Loop antenna
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A ferrite loopstick antenna, a small loop used for AM reception in a portable radio, consisting of a wire wound around a ferrite core; the most common type of loop antenna today.

A loop antenna is a radio antenna consisting of a loop or coil of wire, tubing, or other electrical conductor, that for transmitting is usually fed by a balanced power source or for receiving feeds a balanced load. Loop antennas can be divided into three categories:

Large loop antennas: Also called self-resonant loop antennas or full-wave loops; they have a perimeter close to one or more whole wavelengths at the operating frequency, which makes them self-resonant[a] at that frequency. Large loop antennas have a two-lobe dipole like radiation pattern at their first, full-wave resonance, peaking in both directions perpendicular to the plane of the loop.[b]

Halo antennas: Halos are often described as shortened dipoles that have been bent into a circular loop, with the ends not quite touching. Some writers prefer to exclude them from loop antennas, since they can be well-understood as bent dipoles, others make halos an intermediate category between large and small loops, or the extreme upper size limit for small transmitting loops: In shape and performance halo antennas are very similar to small loops, only distinguished by being self resonant and having much higher radiation resistance. (See discussion below)

Small loop antennas: Also called magnetic loops or tuned loops; they have a perimeter smaller than half the operating wavelength (typically no more than ⁠ 1 /3⁠ to ⁠ 1 /4⁠ wave). They are used mainly as receiving antennas because of low efficiency, but are sometimes used for transmission; loops with a circumference smaller than about ⁠1/ 10 ⁠ wavelength become so inefficient they are rarely used for transmission.[c] A common example of small loop is the ferrite (loopstick) antenna used in most AM broadcast radios.[d] The radiation pattern of small loop antennas is maximum at directions within the plane of the loop, so perpendicular to the maxima of large loops.

Large, self-resonant loop antennas

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For the description of large loops in this section, the radio's operating frequency is assumed to be tuned to the loop antenna's first resonance. At that frequency, one whole free-space wavelength is slightly smaller than the perimeter of the loop, which is the smallest that a "large" loop can be.[2]

Self-resonant loop antennas for so-called "short" wave frequencies are relatively large, with a perimeter just greater than the intended wavelength of operation, hence for circular loops diameters between roughly 175 feet (53 m) at the largest, around 1.8 MHz. At higher frequencies their sizes become smaller, falling to a diameter of about 11 feet (3.4 m) at 30 MHz.

Large loop antennas can be thought of as folded dipoles whose parallel wires have been split apart and opened out into some oval or polygonal shape. The loop's shape can be a circle, triangle, square, rectangle, or in fact any closed polygon, but for resonance, the loop perimeter must be slightly larger than a wavelength.[2]

Shape

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A quad antenna is a self-resonant loop in a square shape; this one also includes a parasitic element.

Loop antennas may be in the shape of a circle, a square, or any other closed geometric shape that allows the total perimeter to be slightly more than one wavelength. The most popular shape in amateur radio is the quad antenna or "quad", a self-resonant loop in a square shape so that it can be constructed of wire strung across a supporting ×-shaped frame. There may be one or more additional loops stacked parallel to the first as "parasitic" director or reflector element(s), creating an antenna array which is unidirectional with gain that increases with each additional parasitic element. This design can also be turned 45 degrees to a diamond shape supported on a +-shaped frame. Triangular loops (△-shaped) have also been used for vertical loops, since they can be supported from a single mast.[2] A rectangle twice as high as its width obtains slightly increased gain and also matches 50 Ω directly if used as a single element.[2]: § 9.6.2 

Unlike a dipole antenna, the polarization of a resonant loop antenna is not obvious from the orientation of the loop itself, but depends on the placement of its feedpoint.[e] If a vertically oriented loop is fed at the bottom, then its radiation will be horizontally polarized; feeding it from the side will make it vertically polarized.

Radiation pattern

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The radiation pattern of a first-resonance loop antenna peaks at right angles to the plane of the loop. As the frequency progresses to the second and third resonances, the perpendicular radiation fades and strong lobes near the plane of the loop arise.[3](p 235)

At the lower shortwave frequencies, a full loop is physically quite large, and its only practical installation is "lying flat", with the plane of the loop horizontal to the ground and the antenna wire supported at the same relatively low height by masts along its perimeter.[2] This results in horizontally polarized radiation, which peaks toward the vertical near the lowest harmonic; that pattern is good for regional NVIS communication, but unfortunately is not generally useful for making continental-scale contacts.

Above about 10 MHz, the loop is approximately 10 meters in diameter, and it becomes more practical for the loop to be mounted "standing up" – that is, with the plane of the loop vertical – in order to direct its main beam towards the horizon. If the frequency is high enough, then the loop might be small enough to attach to an antenna rotator, in order to rotate that direction as desired. Compared to a dipole or folded dipole, a vertical large loop wastes less power radiating toward the sky or ground, resulting in about 1.5 dB higher gain in the two favored horizontal directions.

Additional gain (and a uni-directional radiation pattern) is usually obtained with an array of such elements either as a driven endfire array or in a Yagi configuration – with only one of the loops being driven by the feedline and all the remaining loops being "parasitic" reflectors and directors. The latter is widely used in amateur radio in the "quad" configuration (see photo).

Low-frequency one-wavelength loops "lying down" are sometimes used for local NVIS communication. This is sometimes called a lazy quad. Its radiation pattern consists of a single lobe straight up (radiation toward the ground which is not absorbed is reflected back upward). The radiation pattern and especially the input impedance is affected by its proximity to the ground.

If fed with higher frequencies, then the antenna input impedance will generally include a reactive part and a different resistive component, requiring use of an antenna tuner. As the frequency increases above the first harmonic, the radiation pattern breaks up into multiple lobes which peak at lower angles relative to the horizon, which is an improvement for long-distance communication for frequencies well above the loop's second harmonic.

Halo antennas

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Main article: Halo antenna

A halo antenna is often described as a half-wave dipole antenna that has been bent into a circle. Although it could be categorized as a bent dipole, it has the omnidirectional radiation pattern very nearly the same as a small loop. The halo is more efficient than a small loop, since it is a larger antenna at ⁠1/ 2 ⁠ wave in circumference with its disproportionately larger radiation resistance.[f] Because of its much greater radiation resistance, a halo presents a good impedance match to 50-Ohm coaxial cable, and its construction is less demanding than a small loop, since the maker is not compelled to take such extreme care to avoid losses from mediocre conductors and contact resistance.[4]

At ⁠1/ 2 ⁠ wave, the halo antenna is near or on the extreme high limit of the size range for "small" loops, but unlike most oversized small loops, it can be analyzed with simple techniques by treating it as a bent dipole.

Practical use

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Car-roof-mounted 6-meter halo antenna for mobile amateur radio (WA8FJW). Notice the triple-loop.

On the VHF bands and above, the physical diameter of a halo is small enough to be effectively used as a mobile antenna.

The horizontal radiation pattern of a horizontal halo is nearly omnidirectional – to within 3 dB or less – and that can be evened out by making the loop slightly smaller and adding more capacitance between the element tips. Not only will that even out the gain, it will reduce upward radiation, which for VHF is typically wasted by radiating into space.

Halos pick up less nearby electrical spark interference than monopoles and dipoles, such as ignition noise from vehicles.[5]

Electrical analysis

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Although it has a superficially different appearance, the halo antenna can conveniently be analyzed as a dipole (which also has a half-wave radiating part with a high voltage and zero current at its ends) that has been bent into a circle. Simply using dipole results greatly simplifies the calculations and for most properties are the same as a halo. Halo performance can also be modeled with techniques used for similar, moderate-sized "small" transmitting loops, but for brevity, that complicated analysis is often skipped in introductory articles on loop antennas (unfortunately, this typical omission leaves otherwise well-read persons unaware of the properties of "large" small loops).

The halo's gap

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Some writers mistakenly consider the gap in the halo antenna's loop to distinguish it from a small loop antenna, since there is no DC connection between the two ends. But that distinction is lost at RF; the close-bent high-voltage ends are capacitively coupled, and the RF current crosses the gap as displacement current. The gap in the halo is electrically equivalent to the tuning capacitor on a small loop, although the incidental capacitance involved is not nearly as large.[g]

Small loops

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Although a full 2.7 m (9 feet) in diameter, this receiving antenna is a "small" loop compared to the LF and MF wavelengths it is used with.

Small loops are "small" in comparison to their operating wavelength. Contrary to the pattern of large loop antennas, the reception and radiation strength of small loops peaks inside the plane of the loop, rather than broadside (perpendicular) to it.[3]: 235 

As with all antennas that are physically much smaller than the operating wavelength, small loop antennas have small radiation resistance which is dwarfed by ohmic losses, resulting in a poor antenna efficiency. They are thus mainly used as receiving antennas at lower frequencies (wavelengths of tens to hundreds of meters). Like a short dipole antenna, the radiation resistance is small. The radiation resistance is proportional to the square of the area:

where A is the area enclosed by the loop, λ is the wavelength, and N is the number of turns of the conductor around the loop.

Because of the higher exponent than linear antennas (loop area squared ≈ perimeter to the 4th power, vs. dipole & monopole length squared = 2nd power), the fall in Rrad with reduced size is more extreme.[6]: 5‑11  The ability to increase the radiation resistance Rrad by using multiple turns is analogous to making a dipole out of two or more parallel lines for each dipole arm ("folded dipole").

Small loops have advantages as receiving antennas at frequencies below 10 MHz.[7] Although a small loop's losses can be high, the same loss applies to both the signal and the noise, so the receiving signal-to-noise ratio of a small loop may not suffer at these lower frequencies, where received noise is dominated by atmospheric noise and static rather than receiver-internal noise. The ability to more manageably rotate a smaller antenna may help to maximize the signal and reject interference. Several construction techniques are used to ensure that small receiving loops' null directions are "sharp", including adding broken shielding of the loop arms and keeping the perimeter around ⁠1/ 10 ⁠ wavelength (or ⁠ 1 /4⁠ wave at most). Small transmitting loops' perimeters are instead made as large as feasibly possible, up to ⁠ 1 /3⁠ wave (or even ⁠ 1 /2⁠ if possible), in order to make the best of their generally poor efficiency, although doing so sacrifices sharp nulls.

The small loop antenna is also known as a magnetic loop[citation needed] since the response of an electrically small receiving loop is proportional to the rate of change of magnetic flux through the loop.[8] At higher frequencies (or shorter wavelengths), when the antenna is no longer electrically small, the current distribution through the loop may no longer be uniform and the relationship between its response and the incident fields becomes more complicated.[8] In the case of transmission, the fields produced by an electrically small loop are the same as an "infinitesimal magnetic dipole" whose axis is perpendicular to the plane of the loop.[3]: 235 

Because of their meager radiation resistance, the properties of small loops tend to more often be intensively optimized than are full-size antennas, and the properties optimized for transmitting are not quite the same as for receiving. With full-size antennas, the reciprocity between transmitting and receiving usually makes the distinctions unimportant, but since a few RF properties important for receiving differ from those for transmitting – particularly below about 10~20 MHz – small loops intended for receiving have slight differences from small transmitting loops. They are discussed separately in following two subsections, although many of the comments apply to both.

Small receiving loops

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Small loop antenna used for receiving, consisting of about 10 turns around a 12-by-10-centimeter (4.5-by-4-inch) rectangle.

If the perimeter of a loop antenna is much smaller than the intended operating wavelengths – say ⁠ 1 / 8 ⁠ to ⁠1/ 100 ⁠ of a wavelength – then the antenna is called a small receiving loop, since loop antennas that small are only practical for receiving. Several performance factors, including received power, scale in proportion to the loop's area. For a given loop area, the length of the conductor (and thus its net loss resistance) is minimized if the perimeter is circular, making a circle the optimal shape for small loops. Small receiving loops are typically used below 14 MHz, where human-made and natural atmospheric noise dominate. Thus the signal-to-noise ratio of the received signal will not be adversely affected by low efficiency as long as the loop is not excessively small.

A typical diameter of receiving loops with "air centers" is between 30 and 100 cm (1 and 3.5 feet). To increase the magnetic field in the loop and thus its efficiency, while greatly reducing size, the coil of wire is often wound around a ferrite rod magnetic core; this is called a ferrite loop antenna. Such ferrite loop antennas are used in almost all AM broadcast receivers with the notable exception of car radios,[citation needed] since the antenna for the AM band needs to be outside the obstructing metal car chassis.

Small loop antennas are also popular for radio direction finding, in part due to their exceedingly sharp, clear "null" along the loop axis: When the loop axis is aimed directly at the transmitter, the target signal abruptly vanishes.[9]

Amount of atmospheric noise for LF, MF, and HF spectrum according CCIR 322.[10] The diagram shows how both man-made noise ("interference", "QRM") and natural atmospheric noise ("static", "QRN") both fall precipitously above 20 MHz, but as frequencies fall below 10 MHz their combined power climbs as the frequency drops.

The radiation resistance Rrad of a small loop is generally much smaller than the loss resistance Rℓoss due to the conductors composing the loop, leading to a poor antenna efficiency.[h] Consequently, most of the power delivered to a small loop antenna will be converted to heat by the loss resistance, rather than doing useful work pushing out radio waves or gathering them in.

Wasted power is undesirable for a transmitting antenna, however for a receiving antenna, the inefficiency is not important at frequencies below about 15 MHz. At these lower frequencies, due to atmospheric noise (static) and man-made noise (interference), even a weak signal from an inefficient antenna is far stronger than the internal thermal or Johnson noise generated in the radio receiver's own circuitry, so the weak signal from a loop antenna can be amplified without degrading the signal-to-noise ratio, since both are magnified by the same amplification factor.[10]

For example, at 1 MHz, the man-made noise might be 55 dB above the thermal noise floor. If a small loop antenna's loss is 50 dB (as if the antenna included a 50 dB attenuator), then the electrical inefficiency of that antenna will have little influence on the receiving system's signal-to-noise ratio. In contrast, at quieter frequencies at about 20 MHz and above, an antenna with a 50 dB loss could degrade the received signal-to-noise ratio by up to 50 dB, resulting in terrible performance.

However, as frequency rises, there is no need to suffer bad performance: At the higher, quieter frequencies, the wavelengths become short enough that a halo antenna is small enough to be feasible – at 20 MHz it is a little less than 8 feet (2.4 m) in diameter, and proportionally shrinks as the frequency increases. So the quieter the rising frequency gets, the more convenient it is to replace a small receiving loop with a larger, but still relatively compact, halos. It is mostly a direct substitute for a small receiving loop, but with superior signal reception.[i]

Radiation pattern and polarization

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Radiation patterns of loop antennas. Distance from the origin is proportional to the power density in that direction. The full wave loop (left) emits maximum power broadside to the wires with nulls off the sides, the small loop (right) emits maximum power in the plane of its wires with nulls broadside to the wires.

Surprisingly, the radiation and receiving pattern of a small loop is perpendicular to that of a large self resonant loop (whose perimeter is close to one wavelength). Since the loop is much smaller than a wavelength, the current at any one moment is nearly constant round the circumference. By symmetry it can be seen that the voltages induced in the loop windings on opposite sides of the loop will cancel each other when a perpendicular signal arrives on the loop axis. Therefore, there is a null in that direction.[11] Instead, the radiation pattern peaks in directions lying in the plane of the loop, because signals received from sources in that plane do not quite cancel owing to the phase difference between the arrival of the wave at the near and far sides of the loop. Increasing that phase difference by increasing the size of the loop causes a disproportionately large increase in the radiation resistance and the resulting antenna efficiency.

Another way of looking at a small loop as an antenna is to consider it simply as an inductive coil coupling to the magnetic field in the direction perpendicular to plane of the coil, according to Ampère's law. Then consider a propagating radio wave also perpendicular to that plane. Since the magnetic (and electric) fields of an electromagnetic wave in free space are transverse (no component in the direction of propagation), it can be seen that this magnetic field and that of a small loop antenna will be at right angles, and thus not coupled. For the same reason, an electromagnetic wave propagating within the plane of the loop, with its magnetic field perpendicular to that plane, is coupled to the magnetic field of the coil. Since the transverse magnetic and electric fields of a propagating electromagnetic wave are at right angles, the electric field of such a wave is also in the plane of the loop, and thus the antenna's polarization (which is always specified as being the orientation of the electric, not the magnetic field) is said to be in that plane.

Thus, mounting the loop in a horizontal plane will produce an omnidirectional antenna which is horizontally polarized; mounting the loop vertically yields a vertically polarized, weakly directional antenna, but with exceptionally sharp nulls along the axis of the loop.[j] Size criteria that favor loops with a perimeter of ⁠ 1 / 4 ⁠ wave or smaller ensure the sharpness of the loop's receiving null. Small loops intended for transmitting (see below) are designed as large as feasible to improve the marginal radiation resistance, sacrificing the sharp null by using perimeters as large as ⁠ 1 / 3 ⁠ to ⁠ 1 / 2 ⁠ wave.

Receiver input tuning

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Since a small-loop antenna is essentially a coil, its electrical impedance is inductive, with an inductive reactance much greater than its radiation resistance. In order to couple to a transmitter or receiver, the inductive reactance is normally canceled with a parallel capacitance.[k] Since a good loop antenna will have a high Q factor (narrow bandwidth), the capacitor must be variable and is adjusted to match the receiver's tuning.

Small-loop receiving antennas are also almost always resonated using a parallel-plate capacitor, which makes their reception narrow-band, sensitive only to a very specific frequency. This allows the antenna, in conjunction with a (variable) tuning capacitor, to act as a tuned input stage to the receiver's front-end, in lieu of a preselector.

Direction finding with small loops

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Loop antenna, receiver, and accessories used in amateur radio direction finding at 80-meter (260-foot) wavelength (3.5 MHz).

As long as the loop perimeter is kept below about ⁠ 1 /4⁠ wave, the directional response of small loop antennas includes a sharp null in the direction normal to the plane of the loop, so small loops are favored as compact radio direction finding antennas for long wavelengths.

The procedure is to rotate the loop antenna to find the direction where the signal vanishes – the "null" direction. Since the null occurs at two opposite directions along the axis of the loop, other means must be employed to determine which side of the antenna the nulled signal is on. One method is to rely on a second loop antenna located at a second location, or to move the receiver to that other location, thus relying on triangulation.

Instead of triangulation, a second dipole or vertical antenna can be electrically combined with a loop or a loopstick antenna. Called a sense antenna, connecting and matching the second antenna changes the combined radiation pattern to a cardioid, with a null in only one (less precise) direction. The general direction of the transmitter can be determined using the sense antenna, and then disconnecting the sense antenna returns the sharp nulls in the loop antenna pattern, allowing a precise bearing to be determined.

AM broadcast receiving antennas

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Small-loop antennas are lossy and inefficient for transmitting, but they can be practical receiving antennas in the mediumwave (520–1710 kHz) broadcast band and below, where wavelength-sized antennas are infeasibly large, and the antenna inefficiency is irrelevant, due to large amounts of atmospheric noise.

AM broadcast receivers (and other low frequency radios for the consumer market) typically use small-loop antennas, even when a telescoping antenna may be attached for FM reception.[12] A variable capacitor connected across the loop forms a resonant circuit that also tunes the receiver's input stage as that capacitor tracks the main tuning. A multiband receiver may contain tap points along the loop winding in order to tune the loop antenna at widely different frequencies.

In AM radios built prior to the invention of ferrite in the mid-20th century, the antenna might consist of dozens of turns of wire mounted on the back wall of the radio – a planar helical antenna – or a separate, rotatable, furniture-sized rack looped with wire – a frame antenna.

Ferrite loop antenna

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Ferrite loopstick antenna from an AM radio having two windings, one for long wave and one for medium wave (AM broadcast) reception. About 10 cm (4 inches) long. Ferrite antennas are usually enclosed inside the radio receiver.

Ferrite loop antennas are made by winding fine wire around a ferrite rod. They are almost universally used in AM broadcast receivers.[12](p 23)[d] Other names for this type of antenna are loopstick, ferrite rod antenna or aerial, ferroceptor, or ferrod antenna. Often, at mediumwave and lower shortwave frequencies, Litz wire is used for the winding to reduce skin effect losses. Elaborate "basket weave" patterns are used at all frequencies to reduce inter-winding capacitance in the coil insuring that the loop self-resonance is well above the operating frequency, so that it acts as an electrical inductor that can be resonated with a tuning capacitor, and with a consequent improvement of the loop Q factor.

Inclusion of a magnetically permeable core increases the radiation resistance of a small loop,[1] mitigating the inefficiency due to ohmic losses. Like all small antennas, such antennas are tiny compared to their effective area. A typical AM broadcast radio loop antenna wound on ferrite may have a cross sectional area of only 1 cm2 (0.16 sq in) at a frequency at which an ideal (lossless) antenna would have an effective area some hundred million times larger. Even accounting for the resistive losses in a ferrite rod antenna, its effective receiving area may exceed the loop's physical area by a factor of 100.[13]

Small transmitting loops

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Small transmitting loops are "small" in comparison to a full wavelength, but considerably larger than a "small" receive-only loop. They are typically used on frequencies between 14–30 MHz. Unlike receiving loops, small transmitting loops' sizes must be scaled-up for longer wavelengths, in order to keep radiation resistance from falling to unusably low levels; their larger sizes blur or erase the otherwise especially sharp nulls that small receiving loops provide.

Size, shape, efficiency, and pattern

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A loop antenna for amateur radio under construction

Transmitting loops usually consist of a single turn of large-diameter conductor; they are typically round or octagonal to maximize the enclosed area for a given perimeter, hence maximizing radiation resistance. The smaller of these loops are much less efficient than the extraordinary performance of full-sized, self-resonant loops,[14] or the moderate efficiency of monopoles, dipoles, and halos, but where space for a full wave loop or a half-wave dipole is not available, small loops can provide adequate communications with low-but-tolerable efficiency.[15][16]

A small transmitting loop antenna with a perimeter of 10% or less of the wavelength will have a relatively constant current distribution along the conductor,[1] and the main lobe will be in the plane of the loop, so it will show the null familiar in the radiation pattern of small receiving loops, but more like signal dimming, instead of complete signal loss shown by sub-⁠1/ 10 ⁠ wave direction-finding loops. Loops of any size between 10% and 30% of a wavelength in perimeter, up to almost exactly 50% in circumference, can be built and tuned with series capacitors to resonance, but their non-uniform current will reduce or eliminate the small loops' pattern null. A capacitor is required for a circumference less than a half wave, and an inductor is required for loops more than a half wave and less than a full wave.

Loops in the small transmitting loops' size range may have neither the uniform current of very small loops, nor the sinusoidal current of large loops, and thus cannot be analyzed using the assumptions useful for the small receiving loops nor full-wave loop antennas. Performance is most conveniently determined using NEC analysis. Antennas within this size range include the halo (see above) and the G0CWT (Edginton) loop. For brevity, introductory articles on small loop antennas sometimes confine discussion to loops smaller in circumference than ⁠1/ 10 ⁠ wavelength, since for loops with circumferences larger than ⁠1/ 10 ⁠ wave, the simplifying assumption of uniform current around the entire loop becomes untenably inaccurate. Since the larger halo also has a simple analysis, moderate-sized small-loop antennas and their complicated analysis are often omitted, leaving many otherwise-well-informed antenna builders in the dark regarding the performance obtainable with moderately small loops.

Use for land-mobile radio

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Vertically aligned small loops are used in military land-mobile radio, at frequencies of 3–7 MHz, because of their ability to direct energy upwards, unlike a conventional whip antenna. This enables near vertical incidence skywave (NVIS) communication up to 300 km (190 miles) in mountainous regions. For NVIS, a typical radiation efficiency of around 1% is acceptable, because signal paths can be established with 1 W of radiated power or less – feasible when a 100 W transmitter is used.

In military use, the antenna may be built using a one- or two-conductor 2.5–5 cm (1–2 inches) in diameter. The loop itself is typically 1.8 m (6 feet) in diameter.

Power limits and RF safety

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One practical issue with small loops as transmitting antennas is that a small transmitting loop has not only a very large current going through it, but also a very high voltage across the capacitor – typically thousands of volts – even when fed with only a few watts of transmitter power. The smaller the loop (in wavelengths), the higher the voltage. This requires a rather expensive and physically large resonating capacitor with a large breakdown voltage, in addition to having minimal dielectric loss (normally requiring an air-gap capacitor or even a vacuum variable capacitor).

Corona discharge around an antenna coil. Despite its lurid appearance, high voltage on a loading coil is not as great a threat as the higher voltages seen on tuning capacitors in magnetic loops.

Making the loop larger in diameter will lower the gap voltage, as well as improving efficiency; however, all other efficiency improvements will tend to increase the gap voltage: efficiency may be increased by making the loop from a thicker conductor; other measures to lower the conductor's loss resistance include welding or brazing the connections, rather than soldering. But because reducing loss resistance increases the antenna's Q, the consequence of better efficiency is even greater voltage across the capacitor at the loop's gap. For a given frequency, a smaller small loop is more dangerous than a larger small loop, and perversely, a comparatively efficient small transmitting loop is more dangerous than an inefficient one.

The RF burn and shock problems raised by capacitive loading of small loops is more serious than for inductive loading of short whips or dipole antennas.[l] The high antenna voltage is generally troublesome only on the upper end of a whip's loading coil, since it is spread across the extended coil length, whereas high voltages on a loop's capacitor plates are (ideally) at maximum over all of the plate surfaces. Further, the high-voltage tips of monopoles and dipoles typically are mounted high up and far out of reach, which limits opportunities for radio-frequency burns. In contrast, small-loop / "magnetic" antennas better tolerate being mounted close to the ground,[m] so all parts of loop antennas, including the high-voltage parts, are more often within easy reach.

In summary: the high voltages from high Q pose a greater threat in small loops than most other small antennas, and demand greater caution, even for very low transmit power.

Feeder loops

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In addition to other common impedance matching techniques such as a gamma match, small receiving and transmitting loops are sometimes impedance-matched by connecting the feedline to an even smaller feeder loop inside the area surrounded by the main loop. Although it may still be connected through the ground system, this leaves the main loop with no other DC connection to the transmitter.[16] The feeder loop and the main loop are effectively the primary and secondary coils of a transformer, with power in the near-field inductively coupled from the feed loop into the main loop, which itself is connected to the resonating capacitor and radiates most of the signal power.

If both the main and the feeder loops are single-turn, then the impedance transformation ratio of the nested loops is almost exactly the ratio of the areas of the two loops separately, or the square of the ratio of their diameters (assuming they have the same shape). Typical feeder loops are ⁠ 1 / 8 ⁠ to ⁠ 1 / 5 ⁠ the size of the antenna's main loop, which gives transform ratios of 64:1 to 25:1, respectively. Adjusting the proximity and angle of the feeder loop to the main loop, and distorting the feeder's shape, both make small-to-moderate changes to the transform ratio, and allows for fine adjustment of the feedpoint impedance. For main loops with multiple turns, more often used for mediumwave frequencies, the feeder loop can be one or two turns on the same frame as the main loop's turns, in which case the impedance transform ratio is very nearly the square of the ratio of the number of turns on each loop.

Antenna-like non-antenna loops

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Some so-called "antennas" look very much like genuine loop antennas, but are designed to couple with the inductive near-field, over distances of 1–2 metres (3.3–6.6 ft), rather than to transmit or receive long-distance electromagnetic waves in the radiative far-field. Because of this difference, the near-field "antennas" are not radio antennas at all (when correctly functioning for the purpose they are designed for).

Likewise, coupling coils used for inductive charging systems, regardless of whether they are used at low or high radio frequencies, are excluded from this article, since they are not (or ideally, should not be) radio antennas.

RFID coils and induction heating

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Inductive heating systems, induction cooking stovetops, and RFID tags and readers all interact by near-field magnetic induction rather than far-field transmitted waves. So strictly speaking, they are not radio antennas.

Although they are not radio antennas, these systems do operate at radio frequencies, and they involve the use of small magnetic coils, which are called "antennas" in the trade. However, they are more usefully thought of as analogs to the windings in loosely coupled transformers. Although the magnetic coils in these inductive systems sometimes seem indistinguishable from the small loop antennas discussed above, such devices can only operate over short distances, and are specifically designed to avoid transmitting or receiving radio waves. Because inductive heating systems and RFID readers only use near-field alternating magnetic fields, their performance criteria are dissimilar to the far-field radio antennas discussed in this article.

Footnotes

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References

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Loop antenna

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from Grokipedia
A loop antenna is a radio antenna consisting of one or more turns of wire or other electrical conductor shaped into a closed loop, typically circular, rectangular, or polygonal, used for transmitting and receiving electromagnetic waves.[1] For small loops where the circumference is much less than the wavelength (C << λ), it functions primarily as a magnetic dipole antenna, responding to the magnetic component of the incident field through Faraday's law of induction, which generates an electromotive force (emf) proportional to the rate of change of magnetic flux through the loop area.[2] The induced open-circuit voltage for such a small loop is given by $ V_{th} = \frac{\pi D^2 N f E_0}{2c} $, where $ D $ is the loop diameter, $ N $ is the number of turns, $ f $ is the frequency, $ E_0 $ is the incident electric field strength, and $ c $ is the speed of light.[1] Loop antennas exhibit a radiation pattern similar to that of an electric dipole oriented perpendicular to the loop's plane, with maximum response when the magnetic field is in the plane of the loop and nulls when perpendicular, enabling directional sensitivity.[2] They are classified into electrically small loops (C < λ/10), which have low radiation efficiency but are compact and useful for near-field applications, and larger self-resonant loops (C ≈ λ), which offer higher efficiency and are employed in far-field communications. The radiation resistance for a small single-turn loop is $ R_r = 20\pi^2 (C/\lambda)^4 $ ohms, increasing with the fourth power of the loop's electrical size, while directivity is approximately 1.5 (or 1.76 dB).[3] These antennas find applications in direction finding for radio signal location, where rotating the loop nullifies reception to determine bearing, as demonstrated in setups using two spaced loops to triangulate sources.[2] They are also integral to AM radio receivers, RFID systems for near- and far-field identification, portable transceivers in HF/VHF/UHF bands, and wireless devices like cellular phones due to their compact size and versatility in arrays for enhanced directivity.[4][5][1]

Fundamentals

Definition and Principles

A loop antenna is a radio antenna consisting of a closed loop or coil of wire, tubing, or other electrical conductor that carries radio frequency (RF) current, enabling it to function as both a transmitting radiator and a receiving sensor.[6] These antennas are versatile and low-cost, with the loop's geometry determining its electrical properties, and they operate effectively up to microwave frequencies around 3 GHz.[7] The fundamental principles of loop antenna operation stem from electromagnetic theory, where the near-field region is dominated by the magnetic field generated by the RF current flowing uniformly around the loop, while the electric field primarily results from the voltage drop across the loop, particularly near any tuning elements.[8] In the far field, the radiation pattern resembles that of a short electric dipole oriented perpendicular to the loop's plane, but the fields exhibit magnetic dipole characteristics, with the electric field oriented azimuthally (in the ϕ^\hat{\phi} direction for a loop in the xy-plane) and the magnetic field components reversed compared to an electric dipole due to electromagnetic duality.[9] This duality arises because a small loop (circumference C<λ/3C < \lambda/3) behaves as an infinitesimal magnetic dipole with moment proportional to the loop area and current.[9] Electrically, a loop antenna can be represented by an equivalent circuit comprising the loop's self-inductance LL (from its geometry) and distributed capacitance CC, often supplemented by a tuning capacitor for resonance. The resonant frequency occurs when the inductive and capacitive reactances balance, given by
f=12πLC f = \frac{1}{2\pi \sqrt{LC}}
where resonance tunes out the imaginary part of the input impedance for maximum efficiency.[7] Polarization is linear and depends on the loop's orientation: a horizontal loop produces horizontally polarized waves with the electric field parallel to the ground, while a vertical loop yields vertical polarization; overall, the magnetic dipole nature ensures orthogonality to the polarization of an equivalent electric dipole.[9] Loop antennas trace their origins to the late 19th century, with early applications in receiving electromagnetic waves demonstrated by Heinrich Hertz in 1888 as part of verifying Maxwell's theory.[10]

Comparison to Dipole Antennas

Loop antennas differ structurally from dipole antennas in that they form a closed conductive loop, creating a continuous circuit without an open-ended feed gap, whereas dipoles consist of two collinear arms separated at the center feed point. This closed configuration allows loop antennas, particularly larger self-resonant designs, to be mechanically self-supporting using the loop perimeter for structural integrity, eliminating the need for a central insulator or feed support common in dipoles.[11][12] In terms of performance, resonant loop antennas typically present a higher input impedance of 100 to 200 ohms, depending on shape and size, compared to the standard 73 ohms of a thin half-wave dipole. Radiation patterns also contrast: loops produce bidirectional lobes in the plane of the loop for both small and full-wave configurations, while dipoles exhibit a figure-8 pattern broadside to the wire axis. Loop antennas offer advantages in compactness for high-frequency (HF) applications, where small loops can achieve resonance in limited spaces, and their dominant magnetic near-field coupling makes them less susceptible to detuning by nearby dielectric objects or ground effects than electric-field-sensitive dipoles. However, loops generally have narrower bandwidths, requiring precise tuning for multi-frequency operation.[13][14][15] For specific use cases, loop antennas are often preferred for direction finding due to their deep nulls perpendicular to the loop plane, enabling precise signal localization by rotating the antenna to minimize reception. In contrast, dipoles are better suited for applications needing broad omnidirectional coverage, such as general communication, owing to their simpler pattern and wider bandwidth. A key metric for small loops (circumference much less than wavelength) is the radiation resistance, which quantifies their efficiency as magnetic radiators. This arises from the loop's equivalence to a magnetic dipole with moment $ \mathbf{m} = I_0 \mathbf{A} $, where $ I_0 $ is the current and $ \mathbf{A} $ is the vector area; the time-averaged radiated power $ P = \frac{\mu_0 \omega^4 m^2}{12 \pi c^3} $ (with $ m = I_0 A $) leads to $ R_\mathrm{rad} = \frac{2P}{I_0^2} \approx 31{,}200 \left( \frac{A}{\lambda^2} \right)^2 $ ohms, where $ A $ is the physical area in square meters and $ \lambda $ is the wavelength in meters—far lower than a comparable dipole's $ R_\mathrm{rad} \approx 73 $ ohms, emphasizing the need for low-loss materials in loop designs.[12][11]

Large Self-Resonant Loop Antennas

Shapes and Configurations

Large self-resonant loop antennas, designed to operate at resonance with a perimeter approximately equal to one wavelength (λ), exhibit varying performance characteristics based on their geometric shapes. The circular shape is considered optimal for achieving uniform current distribution around the loop, which contributes to consistent resonance properties, though it is mechanically more challenging to construct due to the need for precise curvature.[13] In contrast, the square shape is widely adopted for its ease of construction using straight segments, facilitating simpler support structures and alignment.[13] Other common polygonal forms include the delta (triangular) loop, which offers a compact vertical profile suitable for space-constrained installations, and the octagonal loop, which provides a slight improvement in current uniformity over the square while remaining relatively straightforward to build.[13] Across these shapes, the total perimeter is typically set to about 1005 feet per MHz (or 306 meters per MHz) to achieve self-resonance, with minor adjustments made for the conductor diameter and environmental factors to fine-tune the operating frequency.[13] Configurations of these antennas are often tailored to propagation goals, influencing both resonance stability and practical deployment. A horizontal orientation, with the loop plane parallel to the ground, is preferred for skywave communications, such as near-vertical incidence skywave (NVIS) propagation, as it promotes high-angle radiation when mounted at heights of 0.1 to 0.3λ above ground.[13] Conversely, a vertical configuration, where the loop plane is perpendicular to the ground and fed at the side center, supports groundwave propagation and low-angle radiation for longer-distance contacts, even at modest heights.[13] Multi-turn variants, involving multiple windings of the loop conductor, can increase the overall inductance to shift resonance to lower frequencies or enhance impedance matching, though this adds complexity to the construction and may require additional spacing between turns to minimize unwanted coupling. Sizing considerations for large self-resonant loops emphasize the perimeter's role in achieving resonance without external loading, typically approximating λ at the desired frequency. For instance, a 40-meter band loop (around 7 MHz) would have a perimeter of roughly 140 feet, scalable proportionally for other bands while accounting for end effects that slightly lengthen the effective electrical length.[13] Wire gauge selection is critical for power handling, with #12 AWG (approximately 2 mm diameter) commonly recommended for HF operations up to several kilowatts, as it balances mechanical strength, low resistance losses, and resistance to sagging under tension or environmental stress.[16] Thicker gauges, such as #10 AWG, may be used for higher power levels to further reduce ohmic losses and improve durability.[16] Construction techniques vary to optimize resonance and structural integrity. Wire is the standard material for most full-wave loops due to its flexibility and low cost, allowing easy forming into shapes like squares or deltas; however, aluminum or copper tubing (1/2 to 1 inch diameter) is preferred for rigid, high-power applications, as it reduces skin-effect losses and supports heavier loads without insulation.[12] For delta loops, maintaining adequate spacing—such as positioning the base at least 3 meters above ground—is essential to prevent capacitive coupling between the loop elements and the earth, which could detune the resonance or introduce losses.[13] A notable variant is the quad antenna, which employs full-wave loop elements in a square or delta configuration, augmented by a reflector loop spaced approximately 0.15λ behind the driven element to achieve directional gain of about 5-6 dB over a dipole.[17] The reflector's perimeter is typically 5% larger than the driven loop to ensure proper phase opposition for enhanced forward radiation.[17]

Radiation Patterns and Efficiency

The radiation pattern of large self-resonant loop antennas exhibits omnidirectionality within the plane of the loop and bidirectional lobes perpendicular to that plane, providing uniform coverage in azimuth for horizontally oriented configurations. This pattern closely resembles that of a dipole antenna, but rotated by 90 degrees, with maximum radiation directed broadside to the loop plane rather than along the axis of a linear element.[18][19] For circular configurations, the gain in the horizontal plane typically reaches approximately 2-3 dBi, offering improved performance over a comparable dipole by 1-2 dB in the broadside direction. The elevation patterns feature high-angle lobes suitable for near-vertical incidence skywave (NVIS) applications, enabling effective short-range communication at HF frequencies by directing energy toward the ionosphere at low takeoff angles.[20] Efficiency in large self-resonant loop antennas benefits from low ohmic losses at HF bands, attributable to their substantial physical size relative to wavelength, which minimizes the impact of conductor resistance compared to radiation resistance. The Q-factor generally ranges from 20 to 50, resulting in a usable bandwidth of 5-10% around resonance, sufficient for many amateur and commercial HF operations without excessive tuning requirements.[6] For full-wave loops, the radiation resistance is typically 100-130 ohms, depending on shape and feed point (e.g., ~126 ohms for square side-fed).[13] Polarization is linear, with the electric field oriented parallel to the loop plane in the broadside direction; symmetric shapes like circular or square loops exhibit low cross-polarization levels, typically below -20 dB, enhancing compatibility with standard HF systems.[6]

Halo Antennas

Design and Practical Applications

The halo antenna is constructed by bending a half-wave dipole into a circular or square loop configuration, with the feed point typically located at the bottom and a small gap positioned directly opposite to facilitate impedance matching to approximately 50 ohms using direct coaxial feed or a simple gamma match. The design originates from US Patent 2,324,462 (1943) by L.M. Leeds and M.W. Scheldorf, assigned to General Electric, for high-frequency directive antennas in FM service.[21][22][23] Practical implementations often utilize aluminum rods or copper tubing for the radiating element, supported by lightweight PVC or fiberglass frames for structural integrity, enabling easy mounting on vehicle roofs via magnetic or lip mounts or on towers for elevated VHF and UHF installations.[24][21] These antennas find widespread use in mobile radio systems and amateur television setups, where their compact footprint—often less than one meter in diameter for 2-meter band operation—provides dipole-like performance with gains of 2 to 5 dBi, offering horizontal polarization that minimizes pickup of vertical noise sources such as ignition interference during vehicular travel.[22][21] Patented in 1943 for FM broadcasting in the 42-50 MHz band, with designs popularized in amateur radio during the mid-20th century, halo antennas remain popular in the 2-meter (144 MHz) and 70-centimeter (430 MHz) amateur bands due to their omnidirectional azimuth patterns and operational simplicity.[25][23] Performance characteristics include a bandwidth of approximately 2-4 MHz with VSWR below 2:1 across the operating segment, supporting efficient transmission without extensive tuning adjustments.[21][26]

Electrical Analysis

The halo antenna can be modeled as a shortened half-wave dipole bent into a circular shape, resulting in input impedance characteristics typically in the range of 50-100 ohms when properly tuned.[27] This impedance is adjustable by varying the feed gap width, which influences the effective electrical length and reactance of the structure.[28] The antenna's behavior is equivalent to that of a shortened dipole, where the circular configuration reduces the effective aperture compared to a straight dipole, leading to a radiation resistance that is lower than the standard 73 ohms but still suitable for direct feed with 50-ohm systems after minor matching.[29] The feed gap, located opposite the feed point, plays a critical role in tuning resonance through capacitive coupling across the opening. This gap, typically sized at 1-5% of the loop circumference, prevents a short-circuit at the feed location and enables balanced feeding while providing the necessary capacitance to cancel the inductive reactance of the loop.[27] The capacitance introduced by the gap can be approximated using the parallel-plate formula:
Cgap=ϵAd C_\text{gap} = \epsilon \frac{A}{d}
where ϵ\epsilon is the permittivity of the medium between the gap plates (air for typical designs), AA is the effective area of the overlapping conductors, and dd is the gap width.[30] This model derives from treating the loop as a transmission line with the gap acting as a lumped capacitive discontinuity, allowing the reactance XX to be tuned for resonance. The input impedance is thus expressed as Zin≈Rrad+jXZ_\text{in} \approx R_\text{rad} + jX, where RradR_\text{rad} is the radiation resistance (around 50 ohms for resonant designs) and XX is adjusted near zero by the gap capacitance.[6] Due to the folded-like geometry of the halo compared to full-wave loops, it exhibits a higher quality factor QQ than traditional large loops, arising from reduced current distribution losses and higher stored energy in the near-field.[31] This results in efficiencies exceeding 90% at UHF frequencies, where ohmic losses in the conductor are minimized, particularly with copper or aluminum tubing.[27] The elevated QQ enhances bandwidth selectivity but requires precise gap tuning to maintain low VSWR across the operating band.

Small Loop Antennas

Receiving Loops

Small loop antennas, with dimensions much less than λ/10, are particularly effective for receiving applications due to their response to the magnetic component of electromagnetic waves. The induced voltage in such a loop arises from the time-varying magnetic flux through its area, as described by Faraday's law of electromagnetic induction. For a multi-turn loop, the open-circuit induced voltage is given by
V=−jωμ0HAN, V = -j \omega \mu_0 H A N,
where ω\omega is the angular frequency, μ0\mu_0 is the permeability of free space, HH is the incident magnetic field strength normal to the loop plane, AA is the loop area, and NN is the number of turns.[6] This formulation highlights the loop's sensitivity to magnetic flux changes, making it ideal for environments where electric field interference is prevalent.[32] These antennas exhibit a high quality factor QQ, typically ranging from 100 to 1000, which results in a narrow bandwidth often less than 1% of the operating frequency.[33][6] To achieve resonance across desired frequencies, a variable capacitor is employed in series with the loop, forming a tuned circuit that maximizes sensitivity at the target frequency.[34] However, the induced signals are typically very low, on the order of microvolts, necessitating a low-noise preamplifier with 20-30 dB gain to boost the output for practical receiver use without introducing significant noise.[35][36] The radiation pattern of a small receiving loop is a figure-8 in the plane perpendicular to the loop axis, with deep nulls broadside to the loop plane (along the axis), providing inherent directionality for noise rejection.[6] For a horizontal loop orientation, the antenna is sensitive to horizontally polarized electric fields in the incident wave.[37] This configuration excels in rejecting noise from nearby conductors, such as power lines, by responding primarily to the magnetic field rather than electric interference. Small loops are commonly integrated with software-defined radios (SDRs) for HF monitoring, where their compact size and noise-rejection properties enhance signal clarity in urban or electrically noisy environments.[8]

Direction Finding

Small loop antennas are widely employed in radio direction finding (RDF) due to their sharply defined nulls in the figure-of-eight reception pattern, allowing precise localization of signal sources.[38] The fundamental technique involves manually rotating the loop antenna until the received signal strength reaches a minimum at the null position, which aligns perpendicular to the direction of the incoming signal wavefront; this indicates the bearing to the transmitter along the line of the loop's plane.[38] However, the bidirectional nature of the pattern creates a 180-degree ambiguity, resolved by incorporating a nondirectional sense antenna—typically a vertical whip—that combines with the loop signal to produce a cardioid pattern, confirming the correct direction.[39] With proper calibration to account for environmental factors and antenna alignment, this method achieves an accuracy of approximately ±5 degrees.[40] In aviation, automatic direction finders (ADFs) utilizing loop-sense configurations provided essential non-directional beacon (NDB) navigation prior to the widespread adoption of GPS, enabling aircraft to home in on ground stations for approach and en route guidance.[41] Similarly, in amateur radio, "foxhunting" events employ portable loop antennas to track hidden transmitters over distances up to several kilometers, fostering practical skills in RDF.[42] To enable remote or fixed-site operation without mechanical rotation, the goniometer technique couples multiple loops to a rotatable sensing coil, balancing signals for null detection via electrical adjustment rather than physical movement.[38] A seminal implementation, the Bellini-Tosi system introduced in 1907, used two orthogonal fixed loops connected to a goniometer, revolutionizing maritime and aerial RDF by eliminating large rotating structures.[43] Enhancements include dual-loop arrays oriented at 90 degrees for continuous 360-degree coverage without ambiguity in open setups, and electronic switching in modern variants to rapidly sample multiple orientations for improved resolution in dynamic environments.[39]

Transmitting Loops

Small transmitting loop antennas, also known as magnetic loops, are electrically small antennas with a circumference typically less than one-tenth of the operating wavelength, making them compact for HF applications but challenging for efficient transmission due to their inherently low radiation resistance.[44] The radiation resistance $ R_{\mathrm{rad}} $ for a single-turn circular loop is given by
Rrad≈31171(Aλ2)2 Ω, R_{\mathrm{rad}} \approx 31171 \left( \frac{A}{\lambda^2} \right)^2 \, \Omega,
where $ A $ is the loop area in square meters and $ \lambda $ is the wavelength in meters; this formula derives from the magnetic dipole radiation model, with the numerical constant incorporating the free-space impedance and other factors.[6] For such small loops, $ R_{\mathrm{rad}} $ is typically much less than 1 ohm, often dwarfed by ohmic losses in the conductor and tuning components, leading to low overall efficiency defined as $ \eta = \frac{R_{\mathrm{rad}}}{R_{\mathrm{rad}} + R_{\mathrm{loss}}} $, which is generally under 10% without careful design to minimize losses.[44][6] Design trade-offs focus on maximizing $ R_{\mathrm{rad}} $ relative to losses; a circular shape optimizes this for a given perimeter by enclosing the maximum area, thereby maximizing the squared area term in the resistance formula.[44] Multi-turn configurations can boost $ R_{\mathrm{rad}} $ by a factor of $ N^2 $ (where $ N $ is the number of turns), enhancing efficiency for very small sizes, but they also increase loss resistance proportionally, requiring low-resistance materials like thick copper tubing to maintain viable performance.[6] The radiation pattern resembles that of a short vertical electric dipole, with maximum radiation perpendicular to the loop plane, but when mounted near ground for practical use, soil losses distort the pattern, particularly suppressing low-elevation angles and emphasizing higher angles suitable for skywave propagation.[44] Despite these efficiency limitations, small transmitting loops find application in near-vertical incidence skywave (NVIS) communications on the 80 m band (3.5–4.0 MHz), where their high-angle radiation supports regional coverage over 100–500 km, even if only a fraction of input power is radiated.[45] This use leverages their compactness and omnidirectional azimuth pattern in horizontal orientations, trading efficiency for portability in emergency or temporary setups.[46]

Ferrite Loops

Ferrite loops, also known as loopstick or ferrite rod antennas, consist of a coil of wire wound around a high-permeability ferrite core, typically in the form of a rod measuring 10-20 cm in length, enabling compact designs suitable for medium-wave AM reception.[47] The ferrite core significantly boosts the coil's inductance through its relative permeability μ_r, which can reach values up to 1000, concentrating the magnetic field lines from incident radio waves and allowing the antenna to achieve performance comparable to larger air-core loops despite its small physical size.[48] This enhancement arises because the effective permeability μ_fe approximates μ_r when the coil closely fits the core, increasing the magnetic flux linkage and thus the induced voltage.[48] Invented in the early 1950s to enable compact antennas in emerging transistor radios, ferrite loops quickly became integral to portable AM receivers, replacing bulkier wire antennas and facilitating the miniaturization of consumer electronics.[49] They were also employed in aviation automatic direction finder (ADF) systems, with widespread use continuing into the 1990s and beyond, though largely replaced by satellite-based alternatives by the 2000s.[41][50] In applications such as portable radios and loopsticks within AM broadcast receivers, ferrite loops are often tuned by adjusting the position of a movable coil slug along the rod, which varies the effective inductance to resonate with the desired frequency when paired with a fixed or variable capacitor.[47] This configuration excels in environments requiring directional selectivity, as the antenna exhibits high directivity with maximum sensitivity perpendicular to the rod axis and a null along it, aiding in rejecting interference.[47] Performance metrics include a quality factor Q typically ranging from 50 to 200 at AM frequencies, balancing bandwidth and selectivity while maintaining low losses in the ferrite material.[51] The sensitivity of these antennas rivals that of full-size whip antennas due to the amplified magnetic coupling, with the effective aperture area A_eff approximated as A_eff = μ_r A_core, where A_core is the physical cross-sectional area of the core; this derivation adjusts the standard small-loop effective area by the permeability factor to account for the flux concentration within the ferrite.[48]

Specialized Configurations

Feeder Loops

Feeder loops serve a critical role in antenna systems by integrating small auxiliary loops at the feedpoint to perform balun-like functions and end-fed impedance matching. These loops facilitate the transition from the unbalanced impedance of the transmission line, typically 50 ohms coaxial cable, to the higher impedance of the main loop antenna, often around 100-200 ohms or more depending on configuration. By employing magnetic coupling, feeder loops help suppress common-mode currents on the outer shield of the feedline, reducing noise pickup and improving overall system balance and efficiency. Common configurations of feeder loops include the small inductive coupling loop used in magnetic loop antennas, where a compact loop—often one-fifth the diameter of the main loop—is positioned inside or adjacent to the primary radiator to transfer energy via mutual inductance. The position and size of this feeder loop are tuned to optimize coupling for the desired frequency range, enabling efficient power injection without direct electrical connection to the main loop. Another configuration involves small loops acting as RF chokes at the feedpoint, wound around ferrite cores or formed from coaxial cable to present high impedance to common-mode signals while allowing differential mode propagation. In delta loop antennas, a gamma match variant incorporates a short section or stub to achieve end-fed matching, adapting the antenna's natural impedance to the feedline. The electrical analysis of feeder loops treats them as inductive transformers, where the effective turns ratio is influenced by the relative areas or geometries of the loops, providing an impedance transformation proportional to the square of this ratio. This coupling mechanism relies on mutual inductance M between the feeder loop (L1) and the main loop (L2), quantified by the coupling coefficient:
k=ML1L2 k = \frac{M}{\sqrt{L_1 L_2}}
Here, M represents the magnetic flux linkage through one loop produced by current in the other, derived from Neumann's formula for mutual inductance integrating the dot product of current elements along the loop paths. Values of k typically range from 0.1 to 0.3 in practical designs, ensuring sufficient energy transfer while avoiding overcoupling that could detune the system or introduce losses. This approach minimizes common-mode currents by confining fields to the differential mode, enhancing pattern integrity and noise rejection.

Non-Radiating Loops

Non-radiating loops, also known as inductive loops or coupling coils, are closed conductor configurations designed primarily for magnetic field generation or coupling in the reactive near-field region, where radiation is intentionally minimized and negligible, typically less than 1% of input power due to their electrical size being much smaller than the operating wavelength (size << λ). These structures function as high-Q inductors, emphasizing energy storage and transfer through mutual inductance rather than electromagnetic wave propagation, distinguishing them from radiating antennas by their focus on quasi-static magnetic fields for applications like power transfer and sensing. In radio-frequency identification (RFID) systems, non-radiating loops serve as coils for near-field magnetic coupling between readers and passive tags, enabling short-range data exchange and power delivery without significant far-field radiation. These coils are typically planar or helical, with dimensions far smaller than the wavelength at frequencies like 13.56 MHz, where λ ≈ 22 meters, ensuring operation in the reactive near-field dominated by magnetic induction. To optimize power transfer efficiency, RFID coils achieve quality factors (Q) greater than 100, which minimizes resistive losses and maximizes stored magnetic energy, as seen in designs using low-loss materials and precise tuning.[52][53][54] Near-field communication (NFC), a subset of RFID, employs standardized loop coils operating at 13.56 MHz under ISO 14443 protocols to facilitate contactless transactions and device pairing within distances of a few centimeters. These loops generate alternating magnetic fields that induce currents in tag coils via mutual inductance, powering the tag and modulating data without relying on radiated waves. The mutual inductance $ M $ between two coaxial loop coils is derived from the Biot-Savart law for the magnetic flux linkage.[52][55][56] Induction heating applications utilize large non-radiating loops to generate eddy currents in conductive workpieces through strong, localized magnetic fields, typically at medium frequencies of 10-100 kHz to balance penetration depth and heating efficiency. At these frequencies, the loop acts as a current-carrying inductor that confines energy to the near-field, inducing ohmic heating via Faraday's law without appreciable radiation, as the structure's size remains much smaller than the wavelength (λ > 3 km). Historical examples include Tesla coils, which employ resonant primary and secondary loops for high-voltage generation through inductive coupling, originally developed in the 1890s for wireless power experiments but exemplifying non-radiating loop principles in their core transformer-like operation.[57][58]

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