RF balanced transmission lines behaviour in a progressive wave regime

Errante's apparatus
for the physics of the balanced transmission lines for radio frequency signals.

The apparatus and the measurement method presented hereby permit to analyze the electric behaviour of balanced transmission lines for radio frequency electric segnals in a progressive wave regime and in particular have the purpose of:

a) demonstrating that the balanced transmission lines are aperiodic;

b) demonstrating that the balanced transmission lines can be converted into unbalanced ones and viceversa, an infinite number of times;

c) demonstrating that it is always possible to generate a virtual ground node at any point of any transmission line;

d) demonstrating that the balanced transmission lines, when perfectly matched, both to the signal source and to the load, DO NOT originate hertzian radiation. II^nd Errante's law.

The balanced transmission lines for radio frequency electric signals are generally formed omogeneously by two identical unshielded electrical conductors running parallel to each other but can also be formed by a larger number of conductors, being them open wires or shielded cables.

A transmission line for electric signals is electrically balanced when it does not intervene to modify the phase difference between the currents traveling on it.
In order for that to be possible it is necessary that all the line's conductors be identical to each other and that the line it-self be perfectly matched both on its input and output ports. That means that the characteristic impedance of the line must be equal to the impedance of the radio frequency signal source and to the impedance of the load, being it reactive or non-inductive. A correctly matched transmission line, when being runned, is in a progressive wave regime and the energy transfer to the load is maximum with no hertzian radiation being originated.

Wherever the transmission line runs at a close proximity of the ground, it is also necessary for its conductors to be equally spaced away from it, in order to keep their capacitive coupling constant to the ground it-self.
If the interaxial distance between the line's conductors is kept constant, decreasing the line distance from the ground, the line's own characteristic impedance decreases accordingly. This is due to the line's conductors capacitive coupling to the ground, this capacitance adds to the the parasitic electrical capacitance between the line's conductors, which is always present.
Balanced transmission lines, if properly isolated, can run along the ground surface or can even be buried underground. In those cases, the close capacitive coupling between the line's conductors and the ground makes the parasitic electrical capacitance between the line's conductors neglectable, to the point that they no longer need to run parallel to each other. However, they still need to be identical to each other, unless they are ment to form an asymmetric balanced line.

Electrically balanced transmission lines can also be geometrically and electrically asymmetric.
An asymmetric balanced line is so defined: "a balanced transmission line for electric signals is asymmetric when it does not intervene to modify the phase difference between the currents traveling on it and it is formed by electrical conductors which do not exhibit the same impedance value with respect to the physical ground or to a virtual groung node. Copyright 2008 Francesco Errante.

Close coupling between the line's conductors and the ground, however, confines the usage of lines running along the ground or underground to low and medium power systems, where voltages involved do not require a great deal of insulation.
With the advancement of the technology for radioelectric constuctions, the coaxial cable unbalanced lines have, progressively, taken the place of the balanced transmission lines in the majority of the applications, except for the very high power ones.

Right from the outset of radio engineering, the most recurrent case of usage of a balanced transmission line is represented by its employment in the feeding of the half a wave length folded dipole antenna. This because, a 300 Ohm balanced transmission line adds ease of construction to the folded dipole's useful properties. (The same can be said for the multiple-wire folded dipoles that have characteristic impedance multiple of the 300 Ohm)

Rough observations made without any scientific rigor and the fact that it is much too easy to feed an half a wave length folded dipole with a a stretch of a 300 Ohm balanced transmission line has led everyone, untill now, to erroneously desuming and/or accepting that balanced transmission lines were them-selves resonant and, therefore, that it was necessary to neutralize their effects by lengthening or shortening them. This desumption is false! Ernst Lecher's experiment erroneous interpretation has done the rest in spreading this misconseption. Lecher's line, infact, shows the electric behaviour of a two-wire line in a standing wave regime and its employment is, instead, of no use in measuring electric wavelengths if the line is in a progressive wave regime (VSWR = 1:1).

The instrumental illusion that balanced lines be resonant is given by the fact that, when a folded dipole is directly fed by a two-wire line, there is no clear cut border between the dipole it-self and the stretch of the bifilar line, therefore, the electric signals will travel on a path which varies with the transmission line length, with the result that the point of resonance of the whole system will move ciclically.

The truth is that, if in a system being formed by a balanced signal source, a balanced line and a radiator, the reactive load gets substituted by a non-inductive load of equal impedance (dummy load) or by a perfectly matched reactive load, the illusion that the balanced line be resonant disappears and the system returns to showing it-self as being aperiodic, as demonstrated in the experimental verifications pictured below:

A step-by-step sequence of all the measurements taken, along with their results is shown here below:

These measurements, with the proper equipment, can be carried out in three different ways:

1) by keeping constant the test signal wavelength while varying the physical length of the balanced line;
2) by keeping constant the physical length of the balanced line while varying the test signal wavelength;
3) by systematically varying both the physical length of the balanced line and the test signal wavelength.

The second method is a great deal more convenient and faster than the others, so that, a 300 Ohm balanced line of a fixed physical length has been used and reflected energy measurements have been taken while varying the test signal wavelength.

Moreover, it should be noted that these measurements can be carried out on any spectrum of radio frequencies, but it is most convenient to perform them on the shortwaves spectrum as they give, amongst other benefits, a larger wavelength excursion for the same frequency span. All the measurements results, therefore, can be extended to the whole spectrum of the radio waves.

NB: all the devices here employed for the obtainement of virtual ground nodes provide a clear cut border for the RF signals between lines and radiators as well as lines and lines, while always offering a total galvanic continuity among all the circuits connected to them, ensuring a solid common ground path, which can, if necessary, connected to the physical ground. See also: A virtual ground node generator for unbalanced lines