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Author Topic: 50 and 75 ohm Coax question  (Read 18977 times)
KD0ZGW
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Posts: 1037




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« on: August 10, 2014, 07:03:23 AM »

doing a lot of research on antennas and I sometimes see an antenna spec calling for 75ohm.  Not sure why you'd want 75ohm feedline to a 50ohm source??

what am I missing?
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WB6BYU
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« Reply #1 on: August 10, 2014, 07:25:38 AM »

Sometimes 75 ohm TV coax is already on hand, or available cheaper, than
50 ohm coax. No reason not to use it in that case.

RG6 75 ohm TV cable has lower losses than some of the common 50 ohm
types, making it a good choice for long runs, especially in receive applications
where the power rating isn't important.

It can also be useful for impedance matching:  a quarter wavelength of 75
ohm line matches a 112 ohm loop antenna to 50 ohms, for example, and two
such lengths in parallel can be used to match a 28 ohm yagi feedpoint.
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KD0SFY
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« Reply #2 on: August 10, 2014, 11:34:07 AM »

doing a lot of research on antennas and I sometimes see an antenna spec calling for 75ohm.  Not sure why you'd want 75ohm feedline to a 50ohm source??

what am I missing?

Impedance matching
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WS4E
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« Reply #3 on: August 10, 2014, 11:49:32 AM »

I personally don't understand why hams don't switch to 75ohm cables and ditch the UHF connector at the same time.  


I have seen 75ohm quad RG6 that is better or as good quality as LMR400 for 1/10th the price.  


Regular RG6 and the old CATV F-connector has been proven more than capable of handling 1500W RF.  

Imagine the money hams would save if they used coax and connectors available at every store in the country for pennies on the dollar compared to custom coax and connectors.  

Btw there is a portion of the ham community doing this.  Remember a dipole is usually about 75ohms anyway if I remember correctly.  

It has always fascinated me why more hams don't think about this and try it.   If enough people tried it, eventually 75ohm might be the standard that radios would be designed for output. 
« Last Edit: August 10, 2014, 11:52:26 AM by WS4E » Logged
G4IJE
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« Reply #4 on: August 10, 2014, 01:47:01 PM »

A dipole in free space is near 75 ohms, but as my spacesuit is in the laundry I find that 50 ohms is nearer the mark for my low antennas ;-)

I find the thin inner conductor of 75 ohm coax isn't so easy to work with as 50 ohm cable.

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AA4PB
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« Reply #5 on: August 10, 2014, 01:59:12 PM »

I personally don't understand why hams don't switch to 75ohm cables and ditch the UHF connector at the same time.  

One reason is because 50 Ohms is the standard for the radio communications equipment industry. Transmitters, receivers, test equipment, etc. are all designed to work in a 50 Ohm system.
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Bob  AA4PB
Garrisonville, VA
WB6BYU
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« Reply #6 on: August 10, 2014, 02:42:32 PM »

At least of my solid-state HF transceivers is specified for "50 - 75 ohms".

75 ohms gives the lowest loss.  Power handling is maximum at some lower impedance, something
like 35 ohms.  50 ohms is a compromise between the two.  In many applications it doesn't make a
lot of difference.
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WT5MW
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« Reply #7 on: August 10, 2014, 02:45:05 PM »

doing a lot of research on antennas and I sometimes see an antenna spec calling for 75ohm.  Not sure why you'd want 75ohm feedline to a 50ohm source??

what am I missing?

Here's a good high level summary of why (From Belden's site, with a little marketing):

http://www.belden.com/blog/broadcastav/50-ohms-the-forgotten-impedance.cfm

If you play with coax, short for coaxial cable, you probably know this it is available in a number of different impedances. The most common is 75 ohm, like video cable or antenna cable, but in fact our products range from 32 ohms up to 124 ohms.

Why all these different numbers? It's not an accident of course, and there is a reason for each one. Today, we're going to take a quick look at 50 ohm coax cable.

Belden makes hundreds of 50 ohm cables, including a whole line of ultra-low loss versions (Belden 7805 to Belden 7977). The two largest versions are HUGE. The 7977 has a diameter of .600" six-tenths of an inch! This is the largest coax cable that we make.

But first of all, why 50, or any other number? The answer can be shown in the graph below. This was produced by two researchers, Lloyd Espenscheid and Herman Affel, working for Bell Labs in 1929.

They were going to send RF signals (4 MHz) for hundred of miles carrying a thousand telephone calls. They needed a cable that would carry high voltage and high power. In the graph below, you can see the ideal rating for each. For high voltage, the perfect impedance is 60 ohms. For high power, the perfect impedance is 30 ohms.

This means, clearly, that there is NO perfect impedance to do both. What they ended up with was a compromise number, and that number was 50 ohms.



You will note that 50 ohms is closer to 60 than it is to 30, and that is because voltage is the factor that will kill your cable. Just ask any transmitter engineer. They talk about VSWR, voltage standing wave ratio, all the time. If their coax blows up, it is voltage that is the culprit.

So why not 60 ohms? Just look at the power handling at 60 ohms - below 50%. It is horrible! At the compromise value of 50 ohms, the power has improved a little. So 50 ohm cables are intended to be used to carry power and voltage, like the output of a transmitter. If you have a small signal, like video, or receive antenna signals, the graph above shows that the lowest loss or attenuation is 75 ohms.

Still, I get a lot of feedback from people who use 50 ohms for small signals; you can see above that they are taking a 2-3 dB hit in attenuation. Excuses I hear are “It's too late to change now!” or “That's the impedance of the box itself.” This is especially true of most test gear, which is universally 50 ohms. You have to buy a matching network to use it at 75 ohms or any other impedance. But there are lots of applications where 50 ohms is the best choice.

Belden 7977 mentioned above, can carry more than 5 kW at 30 MHz and more than 600 watts at 6 GHz. So even a cable this small could be used for TV or FM low power, boosters, translators, two-way radios, life-safety such as police/fire, RPU, many ham frequencies, microwave transmitters up to 6 GHz, and probably hundreds of other applications where signal are being delivered with high voltage and high power.

Most often, these signals end up in antennas. For instance, the sections in transmitters where small output power sections, like an exciter, are fed to a larger power section also require 50 ohm cable. That might be where the physically smaller 50 ohm cable might be used.

For many of these cables, they come in three versions: for outdoor applications, for riser-rated indoor applications, and for water-blocked applications such as direct burial or under-water applications. Some are even approved for shipboard ABS approvals.

These shipboard versions are also LSZH or low-smoke zero-halogen, which is often a requirement in some European countries.

You can get more information and samples by contacting Belden customer service or just drop me a line at steve.lampen@belden.com.



Now to really dig into the math, go here:

http://www.microwaves101.com/encyclopedias/458-why-fifty-ohms







Additional information about using 75 ohm coax and how to compensate is here:

http://www.w9xt.com/page_radio_gadgets_hardline.html




« Last Edit: August 10, 2014, 03:04:54 PM by WT5MW » Logged
W0BTU
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« Reply #8 on: August 10, 2014, 03:19:45 PM »

Well done. I've never seen that graph, that's interesting.

What's also interesting is that the power handling curve of RG-6 is almost identical to RG-213. I can't explain why, even though the center conductor is so much smaller. Amazingly, it'll handle 3 kW all day long at 160 meters.

RG-6 is all I run outdoors. It doesn't even get warm at 1500W. Neither do my F connectors.
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WT5MW
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« Reply #9 on: August 10, 2014, 03:51:54 PM »


What's also interesting is that the power handling curve of RG-6 is almost identical to RG-213. I can't explain why, even though the center conductor is so much smaller. Amazingly, it'll handle 3 kW all day long at 160 meters.


They explain here (not my words):

http://www.microwaves101.com/encyclopedias/458-why-fifty-ohms

For RF signals, resistance per unit length of coax cables is determined by circumferential area of the conductor surface due to skin depth effect, not cross-sectional area. Here's the solution for loss/length for coax cables of arbitrary dielectric constant and metal properties:



The details of this equation are derived on this page.

http://www.microwaves101.com/Coaxloss.cfm

You'd think a fat conductor would always give the lowest insertion loss because it has the most circumferential area (the 1/d component of the above equation decreases loss for increasing d), but no.  The characteristic impedance of the cable (Z0) throws that log(D/d) function into the denominator, it increases for increasing d.

In order to plot loss/length versus characteristic impedance, let's review the coax impedance calculation. The impedance of coax for a given outer diameter and dielectric is solely a function of the diameter of the inner conductor and the dielectric constant of the filler material:



Now we can plot loss/length versus characteristic impedance. It turns out that insertion loss has a minimum around 77 ohms, for any cable with Er=1 (air dielectric). In this example, we chose 10 mm inner diameter of the outer conductor, and calculated loss at 10 GHz.



Peak Power Handling

The peak power handling for air coax is limited by voltage breakdown (as opposed to heating effects which limit average power handling). You'd think that you'd want maximum separation between the opposing conductors (inner wire and outer sheaf) to avoid arcing, so you'd make the inner conductor as thin as possible, but no again! The maximum voltage field in a coaxial cable is quite different than between parallel-plane conductors. Here's the equation for "field enhancement", which is a measure of how much worse the fields are than in parallel plate:

Beta=(a/r)/[ln(1+a/r)]

Here a is the is the gap between the conductors and r is the radius of the inner conductor. This is from from Gilmour's book. Once again, characteristic impedance has to be considered because power depends on V2/Z0.

The way to calculate maximum power handling is to assume a critical electric field can't be exceeded to avoid breakdown. We'll assume 100,000 volts/meter (actually it can exceed 1,000,000 volts per meter, but the whole topic of voltage breakdown deserves a lot more attention so we'll be conservative here for the time being). Next, calculate the field that would be generated across the gap in the coax cable, without regard to the geometry (assume the center and outer conductors are parallel plates). Then apply the field enhancement equation above (which is a number greater than 1). Then the maximum power is equal to Vcritical^2/(2Z0). Why the "2" in the denominator? That's because Vcritical is a peak value, not an RMS value.



The best peak power handling occurs at Z0=30 ohms.

The voltage breakdown of air coax is a function of atmospheric pressure (or altitude), temperature, humidity, and even surface roughness. How do you increase the power handing of air coax? that's easy, fill it with a dielectric such as PTFE! Typical "solid" dielectric withstanding voltage is much higher that the breakdown voltage of air, by a factor of 10 or more. Foamed dielectrics used in cables don't provide much of an increase in voltage handling compared to air, but semi-rigid coax (solid PTFE) can handle 10s of kilowatts, the overall voltage limitation is usually the connectors that are attached to the cables.

The 50-Ohm Compromise

The arithmetic mean between 30 ohms (best power handling) and 77 ohms (lowest loss) is 53.5, the geometric mean is 48 ohms. Thus the choice of 50 ohms is a compromise between power handling capability and signal loss per unit length, for air dielectric.

Why 75 Ohms?

For cheap commercial cables such as those that bring CATV to your home, 75 ohms is the standard. These cables don't have to carry high power, so the key characteristic that should be considered is low loss. The answer to the "why 75 Ohms?" question seems obvious. We just saw that 77 ohms gives the lowest loss for air dielectric coax, so 75 ohms might be just an engineering round-off. We know of one text book that will tell you that is why RG cables are 75 ohms... but they are wrong!

Here's the problem. Commercial CATV cables are filled with PTFE foam, which has a dielectric constant around 1.43. Guess what? The loss characteristic is a function of the dielectric constant (~SQRT(ER)), while impedance is a different function of dielectric constant (~1/[SQRT(ER)]). The opposing contibutions of Er muddy the waters quite a bit.

It turns out that the minimum loss impedance for ER=1.43 is around 64 ohms, as shown in the plot below (purple trace). For the record, for solid PTFE (ER=2.2, yellow line) the minimum loss occurs near 52 ohms. So it's serendipity that when we use 50 ohm semirigid coax cables with solid PTFE, they give nearly the lowest possible loss for ER=2.2!
PTFE was invented by Roy Plunkett in 1938, well after the 50 ohm standard was in place.



So why 75 ohms? Here's our guess. Often the center conductor of cheap cables is made of a steel core, with some copper plating. The lower the impedance, the bigger the diameter of the center core. An impedance of 75 ohms was probably a compromise between low loss and cable flexibility.
« Last Edit: August 10, 2014, 03:55:20 PM by WT5MW » Logged
N3DT
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« Reply #10 on: August 10, 2014, 05:20:45 PM »

Boy, that's a good education.  But I do use some RG6 to feed a 6M dipole up about 50'.  I also use some RG11 to feed the GPS antenna/amp.  It was recommended by Nortel and if you look at the specs it's almost like hardline and you can get 150' of underground rated for about $30 delivered from ebay. You just have to buy some F adapters because it's aluminum foil and you can't solder connectors on it, they have to be crimped. 75 to 50 ohms is only 1.5:1, and usually with a long run you can't see a difference and then it's better.
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K0ZN
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« Reply #11 on: August 10, 2014, 09:37:30 PM »

 Wow!  Thanks for taking the time and effort to go over those details and give a sensible review/explanation of the math involved.  Much appreciated!

 When is your seminar on parallel conductor transmission line ?!   Chuckle.....

 73,  K0ZN
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WT5MW
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« Reply #12 on: August 10, 2014, 09:42:48 PM »

Wow!  Thanks for taking the time and effort to go over those details and give a sensible review/explanation of the math involved.  Much appreciated!

 When is your seminar on parallel conductor transmission line ?!   Chuckle.....

 73,  K0ZN

Don't want to take credit for others work!  I just assembled them here for reference, edited for specific points, and connected images.  Links are at the very tops of the posts to the originals.  Smiley

73 de WT5MW
« Last Edit: August 10, 2014, 09:52:32 PM by WT5MW » Logged
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