J-pole antenna

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J-pole antenna diagram.svg
J-pole antenna showing standing waves 1.svg
J-pole antenna fed by coaxial cable (left) and parallel line (right). The right diagram shows the standing waves of voltage (V, red bands) and current (I, blue bands) on the elements.

The J-pole antenna, more properly known as the J antenna, [1] is a vertical omnidirectional transmitting antenna used in the shortwave frequency bands. It was invented by Hans Beggerow in 1909 for use in Zeppelin airships. [2] Trailed behind the airship, it consisted of a single one half wavelength long wire radiator, in series with a quarter-wave parallel transmission line tuning stub that matches the antenna impedance to the feedline. By 1936 this antenna began to be used for land-based transmitters with the radiating element and the matching section mounted vertically, giving it the shape of the letter "J", [3] and by 1943 it was named the J antenna. [1] When the radiating half-wave section is mounted horizontally, at right-angles to the quarter-wave matching stub, the variation is usually called a Zepp antenna. [4]

Contents

How it works

The J-pole antenna is an end-fed omnidirectional half-wave antenna that is matched to the feedline by a shorted quarter-wave parallel transmission line stub. [5] [1] [6] For a transmitting antenna to operate efficiently, absorbing all the power provided by its feedline, the antenna must be impedance matched to the line; it must have a resistance equal to the feedline's characteristic impedance. A half-wave antenna fed at one end has a current node at its feedpoint, giving it a very high input impedance of around 1 000–4 000 ohms. [5] This is much higher than the characteristic impedance of transmission lines, so it requires an impedance matching circuit between the antenna and the feedline.

A shorted quarter-wave stub, a transmission line one quarter of the wavelength long with its conductors shorted together at one end, has a similar high impedance node at its open end, making a good match to the antenna. The input impedance seen at a point along the stub varies continuously, decreasing monotonically from this high value to zero at the shorted end. So any value of input impedance can be obtained by connecting the feedline to the proper point along the stub. One arm of the stub is extended a half wavelength to make the antenna. By attaching the antenna's feedline to the proper point along the transmission line, the stub will transform this impedance down to match the lower feedline impedance, allowing the antenna to be fed power efficiently. [6] During construction the proper attachment point for the feed-line is found by sliding the connection of the feedline back and forth along the stub while monitoring the SWR until an impedance match (minimum SWR) is obtained. [1] [6] Being a half-wave antenna, it provides a small gain of just under 1 dB over a quarter-wave ground-plane antenna. [7]

Gain and radiation pattern

E-plane gain measurements of J antenna with respect to reference dipole. Gain in the E-plane of a J antenna (SlimJim variation) vs. a reference dipole.svg
E-plane gain measurements of J antenna with respect to reference dipole.

Primarily a dipole, the J-pole antenna exhibits a mostly omnidirectional pattern in the horizontal (H) plane with an average free-space gain near 2.2 dBi (0.1 dBd). [8] Measurements and simulation confirm the quarter-wave stub modifies the circular H-plane pattern shape increasing the gain slightly on the side of the J stub element and reducing the gain slightly on the side opposite the J stub element. [8] [9] At right angles to the J-stub, the gain is closer to the overall average: about 2.2 dBi (0.1 dBd). [8] The slight increase over a dipole's 2.15 dBi (0 dBd) gain represents the small contribution to the pattern made by the current imbalance on the matching section. [8] The pattern in the elevation (or E plane) reveals a slight elevation of the pattern in the direction of the J element while the pattern opposite the J element is mostly broadside. [9] The net effect of the perturbation caused by quarter-wave stub is an H-plane approximate gain from 1.5 to 2.6 dBi (-0.6 dBd to 0.5 dBd). [9]

Environment

Like all antennas, the J-pole is sensitive to electrically conductive objects in its induction fields [10] (aka reactive near-field region [11] ) and should maintain sufficient separation to minimize these near field interactions as part of typical system installation considerations. [12] The quarter wave parallel transmission line stub has an external electromagnetic field with strength and size proportional to the spacing between the parallel conductors. [13] The parallel conductors must be kept free of moisture, snow, ice and should be kept away from other conductors including downspouts, metal window frames, flashing, etc. by a distance of two to three times the spacing between the parallel stub conductors. [4] The J-pole is very sensitive to conductive support structures and will achieve best performance with no electrical bonding between antenna conductors and the mounting structure. [14] [15]

Construction

The antenna consists of two parallel straight metal conductors, one 3/4 of a wavelength and the other 1/4 of a wavelength long at the operating frequency, shorted together at the bottom.[ citation needed ] Typical construction materials include metal tubing, [1] ladder line, or twin-lead. [16] Since the matching section must act as a transmission line, the parallel conductors should be no more than .02 wavelength apart. [17]

The J-pole antenna and its variations may be fed with balanced line. [1] A coax feed line may be used if it includes a means to suppress feed-line RF currents. [14] [18] The feed-point of the J-pole is somewhere between the closed low-impedance bottom and open high-impedance top of the J stub. [1] [3] Between these two extremes a match to any impedance between the low to high impedance points is available. [1] [3]

The J-pole design functions well when fed with a balanced feed (via balun, transformer or choke) and no electrical connection exists between its conductors and surrounding supports. [14] [15] Historical documentation of the J antenna suggests the lower end of the matching stub is at zero potential with respect to earth and can connect to a grounding wire or mast with no effect on the antenna's operation. [1] Later research confirms the tendency of the mast or grounding wire to draw current from the antenna potentially spoiling the antenna pattern. [19] A common approach extends the conductor below the bottom of the J-pole resulting in additional and undesirable RF currents flowing over every part of the mounting structure. [14] This modifies the far field antenna pattern [19] typically, but not always, raising the primary lobes above the horizon reducing antenna effectiveness for terrestrial service. [15] J-pole antennas with electrical connection to their supports often fare no better, and often much worse, than the simpler monopole antenna. [14] A mast decoupling stub reduces mast currents. [19] [20] [21] [22]

Variations

J-pole Antenna and variations of same. J-pole Antenna and variations of same..png
J-pole Antenna and variations of same.
E-plane gain plots of J antenna variations E-plane gain plots of J antenna variations.png
E-plane gain plots of J antenna variations

Slim Jim antenna

A variation of the J-pole is the Slim Jim antenna, also known as G2BCX Slim Jim, [23] that is related to the J-pole in a similar way to how a folded dipole is related to a dipole. [24] The Slim Jim is one of many ways to form a J-Pole. [24] Introduced by Fred Judd (G2BCX) in 1978, the name was derived from its slim construction and the J type matching stub (JIntegrated Matching). [23]

The Slim Jim variation of the J-pole antenna has characteristics and performance similar to a simple or folded half-wave antenna and identical to the conventional J-pole construction. [24] Judd reported that the Slim Jim produces a lower takeoff angle and better electrical performance than a 5/8 wavelength ground plane antenna, [23] however others' test and analyses show Slim Jim antennas to have no performance advantage over a conventional, single-wire J-pole antenna. [9] [24] Slim Jim antennas made from ladder transmission line use the existing parallel conductor for the folded dipole element, [9] but in the copper pipe variation, the Slim Jim requires almost twice as much material, for which it returns no performance benefit. [9]

The approximate gain in the H-plane of the Slim Jim is from 1.5 to 2.6 dBi (−0.6 dBd to 0.5 dBd). [9]

Super-J antenna

The Super-J variation of the J-pole antenna adds another collinear half-wave radiator above the conventional J and connects the two with a phase stub to ensure both vertical half-wave sections radiate in current phase. [25] The phasing stub between the two half-wave sections is often of the Franklin style. [25] [26] [27]

The Super-J antenna compresses the vertical beamwidth and has more gain than the conventional J-pole design. [28] Both radiating sections have insufficient separation to realize the maximum benefits of collinear arrays, resulting in slightly less than the optimal 3 dB over a conventional J-pole or halfwave antenna. [28] [29]

The approximate gain in the H-plane of the Super-J antenna is from 4.6 to 5.2 dBi (2.4 dBd to 3.1 dBd). [29]

Collinear J antenna

The collinear J antenna improves the Super-J by separating the two radiating half-wave sections to optimize gain using a phasing coil. [29] The resulting gain is closer to the optimum 3 dB over a conventional J-pole or halfwave antenna. [29]

The approximate gain in the H-plane of the Collinear J antenna is from 4.6 to 5.2 dBi (2.4 dBd to 3.1 dBd). [29]

E-plane gain patterns of the variations

The graph compares the E-plane gain of the above three variations to the conventional J antenna.

The conventional J antenna and SlimJIM variation are nearly identical in gain and pattern. The Super-J reveals the benefit of properly phasing and orienting a second radiator above the first. The Collinear J shows slightly higher performance over the Super-J.

Dual-band operation near 3rd harmonic

The basic J antenna resonates on the third harmonic of its lowest design frequency. [30] Operating a 3/2 wavelengths this way produces an antenna pattern unfavorable for terrestrial operation. [31]

To address the pattern change a variety of techniques exist to allegedly constrain a J antenna operating at or near the third harmonic so only one half-wave is active in the radiator above the stub. All involve the use of a high impedance choke at the first voltage loop. [31] These methods fall short of the goal as choking a high impedance point with a high impedance allows energy to pass the choke. [31] [32]

Related Research Articles

<span class="mw-page-title-main">Collinear antenna array</span>

In telecommunications, a collinear antenna array is an array of dipole or quarter-wave antennas mounted in such a manner that the corresponding elements of each antenna are parallel and collinear; that is, they are located along a common axis.

In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through the conductor. In other words, it is the length of the conductor measured in wavelengths. It can alternately be expressed as an angle, in radians or degrees, equal to the phase shift the alternating current experiences traveling through the conductor.

In electrical engineering, a ground plane is an electrically conductive surface, usually connected to electrical ground.

<span class="mw-page-title-main">Antenna (radio)</span> Electrical device

In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves. In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.

<span class="mw-page-title-main">Twin-lead</span> Two-conductor flat cable used to carry radio frequency signals

Twin-lead cable is a two-conductor flat cable used as a balanced transmission line to carry radio frequency (RF) signals. It is constructed of two stranded or solid copper or copper-clad steel wires, held a precise distance apart by a plastic ribbon. The uniform spacing of the wires is the key to the cable's function as a transmission line; any abrupt changes in spacing would reflect some of the signal back toward the source. The plastic also covers and insulates the wires. It is available with several different values of characteristic impedance, the most common type is 300 ohm.

<span class="mw-page-title-main">Omnidirectional antenna</span> Radio antenna that sends signals in every direction

In radio communication, an omnidirectional antenna is a class of antenna which radiates equal radio power in all directions perpendicular to an axis, with power varying with angle to the axis, declining to zero on the axis. When graphed in three dimensions (see graph) this radiation pattern is often described as doughnut-shaped. This is different from an isotropic antenna, which radiates equal power in all directions, having a spherical radiation pattern. Omnidirectional antennas oriented vertically are widely used for nondirectional antennas on the surface of the Earth because they radiate equally in all horizontal directions, while the power radiated drops off with elevation angle so little radio energy is aimed into the sky or down toward the earth and wasted. Omnidirectional antennas are widely used for radio broadcasting antennas, and in mobile devices that use radio such as cell phones, FM radios, walkie-talkies, wireless computer networks, cordless phones, GPS, as well as for base stations that communicate with mobile radios, such as police and taxi dispatchers and aircraft communications.

<span class="mw-page-title-main">Rhombic antenna</span> Rhombus-shaped antenna

A rhombic antenna is made of four sections of wire suspended parallel to the ground in a diamond or "rhombus" shape. Each of the four sides is the same length – about a quarter-wavelength to one wavelength per section – converging but not touching at an angle of about 42° at the fed end and at the far end. The length is not critical, typically from one to two wavelengths (λ), but there is an optimum angle for any given length and frequency. A horizontal rhombic antenna radiates horizontally polarized radio waves at a low elevation angle off the pointy ends of the antenna.

<span class="mw-page-title-main">Helical antenna</span> Type of antenna

A helical antenna is an antenna consisting of one or more conducting wires wound in the form of a helix. A helical antenna made of one helical wire, the most common type, is called monofilar, while antennas with two or four wires in a helix are called bifilar, or quadrifilar, respectively.

<span class="mw-page-title-main">Dipole antenna</span> Antenna consisting of two rod shaped conductors

In radio and telecommunications a dipole antenna or doublet is one of the two simplest and most widely-used types of antenna; the other is the monopole. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole with a radiating structure supporting a line current so energized that the current has only one node at each far end. A dipole antenna commonly consists of two identical conductive elements such as metal wires or rods. The driving current from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the two halves of the antenna. Each side of the feedline to the transmitter or receiver is connected to one of the conductors. This contrasts with a monopole antenna, which consists of a single rod or conductor with one side of the feedline connected to it, and the other side connected to some type of ground. A common example of a dipole is the "rabbit ears" television antenna found on broadcast television sets. All dipoles are electrically equivalent to two monopoles mounted end-to-end and fed with opposite phases, with the ground plane between them made "virtual" by the opposing monopole.

<span class="mw-page-title-main">Whip antenna</span> Type of radio antenna

A whip antenna is an antenna consisting of a straight flexible wire or rod. The bottom end of the whip is connected to the radio receiver or transmitter. A whip antenna is a form of monopole antenna. The antenna is designed to be flexible so that it does not break easily, and the name is derived from the whip-like motion that it exhibits when disturbed. Whip antennas for portable radios are often made of a series of interlocking telescoping metal tubes, so they can be retracted when not in use. Longer whips, made for mounting on vehicles and structures, are made of a flexible fiberglass rod around a wire core and can be up to 11 m long.

<span class="mw-page-title-main">Antenna tuner</span> Telecommunications device

An antenna tuner is a passive electronic device inserted between a radio transmitter and its antenna. Its purpose is to optimize power transfer by matching the impedance of the radio to the signal impedance on the feedline to the antenna.

<span class="mw-page-title-main">Beverage antenna</span> Type of radio antenna

The Beverage antenna or "wave antenna" is a long-wire receiving antenna mainly used in the low frequency and medium frequency radio bands, invented by Harold H. Beverage in 1921. It is used by amateur radio operators, shortwave listeners, longwave radio DXers and for military applications.

<span class="mw-page-title-main">Mast radiator</span> Type of radio frequency antenna

A mast radiator is a radio mast or tower in which the metal structure itself is energized and functions as an antenna. This design, first used widely in the 1930s, is commonly used for transmitting antennas operating at low frequencies, in the LF and MF bands, in particular those used for AM radio broadcasting stations. The conductive steel mast is electrically connected to the transmitter. Its base is usually mounted on a nonconductive support to insulate it from the ground. A mast radiator is a form of monopole antenna.

<span class="mw-page-title-main">Loop antenna</span> Type of radio antenna

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. Within this physical description there are two distinct types:

<span class="mw-page-title-main">Monopole antenna</span> Type of radio antenna

A monopole antenna is a class of radio antenna consisting of a straight rod-shaped conductor, often mounted perpendicularly over some type of conductive surface, called a ground plane. The driving signal from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the lower end of the monopole and the ground plane. One side of the antenna feedline is attached to the lower end of the monopole, and the other side is attached to the ground plane, which is often the Earth. This contrasts with a dipole antenna which consists of two identical rod conductors, with the signal from the transmitter applied between the two halves of the antenna.

A radio transmitter or receiver is connected to an antenna which emits or receives the radio waves. The antenna feed system or antenna feed is the cable or conductor, and other associated equipment, which connects the transmitter or receiver with the antenna and makes the two devices compatible. In a radio transmitter, the transmitter generates an alternating current of radio frequency, and the feed system feeds the current to the antenna, which converts the power in the current to radio waves. In a radio receiver, the incoming radio waves excite tiny alternating currents in the antenna, and the feed system delivers this current to the receiver, which processes the signal.

<span class="mw-page-title-main">Folded unipole antenna</span> Antenna used for radio broadcasts

The folded unipole antenna is a type of monopole mast radiator antenna used as a transmitting antenna mainly in the medium wave band for AM radio broadcasting stations. It consists of a vertical metal rod or mast mounted over and connected at its base to a grounding system consisting of buried wires. The mast is surrounded by a "skirt" of vertical wires electrically attached at or near the top of the mast. The skirt wires are connected by a metal ring near the mast base, and the feedline feeding power from the transmitter is connected between the ring and the ground.

<span class="mw-page-title-main">Random wire antenna</span> A radio antenna consisting of a long wire suspended above the ground

A random wire antenna is a radio antenna consisting of a long wire suspended above the ground, whose length does not bear a particular relation to the wavelength of the radio waves used, but is typically chosen more for convenient fit between the available supports, or the length of wire at hand, rather than selecting length to be resonant on any particular frequency. The wire may be straight or it may be strung back and forth between trees or walls just to get as much wire into the air as feasible. Due to the great variability of the (unplanned) antenna structure, the random wire’s effectiveness can vary erratically from one installation to another, and a single random wire antenna can have wildly different reception / transmission strength in one direction than it achieves in another azimuth direction about 70°~140° different, and finally reception / transmission strengths and directions can be wildly different on only moderately different frequencies. Random wire antennas are typically fed at one end against a suitable counterpoise.

<span class="mw-page-title-main">Antenna array</span> Set of multiple antennas which work together

An antenna array is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas are usually connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship. The radio waves radiated by each individual antenna combine and superpose, adding together to enhance the power radiated in desired directions, and cancelling to reduce the power radiated in other directions. Similarly, when used for receiving, the separate radio frequency currents from the individual antennas combine in the receiver with the correct phase relationship to enhance signals received from the desired directions and cancel signals from undesired directions. More sophisticated array antennas may have multiple transmitter or receiver modules, each connected to a separate antenna element or group of elements.

In radio systems, many different antenna types are used whose properties are especially crafted for particular applications. Most often, the greatest effect is due to the size (wavelength) of the radio waves the antenna is to intercept or produce; one competing second effect is differences in optimization for receiving and for transmitting; another competing influence is the number and bandwidth of the frequenc(y/ies) that any single antenna must intercept or emit.

References

  1. 1 2 3 4 5 6 7 8 9 "Very-High-Frequency Antennas". Antennas and Antenna Systems (TM 11-314) (PDF). U.S. War Department. 30 November 1943. pp. 163–164. Retrieved 6 May 2016.
  2. ↑ Beggerow, Hans (19 September 1909). "German patent 225204" (PDF). Zeppelin Antenna. Retrieved 28 January 2016.
  3. 1 2 3 USpatent 2124424,Laurance McConnell Leeds,"Antenna System",published 1938-07-19
  4. 1 2 Hall, Gerald; et al., eds. (1988). The ARRL Antenna Book (15th ed.). Newington, CT: American Radio Relay League. p. 24.25. ISBN   0-87259-206-5.
  5. 1 2 The A.R.R.L. Antenna Book. Radio Amateurs' Library. Vol. 15 (5th ed.). West Hartford, CT / Concord, NH: American Radio Relay League / Rumford Press. 1949. pp. 91–92 – via Google books.
  6. 1 2 3 Brown, George, ed. (July 2001). Radio and Electronics Cookbook. Potters Bar, Herts., UK / Oxford, UK: Radio Society of Great Britain / Newnes. pp. 149–150. ISBN   9780750652148 – via Google books. ISBN   0-7506-5214-4
  7. ↑ Huggins, John S. (6 November 2008). "1/4 wave monopole vs. 1/2 wave J-pole EZNEC shootout". Ham Radio: Magnum Experimentum (hamradio.me). Retrieved 30 January 2012.
  8. 1 2 3 4 Cebik, L.B. "Some J-poles that I have known, Part 1: Why I finally got interested in J-poles, and some cautions in modeling them". Cebik.com. Archived from the original on 22 April 2014. Retrieved 1 October 2015.
  9. 1 2 3 4 5 6 7 Huggins, John S. (19 August 2015). "Slim-Jim vs. traditional J-pole antenna". Ham Radio: Magnum Experimentum (hamradio.me). Retrieved 28 August 2015.
  10. ↑ Griffith, B. Whitfield (1962). Radio-Electronic Transmission Fundamentals. New York, NY: McGraw Hill. pp. 322–323.
  11. ↑ Balanis, Constantine (1982). Antenna Theory. Harper & Row. pp. 116–118. ISBN   0-06-040458-2.
  12. ↑ Collins, Brian (1984). "VHF and UHF communication antennas". In Johnson, Richard (ed.). Antenna Engineering Handbook (2nd ed.). New York, NY: McGraw-Hill. pp. 27.21–27.22. ISBN   0-07-032291-0.
  13. ↑ Griffith, B. Whitfield (1962). Radio-Electronic Transmission Fundamentals. New York, NY: McGraw Hill. pp. 243–244.
  14. 1 2 3 4 5 Huggins, John S. (28 January 2012). "J-pole antenna: Should I ground it?". Ham Radio: Magnum Experimentum (hamradio.me). Retrieved 30 January 2012.
  15. 1 2 3 Richardson, Dan (March 1998). "The J-pole revisited" (PDF). CQ Magazine . pp. 34–41. Retrieved 30 January 2012.
  16. ↑ Fong, Edison (March 2007). "The DBJ-2: A Portable VHF-UHF Roll-Up J-pole Antenna for Public Service". QST. Newington, CT: ARRL, Inc.
  17. ↑ Teeters, Chuck (December 2005). "The trouble with J antennas". The Splatter, December 2005 edition. Amateur Radio Club of Augusta website, Augusta, Georgia. Retrieved 15 November 2021.
  18. ↑ A folded-balun, sleeve balun, or common-mode choke will suppress feed-line RF currents. See: Straw, Dean (2007). "26 - Coupling the Line to the Antenna". The ARRL Antenna Book. Newington, CT: The ARRL, Inc. ISBN   978-0-87259-987-1.
  19. 1 2 3 Huggins, John S (27 February 2015). "Have your J-Pole and ground it too" . Retrieved 4 March 2015.
  20. ↑ Huggins, John S. (17 June 2015). "Mast Mountable J-Pole Antenna" . Retrieved 17 June 2015.
  21. ↑ USpatent 10468743,"Antenna",issued 2019-11-05
  22. ↑ USpatent D798847,"Antenna",issued 2017-10-03
  23. 1 2 3 Judd, Fred (1978). "Slim Jim - 2 metre aerial". Practical Wireless - Out of Thin Air: 37–39. Retrieved 24 April 2014.
  24. 1 2 3 4 Cebik, L.B. "What is a Slim Jim?". Cebik.com. Archived from the original on 24 April 2014. Retrieved 30 January 2012– via net46.net.
  25. 1 2 Steve Cerwin (2007). "Mobile and Maritime Antennas - The Super-J Maritime Antenna". In Straw, Dean (ed.). ARRL Antenna Book (21st ed.). Newington, CT: The American Radio Relay League, Inc. pp. 16.23–16.26. ISBN   978-0-87259-987-1.
  26. ↑ Franklin, Charles (1924). "Franklin Antenna" (PDF). Retrieved 28 January 2016.
  27. ↑ Collins, Brian (1984). "VHF and UHF Communication Antennas - Base-Station Antennas". In Johnson, Richard; Henry Jasik (eds.). Antenna Engineering Handbook (2nd ed.). New York: McGraw-Hill. p. 27.14. ISBN   0-07-032291-0.
  28. 1 2 Cebik, L.B. "Some J-Poles that I have known, Part 4: Some things we can and cannot do with a J-Pole". Cebik.com. Archived from the original on 22 April 2014. Retrieved 21 April 2014.
  29. 1 2 3 4 5 Huggins, John S. (5 August 2012). "Improving the Super J-Pole Antenna" . Retrieved 21 April 2014.
  30. ↑ Huggins, John (17 December 2008). "Can a 2m J-Pole be used at 440?". Hamradio.me. Retrieved 12 June 2019.
  31. 1 2 3 Huggins, John (29 December 2018). "Antenna radiator decoupling stub flub?". Hamradio.me. Retrieved 12 June 2019.
  32. ↑ Huggins, John (28 December 2018). "Where quarter-wave radiator decoupling stubs work ... and don't work". Hamradio.me. Retrieved 12 June 2019.
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