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The 5/8λ vertical it quite popular, being ascribed some magic pattern properties. Objectively, a change in the pattern distribution occurs for a vertical monopole as its length increases past about 60% of a wavelength. Installed over an excellent ground system, it offers a small amount of gain in a major lobe at quite low elevation.
Whilst it might offer a good pattern, it does not have a feed point impedance that is at all suited to direct connection to a 50Ω feed line.
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Fig 1 shows the feed point impedance of a vertical monopole over a perfect ground plane from an NEC model. The models were created with a 10m high conductor, 50mm in diameter, and at frequencies from 13 to 22MHz. Note that the radiator exhibits a parallel resonance at λ/2 and a series resonance at 3λ/4. In between, it exhibits a resistance and capacitive reactance quite dependent on length.
Importantly to the design of a matching network, the R component in the region of 0.6λ is significantly greater than 50Ω. This shapes the likely impedance matching solutions.
The simplest solution for many applications is a low pass L network with the shunt C on the load side. The strategy is to add sufficient shunt C at the feed point so that the series R of the combination is just less than 50Ω, then a series L to tune out the residual reactance.
For example, if at 14MHz, the impedance at the feed point was say 100-j300Ω, a shunt capacitance of about 16pF will change the impedance to about 49-j215Ω. A series inductor of about 2.4µH will cancel that reactance, and its small loss resistance will raise total R to about 50Ω. In practice, both L and C would be adjusted for a perfect match at some preferred frequency.
This solution is often proposed in ham discussions, but apparently with little understanding of how it works. Perhaps the popularity derives from its promotion in various ARRL publications.
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Fig 2 shows a diagram from (Straw 2007) illustrating a project for a 5/8 vertical for the 2m band. The tapped inductor can be translated to an equivalent network of two uncoupled inductances, some stray capacitance represented by a shunt capacitance from the base of the vertical to ground.
This network depends on the stray capacitance for its operation, it is not possible to transform the feed point impedance with R component greater than 50Ω using just two inductors. The design of the project base insulator results in a higher stray capacitance than that due to the coil alone.
An equivalent stray capacitance of just a little over 1pF is sufficient to bring the R component to less than 50Ω. At that point, a simple series inductor could be used to tune out the residual reactance, but they have chosen a more complicated tapped inductor.
If one studies the tapped inductor, it is tapped quite high, and the inductance of the lower section is so high that it doesn't have much bearing on the match, the effect of adjusting the tap is principally from the change in the inductance of the top section of the coil.
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Fig 3 shows the base assembly from the project. The projection of the vertical into the top turns of the coil, and the routing of the top turn through the insulator and near to the vertical helps to increase stray capacitance, and the very high coil tap can be seen. The inductance of the common section of the coil is probably around 450nH, a reactance of over 400Ω, so it has little impact on the match.
None of this is to question whether it works, but to offer an explanation of why it works.
The scheme does not scale well to lower frequencies, a coil with higher inductance will typically be a larger diameter, and have less stray capacitance, and even less capacitive reactance. For example, it is unlikely that a 5/8λ vertical will match up on the 20m band without some additional capacitance across the feed point. It may only require 10 to 20pF of shunt capacitance (depending on the R component of a real vertical) to allow a match. There is no need for a tapped inductor (either for 2m or 20m), an adjustable series inductor in concert with an adjustable shunt C will allow a perfect match the frequency of choice.
Some types of heavy duty mounts for HF verticals (eg for a 20m 5/8λ) may have more than sufficient built in stray capacitance to get the R component of feed point impedance below 50 ohms, and a tapped inductor may be quite practical.
A variation on the L match is to connect a short length of coax to the feed point, and then insert a series inductor between that line section and the main feed line.
For example, if at 14MHz, the impedance at the feed point was say 100-j300Ω, 160mm of RG213 will have an input impedance of 49-j212Ω. A series inductor of about 2.4µH will cancel that reactance, and its small loss resistance will raise total R to about 50Ω. In practice, both L and the length of the short line sections would be juggled for a perfect match at some preferred frequency. (The loss in the coax section is negligible at about 0.15% of input power.)
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Fig 4 shows the solution on a Smith chart. X marks the feed point impedance, a line section of about 4° at constant VSWR intersects the R'=1 circle, then sufficient series inductance to follow around the R'=1 line to deliver an input impedance of Z'=1+j0, or Z=50+j0Ω.
The matching methods discussed here are applicable to an antenna where the feed point impedance R component is greater than 50Ω, possibly much greater, with or without a substantial X component.
An example is the Ringo Ranger antenna, an end fed half wave. The raw half wave is likely to have R somewhere around 1000Ω at resonance, and X from +500 to -500 either side of resonance. Most antennas of this type incorporate some equivalent capacitance in the base insulator construction , and possibly some further transmission line transformation in the connection to the tapped inductor.
Straw, Dean ed. 2007. The ARRL Antenna Book. 21st ed. Newington: ARRL. 16.27-16.29.
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