used as an approximation for a dipole antenna.

The techniques described and demonstrated can be incorporated into most computational electromagnetics models with little effort to provide those interested in investigating localized radiation behavior for various situations. Such techniques will be of value in a teaching setting since they will give students a learning tool and unique insight into a fundamental aspect of the electromagnetic discipline. A variety of examples throughout will demonstrate geometrical features that cause charge acceleration or radiation. As a specific example, various published observations that associate current decay along a straight wire with radiation are confirmed to be due to charge reflection, caused by a wave-impedance variation with distance.

The Lienard-Wichert potentials show that radiation is caused by charge acceleration. The question arises about where charge acceleration occurs on the most basic of antennas, a center-fed, perfectly conducting dipole for which there are two obvious causes. One is the feedpoint exciting voltage that sets into motion an outward-propagating charge and current wave at light speed c in the medium. A second is at the dipole ends where the outgoing wave is totally reflected producing a change in charge speed of 2c. A third, possibly less-obvious cause is the deceasing amplitude of the propagating wave with distance due to its partial reflection along the wire. That reflected charge also undergoes a speed change of 2c. This is the reason why the decay of current flowing along a straight wire antenna has been attributed as being due to radiation. Radiation caused by these and other kinds of charge acceleration due to resistive loads, right-angle bends, and radius steps are investigated.

These phenomena are examined primarily in the time-domain where they are more observably separable in time and space than in the frequency domain. The current and charge induced on an impulsively excited wire antenna and its broadside radiated E-field are computed using a time-domain, integral-equation model, thin-wire time domain (TWTD). The computed results are used to derive a numerical relationship between the amount of accelerated charge and its radiated field. This relationship is denoted as an acceleration factor (AF) and is derived for various charge-accelerating features of a generic wire object. Their values are normalized to those of the exciting sources to standardize their respective values.

Footnote: This chapter is largely based on "The Proportionality between Charge Acceleration and Radiation from a Generic Wire Object," Progress In Electromagnetics Research, Vol. 162, 2018, 15-29, by E. K. Miller, with some additions and deletions including correction of acceleration factors for resistance-loaded and bent wires that were too low by a factor of 2.

The Lienard-Wiechert potentials show explicitly that charge acceleration, i.e. a change in charge velocity, causes radiation of an electromagnetic field. The goal of this chapter is to explore the rate of energy loss due to radiation from current and charge flowing on a circular loop as a function of the loop's curvature and wire radius. The results presented are obtained using a thin-wire, time-domain (TWTD) computer model for Gaussian-pulse excitation. Some results for a straight wire are also presented for comparison. Analytical estimates for the curvature and wire-radius effects are developed from best-fit expressions to the computed results using model-based parameter estimation (MBPE).

Footnote: This chapter is based on "The dependence of time-domain radiation loss on the circumference and wire radius of a circular loop antenna," Progress In Electromagnetics Research M, vol. 92, 2020, 1-9, by E. K. Miller.

The procedure called FARS (Far-Field Analysis of Radiation Sources ha been briefly introduced in earlier chapters of this book. It is a technique for determining the quantitative distribution of power or energy radiated from a perfect electric conductor. FARS is based on a source-integral expression for the fields of an object of interest for which both time-domain (TDFARS) and frequency-domain (FDFARS) versions have been developed. These two versions provide complementary perspectives of general electromagnetic phenomena. While a frequency-domain result explicitly demonstrates the effects of standing waves, for example, a time-domain result has the advantage of separating various contributions to the far field due to their different time delays. The motivation for both FDFARS and TDFARS is to provide information about radiation from a perfect electric conductor. A brief description of TDFARS is given here and demonstrated for some simple wire geometries.

Time-domain far field analysis of radiation sources (TDFARS) and frequency-domain far field analysis of radiation sources (FDFARS) have been shown in Chapters 7 and 8 to determine the quantitative distribution of radiated power and radiated energy on a variety of wire objects. The FDFARS results reveal their frequency dependence through a series of lobes related to the wavelength. For antennas, there are nominally 2 lobes per wavelength with larger maxima at the feedpoint and ends. For scattering the lobe structure can vary from 1 to 2 lobes per wavelength. Similar lobe structure is found for other wire objects. The TDFARS results, on the other hand, are not lobed but vary smoothly over an object with maxima at the open ends of a wire and at the feedpoint as well as opposite the feedpoint of a circular or square loop. The absence of lobes is because the time-domain current and charge are not standing waves.

The comparisons included here are normalized to a 1-W total power or 1-J total energy on a per-segment basis for a nominal spatial sampling density of 20 per m. Discussion is limited here to wires of several wavelengths so that physical features that may not be as pronounced for shorter objects are observable.

Incremental versions of far-field analysis of radiation sources (FARS) and the induced electromotive force (IEMF) method are implemented in this chapter in connection with moment-method models for two reasons. One is to provide a more geometrically detailed way of determining the power-density distribution of radiation from over the surface of an object. A second is to make this possible without the need to integrate the power flow over the entire far-field sphere. The generalizations of these two methods are denoted here as incremental FARS (IFARS) and incremental IEMF (IIEMF). These incremental procedures are developed and their application demonstrated using various NEC models. Both involve determining the pairwise interaction between current samples on a PEC object. Mutual validation of both techniques is confirmed by the agreement shown between their numerical results in the following.

The electric field of a sinusoidal current filament (SCF) is one of the relatively few problems in electromagnetics whose solution can be developed in closed form. This is why the SCF was routinely used to approximate the radiation characteristics of the thin-wire, center-fed, dipole antenna. This proved to be useful because the current on a perfect electric conductor (PEC) wire of near-zero radius (NZR) closely approximates a sinusoidal current as does its radiation patterns.

However, while the SCF and NZR dipole are very similar in some respects, they are quite different in others as will be show here. These similarities and differences are explored below and how these two sources actually produce a far radiation field is explained.

A brief description of thin-wire time-domain (TWTD) is presented together with a sampling of some of the results a time-domain model can generate. The code is based on a time-domain version of the electric-field integral equation specialized to thin wires. It originated in the late 1960s inspired by time-domain results reported at the 1968 IEEE AP-S conference. Its initial use was for simple wire antennas and scatterers and subsequently for ElectroMagnetic Pulse (EMP) applications. For the latter problems, a circuit capability was added to evaluate the damage that an EMP might do to electronic systems. This later feature was exploited in later research to design passive electronic tags for radio-frequency identification (RFID).

No Abstract available.