Classical, impedance-quadrupling BalUn transformer.

Some readers might ask themselves, ‘What the heck is a Balun transformer?’ And the answer is that, in certain high-frequency applications, this term gets used for a Balanced-to-Unbalanced (impedance-matching) transformer, often implemented as a transmission-line transformer. One common place they did get used in years gone by was, to allow people to connect 300Ω twin-lead TV antenna cable, to the 75Ω coax inputs of more-recent TVs. Actually, what was inside those little adapters was, a toroidal ferrite core, with a piece of sheet-metal (probably aluminum) stamped around it in a clever way, so that this stamped sheet of metal also acted as the ~windings~ of the transformer.

Really, this type of transformer does the same thing that an ‘autotransformer’ does, only, at much higher frequencies. If the reader is picturing a (center-tapped) autotransformer with many windings, then he or she should also picture how many implicit, internal capacitors those have (between the windings), and how capacitors become increasingly conductive, at higher frequencies… Traditional, wound transformers start to become useless well before 100MHz has been reached.

If people look this subject up elsewhere on the Web, They might find diagrams of various types of transmission-line transformers. But, it’s easy to get confused about the way those need to be connected, so that one possible result could be, a transformer that does not work correctly. For that reason, I have just reconstructed how I remember them to have been configured in the past:




I suppose that another piece of possibly related trivia could be, that an impedance of, say, 150Ω, connected to a voltage of zero, is equivalent to 300Ω, connected to a relative voltage of (-1). Another related assumption is, that such transmission lines are indeed wound on effective ferrite cores, capable of choking their net current to zero.


Now, there’s another, related application of transmission-line transformers, which could be, that a number of transistorized output drivers might only be able to handle some higher (load-) impedance (each), but that the goal is to combine their amperage, so that a divided output-impedance also results, at minimal waste of energy. Additionally, some small mismatch in the outputs could be expected, which should be absorbed, and not result in reflected waves…

(Updated 6/02/2021, 9h15… )

On those assumptions, the following would seem like the sought configuration:




(Revised 6/01/2021, 15h30. ) (:1)


(As of 5/30/2021: )


The sketches suggest, what the ideal line impedance of each coax cable would be, that is to be wound on a core. However, practical explorers might discover that ~150Ω coax cable~, etc., would be hard to find. In fact, because such transmission lines need to be choked, practicality might require – subminiature 50Ω coax. This is one of the few situations where, Within reason, such substitutions are acceptable. They will only have as consequence, that each ferrite core becomes active, and, in the case of combining considerable output power, the cores could heat up.

For frequencies up to 100MHz, the fact that the transmission lines can be choked, is more important, than the idea that each transmission line have its ideal impedance.


What observant readers might notice is the fact that ~television antennae~ work all the way up to UHF frequencies, which by definition extend beyond 100MHz. In those cases, all the manufacturers needed to do was, to calculate the area of the aluminum sheet metal, so that the capacitance between its surfaces corresponded to a reactive impedance of ~150Ω. At 500MHz, that requires 2pF. Actually, at low frequencies, all that would have been revealed was conductivity.

However, in designing their 300Ω – 75Ω (TV) antenna adapters, companies could hypothetically have been apathetic in reducing the internal capacitance below 4pF, which should have resulted in an inability to receive any stations higher than ~Channel 30 or so~.


Now, the usage scenario could change again. This time, the assumption could be, that a 50Ω coax cable were connected to a circuit-board, but, that the circuit-board traces had an impedance of, say, 200Ω, as defined by their width, the dielectric constant of the circuit-board insulator, and the thickness of the circuit-board, if there is a solid Ground Plane etched onto its opposite face. Further, the goal might be, not to waste ¾ the signal energy, by just connecting a ~65Ω resistor in parallel with any incoming signal. In that case, the following circuit should be connected within 1cm of where the coax cable connects. It will double the signal voltage, quadruple the impedance once, and not waste much signal energy:




Now, if the hobbyist finds that his or her circuit-board traces have 400Ω and not 200Ω, they can still connect a 400Ω resistor in parallel with (a 200Ω resistor in series with) the higher-impedance side. They’d ‘only’ be cutting the power to ½ the input (output) power then, not, to ⅛.


(Update 5/31/2021, 7h35: )

There is a distinction between how coax cables are usually connected to Printed Circuit Boards (PCBs), and how this posting proposes to do so. Normally, what electronics hobbyists, even, want from a coax cable is, frequency response into the Gigahertz range, which requires attaching bulky connectors to the PCB.

My Transmission-Line Transformers (TLTs) require that a length of coax cable, such as the (miniature) 50Ω ‘RG174′, be looped through a ferrite core at least once – preferably multiple times – and then, back to a location on the PCB which is very close to where the other end was.

What this means is twofold:

  • The TLTs suggested in this posting can only operate at much lower frequencies… Up to 100MHz, And
  • The way they need to be connected to the PCB is, to be soldered directly on or in. In some cases people might have the dexterity, to surface-mount the ends of the coax, but this is actually unlikely. And so, the only alternative that actually remains is, to strip the coax, and to bundle the braided external conductor to one side of the centre conductor. Then, the braided bundle and the centre conductor could, in principle, be fed through two holes in the PCB, and soldered in.

And this is the only practical way I see people perhaps putting these TLTs on a PCB.


(Update 5/31/2021, 19h15: )

One fact I’m keenly aware of is, that industrial manufacturers will put Surface-Mount Packages of ICs, which have distances between their leads of ~0.5mm, onto multi-layered PCBs, for operation up to 100MHz, with no Ground Plane. I would estimate that the characteristic line impedance of the resulting 0.25mm traces is close to ~200Ω. It will stay consistent with itself.

However, certain microwave technologies work, because they put a Ground Plane. If the packages mentioned above are positioned opposite such a 2-layered PCB’s Ground Plane, according to the calculator I linked to above (all other parameters left at their defaults or set to standard values), that impedance will precisely become 134.5Ω. It will be consistent with itself again. But it won’t equal the previous value. Doing so might overload the chip’s output drivers.

The traces’ free impedance can be verified, by subsequently setting the calculator’s “Isolation Height” to 1cm.

I’m also assuming that stretches of ~arbitrarily thin wire~ no longer than 1cm, can connect two terminals in a functioning way, when each of those terminals has an impedance of 50Ω.


(Update 6/02/2021, 9h15: )


Concerning the power-combining transformer, I calculated the ideal impedance of each transmission line, for the hypothetical scenario, that an infinite number of inputs were to be combined. If instead, 4 inputs are to be combined, then this ideal impedance would get closer to (Z/2).

And No, this cannot be used as a splitter, as shown.




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