Neither electromagnetic theory nor calculations of any kind, just practical experimentation. As we know, the number one enemy of Dxers and shortwave radio listeners is man made noise.
Dirty electric power grids, low quality transmission lines, made in chinese electronic bulbs plague, and we have a chaos in the HF spectrum, also in MW.
How to chase it ?
Place antennas away from potential noise sources and use a transmission line shielded to input the signal into the receiver is a good and efficient approach.
Transformer circuit diagram for 9:1 impedance matching
To achieve this the use of a impedance match transformer is a powerful tool. Put your random wire in some safe place, install a balun to couple the wire that acts as antenna into a coaxial cabling that will be the transmission line that is supposed to not capture noise up to your receiver placed indoor.
The random wire typically presents hire impedance, depending on its weight and length, and we can estimate in average 500 Ohms, while the coaxial cable presents 50 Ohm impedance, that is the most common input impedance of tabletop receiver and also portables like Sony and Sangean.
Transformer schematic using a toroid core of ferrite for 9:1 coupling
So, to make the correct energy transference between the antenna and the receiver input, we should transform both impedances to avoid attenuation in the transmission line.
The theory of maximum energy transfer is quite simple, just think in a battery providing power, and this battery has an internal resistance value, so if the load presents the same internal resistance, maximum power transference will occur.
The same principle applies to receiving RF signals. And the so called magnetic coupling, impedance matching or transformer, will provide a ratio between the random wire impedance and the internal impedance of receiver’s front end input.
The 9:1 ratio will provide about 500 Ohm impedance of random wire be divided by 9, so the final impedance should be next 50 Ohms, the same of coaxial cable and receiver’s input.
Ferrite core in toroid shape
The use of ferrite core is mainly for increasing the inductance value of the coil, and toroid shape helps magnetic coupling of the transformer and also isolates from other magnetic fields nearby.
Using enameled wire is just an option, because in this kind of assembly the wire used is not critical, because this balun is intended just to receive signals not transmit.
This toroid is really big, and in practical terms it is not necessary this way just to receive RF signals, but I have purchased 3 units in surplus conditions, so I have not had a choice to choose a specific ferrite toroid.
In fact, it can be used larger powered iron toroids to wind inductors, however, they can also be wound on ferrite cores or be air-wound. The core size, wire gauge and type of inductor used can affect the insertion loss of the transformer (balun), however for practical receiving purposes it is not a major concern.
And that makes the hobby more interesting: use the theory, but make experimentations … always.
Balun construction using a strong alloy case used on VSAT stabilized systems offshore
The case to assembly the balun can be whatever material available, I have chosen a robust alloy case used as a modem for some VSAT systems. It’s mechanical features allow it to be installed virtually anywhere and placed to resist weather and very long wire that causes tension over the connector.
Final assembly of magnetic coupling for random wire antennas
This case will never be broken, just that simple.
This balun is also called UN-UN (unbalanced – unbalanced) because it couples a random wire and uses a coax as transmission line, and both component are unbalanced related to ground.
If we use an antenna dipole, so, the proper balun should be balanced-unbalanced in this way.
More to come, I have two toroid units available yet to test other coil configurations and ratio transforming.