Short, Coil-Loaded, Ground-Mounted, Vertical or Slanting Antennas

Author: R.J.Edwards G4FGQ © 28th November 2000

The feedpoint impedance of a short vertical antenna has a high capacitive reactance. To present a purely resistive load to the transmitter somewhere in the system there must be an inductive reactance to cancel it. All coils have a loss resistance and the question arises - where in the system can a large coil be conveniently located such that power-radiating efficiency is maximised?

Loss resistance decreases as the coil's physical size increases. There may not be sufficient room available to accommodate a large coil indoors or inside a vehicle. Locating a coil in the antenna itself poses construction problems but for a given size of coil there is always a height of coil at which efficiency is maximised. At a given frequency, other factors influencing coil height are overall antenna height and the loss resistance of the ground electrode system.

As antenna height increases, optimum coil height decreases. As antenna height approaches about 1/5th wavelength the difference in efficiency between a high and a low coil is so small the coil can be located in the most mechanically convenient place - at the bottom of the antenna. This program assists with coil design and computes the most efficient height of coil above feedpoint.

Factors Affecting radiating Efficiency

1. A design objective is to maximise the ratio of radiation resistance Rr to the sum of all the loss resistances. There are several conflicting factors.
2. As the coil is moved higher up the antenna the current is more uniformly distributed along its length and radiation resistance increases until the coil nears the top of the antenna where Rr falls rapidly to near its no-coil value.
3. As coil height increases, antenna length above the coil decreases and to maintain resonance coil inductance must be increased. This needs more turns of thinner wire and coil loss increases even though coil Q may remain unchanged.
4. Coil Q increases with physical size of coil and except for the effect of coil self-capacitance Q tends to be independent of height. But at the antenna top there is only coil self-capacitance to tune it. The internal circulating current results in high power loss in the coil and the effective series loss resistance is much increased. Antenna current reverts to a triangular distribution
5. So as height above base increases, radiation ohms initially increases faster than coil ohms but eventually coil loss predominates. This occurs well before the loading coil disassociates itself from the antenna due to the small difference between operating frequency and the coil's self resonant frequency.
6. The height at which maximum efficiency occurs also depends on ground loss resistance. If ground loss swamps coil loss then the coil can be moved further up the antenna to increase Rr but with only a small proportional effect on the total circuit resistance. Efficiency = Rr/(Rr+all other ohms) provided values have all been transformed to a common point such as the antenna feedpoint.
7. Although the loading coil tunes out the high antenna reactance to leave a low feedpoint resistance, a matching L-network for 50 ohms may still be needed and the coil in the L-network will introduce a small additional loss. If feed-point resistance is less than 50 ohms then the L-match coil will be in series with the antenna and so it can be incorporated in the antenna itself by adding a few more turns to the loading coil. The L-match fixed capacitor is then connected across the antenna feedpoint and in shunt with the coaxial feedline.

Operating Notes
The program allows coil height and other input data to be varied in small increments from the keyboard by using two adjacent up/down keys while observing radiating efficiency and other computed values of interest. See data screen menu

The ends of the coil cannot protrude beyond the top and bottom of the antenna. Height is entered as a percentage of the distance between the upper and lower possible extreme positions of the coil's midpoint. Actual height is computed.

To avoid computational problems associated with impossible coil turns and wire diameter the program will not accept overall antenna heights greater than 0.24 wavelengths. Also program modeling accuracy is poor for the effects of a self-resonant coil at the top of a nearly resonant antenna.

Coil lengths greater than 1/3 of overall height are allowed but the accuracy of computing radiating efficiency and coil turns is impaired. The program is not recommended for accurate modeling of helical antennas.

When the difference in efficiency between a coil at moderate height and a base loading coil is less than 1 dB the inconvenience, cost or fragility of a high coil may not be considered justified and the antenna can be loaded with a coil incorporated in a tuning unit located immediately at the antenna's feedpoint.

Computed coil wire diameter is for a wire diameter/winding-pitch ratio of 0.66. This is not a critical value and may be between 0.6 and 0.72 or to the nearest wire gauge. Close wound coils of enameled (magnet) wire are not recommended.

When an antenna is mounted on a road vehicle the vehicle itself forms part of the radiating system which is coupled to ground via capacitance. Ground losses may be small but the additional feedpoint reactance may need tuning out with a few more turns on the coil than the computed number. Or simply adjust length of the antenna top section for resonance in the required frequency band.

Ground Loss Resistance - Crude Guesstimates
The most uncertain of the program's input data is ground loss resistance. The best way to determine it is to erect a 1/4-wave resonant antenna and measure feedpoint resistance. Then use the program to vary ground loss resistance till measured and computed feedpoint resistances are equal.

Loss resistance of vehicle roof-mounted antennas varies between 2 and 12 ohms, being greater for small vehicles. But surface soil resistivity has an effect.

A shallow-buried circular close-mesh mat has a loss resistance not less than 0.5*(Soil Resistivity)/(Mat Diameter in metres) ohms. The table below is for a soil resistivity of 100 ohm-metres = 10 mS. N = Number of shallow-buried 12- gauge radials. Length is in metres. Ohms = resistance-to-ground at the focus.

N		Len	Ohms		Len	Ohms		Len	Ohms		Len	Ohms		Len	Ohms
4		2	28		3	20		4	15		6	11		12	6
8		2	20		3	14		4	11		6	8		12	4
16		2	17		3	11		4	9		6	6		12	3
32		2	14		3	10		4	8		6	5		12	3
64		2	14		3	9		4	7		6	5		12	2
128		2	13		3	9		4	7		6	4		12	2

Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link LoadCoil then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.

Discuss, debate and ask questions about short, coil-loaded, ground-mounted, vertical or slanting antennas in the Ham Radio Technical Forum.