Rumsey / Booker / Declaris Frequency Independent Antennas

1. Auflage 2014
ISBN: 978-1-4832-8222-0
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 160 Seiten

Frequency Independent Antennas provides a reasonably complete coverage of frequency independent antennas from its inception until the middle of 1965. Most of the contents have not previously been published, except in scattered journal articles, and some are original. The first six chapters are written at a fairly easy level-about the level of a beginning graduate student or the more advanced undergraduate. The last two chapters, which deal with solutions of Maxwell's equations, are at a somewhat higher level. The book opens with a discussion of some fundamental ideas about antennas. It shows how typical measurements can be understood in terms of classical electromagnetic theory: in other words, how to make sense of measured data, how to set up apparatus to get meaningful data, and how to test their significance. Separate chapters follow on the features of frequency independent, plane-sheet, spiral, and log-periodic antennas. Subsequent chapters discuss how the periodic structure theory provides a way of understanding the peculiarities of frequency independent antennas; and solutions of Maxwell's equations for idealized spiral and idealized sinusoidal structures.

Autoren/Hrsg.

Rumsey, Victor H.

Booker, Henry G.

Declaris, Nicholas

Leseproben

1

ELEMENTARY PRINCIPLES

Publisher Summary

This chapter discusses the way by which typical measurements can be understood in terms of classical electromagnetic theory; the way to make sense of measured data, the way to set up apparatus to get meaningful data, and the way to test their significance. The dipole has been chosen in the chapter for the sake of illustration because it is probably the most familiar type of antenna. It consists of two collinear wires each about a quarter of a wavelength long, the gap between them forming the terminal region. There are two ways of understanding its working. In the conventional way, it is pictured as a resonator. Current is thought of as traveling along the wire with the velocity of light, being reflected from the end with phase reversal, and so coming back to the terminals exactly in resonance with the outgoing wave. The distribution of current is consequently sinusoidal, being zero at the ends and maximum at the center. Alternatively, the current can be thought of as continuously leaking out of the wire into the surrounding medium so that none is left at the end. This explains, in quite a different way, why the current changes with distance along the wire.

To open the subject we shall discuss a few fundamental ideas about antennas. Doubtless this is not the most enticing introduction, nor is it necessary for the reader who wants to go straight to the heart of the matter. Chapter 2 would be the place for him to start. But a careful discussion of fundamentals will finally be needed, and Chapter 1 is the logical place for it. Our aim here is, then, to show how typical measurements can be understood in terms of classical electromagnetic theory: in other words, how to make sense of measured data, how to set up apparatus to get meaningful data, and how to test their significance.

1.1 Dipole Antennas

The dipole has been chosen for the sake of illustration because it is probably the most familiar type of antenna. It consists of two colinear wires each about a quarter of a wavelength long, the gap between them forming the terminal region. There are two ways of understanding how it works.

(1) In the conventional way it is pictured as a resonator. Current is thought of as traveling along the wire with the velocity of light, being reflected from the end with phase reversal, and so coming back to the terminals exactly in resonance with the outgoing wave. The distribution of current is consequently sinusoidal, being zero at the ends and maximum at the center. Thus far the picture is clear, but now it is difficult to see how this causes a signal to be picked up on some receiving antenna far away, although there are straightforward formulas for calculating the result.

(2) Alternatively, we can think of the current as continuously leaking out of the wire into the surrounding medium so that none is left at the end. This explains in quite a different way why the current changes with distance along the wire. It also shows directly how current passes into the surrounding medium and so flows out to the distant receiving antenna.

Method (1) is approximate, because there is an infinite number of modes for propagation of current along a wire. What spectrum of this infinite set will actually be set up depends on the physical details of the terminal region. But if the wire is thin compared to the wavelength, all except the mode that travels with the velocity of light are rapidly attenuated. So, for sufficiently thin wires, the approximation is good except in the immediate vicinity of the terminals.

Method (2) is exact but is of little value for quantitative purposes: its value is conceptual. It is justified by the Maxwell equation

CH·dl=?S(s+j??)E·n dS

using the time convention, being the edge of surface and n being the unit vector normal to . The symbols E, H, s, e, and ? have their usual significance. The expression (or + ?e)E represents the total current J, the combination of conduction and displacement currents. When is a closed surface, the perimeter of shrinks to zero. So

sJ·n dS=0

This means the total current J is continuous everywhere: in particular it is continuous in crossing a metal surface. Hence the reduction in conduction current with distance along the wire must equal the flow of displacement current out of its surface [hence method (2)].

If we accept the fact that the velocity of light is independent of frequency, method (1), although approximate, correctly expresses the scaling principle. It shows that the current distribution remains fixed if the size of the antenna and the wavelength are changed by the same fraction. Because this is the key to frequency-independent-antenna design, it is important that we establish it rigorously. The proof depends on Maxwell’s equations and a theorem derived from them which says that the field radiated from some antenna is uniquely determined by tangential E on any surface that encloses the generator. We take the surface so that it follows the surface of the antenna and runs across the gap between the terminals. If the gap is small enough and if the antenna is perfectly conducting, tangential E will be zero on except at the gap, where it will represent the applied voltage.

Turning now to Maxwell’s equations, we express them in the form

×E=-j?µH?×H=j??E

We are therefore considering a perfectly lossless medium with µ and e independent of frequency. Let

=?(µ?)1/2=2p/?Z0=(µ/?)1/2

We transform the equations so that the unit of length is the wavelength ?, the new equations being indicated by a prime. Thus = ?', = ?, and = ?'. The result is

'×E=-Z0H?'×H=Z0-1E

Now 0 is independent of ?. Therefore the field is independent of ? if tangential E on , and itself, are fixed in the primed system; that is, ?. Note that the antenna must be perfectly conducting and the surrounding medium must be perfectly lossless. In practice, a copper antenna surrounded by air easily fits these requirements. Note also that the surrounding medium does not have to be uniform: µ and e can be functions of position but, to fit the scaling principle, when expressed as functions of they must be independent of ?. Thus any lossless system composed of a mixture of dielectrics and metals fits the geometric scaling principle; that is, the entire electrical performance is frequency-independent if length dimensions are scaled in inverse proportion to frequency.

1.2 Characteristic Impedance

A major step toward an understanding of antennas was made in 1941 by Schelkunoff in his analysis of biconical structures.4 Its effectiveness is largely due to the fact that the principal mode for two metal cones with a common apex fits the simple formulas for propagation along a uniform transmission line. This holds for cones of arbitrary cross section5, but for the sake of simplicity let us take up the special case of circular cones with a common axis (as well as common apex). Imagine that the apices are separated by an infinitesimal gap so that they form the input terminals—see Fig. 1.1. Then Maxwell’s equations are satisfied by

FIG. 1.1 Coaxial biconical structure.

=E0e-jkr?ˆrsin?,H=E0e-jkr?ˆrsin? (1.1)

(1.1)

0=Z0H0 (1.2)

(1.2)

?? being a standard set of spherical coordinates and and the corresponding unit vectors. The symbols and 0 are the intrinsic propagation factor and impedance for the medium between the cones, as used in Section 1.1. It should be noted that this is not a general solution. It is only one of an infinite number of possible solutions which make E normal to the metal cones. To proceed, we define and by

=??1?2E?r d?=E0e-jkrlntan(?2/2)tan(?1/2) (1.3)

(1.3)

=H?2prsin?=H0e-jkr2p (1.4)

(1.4)

00=VI=Z02plntan(?2/2)tan(?1/2)[Z0=(µ/?)1/2] (1.5)

(1.5)

Evidently when ? 0, and represent the input voltage and current. Thus for this solution (or mode) the input impedance is independent of frequency and is a pure resistance. If the cones extended to infinity, only this mode would be excited by a generator at the input, and so the input...