Q5Antenna And Wave Propagation

(a) Comparison of Half-Wave Dipole, Folded Dipole, and V-Dipole

Half-wave dipole: the most fundamental and widely used practical wire antenna, consisting of a straight conductor of total length approximately lambda/2 (slightly less, around 0.47-0.48 lambda, after accounting for the end-effect/thickness correction), fed at its center. Its design is the simplest of the three antennas being compared, requiring no special impedance-transformation structure and no unconventional geometric shaping. Its radiation resistance at resonance is Rr=73 ohms (73.1 ohms more precisely), a moderate value reasonably close to common 50-75 ohm coaxial transmission line impedances, allowing reasonably direct feeding without an elaborate matching network. Its radiation pattern is omnidirectional in the azimuthal plane (uniform radiation in all directions perpendicular to the dipole's own axis) and follows the characteristic figure-eight-shaped pattern in the elevation (E-)plane containing the dipole axis, with maximum radiation broadside to the dipole and nulls exactly along the dipole's own axis. Its bandwidth is relatively narrow (typically only a few percent of the center frequency for a simple thin-wire dipole), since its input impedance varies fairly rapidly with frequency away from resonance.

Folded dipole: constructed from two parallel half-wave conductors of the same length, connected together at both end tips, with the feed applied at the center of only one of the two parallel conductors (or equivalently modeled with feed current split between both conductors) — this configuration produces exactly the same overall radiation pattern shape as an ordinary half-wave dipole (since the folded dipole's overall current distribution and physical extent closely resemble the simple dipole case), but with a feed-point impedance that is stepped up by a factor of four compared to the ordinary half-wave dipole, giving Rr approximately 4*73=292 ohms. This impedance step-up makes the folded dipole particularly convenient for direct connection to 300-ohm twin-lead transmission line (historically standard for television and FM broadcast reception antennas), avoiding the need for a separate impedance-matching transformer that an ordinary 73-ohm half-wave dipole would otherwise require for use with such feeders. The folded dipole also exhibits a noticeably wider input-impedance bandwidth than a simple half-wave dipole of the same overall length, since its two-conductor parallel structure behaves partly as a low-impedance transmission-line stub in parallel with the radiating structure, broadening the overall frequency response — this wider bandwidth, combined with its convenient impedance level, is why folded dipoles are very commonly used as the driven element in Yagi-Uda antenna arrays.

V-dipole (V-antenna): consists of two straight wire arms, each of some chosen length, joined at a common feed-point apex but opened out at an angle (rather than in a single straight line as in the ordinary dipole), so that the two arms are tilted symmetrically about the antenna's own bisecting axis. By adjusting the tilt (included) angle between the two arms and the individual arm lengths, the individual radiation contributions from each tilted arm can be made to reinforce constructively along the antenna's bisecting axis direction, increasing the directivity along that particular direction compared to what either arm alone (or a simple straight dipole of the same total length) would achieve — V-antennas are also frequently operated as travelling-wave antennas (each arm terminated in a matched resistive load to suppress standing-wave reflection, particularly for the long-wire V-antenna variant used at HF), useful for directive long-distance point-to-point HF communication links, where the V geometry allows a specific, adjustable directive gain to be achieved from a comparatively simple and inexpensive two-wire structure.

(b) Characteristic Features and Far-Field Expressions of Circular and Square Loop Antennas

Small loop antennas (circular and square) are electrically small radiating structures (with overall loop circumference/perimeter much less than a wavelength) that behave, in terms of their far-field radiation characteristics, as magnetic dipole radiators, in direct contrast to a short linear dipole (which behaves as an electric dipole radiator) — this magnetic-dipole-like behavior means the loop's far-field pattern shape is identical in form to that of a short electric dipole (a sin(theta)-type pattern, with theta measured from the loop's own axis, i.e., the direction perpendicular to the plane of the loop), but with the roles of the E-field and H-field interchanged relative to the electric-dipole case (the loop's far electric field E_phi is analogous in pattern shape to a short dipole's far magnetic field, and vice versa).

Far-field expression: for a small loop antenna (circular or square) carrying a uniform loop current I, the far-zone electric field has only a phi-component, varying with observation angle theta (measured from the loop axis) and falling off with distance r as:

with the exact proportionality constant depending on the loop's area, the operating frequency, and the loop current magnitude — this sin(theta)/r far-field dependence gives the small loop its characteristic donut-shaped (magnetic-dipole) radiation pattern, with maximum radiation broadside to the loop's plane (theta=90 degrees from the loop axis) and a null exactly along the loop's own axis (theta=0/180 degrees).

Radiation resistance: for a small circular loop of circumference C (C much less than lambda), the radiation resistance is:

showing the characteristic fourth-power dependence of a small loop's radiation resistance on its electrical circumference (C/lambda) — this fourth-power scaling means a small loop's radiation resistance falls off extremely rapidly as its physical size is reduced relative to the wavelength (much more rapidly than a short dipole's radiation resistance, which scales only as the square of its electrical length), making small loop antennas typically have very low radiation resistance and hence generally lower radiation efficiency than a comparably-sized short dipole, unless specifically compensated for with multiple turns or a ferrite core to boost the effective radiation resistance. A small square loop antenna of equivalent perimeter/circumference follows essentially the same fourth-power circumference-to-wavelength scaling law for its own radiation resistance, since the detailed derivation depends primarily on the total enclosed loop area (equivalently, the loop's magnetic dipole moment) rather than the loop's precise geometric shape (circular versus square), so a circular and a square loop of equal enclosed area produce very similar radiation resistance and far-field characteristics.

Applications: because of their characteristic magnetic-dipole radiation pattern (with a sharp null exactly along the loop axis), small loop antennas are extensively used for radio direction-finding (RDF) applications, since rotating a small loop antenna until the received signal strength reaches its sharp null provides a precise bearing indication toward (or away from) a transmitting station; small loop antennas are also widely used as compact receiving antennas (such as the ferrite-core loop antennas built into portable AM broadcast radio receivers), where their small physical size, combined with a ferrite core to boost effective radiation resistance and received signal pickup, makes them a practical, low-profile receiving antenna solution despite their inherently low radiation efficiency in transmit-mode use.