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Why do we have 50, 75, 62 and 92 Ω coaxial cable, to name a few? Why not just one standardised cable? Is there some technical reason or did Mr. Coax and Mr. Cable have a disagreement, like Mr. Tesla and Mr. Edison?

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Glad to see this question posted! This has a really interesting answer which I'm not qualified to write a comprehensive answer to, so here's a rather unsupported answer to help you along until someone writes a better one.

There are several reasons why coaxial cable is used in several different impedances.

  • On basic principles: if a device on one end of the cable inherently has a specific impedance, then using a cable matched to that impedance means you don't need a matching network at least at that end.

  • Different choices of impedance result in different characteristics of the cable, given the available choices of material and construction techniques.

    It is said (I don't have a citation) that 50 Ω was chosen as a compromise between power handling capability (lower impedance would be better) and attenuation per length (higher impedance would be better). In high-power applications, 50 Ω is used to allow use of the smallest cable possible for the power (minimizing cost and bulk).

    On the other hand, if you are not intending to transfer significant power, i.e. your application is very low-power or receive-only, then you only care about attenuation and so you choose the higher 75 Ω to optimize for least attenuation.

  • Even if there was one best line impedance to use, you would still want to have available cables of other impedances. This is because RF circuits that use transmission lines as impedance transformers don't need any specific impedance, but they do need to have an impedance that is different than the impedance of the incoming/outgoing lines. For example, in this Wilkinson power divider implemented using coax:

    Wilkinson power divider

    (Image credit: SpinningSpark on Wikimedia Commons)

    If your lines are 50 Ω then you need 71 Ω in the divider. If your lines are $x$ Ω then you need $\sqrt{2}x$ Ω in the divider. No single type of coax can do this.

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    $\begingroup$ I was told once by a very old man, radio operator for the Army during WWII, that 50-ohm coax cable became standardized with a lot of modern (that is, anything after WWII) transmitters because it was used for most military radio equipment and the war effort created tons of 50-ohm coax which made its way into the amateur radio arena. However, that was a single source. Anyone else know whether it is true? $\endgroup$ – K7PEH Jun 25 at 5:00
  • $\begingroup$ @K7PEH I don't know about the surplus equipment aspect of that, but certainly, the fact that a lot of companies agreed on a common impedance will have a lot to do with military customers. $\endgroup$ – Marcus Müller Jun 25 at 6:26
  • $\begingroup$ @MarcusMüller -- I forgot to add another part of what that old man told me. He was a ham operator before WWII and he said that everyone he knew in the hobby used ladder line (usually home-brew) for their antennas. Coax he said was used at all that he could remember until after WWII. Of course, one person's opinion. I used to chat with this guy on the 80-meter band late at night on an almost regular basis several times a week. He passed away about 10 years ago. $\endgroup$ – K7PEH Jun 26 at 5:03
  • $\begingroup$ @K7PEH I really agree that WWII changed the economics of RF. My point was just that economics alone doesn't imply that all manufacturers suddenly agree on 50Ω. I was assuming it was the fact that the military customers pressed for standardization. $\endgroup$ – Marcus Müller Jun 26 at 5:41
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RF Cafe cites quotes Harmon Banning of W.L. Gore & Associates, Inc.:

In the early days of microwaves, around World War II, impedances were chosen depending on the application. For maximum power handling, somewhere between 30 and 44 Ω was used. On the other hand, lowest attenuation for an air filled line was around 93 Ω. In those days, there were no flexible cables, at least for higher frequencies, only rigid tubes with air dielectric. Semi-rigid cable came about in the early 50s, while real microwave flex cable was approximately 10 years later.

Somewhere along the way it was decided to standardize on a given impedance so that economy and convenience could be brought into the equation. In the US, 50 Ω was chosen as a compromise. There was a group known as JAN, which stood for Joint Army and Navy who took on these matters. They later became DESC, for Defense Electronic Supply Center, where the MIL specs evolved. Europe chose 60 Ω. In reality, in the U.S., since most of the "tubes" were actually existing materials consisting of standard rods and water pipes, 51.5 Ω was quite common. It was amazing to see and use adapter/converters to go from 50 to 51.5 Ω. Eventually, 50 won out, and special tubing was created (or maybe the plumbers allowed their pipes to change dimension slightly).

Further along, the Europeans were forced to change because of the influence of companies such as Hewlett-Packard which dominated the world scene. 75 Ω is the telecommunications standard, because in a dielectric filled line, somewhere around 77 Ω gives the lowest loss. (Cable TV) 93 Ω is still used for short runs such as the connection between computers and their monitors because of low capacitance per foot which would reduce the loading on circuits and allow longer cable runs.

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  • $\begingroup$ I thought it was something like that.The lower impedance was better for power transfer but a higher impedance is better at low signal levels. We learn something every day! $\endgroup$ – R Johnson Jun 26 at 23:55
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    $\begingroup$ "93 Ω is still used for short runs ... [to] allow longer cable runs." ?! $\endgroup$ – Phil Frost - W8II Jun 27 at 15:04
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Nearly all coax is either 50 or 75 ohms. 50 ohms is standard for radio applications, and 75 ohms for CATV and video applications.

Everything else is a specialty item.

One use of odd impedance feedlines is to match impedances. Any two impedances can be matched by a 1/4 wavelength section of feedline having a characteristic impedance that is the geometric mean of the two to be matched. For example, to match 300 ohms to 50 ohms, a 1/4 wave selection of $\sqrt{300 \times 50} = 122$ ohms can be used.

Certain devices, like a Wilkinson power divider, require transmission lines of peculiar impedances.

Or the application may be one where there's no particular need to accomodate any existing standard, and the system impedance is already set by some other design constraint. For example, antennas don't usually have a 50 ohm impedance feedpoint, and printed feedlines are not often 50 ohms either. The coax impedance is determined by its geometry, so perhaps for mechanical reasons a particular geometry is preferred and this dictates an unusual characteristic impedance.

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92Ω coax has been used for many decades in cars and trucks between the radio and the non-resonant antenna. 75Ω or 50Ω coax would attenuate the signal more than 92Ω would.

The reason is the same: because of its lower capacitance per foot which helps minimize losses in the cable under such a mismatch.

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