# Input Impedance of Inverted-L, Vertical & Dipole Antennas

Author: R.J.Edwards G4FGQ © 10th June 2006Radio amateurs often begin and very often remain with simple wire antennas. The most important characteristic of a simple antenna is its input or feedpoint impedance, Zin. Zin may need to be transformed in some way to be connected to the transmitter and/or receiver. Transmitters prefer to be loaded with a pure resistance of about 50 ohms. The input impedance of receivers is usually around 50 ohms. However, 50 ohms is an arbitrary standard and does not always apply.

Antenna Zin varies widely with wire length and frequency. It is measured as Zin = Rin+jXin, where Rin is the series resistive component and jXin is the series reactive component. The sign of jXin may be either +ve or -ve. When the sign is +ve the antenna can be tuned to a pure resistance with a variable capacitor. When the sign of jXin is negative the antenna can be tuned with a variable or fixed inductance or coil. The effect of tuning changes Zin to to a pure resistance equal to Rin. Although Rin may not be equal to the 50 ohms needed by the transmitter it is at least purely resistive. Varying antenna wire lengths and/or frequency changes feedpoint Resistance.

This program models an inverted-L, end-fed, antenna which includes a connecting wire to ground. It is a very common arrangement. From the feedpoint there is a vertical wire. From the top of the vertical wire there is a horizontal wire. From the ground side of the feedpoint there is a grounding wire which can be assumed to be vertical. The ground wire radiates. It is part of the radiating system. Lengths of all three wire sections can be varied in terms of metres and free-space wavelengths. Free-space wavelength = 300/F metres, with F in MHz.

In addition to an inverted-L, other antenna configurations can be chosen. By setting the length of the horizontal top section to zero, we have a purely vertical antenna with a zero length or longer connection to ground.

If the ground connection is removed by increasing the ground loss resistance to 1 Megohm or greater, depending on frequency the length of the ground wire can then form the lower half of a vertical half-wave dipole.

When the vertical and ground wires are of unequal lengths we have an off-centre-fed dipole which can be considered to be either vertical or horizontal.

The resonant frequencies of all antenna configurations can be found by varying frequency, fast and slow, until the reactance jX of the antenna feedpoint impedance is very near or equal to zero.

Or the frequency can be left fixed and resonance found by varying the lengths of antenna wires. Fine adjustments can be made by slowly varying frequency.

When feedpoint reactance is -ve without the coil, resonance can be achieved by varying the number of turns on the loading coil. The act of varying the number of turns greater than 1 turn connects the coil in circuit. Adjust coil dimensions to allow a suitable, practical, gauge of wire to be wound on the coil.

When feedpoint reactance is +ve, resonance can be achieved by setting a variable capacitor to the computed value which will neutralise +Xin. The program does not allow the loading capacitor actually to be connected in circuit. You will have to use your imagination.

Whether the feedpoint reactance has a +ve or -ve sign depends on the overall length of the antenna + grounding wire as measured in wavelengths. If overall length of the wire is less than 1/4-wavelength then a loading coil will be needed for resonance. If the overall length of wire is between 1/4 and 1/2 wavelengths then a series loading capacitance will be needed. Between 1/2 and 3/4 wavelengths a coil will again be needed ... and so on.

This program, in addition to its practical value of calculating feedpoint impedance, also will be of educational value to newcomers to amateur radio.

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