Antenna Factor of short tuned vertical with concentrated loading

This is a simple calculator to estimate the Antenna Factor of a short (< 0.25λ) vertical tuned with a concentrated inductor placed along its length, and installed over ground.

Antenna Factor is the ratio of the incident electromagnetic electric field strength to the voltage at the receiver input terminals.

Title:

Height from base to centre of short loading coil (m)
Height from centre of short loading coil to tip (m)
Frequency (MHz)
Termination loss (dB)

Example 1: A centre loaded whip for 7MHz has a loading coil 1.6m above the base, and a whip section of 1.4m above the loading coil. Termination loss is 6dB. The estimated Antenna Factor is -1.11dB.

Assumptions

The calculator assumes:

  1. the loading coil is of zero length;
  2. the current distribution below the loading coil is cosine in  form;
  3. the current tapers linearly from the loading coil to zero at the tip;
  4. no matching networks or transformers are used;
  5. the vertical is mounted at ground level; and
  6. no ground reflection effect.

The Termination loss reflects the loading effect of the receiver on the open circuit voltage induced in the antenna. Typical values will be close to 6dB, since the source impedance of most practical verticals of this type will be close to 50Ω (radiation resistance, conductor and inductor loss resistances, and earth resistance). A more accurate estimate for a resonant antenna (where load resistance is less than 50 ohms) could be made as Termination loss = 20*log(1+1/VSWR) where VSWR is the measured antenna VSWR.

Verticals loaded with a capacity hat will violate assumption 3 to some extent, and this model would underestimate the Antenna Factor by an amount depending on the contribution of the capacity hat.

A continuously or helically loaded vertical is complex to describe and model. Helices will not comply with assumptions 1, 2, and 3. A common design objective of a helically loaded vertical is higher radiation resistance achieved by a higher current moment, which would have the effect of increasing the Antenna Factor compared a centre loaded vertical of the same height. Common short resonant helices will have an Antenna Factor somewhat similar to that of a centre loaded vertical of the same overall length, possibly a little higher, dependent on the actual implementation.

Vehicle mounted antennas will violate assumption 5 to some extent, especially where the mounting is asymmetric such as low bumper mounted antennas near to bodywork. Results may be a good guide for verticals mounted symmetrically in the clear on a vehicle roof.

There is a relationship between antenna gain and antenna factor for a lossless impedance matched antenna. That relationship does not apply to a lossy short tuned vertical with concentrated loading, so this calculator should not be used to infer gain of an antenna.

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