# Relationship between radiation efficiency and minimum VSWR for common short helically loaded verticals

For clarity, $${RadiationEfficiency}=\frac{FarFieldPower}{InputPower}$$.

Such antennas are often advertised with a “minimum VSWR” or “VSWR at resonance” figure, but rarely show gain figures. One might wryly make the observation that that is how one might sell dummy loads rather than antennas.

Well, these things do radiate, so they are not very good dummy loads. Lets explore a theoretical example on the 40m band to inform  thinking.

Above is a NEC5.2 model of a vertical on a wagon roof.

Key parameters are:

• 7MHz;
• unloaded 1.2m lossless whip in centre of wagon roof;
• lossless vehicle body structure; and
• real ground (σ=0.005, εr=13).

Key model results:

• average power gain=0.313 (-5dB);
• maximum power gain=-3.5dB;
• resistance component at the feedpoint = 1.7Ω;
• Radiation Resistance (Rr) calculated as 0.53Ω.

Such an antenna is not suited to be directly connected to the transmitter using 50Ω coax.

Loading the antenna ‘cancels’ the substantial capacitive reactance of the short antenna, introduces some loss resistance in the helix conductor, and changes the current distribution which increases Rr.

We might expect that with continuous helical loading, the Rr component might be nearly doubled, lets assume 1.0Ω.

If we make an assumption that the specified minimum VSWR (ie at resonance) for a very short antenna implies a feed point resistance lower than 50Ω and therefore $$R_t=\frac{50}{{VSWR}_{min}}$$.

Above is a plot of calculated Radiation Efficiency against minimum VSWR where Rr=1Ω.

Readers will not that the lower the specified minimum VSWR, the lower the Radiation Efficiency… because a lossier helix is used to increase the feed point resistance and so improve VSWR.

So, if such an antenna had minimum VSWR of 1.5 (as commonly specified), Radiation Efficiency is 3.0% or -15.2dB.

We can then adjust the lossless gain model for expected structure loss, so $$G_{max}=-3.5-15.2= -18.7 \text{ dB}$$.

Above, calculated feed point resistance is decomposed into three components:

• Rr;
• Rg (ground loss);
• and Rloss (structure loss, helix wire loss resistance).

This type of antenna is often intended to be directly connected to the transmitter using 50Ω coax. The are usually best optimised simply by adjustment of the vertical length to achieve minimum VSWR at the desired operating frequency.

## More generally

We can generalise this solution to the wider range of electrically short helically loaded verticals with specified VSWR at resonance.

Above is the same chart with a family of curves for different value of Rr.

## Delivering the rated load to the transmitter

Most modern transmitters are rated for a maximum load VSWR50, often between 1.5 and 2.0. That is not to say they deliver rated power into such a load, but that it is safe to use.

So, depending on the antenna specification, it might suit the transmitter, albeit over a quite narrow bandwidth. It is often overlooked that an antenna with minimum VSWR=1.5 might only suit a transmitter requiring maximum VSWR=1.5 at just one frequency, not very practical. Minimum VSWR is not the same as saying VSWR<x over some given / useful bandwidth.

The actual power obtained from the transmitter is not easily predicted for arbitrary loads. Measure forward and reflected power with a good directional wattmeter and calculate $$P=P_{fwd}-P_{ref}$$.

Higher efficiency helical verticals may need some additional impedance transformation to adapt a higher load VSWR to the transmitter.

## An approach to impedance matching

Looking for the resonance point is going to be located at the point where reactance is closest to Zero and not where SWR is at it’s lowest. I look for Zero reactance on the Smith chart. Set you resonance in the center of your operating range then match the impedance with a transformer like the MFJ-907.

On the surface, this might look like ham homage to the resonant antennas thing though from the context of the discussion resonance appears to be being observed looking into the feedline which is not necessarily the same as radiator resonance.

But look more closely at the reference to the MFJ-907. It is a tapped transformer intended to transform a resistive load less than 50Ω to 50Ω to suit the transmitter… so it needs a resistive load and hence this poster’s method of setting X=0 at the point where the transformer is deployed.

This of course may require shifting the antenna resonance well away from the operating frequency due to the transformation on the feed line section, and possibly beyond the range of the antenna adjustment. This method will tend to work better if the MFJ-907 is very close to the feed point, but that may not be practical for many roof mount scenarios (such as described above).

## A sanity check

The results given here are quite consistent with measurement of a real 1.5m helical vertical and calculation of radiation efficiency from field strength measurements, see Field strength survey of an M40-1 short helical vertical on 40m .

## Disturbing the thing being measured – coax line

Keep in mind that the most relevant VSWR measurement from the view of the transmitter is that at the transmitter.

Remember the possible common mode current path, see Disturbing the thing being measured – coax line.

## Conclusions

Helically loaded short vertical antennas are popular because many can be directly connected to a transmitter using 50Ω coax without further impedance matching, albeit with degraded radiation efficiency and narrow bandwidth.

Optimisation of the simple configurations where the feed point is directly connected to the transmitter using 50Ω coax is simple, tune for minimum VSWR at the desired operating frequency.

Other configurations use more complex matching schemes and adjustment depends on the method used.