
Why 50 Ohms? - segfaultbuserr
https://www.microwaves101.com/encyclopedias/why-fifty-ohms
======
phkamp
The choice of 75 Ohm is documented in ultimate detail in Bell Systems
Technical Journal.

Here is a 1934 article as an example, long before anybody had even named
microwaves:

[https://archive.org/details/bstj13-4-532](https://archive.org/details/bstj13-4-532)

75Ohm gave the lowest loss and thus the longest distance between repeater-
amplifiers on the trans-continental carrier-telephony coax-cables.

These same cables (and their brethern: microwave links) also carried
television, thus enabling the first "television networks" as opposed to
"television stations".

In many cases even the stand-alone television stations paid AT&T to connect
their down-town studios to the hill-top transmitter.

So television uses 75Ohm because AT&T did.

And AT&T did to minimize the number of repeater amplifiers across USA, because
75Ohm has the lowest loss.

~~~
jacquesm
I'll tell you a neat story about coaxial cables. I worked with quite a few
high power transmitters. If you go topside and check the cables to figure out
why transmitter power is lost it isn't rare at all to see the cables brittle
every half wave. The high frequency does _mechanical_ damage to the cables to
the point where the outer mantle will become porous enough to allow water to
enter. After that it's only a matter of time, presumably a bit of water will
not help with reflected power and speed up the process of desintegration. You
can easily tell roughly what band the transmitter is running at just by
measuring the distance between two such porous points. That's exactly a half
wave length.

~~~
taneq
> The high frequency does _mechanical_ damage to the cables

How does it do this? Like, is it physical vibration driven by the EMF or what?

~~~
someguydave
The current and voltage in coax feedlines varies with length - he is probably
looking at spots where current peaks and thus ohmic heating causes physical
damage.

~~~
CamperBob2
The only way there should be significant nodes and antinodes along a
transmission line is if the load match is (very) bad. Not sure why this
phenomenon would ever happen in the real world, unless there's a mismatch
problem.

This is basically the definition of VSWR. No mismatch = no standing waves. If
you're seeing a pattern of degradation due to uneven heating in a piece of
coax, check the antenna.

~~~
nullc
Even if the antenna is well matched when it's set up... is it still well
matched while it's loaded with snow?

~~~
jacquesm
At high enough power levels that doesn't even matter. No antenna is perfect
and even if it is when it is installed it won't remain so over time.

------
IndrekR
There is also another story [1]. That standard air-core coax lines were built
using regular plumbing pipes in US. As the impedance of a coax is proportional
to _log(inner diameter of the shield /outer diameter of the core)_ this
generated standard impedance around 50 ohms for many different tube
configurations.

(10 minutes later)

However, I just calculated this for standard copper tubing size [2] and this
probably is just a myth, except for few specific tube sizes like 1/4+5/8 or
1.5+3.5 inches.

For some reason, tubing is still mostly given in inches and neither its OD nor
ID correspond to tube size. OD is always 0.125in larger than tube size.

[1] [http://www.rfcafe.com/references/electrical/history-
of-50-oh...](http://www.rfcafe.com/references/electrical/history-
of-50-ohms.htm)

[2] [https://www.petersenproducts.com/Copper-Tubing-
Sizes-s/1979....](https://www.petersenproducts.com/Copper-Tubing-
Sizes-s/1979.htm)

~~~
XorNot
Trying to figure out what pipe to ask for when I have the physical
measurements in hand is one of the ongoing mysteries of the world for me. "Oh
that pipe is <some number you will not get with any type of measuring tool>"
is one of the most bizarre conventions out there.

That said, this isn't even the only place it turns up - there are timber sizes
which are specified as one dimension and just "commonly known" to actually be
a different one: [https://www.thesprucecrafts.com/why-
isnt-a-2x4-a-2x4-3970461](https://www.thesprucecrafts.com/why-
isnt-a-2x4-a-2x4-3970461)

~~~
heavenlyblue
Technically HDD manufacturers are doing exactly the same.

~~~
Stratoscope
Can you explain what you mean?

~~~
gugagore
HDD manufactures often report a storage capacity that is larger than the
effective capacity, since some capacity is used for formatting information, or
error correction. This is the same situation with protocols (like gigabit
Ethernet).

There's also "punning" between the SI préfixes, where e.g. "kilo" can be used
to mean 1000 or 1024. See
[https://en.m.wikipedia.org/wiki/Kibibyte](https://en.m.wikipedia.org/wiki/Kibibyte)

~~~
Stratoscope
I think modern HDD and SSD manufacturers have been pretty honest about the
actual capacity of their drives. They have no way of knowing what kind of
filesystem you will be putting on the drive and how much overhead it has, or
whether you might be putting it in a RAID 1 array (which cuts the effective
capacity per drive according to the number of drives in the array).

The number of bytes they specify is the actual number of bytes available to
your operating system. It seems like a pretty fair measurement.

The 1000 vs. 1024 thing is an unfortunate point of confusion. Terms like
kibibyte and such were an attempt to solve it, but they never took off. (If
you were to ask me which number a kilobyte or kibibyte was, I would have to go
look it up!)

Even if we did use the kilo vs. kibi terms, HDD and SSD manufacturers are the
ones who are getting it right. As the article you linked notes:

> _1 kibibyte (KiB) = 2^10 bytes = 1024 bytes_

> _The kibibyte is closely related to the kilobyte. The latter term is often
> used in some contexts as a synonym for kibibyte, but formally refers to 10^3
> bytes = 1000 bytes, as the prefix kilo is defined in the International
> System of Units._

The same applies as you go up in the units. One mega-anything is 1,000,000 of
those things, giga- is 1,000,000,000, and tera- is 1,000,000,000,000 things.

So a one-terabyte HDD or SSD should have a true capacity of 1,000,000,000,000
bytes, before any operating system or RAID overhead. Of course its actual
_physical_ capacity has to be higher, to support remapping of failing sectors
or flash blocks and such. But that's all hidden by the drive controller.

I think it's the memory people who got this wrong, by co-opting a "kilobyte"
to mean 1024 bytes, contrary to the standard definition. It was a handy
coincidence of terminology at the time, but the error was amplified as we got
into multiples of that size.

And then the operating system and utility people (or many of them) completely
messed up by using the power-of-two definitions for disk/flash storage instead
of the correct power-of-ten definitions.

This is why, for example, every single Amazon listing of a 1TB drive (HDD,
SSD, flash card) which honestly provides the correct 1,000,000,000,000 bytes
of storage to the OS will have at least one review complaining:

> _Claims to have 1TB but only has 931GB as reported by my operating system._

The "missing" 69GB isn't due to formatting or any misdoing on the part of the
drive manufacturer, it's because the OS is using the wrong units.

~~~
Dylan16807
> Even if we did use the kilo vs. kibi terms, HDD and SSD manufacturers are
> the ones who are getting it right.

I'd remove that "even".

If we used both terms, then they'd be getting it right.

But since we're not, they're being misleading compared to the typical use.

> I think it's the memory people who got this wrong

The memory people? It's pretty much everyone that uses "gigabyte" and isn't
selling you a storage device.

------
aj7
The coolest coax cable is the YK-217 cable. 14.8 ohm impedance. 25kv. The
center conductor was a 6mm plastic rod. Then came the braided inner conductor,
covered with some very thin black plastic shit. Then some serious HV
insulation, followed by the outer conductor and a thick outer protective
jacket. The cable was about 16mm in outside diameter. I had to strip 100 of
these cables, with the inner conductor extending about 35mm from the outer
conductor. The only way to do this accurately was on a lathe. In my youth, I
spent all afternoon and evening doing this, then went to a concert at
Winterland in San Francisco. From these cables, and a ton of other machining
and one large 50nF capacitor, I built a nitrogen laser reliable enough to use
in my thesis experiment. Every once in a while, a cable would short, always
where my lathe knife had gone a tad too deep. As the laser pulsed at 17Hz, it
sounded like a machine gun when this happened. I stopped the laser, used my
grounding hook to discharge everything, and calmly unclamped the offending
cable and threw it away. The laser ran perfectly well with 99, 98,97… cables.
That’s why I used cables.

------
exabrial
I'd really like to understand impedence some day. I understand the text book
definition is resistance to A/C, but I fail to understand impedence matching,
coax cable ratings, high impedance inputs, and pretty much anywhere else the
term is used.

~~~
elevation
Impedance matching is a technique required because equivalent amounts of
energy can take many different forms, such as low power for a long time, or
high power for a short time. In electronics, the term "impedance" is most
often understood in terms of an ohms law tradeoff (higher current at lower
potential or lower current at higher potential), and the related formulas are
easy to find. But the requirement to match impedance is easier to grasp if you
understand how energy could be transformed from one form to another and why
that would be desirable.

Consider a system in which we have raised 100 baseballs to a height of 10
centimeters. The amount of potential energy stored in this system is
equivalent to the energy in a system with a single baseball raised to a height
of 10 meters. We could say that these systems, while storing equivalent
potential energy, would have a different kinetic impedance when the energy is
released. Imagine how different it would feel to be laying underneath a
blanket of baseballs dropped from a few centimeters versus standing underneath
a baseball dropped from several stories! One would be uncomfortable, the
other, barely survivable. This is the impact that mismatched impedance can
have on an electrical device.

Like baseballs, electrons in their orbitals have a certain potential energy
"voltage" relative to another nucleus. This energy is released (electrical
current flows) when there is a conductive path for electrons at a higher
potential to move to a lower potential. A system with 10 billion electrons at
1 volt potential has the same energy as a system with 10 million electrons at
potential of 1000 volts, but the one with the higher voltage would have
proportionally less current (fewer electrons) than the one with the lower
voltage. We would describe these two systems as having different electrical
impedance.

In practice, electrical impedance is more complicated than a simple ohms law
exchange because of the wonderfully useful property that impedance varies with
frequency in all natural materials. This makes analysis less straightforward,
but allows us to build filters.

If "electrons with potential" seems abstract, it can be conceptually
worthwhile to examine the many analogs to impedance matching in the mechanical
realm which are easiest to see when a natural or convenient energy source is
transformed into a more useful form. No energy is created (indeed, energy is
lost to heat due to inefficiencies); only the impedance is transformed, as we
see in the following examples:

An automotive transmission is just an impedance transformer, taking the
engine's optimal energy output at 1500-2000 RPM at low force and delivering it
to the wheels at a lower RPM with higher force. The transmission matches the
output impedance of the engine to the impedance of the car on the road so the
engine doesn't stall under too high a load or burn too much gas under too low
a load.

A butter knife is an impedance transformer (transforming the low pressure in
your hand across the large area of the knife handle into 100X the pressure
across the tiny 1/100th area of the blade.) The knife matches the pressing
impedance of your hand to the slicing impedance of the butter.

A nut-cracker is an impedance transformer that transforms your hand's low
force over a long distance into a very high force over the very short distance
required to crack the nut. It matches the impedance of your grip strength to
the cracking impedance of the nut.

An electrical utility transformer is an impedance transformer, transforming
high-voltage low current into low voltage, high current. It matches the
impedance of the utility line to the impedance of your toaster.

A hydro electric dam usually takes the high cross sectional area and low speed
water flow of a river and chokes it into a single point with a much lower
cross sectional area and a much higher speed where it can drive a turbine. The
dam transforms the impedance of the river to the impedance of the turbine.

Even an air conditioner compressor could be said to be an impedance
transformer; the coolant starts at room temperature and at a regular volume.
Compressing the coolant increases its thermal potential while decreasing its
volume. When the higher potential energy is radiated out through the exchanger
coils, the coolant is cycled back inside and decompressed, but since it has
lost energy to radiation, it is cooler. The air conditioner matches the
impedance of the coolant to the thermal radiation impedance of the exchanger
coil.

With the exception of the compressor example, all of these devices are simple
and passive: some gears, a knife, a lever, some coils, a funnel... impedance
transformers are everywhere, doing the simple and passive task of matching the
form of energy you have into the form that you need.

~~~
dr_dshiv
Really nice description.

One way that I think about impedance matching is with the idea of resonant
coupling. If one wants to record a heartbeat, the microphone needs to resonate
and couple with the heart. But since sound waves don't transfer well across
gaps of materials with different impedance, to enhance resonant coupling, the
microphone is embedded within another device that can better couple with the
skin -- e.g., through increased surface area or with material that is
acoustically similar to the skin. The use of acoustically similar materials is
also called impedance matching.

This article is nice, especially the illustration of how air ducts can be used
to create low/high-pass and bandpass filters.
[https://www.britannica.com/science/sound-
physics/Impedance](https://www.britannica.com/science/sound-physics/Impedance)

------
eebynight
What a great article. I would love to see more hardware/electrical articles to
balance out all the software ones.

~~~
segfaultbuserr
Thanks, this is my intention.

Hardware and electronics was an important area in computer engineering, and
many early hackers were hardware hackers. Today, the field has shifted as
software development at large, but hardware and electronics is still an
indivisible part of the hacking community. It can be seen from the fact that
EECS is still taught at schools, the fact that embedded electronics is having
increased popularity due to IoT, and the renewed interests within free and
open source community.

I'll keep submitting more hardware/electrical articles which I find
interesting.

------
mNovak
For those nostalgic over classic 90's websites, the RF community has you
covered: [1] rfcafe.com [2] antenna-theory.com

~~~
superkuh
Yeah, it's nice to see a website that loads instantly, is accessible for those
with disabilities, doesn't require executing code, and who's design is based
around content rather then the other way. The amateur radio community is
generally pretty good at this.

------
tyingq
I guess the follow-on might be _" Why 50 ohms for 10b2 Ethernet, which isn't
microwave band?"_

~~~
k0stas
Ethernet transmission is broadband not tuned like a radio but the same
equations as presented in the article hold across most of the bandwidth (where
the skin effect holds). Actually, I am not sure whether the article is
referring to tuned or broadband communication but in a sense it is irrelevant
because practically, a large proportion of the energy transmitted in a modern
broadband system is in the skin effect domain. If this wasn't the case, the
system would be highly inefficient in the use of available bandwidth.

~~~
tyingq
The carrier frequency for 10b2 is 10Mhz.

~~~
gugagore
It's not a modulated signal encoding. There's no modulation, and so there's no
carrier.

The bandwidth is probably 20MHz, due to the Manchester encoding.

~~~
tyingq
It is Manchester encoding on a 10MHz clock signal. Perhaps carrier isn't quite
the right word.

~~~
gugagore
I take back by correction. Thanks, and sorry. Manchester encoding really is a
form of phase modulation (BPSK). It makes sense to think of it as a 10MHz
baseband signal modulated by a 10MHz carrier, and therefore having a 20Mhz
bandwidth.

------
jojobas
Coincidentally, 50 Ohms is also impedance of a typical whip antenna near
ground.

~~~
mNovak
Roughly.. If I recall, a quarter-wave monopole will be 37 ohms

~~~
jojobas
That would be without ground or something.

------
walrus01
With very modern point to point microwave systems there are zero 50 ohm
coaxial connectors at all. The radio unit has a direct waveguide flange
interface and mounts directly on the rear of a dish.

------
dillonmckay
What where the old pigtail connectors to TVs?

Was that 300 ohm to 75 ohm?

~~~
Pick-A-Hill2019
Short answer, yes. Techie answer is that 75 ohms is best for receiving
signals. For air dielectric coax, 77 ohms provides the lowest loss of signal.
'...the standard coax impedances is 75 ohms because that is the impedance you
end up with after you run a 300 ohm 1/2 wave folded dipole impedance through a
classic 4:1 hairpin balun. You've got folded dipole, you gotta have a balun,
and baluns don't come any simpler than the hairpin balun (and there isn't any
easy way to get to 50 ohms from 300 ohms)'. Modern (US) coax cable is foam
filled PTFE which works best at 50 ohms.

------
madengr
Interestingly for coax, as the frequency approaches DC (say a few 100 kHz),
the Z0 jumps slightly.

