Why 50 Ohms?

https://www.microwaves101.com/encyclopedias/why-fifty-ohms

by segfaultbuserr • 7 years ago

242 89 7 years ago

microwaves101.com

tyingq4• 7 years ago

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

fsh• 7 years ago

Because they were using existing BNC connectors and cables.

bcaa7f3a8bbc• 7 years ago

Because 50 ohms is an universal standard for most radio frequency equipment, not just microwave. It (often) doesn't make sense to invent your own coax, connectors, transformers, and chips. At the end of the day, the selection had its rational back in the days, but it eventually became an agreed convention that everyone just follows.

whoopdedo• 7 years ago

The convenience of existing cables and connectors seems to be the motivation.

The first Ethernet used 9.5-mm coaxial cable, also called ThickNet, or as we used to curse it as we tried to lay out the cables, Frozen Yellow Snake.
To attach a device to this 10Base5 physical media, you had to drill a small hole in the cable itself to place a "vampire tap."
So-called Thinnet (10Base2) uses cable TV-style cable, RG-58A/U. This made it much easier to lay out network cable.

https://www.hpe.com/us/en/insights/articles/the-birth-and-ri...

k0stas• 7 years ago

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.

tyingq4• 7 years ago

The carrier frequency for 10b2 is 10Mhz.

IndrekR• 7 years ago

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...

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

XorNot• 7 years ago

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

heavenlyblue• 7 years ago

Technically HDD manufacturers are doing exactly the same.

petschge• 7 years ago

The sizes for timber come the actual physical size early in the production process as your link nicely explains. Where to the "commonly known as" sizes for pipes come from?

jacquesm9• 7 years ago

The timber sizes are different because you are buying planed timer, rough timber would have the exact dimensions you are looking for. So a 2x4 rough is really 2x4"

kube-system2• 7 years ago

Pipe was originally measured by inside diameter.

Anyway, over the past 100 years, metallurgy got better and they could make the same strength pipe with thinner walls.

So now, because of the thickness change, the old pipes that measured 1/2” inside and the fittings for those pipes were the right size for new pipes that measured about 3/5” inside. They had the same outside diameter, but a larger inside diameter.

Instead of confusing everyone and requiring them to remember compatibility charts for every size pipe (and guessing about the age of the pipe), they just “solved” the problem by selling the new pipes under the name of the old size they were compatible with.

Tl;dr: Plumbers have technical debt that goes way back.

phkamp2• 7 years ago

Some of the first experiments with coaxial lines were indeed made by pulling a center-conductor into standard copper pipes.

There are several articles about that in BSTJ, with pictures.

eebynight• 7 years ago

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

segfaultbuserr2• 7 years ago

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.

dillonmckay• 7 years ago

What where the old pigtail connectors to TVs?

Was that 300 ohm to 75 ohm?

dsr_• 7 years ago

Yes -- the ones with two flat spade connectors on one side of a box, and a coaxial screw-in connector on the other.

Pick-A-Hill2019• 7 years ago

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.

jojobas2• 7 years ago

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

mNovak2• 7 years ago

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

jojobas2• 7 years ago

That would be without ground or something.

mNovak2• 7 years ago

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

gus_massa• 7 years ago

[Remember to add the "http" part to trigger the magic autolink http://rfcafe.com and http://antenna-theory.com ]

superkuh• 7 years ago

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.

madengr• 7 years ago

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

phkamp2• 7 years ago

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

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.

jacquesm9• 7 years ago

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.

aidos3• 7 years ago

That half wavelength damage is deviously pleasing somehow.

taneq3• 7 years ago

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?

guenthert• 7 years ago

75Ohm gave the lowest loss

The lowest loss of a selection of cable diameters I presume. I'd think lower loss can be achieved with greater diameters (lower specific capacitance), but costs will be prohibitive.

walrus01• 7 years ago

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.

exabrial• 7 years ago

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• 7 years ago

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.

disqard• 7 years ago

That was a beautiful explanation! Thank you for sharing those examples.

dr_dshiv• 7 years ago

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

rocqua2• 7 years ago

The way I rationalize impedance matching is like the Index of refraction.

The analogue to two pieces of wire with different impedance is two pieces of glass with different index of refraction. What happens when you shine in light is a partial reflection at the boundary of the two pieces of glass, which also means less light gets through.

Impedance matching is just trying to match these indices of refraction to me. Sadly, I have no good analogue for a balun or impedance matching circuit.

I have no idea whether this is mathematically correct, but it gives me some intuition for why it matters.

MayeulC• 7 years ago

It is technically correct, but might not be the easiest way to understand it intuitively (this will be different for everyone, but I didn't quite get the explanations in the thread).

I'll try to make it simple: for now, let's admit impedance is resistance. It is just a way to express how much the medium will slow a propagation down.

This works with multiple fields: thermal resistance, soundwaves, lightwaves (refraction index is c/v), or you can just imagine yourself going trough different mediums: when diving, you encounter some resistance where the medium starts slowing you more. You lose energy there. If instead the resistance was the same all the way (if you were already swimming), there would be no interface to lose energy at. Diving championships use bubblers to soften the water, that's adapting impedance, in a sense.

Of course, this analogy is a bit extreme at our scale, due to the high absorption and terminal velocity differences between the two mediums. But you have the same with soundwaves: a wall will reflect your speech because sound has a lot higher speed in concrete. Some surfaces will do it better than others. And to avoid that kind of parasite reflection during ultrasound imaging, a gel is employed to match impedance between the emitter and the body [1] (avoiding a thin air layer in between).

OK, now for real (actually complex) impedance, you have to take into account that the speed inside the medium varies based on frequency. That's called dispersion in optics and acoustics, and is sometimes compensated by employing mediums with an inverted dispersion relationship [2].

OK, I'll admit that propagation speed isn't strictly what impedance is, but it is pretty close, and they probably have an intimate relationship (which I can't reflect on right now, but feel free to elaborate below, if you feel like it).

This actually sent me down a small rabbit hole in wikipedia: https://en.wikipedia.org/wiki/Impedance_analogy

[1] https://en.wikipedia.org/wiki/Medical_ultrasound [2]: https://en.wikipedia.org/wiki/Dispersion_(optics)#Dispersion... [2]: http://www.m2optics.com/blog/bid/61431/Chromatic-Dispersion-...

segfaultbuserr2• 7 years ago

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.

Actually, it's easy to understand the basic concepts in pure DC. Let's see...

high impedance inputs - this is the easiest one to explain. A device with high-impedance input only allows a small, often negligible amount of current to flow into it, as if nothing is connected.

Imagine a 5-volt power source followed by an 10k ohm output resistor in series, and we put it in a blackbox. If you connected another 10k ohm resistor across the blackbox, you create a voltage divider, and the voltage across your resistor would be 5 x (10k / (10k + 10k)) = 2.5 volts, and a current of 0.25 mA flows.

But if you increase the value of your inserted resistor to, e.g. 10M ohm, now the 99.9% of the voltage is now across your resistor, and you get 4.995 V, and there is almost no current flows across the power source, as if nothing is connected, minimizing the "observation effect".

This allows you to measure the voltage without disturb it by drawing power from a circuit. Example:

ideal voltmeter - gives a voltage measurement.

ideal oscilloscope probe - just an ideal voltmeter that takes many measurements and display a line on a chart.

ideal ADC - just an electronic voltmeter.

ideal transistor switch and logic gate - output only depends on the voltage reading of the input, it doesn't absorb power.

ideal buffer and operational amplifier - measures the voltage at the input without affecting it, and creates a replica of this voltage by using its own power source.

impedence matching - This one is difficult if we're talking about reflections, S-parameters, and standing waves, but it's easy understand if we only talk about impedence matching for maximum power transfer. People often say that, to get the maximum power transfer, the impedance of the source and the load should be matched. But it's misleading. Theorem of Maximum Power Transfer is actually telling us how to choose our load, given a known source, not vice versa.

Imagine an ideal 5-volt DC voltage source. The maximum available power from such a power source is infinite, and only depends on the impedance of your load. By connecting an infinitesimal resistor, infinite power will be absorbed by the resistor.

Now imagine an ideal 5-volt DC voltage source followed by 10 ohm of output resistor in series. This is closer to a real power supply, or a signal generator, or a radio antenna, whose internal impedance sets an upper limit of available power.

What the Theorem of Maximum Power Transfer is telling is that, if we want to absorb the maximum available power out of this power source, our load must be equal to the source impedance, in this case, 10 ohm.

If our load has the same impedance as our source, the voltage across our load will be Vcc x R2 / (R1 + R2), or 5 x 10/(10+10) = 2.5 V, and the power is absorbed by our load is V^2 / R, or 0.625 W.

If our load is much smaller than the source, there will be more current but less voltage. A 1-ohm load will get a voltage of 5 x 1/(1+11) = 0.416 V, and absorb only 0.173 W.

If our load is much bigger than the source, there will be more voltage but less current. A 100-ohm load will get a voltage of 4.54 V, and absorb only 0.206 W.

It's simple if the following misconceptions are cleared.

* Misconception 1: If I have a 300-ohm load, the output impedance of the power supply should be matched to 300-ohm for maximum efficiency.

False. Maximum Power Transfer does not imply Maximum Efficiency. Efficiency is the ratio, Useful Power / (Useful Power + Wasted Power), and it has nothing to do with maximum power transfer.

Recall the example above, when a 100-ohm load is connected to a 10-ohm power source, the voltage across the load is 4.54 V, drawing 0.206 W. Meanwhile, the voltage across the internal impedance of the power is 0.46 V, drawing 0.021W. The efficiency is 91%. But when impedance is matched, 100-ohm load is connected to a 100-ohm power source, the efficiency is "only" 50%.

Often, the efficiency is the best when there's low power transfer. You don't waste a lot of power if you don't take away a lot of power.

* Misconception 2: If I have a 300-ohm load, (e.g. a headphone), the output impedance of the power supply (e.g. a headphone amplifier) should be 300-ohm for maximum power transfer.

False. Maximum Power Transfer is only about how to select our load to absorb maximum power when we have no control over a given source, not vice versa. In real-life, for non-RF circuit, if we have control over the source, the solution is to make the output impedance of the power source close to zero.

For a 5-volt DC source with a 300-ohm impedance, connected by a 300-ohm load, only 0.02W of power comes out because there's only 2.5 V across the load. But if we have the output impedance to be 0.1-ohm, 4.998 V is now across our load, and drawing 0.083 W of power.

This is called impedance bridging, and it's how power supplies and modern headphone amplifiers are designed - they are designed for maximum efficiency by minimizing their output impedance, while the headphones themselves only draw a little bit of power.

On the other hand, a radio receiver is a good example when we have no control over the source impedance, given the same antenna, it cannot be changed. In this case, the better our receiver is matched to the impedance of the antenna, the higher its sensitivity.

BTW, in RF-circuit, even if we have control over a signal source, we use matched impedance, in this case, the purpose is not to get the maximum power transfer, but for avoiding reflections, a completely separate issue.

* Misconception 3: 50-ohm coax cable has 50-ohm of electrical impedance.

False. The "50 ohm" and "75 ohm" for coax cable is its characteristic impedance, not electrical impedance.

This is when things get complicated and when we must think electrical signals as waves. But the other comment has a good explanation, so it won't be repeated. In short, when a wave hits an impedance discontinuity in its medium of propagation, some of the energy is reflected, so in an RF system, 50-ohm everywhere is desirable.

A small piece of lossless coax cable can be modeled as an inductor in series and a capacitor in parallel, it's the radio of the inductor and the capacitor that determines its characteristic impedance that we can match to avoid a discontinuity in the circuit, thus avoiding reflection. Or we can say that the characteristic impedance is the input impedance when the length of the lossless coax is infinite.

It's not an actual electrical impedance that we can measure by an ohmmeter. A 10-meter coax has an electrical impedance of less than 1 ohm.

fuzzfactor• 7 years ago

Audio frequencies are a much more limited band than RF and it can be intuitive to look at a simple hardware consideration.

Such as your speaker's voice coil, which is a fairly low-resistance length of thin copper wire commonly wrapped around a hollow paper core an inch or two in diameter and enameled in place. The paper form is cemented to the center of the suspended speaker cone, with the coil itself free to move back & forth within the matched gap of the speaker magnet.

When the audio signal (which is a series of waves, therefore an AC voltage) comes in on the wires, the coil moves the cone in response to the signal.

DC voltage is not allowed to pass to this kind of speaker since DC would just displace the cone in a single direction for the duration of DC voltage application.

But when you measure the resistance in Ohms of an individual _8-Ohm_ speaker, it is always less than 8 Ohms, sometimes between 6 & 7 Ohms because regular Ohmmeters are measuring DC resistance using a DC battery inside the Ohmmeter as a reference.

The DC resistance of the coil is no different than it would be if the whole coil was unwound, it basically depends on the length of the wire and the diameter of the wire, similar to the way precision wirewound resistors are available for lower Ohm service. Thinner wire and longer wire has higher resistance to current flow.

But when audio is passing through the coil alone in free air, IOW no magnetic or ferritic core is present, there will be slight additional resistance to the audio AC (over and above the fundamental DC resistance measurable with the regular Ohmmeter), simply because of the wire being shaped into a coil. This total working resistance to AC is what is referred to as impedance. When a ferritic or magnetic core is in place, there will be that much more of a challenge for the audio signal since it needs to then reverse polarity against the inertia of the magnetic material at whatever frequency it happens to be operating at. This magnetic bump in AC resistance is significant and causes a nominal 6-Ohm-resistance speaker to operate as a characteristic 8-Ohm-impedance audio load.

Speakers do work really well with much higher than 8-Ohm voice coils, provided a matching amplifier is available. Practically this is not done since the speaker wires from the power amplifier to the speakers in a high-power system would then be required to carry audio AC voltages as dangerously high as the line voltage coming in to the amplifier.

So using the everyday low-impedance speakers we are stuck with, a slightly poor connection having an extra 1-Ohm of unwanted resistance, due to corrosion for instance, will result in that connection dissipating a significant percentage of the power passing through it, as heat, in many cases accelerating a corrosive source of power loss.

aj7• 7 years ago

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.

Why 50 Ohms?

Related Stories