# Matching a 5/8λ vertical - example 1

Mark, M6AWG, wanted to try a 5/8λ vertical on the 20m band.

A lot of magic is ascribed to 5/8 verticals by hams, many drawing inferences from their use on the AM MW broadcast band. Many of the claims are not realised in implementation.

If the radiation pattern of a vertical monopole over a perfectly conducting ground is studied, at a little over λ/2, the main lobe divides. This point is often taken as 5/8λ (0.625λ), but it is just a little less. So, in practice, a radiator of 0.6λ is quite sufficient.

Mark's need is for an elevated feed point, at about 2.7m above natural ground. That is fine, it means that the radials will be sufficiently clear of soil as to have low loss and three quarter wave radials should be quite sufficient to provide good decoupling of the feed line (ie low common mode current) and minimal distortion of the radiation pattern.

The matching system chosen was the Transmission line section and series L described at (Duffy 2012).

Fig 1 shows the concept, the dimensions are in metres. The length of the 50Ω line section attached to the feed point, and the series inductor form the matching network to deliver a load of 50+j0Ω to the main feed line. The short coax section is sized to transform the feed point impedance of something like 100-j300Ω to approximately 50-jX, and the coil reactance cancels X.

An NEC model was constructed of a 0.6λ base fed vertical with three λ/4 equally spaced radials, the base located at 2.7m above 'average' ground. The model also incorporates the matching components.

Fig 2 shows the antenna structure as modelled. In reality, the antenna will be erected very close to a building and trees, but the model above provides sufficient insight into the antenna system to be worthwhile.

The model enables calculation of the feed point impedance and matching network.

Fig 3 shows the VSWR curve from the model.

The modelled feed point impedance is 120-j445Ω. The matching components are a series section of 50Ω line with vf=0.67 of length 143mm, and a 3.2 µH series coil. These are starting points for in-situ adjustment of the real antenna.

It is prudent to install an effective current balun on the main feed line near the matching circuit.

Mark has made a 1:1 Guanella current balun from 9 turns of RG58 on a TF240-43 core.

Fig 4 shows the expected impedance vs frequency characteristic for the balun. It has excellent choking impedance at 14MHz, and is well suited to the task.

Fig 5 shows the elevation pattern, maximum gain is at 14° elevation. System efficiency (including matching network loss, but not the main feed line loss) with 1mm diameter copper wire is 96%. Thinner wire for 'stealth' will increase losses, whereas thicker wire or tube will decrease losses. There is negligible distortion of the azimuth pattern.

The pattern shows the reality of 5/8λ verticals over real ground, maximum gain is not at 0° elevation, but somewhat higher than that.

# Alternatives

## Single stub matching

Mark's original posting (QRZ 2102) sought a solution for a single stub tuner in the style of (Carr 2001).

Fig 6 shows Carr's matching arrangement. (His annotation of the radial length is confusing, labeling them as both λ/4 and λ/8. His matching solution is for the λ/4 case.)

If the solution is calculated for say RG58 coax (his preference), L1 would be 2.65m, L2 0.61m, and loss in the single stub tuner is 1.58dB. 30% of the power reaching the single stub tuner is converted to heat in the tuner, system efficiency is below 70%, it is a poor solution. Very low loss cable is needed in this instance to obtain good efficiency, eg LDF4-50A would have losses of about 8%.

Nevertheless one poster explained how to set such a matching system up as follows.

That "stub" is actually two stubs, one series section transformer (L1) and one shorted parallel stub (L2). The series section transformer (L1), which carries a very high SWR, transforms the feedpoint impedance from e.g. 150-j500 ohms to e.g. 50-j300 ohms. The shorted parallel stub is inductive with a reactance equal to +j300 and neutralizes the capacitive reactance in the above 50-j300 ohm impedance thus leaving 50 ohms resistive and a 1:1 SWR on the coax to the transmitter. That is ideally how it works perfectly.

If one has an antenna analyzer, like the MFJ-259B, one can adjust L1 for a 50-jX value and then adjust L2 for a +jX value. That's why I love my MFJ-259B.

This is nonsense, the series section (L1 in Fig 6) is adjusted for an admittance looking into it of 1/50+jB, not an impedance of 50+jX as suggested. The MFJ259B does not directly read admittance (it will need to be computed for each R,X), the poster could not have ever actually performed the procedure successfully as he described, and shows a lack of understanding of how such a tuner works. (See Setting up shunt matching with an MFJ259B or the like for a practical method of adjustment of such a matching system.)

(Carr 2001,p86,87) gives an explanation of a single stub tuner which has exactly the same flawed thinking as the poster quoted above. In Fig 3-10A, he places a s/c stub of X=0+j20Ω in shunt with a load of 50-j20Ω which actually results in Z=8+j20Ω, not 50+j0 as asserted.

### L network

Another poster (QRZ 2012) offered I would use an LC network, about 4 uH series to the antenna and 10 pf across the coax. That will not work, he probably intended that the 10pF be in shunt with the feed point, which will work though a high voltage capacitor must be used. The actual values required for the modelled antenna are 14pF and 3.3µH, but note that some stray capacitance existing at the feed point will reduce the actual C needed.

### L network with TL element

Another variation on the L network is to use a TL element in place of the C, so 3.5° of 50 coax as an shunt o/c stub at the feed point, and a series coil of 3.3µH from main feed line inner conductor to the vertical's feed point. This approach avoids the need for a high voltage capacitor.

This o/c stub could be formed by telescoping a tube for the vertical radiator inside a mount tube for a short distance at the base.