Understanding RG6-75 ohm Cable Impedance

Question

Here is my measurement to a piece of RG6 cable. It is around 30cm cable. On the shield is written COAXIAL CABLE 5C-2V 75 ohm. From my measurement I got data as below:

From that table, we can see that there is significant impedance of the cable. If we calculate the inner and the outer impedance using formula Z=R+j(XL-XC), where XL=j2pifL, and XC=j/(2pifC), L in Henry, C in Farad, f in Hertz, and pi=3.14159265358979. Calculation with the data below and using 2,100 MHz frquency, I got as below:

• Z inner=5+j2638.9 ohm, and
• Z outer=6+j1319.5 ohm.

Then my question is:

• What is the 75 ohm meaning (written at the the cable shield)?
• What is those two impedance meaning to the antenna?
• If we got data in real cable, what to do to match the impedance?

Edit: The cable was just used for C-Band parabolic antenna.

Answer 1

You have mixed up the characteristic impedance of a coaxial cable with the DC impedance measured from a piece of that cable. So I'll tell you what you measured and then what you could have done instead.

• First of all, I have no idea what does it mean to measure a capacitance with a multimeter when you have connected both measurement leads to the same piece of wire. Probably your multimeter doesn't know either and that's why you got the wildy swinging numbers. Capacitance is a measure of how much electric charge (electrons) is stored in a capacitor. If you would have a bit of ripple in any voltage, this charge could be used to "even out" the variations. If you measure the capacitance between the inner and outer wire, it would be more useful. I would forget your measurement results completely.

• The inductance measurement already makes more sense: it tells you how strongly anything (your cable in this case) fights against the current from changing. Again, inductance can be useful in a filter. Longer cable means more inductance. In your measurement, probably a great deal of measured inductance is created by the fact that the measurement leads form a loop. If you repeat the "L outer" measurement and start turning the cable in all kinds of crazy shapes, you'll get much higher inductances.

• The resistance you have measured tells us about the losses in your circuit. It basically tells you how much is the voltage loss along the cable if a known current goes through the cable. If you have a longer cable, there will be more losses.

So that's what you measured, and I'm sorry to say but all of that was nonsense. When we are talking about characteristic impedance of a coaxial cable, we mean the ratio of current going along the wire and the voltage between the inner and outer conductor. Although the wire has impedance of $75 \Omega$, this doesn't say anything about losses. As others have pointed out, you can measure the capacitance per unit length and the inductance per unit length and then calculate the characteristic impedance of the cable from $Z=\sqrt{L/C}$, but the multimeter accuracy is just not enough.

• What is the 75 ohm meaning (written at the the cable shield)? The characteristic impedance is a property of the raw cable that tells you the ratio of voltage and current of a wave travelling through the cable.
• What is those two impedance meaning to the antenna? In this case (I assume you have a commercial satellite TV dish antenna) the only importance is that all components in the chain must have the same impedance: the antenna has been "matched" so that the output impedance is $75 \Omega$, your cable is $75 \Omega$, and finally the actual receiver is designed so that it works best when it sees $75 \Omega$ impedance. Changes in impedance mean that power is reflected (and then lost).
• If we got data in real cable, what to do to match the impedance? You can trust the impedance written in the cable jacket. You don't match impedance of the cable, you must match the impedance of the antenna as seen through the cable. If you can measure the actual impedance (at RF frequency, not multimeter) of the system of antenna and cable, maybe you can ask a new question on how to match that to $75 \Omega$ or $50 \Omega$ (or what ever impedance you choose to use in your system).

Answer 2

See a description of 50 vs 75 Ω here:

https://www.eham.net/ehamforum/smf/index.php/topic,98296.msg776787.html#msg776787 :

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.

[...]

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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