# Coil-Loaded Vertical Antennas Operating in Quarter-Wave Resonance

Author: R.J.Edwards G4FGQ © 1st January 1998Coil-loaded antennas are constructed from three contiguous cylindrical sections: mast, coil and rod; the length and diameter of each part being set by the experimenter. This program computes the number of loading-coil turns needed for a given resonant frequency.

The proportional height of the coil can be adjusted by changing lengths of the mast and rod while keeping their sum constant. A lumped loading coil may be a short, fat, single-layer solenoid. When the lengths of both the mast and rod are set to zero and the coil is long and narrow, a simple helical antenna results. If the sum of the three sections equals a free-space quarter-wavelength, then the number of coil turns will be zero and a simple quarter-wave vertical results.

The program input data consists of six cylindrical dimensions, the coil wire diameter, the earth connection loss resistance, the operating frequency and the feed-line impedance. The length or height must be stated in metres. All diametersmust be given in millimetres. Take particular care when entering the coil dimensions.

When an impossible condition arises, such as a wire diameter being greater than the winding pitch, a warning is issued. Also, if the overall height exceeds a quarter-wavelength, the coil would have to be replaced by a capacitor to maintain resonance. Enter all menu selections and input data on bottom line against the cursor.

When a warning message is present on the screen the computed results are not valid and will remain so until the condition is corrected.

The results include inductor and capacitor values of an L-network to match the feed-point input resistance to the transmission line impedance. The antenna tuning unit (ATU) inductor is always connected directly between the feed-point and transmission line. The capacitor is always connected in parallel with the higher of the two impedances.

RF input power is dissipated in five resistances: the earth connection, the coil, the mast, the rod, and the radiation resisitance which are each distributed throughout various parts of the system. The program transforms these losses to a common point, *the feed-point*, such that their sum is then equal to the resonant input resistance. The experimenter can see immediately from the resistance values what will happen to the input power and make appropriate changes.

The greatest source of error in the analysis will be uncertainty in the ground connection resistance. If an experimenter has no idea what the earth loss is, an accurate value is obtained by measuring an actual antenna input resistance at resonance and subtracting the computed antenna components. Measurements can be made at the quarter-wavelength resonant frequency of any random length of wire plus a bottom-end loading coil. Soil characteristics do not change rapidly vs. frequency.

Check carefully that all input data is correct before relying on the program output data.

A crude estimate of the ground connection resistance for a vertical antenna may be obtained from the following examples assuming ordinary garden/pastoral soil with a typical resistivity of 100 ohm-metres,:

- Sixteen buried radial wires, 10-metres long, 2-mm dia, 100-mm depth: 4 ohms
- One, 10-metre long radial wire, 2-mm dia, 100-mm depth: 20 ohms
- One buried square plate with 1-metre sides: 20 ohms
- One earthing rod or spike, one metre deep, 25-mm dia: 80 ohms
- A square, coarse, wire-mesh mat each side equal to S-metres: 50/S ohms

For moist, highly-fertile soils, divide the above figures by three. For dry sandy rocky soils, multiply them by four. It will be seen, for a given amount of copper or aluminium in the ground, it is most efficiently buried in the form of wire. Two earth electrodes in parallel do not behave as such unless spaced apart by at least twice their longest linear dimension. If this electrode pair is considered as one, then another pair of electrodes would need to be spaced even further apart to be fully effective if all four are connected in parallel.

Earth loss resistance for a short antenna mounted in the centre of a car roof will usually be between 4 and 12 ohms, being smallest for shorter antennas and larger cars.

An ohm-metre is the resistance between the opposite faces of a 1-metre cube.

Restrictions on Program Input Data

- Lengths and diameters of masts and rods: not less than 1 mm
- Length of coil: not less than 25 mm
- Diameter of coil: not less than 25 mm
- Diameter of wire on coil: not less than 0.01 mm
- Frequency: not less than 50 kilohertz

Program Limitations

The computed coil data will not be reliable when placing a short loading coil immediately at the top of a tall antenna without a capacitance loading rod above it. This arises for the same reason as a problem will arise in practice. The capacitance associated with the coil is mainly its own self-capacitance and, in almost parallel self-resonance, it will draw so little current up the mast there will be no point in having it.

Note that the overall efficiency can be improved by placing a loading coil higher up the antenna only when the earth loss resistance is several times greater than that of a bottom-end loading-coil. This is because the coil resistance increases faster than radiation resistance as coil height increases.

For minimum values, enter zero. The program will do what else is necessary.

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 VertLoad 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.

Search other ham radio sites with Ham Radio Search