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

Foreword: although when referring to balanced transmission lines our thougth goes to a pair of identical electrical conductors beign parallel to each other, commonly known as a "bifilar line" , it must be said that balanced transmission lines can also be formed by any even number of conductors carrying the same number of currents in a multi-phases arrangement. (Poly-phase currents arrangement were first introduced in the electrical engineering by Nikola Tesla)
Balanced transmission lines can be either symmetric or asymmetric.

Francesco Errante

Definition of a balanced transmission line:   "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 and each and every of its conductors transfer the same amount of energy per time unit (power)."

Francesco Errante

Definition of a symmetric balanced transmission line:   "an electrically balanced transmission line for electric signals is symmetric when it is formed by electrical conductors which exhibit the same impedance value with respect to the physical ground or to a virtual ground node."

Francesco Errante

Definition of an asymmetric balanced transmission line: "an electrically balanced transmission line for electric signals is asymmetric when it is formed by electrical conductors which DO NOT exhibit the same impedance value with respect to the physical ground or to a virtual ground node."

Francesco Errante

Ist Errante's principle for the transmission lines:   "a transmission line for radioelectric signals, being it balanced or unbalanced, when in a progressive wave regime, is always aperiodic."

Francesco Errante

IInd Errante's principle for the transmission lines: "any transmission line for radioelectric signals, may be converted from being a balanced one to an unbalanced one and viceversa, an infinite number of times."

Francesco Errante

IIIrd Errante's principle for the transmission lines: "it is always possible to generate a virtual ground node anywhere along a transmission line for radioelectric signals ."

Francesco Errante

IInd Errante's law applied to the transmission lines "a transmission line for radioelectric signals, being it balanced or unbalanced, when in a progressive wave regime, does not originate hertzian radiation."

Francesco Errante

 

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.  IInd Errante's law.

 

Errante's balanced-to-balanced measurement test set being checked for frequency response flatness
S.W.R. measurement on a 300 Ohm balanced transmission line terminated onto a 300 Ohm reactive balanced load
Errante's 300/300 Ohm balanced virtual ground node generator being checked for frequency response flatness

 

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.  

VIRTUAL GROUND HF MONOPOLE ANTENNA - Antenna Errante

An example of an electrically balanced line employing a pair of individually shielded coaxial cables(7) - Copyright © 2003- Francesco Errante

 

Errante's capacitive RF earth grounding system applied to the RF transmission line

Errante's ONE-WIRE UNBALANCED RF TRANSMISSION LINE, employing Errante's CAPACITIVE RF EARTH GROUNDING SYSTEM - Copyright © 2009 - Francesco Errante

 

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

Experimental verification of the balanced lines aperiodic behaviour, when in a progressive wave regime

PRELIMINARY OPERATION: the balanced-to-balanced measurement network is tested for frequency response flatness within the test spectrum.

the balanced-to-balanced measurement network is tested for frequency response flatness within the test spectrum

From left to the right: 50 Ohm co-axial TX line - S.W.R. probe - 50/300 Ohm BalUn - short stretch of a symmetric bifilar transmission line - 300/50 Ohm BalUn - 50 Ohm dummy load.
Test Freq.: from 1,8 to 30 MHz in 100 KHz steps
RF power : 1 KW cw
Measured S.W.R.:   1:1   over the whole spectrum
Result: OK! The network exhibits a flat response over the whole test frequency spectrum.


 

Network analysis of a 300 Ohm balanced line, fed by a 300 Ohm balanced signal source, terminated on a 300 Ohm dummy load.

Network analysis of a 300 Ohm balanced line, fed by a 300 Ohm balanced signal source, terminated on a 300 Ohm dummy load

From left to the right: 50/300 Ohm BalUn - a random (4 m ca.) stretch of a 300 Ohm symmetric bifilar transmission line - a 300 Ohm dummy load.
Test Freq.: from 1,8 to 30 MHz in 100 KHz steps
RF power : 1 KW cw
Measured S.W.R.:   1:1   over the whole spectrum
Result: the line shows an aperiodic behaviour over the whole test frequency spectrum. The line aperiodic behaviour is VERIFIED.
N.B. All the measurements have been repeated with the line being held up in the air.


 

The line shows the same aperiodic behaviour as in the previous test, even if it is terminated on a non-radiating reactive load (Errante's BalUn and a dummy load) as shown below:

Network analysis of a 300 Ohm balanced line, fed by a 300 Ohm balanced signal source, terminated on a 300/50 Ohm BalUn and a dummy load.

Network analysis of a 300 Ohm balanced line, fed by a 300 Ohm balanced signal source, terminated on a 300/50 Ohm BalUn and a dummy load

From left to the right: 50 Ohm co-axial TX line - S.W.R. probe - 50/300 Ohm BalUn - a random (4 m ca.) stretch of a 300 Ohm symmetric bifilar transmission line - 300/50 Ohm BalUn - 50 Ohm dummy load.
Test Freq.: from 1,8 to 30 MHz in 100 KHz steps
RF power : 1 KW cw
Measured S.W.R.:   1:1   over the whole spectrum
Result: the line shows an aperiodic behaviour over the whole test frequency spectrum. The line aperiodic behaviour is VERIFIED.
N.B. All the measurements have been repeated with the line being held up in the air.


 

The line, again, shows the same aperiodic behaviour as in the previous tests, even if it is terminated on a dummy load through a reactive RF network as shown below:

Network analysis of a 300 Ohm balanced line de-coupled from a non-reactive non-radiating load (300 Ohm dummy load) by means of a 300/300 Ohm Errante's balanced virtual ground node generator.

Network analysis of a 300 Ohm balanced line de-coupled from a non-reactive non-radiating load (300 Ohm dummy load) by means of a 300/300 Ohm Errante's balanced virtual ground node generator

From left to the right: 50/300 Ohm BalUn - a random (4 m ca.) stretch of a 300 Ohm symmetric bifilar transmission line - Errante's 300/300 Ohm B.V.G.N.G - 300 Ohm dummy load.
Test Freq.: from 1,8 to 30 MHz in 100 KHz steps
RF power : 1 KW cw
Measured S.W.R.:   1:1   over the whole spectrum
Result: the line shows an aperiodic behaviour over the whole test frequency spectrum. The line aperiodic behaviour is VERIFIED.
N.B. All the measurements have been repeated with the line being held up in the air.


 

Finally, by employing a virtual ground node generator for electrically balanced systems, it has been dimostrated that balanced lines, if properly decoupled from the radiators, always exhibit an aperiodic behaviour, as shown hereafter:

Network analysis of a 300 Ohm balanced line de-coupled from a reactive and radiating load (300 Ohm folded dipole) by means of a 300/300 Ohm Errante's balanced virtual ground node generator

Network analysis of a 300 Ohm balanced line de-coupled from a reactive and radiating load (300 Ohm folded dipole) by means of a 300/300 Ohm Errante's balanced virtual ground node generator.

Ist test:
Purpose: finding the test dipole natural resonance

Conditions: test dipole fed through a 50/300 Ohm virtual ground BalUn.
Test frequency: test dipole center frequency - MHz 22,9
RF Power: 1 KW cw
S.W.R.:   1:1   @ MHz 22,9
Result: the test dipole center frequency found to be MHz 22,9



IInd test:
Purpose: finding the new test dipole center frequency once its feeding system changed

Conditions: test dipole fed directly by a stretch of a 300 Ohm balanced transmission line
Test frequency: NEW test dipole center frequency - MHz 23,5
RF power: 1 KW cw
S.W.R.: 1:1   @ MHz 23,5
Result: the test dipole center frequency has been found to have shifted to MHz 23,5



IIIrd test:
Purpose: finding the new test dipole center frequency once it has been de-coupled from its balanced transmission line

Conditions: test dipole is de-coupled from its 300 Ohm balanced transmission line through a 300/300 Ohm balanced virtual ground node generator
Test frequency: test dipole center frequency found to be back on MHz 22,9
RF power: 1 KW cw
S.W.R.:   1:1   @ MHz 22,9
Result:
1) test dipole center frequency has been restored to its natural resonance value.
2) it has been verified that the balanced transmission line exhibits an aperiodic behaviour.


 

 

Experimental verification of hertzian radiation ABSENCE on a balanced transmission line in a progressive wave regime.
IInd Errante's law

 

A perfectly adapted balanced transmission line being runned with 1 KW RF has been tested for hertzian radiation emission by means of radioluminescence.
It has been observed and at the same time demostrated the absence of hertzian radiation emission on a transmission line while in a progressive wave regime.

 

A properly adapted 300 Ohm balanced transmission line terminated on a reactive but non-radiating load undergoing a radiation test by means of a radiofluorescent detector.

A properly adapted 300 Ohm balanced transmission line terminated on a reactive but non-radiating load undergoing a radiation test by means of a radiofluorescent detector. Experimental verification of the IInd Errante's law applied to the transmission line
A properly adapted 300 Ohm balanced transmission line terminated on a reactive but non-radiating load undergoing a radiation test by means of a radiofluorescent detector. Experimental verification of the IInd Errante's law applied to the transmission line

From left to the right: a 50 Ohm dummy load - 50/300 Ohm BalUn - a random stretch of a 300 Ohm symmetric bifilar transmission line, about 4 m. long
Test frequency: from 1,8 to 30 MHz in 100 KHz steps
RF power: 1 KW cw
Measured S.W.R.:   1:1   over the whole spectrum
Result: the line does NOT radiate.


 

A properly adapted 300 Ohm balanced transmission line terminated on a 1/2 wavelenght folded dipole, through a balanced virtual ground node generator , undergoing a radioscopic detection. Measurements performed both on low and high RF power (Freq. 25,5 MHz - 1 KW cw).

A properly adapted 300 Ohm balanced transmission line terminated on a 1/2 wavelenght folded dipole, through a balanced virtual ground node generator, undergoing a low power radioscopic detection. Experimental verification of the IInd Errante's law applied to the transmission line
A properly adapted 300 Ohm balanced transmission line terminated on a 1/2 wavelenght folded dipole, through a balanced virtual ground node generator, undergoing an high power radioscopic detection. Experimental verification of the IInd Errante's law applied to the transmission line
A properly adapted 300 Ohm balanced transmission line terminated on a 1/2 wavelenght folded dipole, through a balanced virtual ground node generator, undergoing an high power radioscopic detection. Experimental verification of the IInd Errante's law applied to the transmission line

 

Hertzian radiation emission by a balanced transmission line, intentionally placed on a standing wave regime.

A standing wave regime (S.W.R. 1:1,7) has been imposed on the transmission line previously used, by substituting the 50/300 Ohm load balun with a 50/150 Ohm one.
It has been observed and at the same time demostrated the PRESENCE of hertzian radiation emission on a transmission line while in a standing wave regime.

A bifilar transmission line in a standing wave regime undergoing a radioscopic and reflection measurement

From left to the right: a 50 Ohm dummy load - 50/300 Ohm BalUn - a random stretch of a 300 Ohm symmetric bifilar transmission line, about 4 m. long
Test frequency: from 1,8 to 30 MHz in 100 KHz steps
RF power: 1 KW cw
Measured S.W.R.:   1:1   over the whole spectrum
Result: the line RADIATES.

A bifilar transmission line in a standing wave regime undergoing a radioscopic and reflection measurement

Another view of a stretch of the bifilar line in a standing wave regime.

 

 

 

An interactive impedance mismatch spectral simulation
by
Agilent Technologies

General Instructions

This spectral simulation is an interactive Java applet. You can change parameters by clicking on the vertical arrow keys. The five control buttons at the lower right are used to start (triangle) and pause (square) the simulation, to skip forward or back one section at a time (double triangles), and to change speed (+ and -).

After the simulation is complete, the start button takes you back to the beginning of the simulation. You may experience a delay at this point.

Wave Propagation along a Transmission Line

When a sine wave from an RF signal generator is placed on a transmission line, the signal propagates toward the load. This signal, shown here in yellow, appears as a set of rotating vectors, one at each point on the transmission line.

In our example, the transmission line has a characteristic impedance of 50 ohms. If we choose a load of 50 ohms, then the amplitude of the signal will not vary with position along the line. Only the phase will vary along the line, as shown by the rotating vectors in yellow.

If the load impedance does not perfectly match the characteristic impedance of the line, there will be a reflected signal that propagates toward the source. At any point along the transmission line, that signal also appears to be a constant voltage whose phase is dependent upon physical position along the line.

The voltage seen at one particular point on the line will be the vector sum of the transmitted and reflected sinusoids. We can demonstrate this by looking at two examples.

Example 1: Perfect Match: 50 Ohms

Set the terminating resistor to 50 ohms by using the "down arrow" dialog box. Notice there is no reflection. We have a perfect match. Each rotating vector has a normalized amplitude of 1. If we were to observe the waveform at any point with a perfect measuring instrument, we would see equal sine wave amplitudes anywhere along the transmission line. The signal amplitudes are indicated by the green line.

Example 2: Mismatched Load: 200 Ohms

Now let's intentionally create a mismatched load. Set the terminating resistor to 200 ohms by using the down arrow. Hit the PLAY button and notice the change in the reflected waveform. If it were possible to measure just the reflected wave, we would see that its amplitude does not vary with position along the line. The only difference between the reflected (blue) signal, say at point "z6" and point "z4", is the phase.

But the amplitude of the resultant waveform, indicated by the standing wave (green), is not constant along the entire line because the transmitted and reflected signals (yellow and blue) combine. Since the phase between the transmitted and reflected signals varies with position along the line, the vector sums will be different, creating what's called a "standing wave".

With the load impedance at 200 ohms, a measuring device placed at point z6 would show a sine wave of constant amplitude. The sine wave at point z4 would also be of constant amplitude, but its amplitude would differ from that of the signal at point z6. And the two would be out of phase with each other. Again, the difference is shown by the green line, which indicates the amplitude at that point on the transmission line.

The impedance along the line also changes, as shown by the points labeled z1 through z7.

VSWR

The VSWR, or Voltage Standing Wave Ratio, is the ratio of the highest amplitude signal to the lowest amplitude signal, as measured along the transmission line. A "perfect" VSWR is 1.

© Agilent 1997-

 

A transmission line calculator

 

 

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All the concepts, methods, designs and devices presented on this web site
are the original novelty works of FRANCESCO ERRANTE.
Patents & Copyright © 2003- of FRANCESCO ERRANTE.

Material is governed by the Copyright, Designs and Patent Act.
No reproduction, in whole or in part, without written permission.
Copies of these documents made by electronic or mechanical means, including information storage and retrieval systems, may only be employed for personal use.
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