Antenna Design
Antenna Design Software

# End-Fed Antennas, Ground Systems, Tuning & Matching

Author: R.J.Edwards G4FGQ © 21st June 1998

This program models a wide range of end-fed antennas used with a ground system of radial wires. For each model the inductance and capacitance values of three alternative impedance matching networks are computed to match to a 50-ohm line. Results include RF power losses in the principal parts of the radiating system and overall radiating efficiency. The input impedance of the ground electrode is estimated.

Antennas are defined in terms of height H of the vertical section, length L of the horizontal section, and conductor diameter. The length S of a heavy wire or strap between the antenna feedpoint and ground radials is also allowed for. Natural resonant frequencies depend on the overall length H + L + S. When L = 0 and S = 0 a simple vertical results. A sloping wire is simulated when H = average height of the sloping section and L is adjusted such that the sum of H + L + S is always equal to the actual overall length.

The ground electrode system is defined by a number of shallow-buried bare wires radiating from a common connection not necessarily near the antenna feedpoint. Other systems of ground rods and plates behave similarly provided appropriate dimensions are entered into the program. The effects of various soil conditions on feedpoint impedance and radiating efficiency is included in the model.

A System of Buried, Copper or Aluminium, Uninsulated, Radial Wires
The program requires the length, diameter and number of radials to be entered. Other types of electrodes can be approximated in that form. E.g., a single earth rod may be described as a radial of length equal to the depth of the rod and of the same diameter. A number N of spaced rods are equivalent to N radials. When rods are not all of the same dimensions enter averages. If a connecting wire to a rod is shallow-buried then add its length to that of the rod. A metal water supply pipe may be used as a radial but its effective length in damp soil will be only 5 to 10% of the free-space wavelength and unrelated to actual length.

A thin rectangular plate is equivalent to a cylinder with a length equal to the plate's diagonal and a diameter equal to half of the plate's shorter side. This equivalence applies also to radials formed from long flat strips which are more economical in the amount of metal used than solid circular conductors.

Radials are assumed to be at a depth of 200mm = 8". But input Z is insensitive to depth changes. Zin is also insensitive to non-uniform radials distribution. The case of N radials being distributed only over a semi-circle may be compensated by entering 0.7N radials into the program. The most important dimension of an electrode is length. When considering equivalent electrodes, directions and depths may be changed but not lengths. Inaccurate estimation of the ground system parameters will not very seriously affect computed Tx performance.

Soil Characteristics in Vicinity of the Antenna
The electrical behaviour of soil depends on two parameters:- Resistivity R and Relative Permittivity K. Resistivity in ohm-metres is the resistance between opposite faces of a 1-metre cube of the material. Sometimes soil is defined in terms of its conductivity in Siemens. Capacitance between opposite faces of the cube is 8.83*K pico-F in parallel with R. So soil impedance decreases as frequency increases - and so does the all-important equivalent series loss resistance.

The program user selects a type of ground or soil from the following list:

Type of Ground or SoilRK
Salt Sea Water away from fresh-water river estuaries0.2281
Very Good: damp, highly fertile loam as in agricultural plains3020
Average: some clay perhaps, but gardens, parks, lawns, trees10015
Poor: sandy, but rainfall, weeds, flowers, hardy grasses30012
Fresh Water Lakes: deep, unpolluted, slow flowing, fish, weeds90080

Alternatively, if resistivity and permittivity are known, they may be entered directly.

Percentage moisture content and dissolved salts are the principal affecting factors. An arid sand desert with negligible rainfall and sparse vegetation may have R = 30,000 ohm-metres or more and K = 3. This program does not cater for such extreme conditions where a different type of antenna would be used.

Feedpoint Input Impedance and Series Tuning Component
Feedpoint impedance is shown as a resistance R in series with a reactance jX ohms. It is the sum of the antenna and ground electrode input impedances as modified by the length of the grounding strap. The latter is treated as a low-loss single-wire transmission line.

The computed value of a series tuning component, L or C, when used to cancel jX will change feedpoint impedance to a pure resistance of R ohms. If overall antenna length is such that R lies between 35 and 65 ohms, a more complicated antenna tuning network may be unnecessary. The T and L-networks are designed on the assumption that this series tuning component is omitted.

T-Network Antenna Tuning/Matching Unit
In the T-match network the central component is always a shunt inductance with its lower end grounded. It need not be continuously variable but may require switching to a different value for each frequency band. The component in series with the 50-ohm coax from the transmitter is always a capacitor. It should be continuously variable. The program automatically sets the shunt inductance to a value which ensures this capacitor does not exceed 300 pF on any band. The component at the antenna-end may be either a capacitor or a coil. If a capacitor then its value will not exceed 300 pF either. The C's can be a matched pair.

Two Alternative L-Network Antenna Tuning/Matching Units
Each of these networks has two components, two L's, or two C's, or one of each. Either network will transform the complex feedpoint Zin to a pure resistance of 50 ohms. A choice may be made on the basis of mechanical or electrical convenience. When L networks consist of a coil and a capacitor, either the low-pass or high-pass configuration may be selected as being the more desirable option.

Computed component values of a network are displayed in 2 of 3 positions on one line of the screen. The centre value is always the series component connected directly between the 50-ohm line and antenna terminals. The circuit location of the shunt component (with one end grounded) is indicated by the position along the line of its computed value. The unused circuit position is always blank.

Performance of a Buried Radial Wire System
The DC input resistance of a system is useful as a periodic maintenance check. Or if the DC resistance has been measured, the program may be inverted and used to estimate local soil conductivity. Radials behave as very lossy transmission lines at RF. Propagation velocity is only a fraction its free-space value and there is little to be gained by making radials longer than 12/Sqrt(MHz) metres in good soil. The objective is a low value of RF input resistance which is easier achieved by having more radials rather than by increasing their length.

Radiated RF power is assumed to be all that is not dissipated within the near field of the antenna system, regardless of direction and ray elevation angle. Power lost in the near field is apportioned percentage-wise between components.

ATU loss is computed for the T-network because it always contains a coil in which nearly all ATU losses occur. The L-networks may contain only capacitors. The ATU coil Q is assumed to be 300 - a typical value for a good quality unit. Copper wire is assumed for antenna conductor loss. If aluminium wire is used the difference will be negligible. If a vertical antenna is a self-supporting metal tube or angle, enter in the program its equivalent diameter given by 1/3 of its overall perimeter. Conductor loss will be small whatever the material.

Losses in the soil in the vicinity of the antenna are assumed to consist of two independent components. The first is always present and is the power dissipated in the ground electrode input resistance. Input reactance is immaterial and is is tuned out simultaneously with antenna reactance.

The second soil loss component occurs when a short vertical wire is extended horizontally. Due to the mutual impedance between wire and ground a current is induced in the resistive soil. Antenna feedpoint impedance is also affected. With long, low, inverted-L antennas, most of the loss may occur in this manner.

Length of Grounding Strap between Antenna Feedpoint and Ground Electrode
Although highly desirable it is frequently inconvenient, sometimes impossible to keep this important grounding strap very short. Its input impedance when terminated by the ground electrode is in series with the antenna insofar as the matching/tuning networks are concerned. Its conductor resistance will be very low and power loss will negligible. But depending on length and height above ground, indoors or outdoors, it will contribute to the total power radiated.

The program treats the strap as a low-loss transmission line and requires only its length to be entered. To estimate its radiation contribution it is assumed the effective height of the whole antenna above ground is increased by half of the length of the strap and this allows for the strap to be sloping. It usually will be. The program user should NOT attempt to compensate for this by changing any conductor lengths, H, L or S. An increase in program complexity to include more details in the model would not significantly improve overall accuracy.

A common arrangement is an inverted-L antenna wire with the transmitter and ATU in a room on the first floor. A number of radials, rods or plates terminate at a common point in the garden near the bottom of an outside wall. A single heavy conductor extends the ground connection up to the ATU and other equipment. If the length of this strap is less than 1/20-wavelength computed results will be sufficiently accurate for station planning purposes.