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I've come across the Shannon-Hartley theorem, so I assume that a "signal" must have some notion of strength or "power" that can be referenced to some noise level (and whose power can be varied at the signal source). But what form does that power take on a coaxial cable?

E.g., is it a maximum voltage that can be observed between the conductor and the shield? Or something else?

And what is a typical value for this power measure or limit – say, as applied to RG6 cable for residential data transmission?

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The SNR used in the Shannon-Hartley theorem is the ratio of the signal power to the noise power.

So you want to use the power in watts or milliwatts to plug in to the formula.

Of course, if you have the power in dBm, you can convert that to milliwatts.

Or if you have the voltage amplitude (and the characteristic impedance of the system) you can also use that to find the signal power.

In practice, I've seen all of the following used to describe signal powers:

  • Power in watts
  • Power in milliwatts
  • Power in dBm
  • Voltage amplitude
  • Voltage peak-to-peak
  • Voltage rms

You should be prepared to convert any of these to the others to be able to compare specifications provided by different vendors or customers.

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The Shannon-Hartley theorem couples Bandwidth and Signal to Noise ratio to how much information can be transferred over a medium.

Let's just assume that there is a certain Bandwidth available, it doesn't really matter what it is. Then the Signal to Noise ratio becomes the only important factor. Note how it is a ratio where Signal and Noise both have to be expressed as power.

A coaxial cable is a from of a transmission line where both ends of the line (cable) have to be terminated properly. Most Coaxial cables you will encounter in the real world have a characteristic impedance of 50 ohms. That 50 ohms determines the ratio of voltage and current. Also, if you know the power of a signal going through that cable you can calculate the voltage and current.

So the signal (or noise, noise is also just an unpredictable signal) going through the Coaxial cable is just voltage and current, same as with any other cable. The cable is also just a "medium" for transport of the signal. Ideally the cable doesn't care about the voltage, current or power level. In practice there will of course be limits to what a cable can handle but usually we can ignore these limitations.

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    \$\begingroup\$ Why is the power level on a 50-ohm coax data cable not a practical consideration? What voltage or current levels will we observe in practice, and if we're not pushing the power limits of the cable then why are they not higher so that we can get more data across? \$\endgroup\$ – feetwet Jan 29 '18 at 21:26
  • \$\begingroup\$ Why would the power level be a practical consideration? You cannot only talk about power, it is Signal power over Noise power (S/N) that is important. Indeed if you'd use more power without increasing the noise, S/N would increase so the datarate can increase. The power limit is not in the cable but the device sending the data and the device receiving the data. There are practical limits on S/N we can use and these aren't in the cable but in the transceiver electronics. \$\endgroup\$ – Bimpelrekkie Jan 29 '18 at 21:40
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    \$\begingroup\$ I would say that 75-ohm coax is more likely to be encountered in everyday life (cable television, cable internet) for the average person. \$\endgroup\$ – davidmneedham Jan 29 '18 at 21:43
  • \$\begingroup\$ Right, there's no point in increasing signal power unless you can do so without increasing noise power. It sounds like you're saying that in practice most of the noise on a data cable comes from the transceivers, rather than the cable and its environment. But I'm astonished to learn that state-of-the-art data devices are sending signals measured in milliVolts across an 18AWG conductor (which means the current couldn't be more than a few Amps). Is there a clear reason the powers are kept to such low levels? \$\endgroup\$ – feetwet Jan 29 '18 at 22:36
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    \$\begingroup\$ @feetwet , I imagine the signal levels for cable TV systems are the range that they are due to the need to be similar to the levels for over-the-air antennas. \$\endgroup\$ – davidmneedham Jan 29 '18 at 22:40
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For cable modems, Arris gives example signal levels of -2 dBmV and SNR of 29 dB.

To give practical values for loss of RG-6 coax (more correctly referred to as Series 6 coax since RG-6 refers to an obsolete military specification), you can consult the Society of Cable Telecommunications Engineers' standard for drop cable, ANSI/SCTE 74.

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At 55 MHz, the insertion loss of 100 meters of Series 6 coax is 5.25 dB. So a signal level of 3.25 dBmV (1.45 mV) travelling 100 meters becomes -2.00 dBmV (0.794 mV) at the cable modem.

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  • \$\begingroup\$ Wow ... milliVolts is lower than I was expecting! And can you confirm that the voltage in such a specification would refer to the the peak voltage between core conductor and cable shield? \$\endgroup\$ – feetwet Jan 29 '18 at 22:20
  • \$\begingroup\$ The voltage levels would be measured as RMS values between the center conductor and the shield. \$\endgroup\$ – davidmneedham Jan 29 '18 at 22:30
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as you noticed, the theorem is about ratio of powers. A power is, for a linear medium, proportional to the square of voltage. However, in cases where you deal with coax cables, it's rather unusual to calculate in voltages, anyway; most things are defined as powers, as this makes handling easier (and also, the proportionality is given by considering the characteristic impedance).

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