Equivalent circuit of an antenna system

Common practice is to treat antenna systems as a two terminal device in free space.

Pickup most handbooks, and even text books, and antennas and often antenna systems are described in this way.

That model is quite inadequate for many or most antenna systems installed in proximity of natural ground. For example, a two terminal dipole and feed line system representation cannot have feed line common mode current, and it follows that thinking in terms of two terminal models denies a full understanding of the antenna system.

A three terminal model of an antenna system

(Schmidt nd) sets out a three terminal model of an antenna system in presence of ground using quite conventional linear circuit theory.

Above is Schmidt’s Y network based on values of three intermediate impedances, ZD, ZU, and ZC. These are found from measured values Za, Zb and ZC as explained by Schmidt:

I measure ZC by connecting both leads of the twinlead together and measuring the impedance to ground. Next I connect wire 2 to ground and measure the impedance between wire 1 and ground and call this Za. Reversing the connections, by grounding wire 1 and measuring between wire 2 and ground gives Zb.

Measurements

An adapter was used to allow measurement of Zz, ab, and Zc reported below. Above, it is attached to a FA-VA5 antenna analyser… the worst instrument I have ever used, but never mind, it might get fixed with firmware updates over the coming years… though experience says that is probably wishful thinking.

Examples

G5RV Inverted V with 10m of open wire feed line at 7.1MHz

The antenna system is a reasonably symmetric Inverted V configuration of the G5RV with tuned feeders, where the feed line to the point of measurement is 10m of 560Ω open wire line.

Above are the direct measured values and calculated results.

The calculations are a bit tedious, a handy online calculator can perform them more conveniently.

The unbalance impedance Zu is not trivial, though the real component is small, the imaginary component is significant suggesting that although the wires are symmetric, there is some asymmetry perhaps due to ground height variation, soil type, soil water content, vegetation etc.

G5RV Inverted V with 10m of open wire feed line at 3.6MHz

The antenna system is a reasonably symmetric Inverted V configuration of the G5RV with tuned feeders, where the feed line to the point of measurement is 10m of 560Ω open wire line.

Above are the direct measured values and calculated results.

The unbalance impedance Zu is not trivial, and worse that the previous case. again a significant imaginary component suggesting that although the wires are symmetric, there is some asymmetry perhaps due to ground height variation, soil type, soil water content, vegetation etc.

Using the measured / calculated values

Readers will often see back of the envelope calculations of the effectiveness of a common mode choke. The article Using Ohms law on antenna baluns deals with some of the junk science that masquerades as fact. Some back of the envelope analyses assume the common mode driving voltage is that of a 50Ω unbalanced source, and the load is simply a common mode choke whereas if an ATU is between the 50Ω point and feed line, voltages and currents are transformed, the series common mode impedance of the ATU and any balun(s) are relevant as is ZC of the antenna system as measured above.

To obtain valid results, the model must be valid, and that starts with including all of the elements that are relevant. Such a model can give a good prediction of the impact of a common mode choke of known Zcm at the point at which the measurements were made.

Such models are complex, and mathematical (high school maths + complex numbers), but solvable with the requisite knowledge.

A simpler approach is to simply directly measure the common mode current, and try common mode chokes with high Zcm to reduce it to an acceptable level. In most cases, the priority in addressing high common mode current is to examine the root cause, can the system symmetry be improved?

Links / references