What causes variations in delay in coax cable of the same length?

[Twigg]

Hey all,

I was doing some tests in lab when I noticed that between two 4.5m RG174 SMA cables, there was a 1ns difference in delay at 4MHz between the two cables. To clarify, theory says 4.5m of RG174 (66% velocity factor) at 4 MHz should have a delay of 22.7ns. I measured one cable at 22ns and the other at 23ns. I know, they only differ in the last digit, but I have other data that suggests the difference is real but I don't have time or a good excuse to do a better measurement of the delay. I also observed no measurable difference in the delay time when I try to bend or coil the cables. What is the main source of variations like this? Is it the connector joints? Wear and tear? 5% variation just seems high. Thanks!

Edit: both cables were at room temperature, in air (not in a harness or in a server rack or anything that would insulate them)

 

[berkeman]

RG174 (66% velocity factor)

Do they specify a tolerance on the velocity factor or $Z_0$ ? +/-5% is not an unreasonable tolerance on those values for many transmission line cables (coax, twisted pair).

 

[berkeman]

BTW, how are you measuring these delays? Are you using a TDR setup?

At 4MHz it's pretty easy to measure $Z_0$ with just a multi-turn potentiometer on the far end of the cable and a TDR driving the near end -- you could see if the differences in $Z_0$ values tracked the difference in velocity factors values...

 

[Joshy]

If you redo the calibration do you see the same measurement and difference in time?

 

[Twigg]

Do they specify a tolerance on the velocity factor or Z0 ? +/-5% is not an unreasonable tolerance on those values for many transmission line cables (coax, twisted pair).

Confession time, this is my first time actually thinking about coax cable specs. I don't actually know the manufacturer or datasheet for the cable (the joys of inheriting someone else's work when they're long gone), I just quoted 66% because I looked up a bunch of RG174 cables and they all seem to have the same velocity factor so I assumed it was a standard. I have no clue about the tolerance, but it's good to know that 5% would be considered not unreasonable. Also, what is $Z_0$ here?

BTW, how are you measuring these delays? Are you using a TDR setup?

If you redo the calibration do you see the same measurement and difference in time?

Nope, no specialized equipment. Just a function generator and an oscilloscope. I put a tee on Ch1 of the scope, connect one end to the function generator, one end to the 4.5m cable, then I run the other end of the cable to ch2 of the scope (with a tee and a 50ohm terminator, for impedance matching). I measure the delay by measuring the distance between zero-crossings of the two waveforms on the scope. I was winging it.

Good to know though, that a TDR is the right tool for the job!

 

[berkeman]

I put a tee on Ch1 of the scope, connect one end to the function generator, one end to the 4.5m cable, then I run the other end of the cable to ch2 of the scope (with a tee and a 50ohm terminator, for impedance matching)

I'm not understanding your setup, but a "coax tee" is not usually a valid way to split a transmission line. You need to use an actual splitter to do that. In this case with the low frequencies involved it may not matter, but I'd have to see a diagram of the setup to be sure.

I did some searching for a good datasheet for your coax, but I haven't found any with tolerances listed (ack).

 

[Twigg]

Sorry for the rushed schematic, I'm out the door for a trip. If it's still an issue, I'll get you a better one early next week.

The reason I used the splitters was because the scope has high impedance inputs. I can confirm this because I saw almost equal amplitude on Ch1 and Ch2, and that amplitude was almost exactly what I set the function generator to produce (100mV).

 

[berkeman]

I know you're out the door, but at some point you could switch your signal generator to square wave output, and look for any ringing in the 'scope waveforms. That would indicate that reflections are coming into play.

 

[Tom.G]

The cables are most likely from different manufacturing batches, and/or different manufacturers. At 4.5m meters, there are probably markings on them, compare the markings for further information.

Also age, misuse, storage conditions, and moisture can degrade them.

 

[alan123hk]

What is the main source of variations like this? Is it the connector joints? Wear and tear? 5% variation just seems high

Please refer to page 11 of the RG174 specification below. The impedance $\left( \sqrt \frac L C \right) ~$ is 50+/-2 Ohm. Although they do not specify the tolerance of the velocity, if estimated based on the tolerance of impedance, the tolerance of the velocity $\left( \sqrt \frac 1 {LC} \right)~$may also reach about +/-4%. So if the theoretical value is 22.7ns, even if the cable is provided by the same manufacturer, the actual value range may be from 21.79ns to 23.61ns. But of course, if it is from the same roll of cable or the same batch from the same manufacturer, their tolerances may be much smaller.

https://www.radiall.com/media/files/RFCableAssemblies D1C004XEe.pdf

 

[Baluncore]

Although they do not specify the tolerance of the velocity, if estimated based on the tolerance of impedance, the tolerance of the velocity Sqrt(1/LC) may also reach +/-4%.

Not necessarily.
So long as the ratio of L/C remains constant, the impedance will remain constant.
But the velocity factor comes from the product of L*C, so you cannot assume a flat impedance line will have a flat vf.

A TDR sees only reflections from changes of line impedance. It cannot see changes in vf.
When you stretch a coaxial cable, the braid increases inductance, while the line capacitance also increases, so the impedance tracks approximately. But the velocity factor is lower, and the cable is longer, which makes for big changes in vf.

 

[alan123hk]

Not necessarily.
So long as the ratio of L/C remains constant, the impedance will remain constant.
But the velocity factor comes from the product of L*C, so you cannot assume a flat impedance line will have a flat vf.

Your argument is of course mathematically correct and logical.

I assume that the correlation coefficient between L and c is very small during the manufacturing process of the cable. I believe that they are likely to have relatively independent probability distributions, because each of them is determined by different materials and geometries at different locations on the cable, and these materials/components are likely to be made separately and then assembled together.

But I agree that everything is still hypothetical before the manufacturer confirms

 

[Twigg]

Sorry for dropping this thread for so long. We were focusing on other things in lab for a while. You know how it is.

This week, I'll hopefully be trying to do the square-wave measurement @berkeman recommended.

I have another question, based on the datasheet @alan123hk shared. I attached a partial screenshot.

(highlight mine)
What does this "shielding effectiveness" mean? Does that mean that if there is RFI, there will be 40dB less pickup in the core than in the shielding? (Wouldn't that actually be terrible for the RF signal?) Or does that mean that RFI, as measured differentially between the shielding and core is suppressed by 40dB? If that's the case, what's the 40dB relative to?

Thanks again!

 

[Tom.G]

Sorry for dropping this thread for so long. We were focusing on other things in lab for a while. You know how it is.

This week, I'll hopefully be trying to do the square-wave measurement @berkeman recommended.

I have another question, based on the datasheet @alan123hk shared. I attached a partial screenshot. View attachment 291414
(highlight mine)
What does this "shielding effectiveness" mean? Does that mean that if there is RFI, there will be 40dB less pickup in the core than in the shielding? (Wouldn't that actually be terrible for the RF signal?) Or does that mean that RFI, as measured differentially between the shielding and core is suppressed by 40dB? If that's the case, what's the 40dB relative to?

Thanks again!

Consider the shield as you would consider tinted glass for light. Any external interference will be reduced by 40db by the time it gets thru the shield to the core conductor; that's a factor of 100 reduction.

Sounds pretty decent to me, how many pieces of your read-out equipment have an amplitude resolution and accuracy of <1%?

Cheers,
Tom

 

[Baluncore]

What does this "shielding effectiveness" mean? Does that mean that if there is RFI, there will be 40dB less pickup in the core than in the shielding? (Wouldn't that actually be terrible for the RF signal?) Or does that mean that RFI, as measured differentially between the shielding and core is suppressed by 40dB? If that's the case, what's the 40dB relative to?

The signal inside a coaxial cable propagates as two equal and opposite currents. One current flows on the outside of the central conductor, with the other exactly opposite current, flowing on the inside of the braid. That common mode signal is almost inside a world of it's own.

There is another world outside the cable. The currents that flow on the outside of the braid are exactly mirrored by currents flowing on the surfaces in the external conductive world.

When measured in wavelengths, the holes in the braid are too small to pass much energy, so to a first approximation, the inside and outside of the braid form two distinct conductors. The shielding effectiveness specifies the attenuation between those two distinct surfaces of the braid.

The leakage through the shielding braid, is specified relative to the signal propagating on the source side of the braid. 40 dB of shielding represents an attenuation of the voltage or current by a factor of 100 when passing through the braid. That is equivalent to a power ratio of 10,000.

 

[Twigg]

The signal inside a coaxial cable propagates as two equal and opposite currents. One current flows on the outside of the central conductor, with the other exactly opposite current, flowing on the inside of the braid. That common mode signal is almost inside a world of it's own.

There is another world outside the cable. The currents that flow on the outside of the braid are exactly mirrored by currents flowing on the surfaces in the external conductive world.

Ok, so if I understand correctly, I should think of the RF cable as 3 channels:
1) the RF current on the core conductor
2) the opposing RF current on the inside of the braid
3) the image current on the outside of the braid that cancels all RFI fields inside the braid

Am I understanding this correctly?

The leakage through the shielding braid, is specified relative to the signal propagating on the source side of the braid.

So 40dB is the ratio of the current of channel 3 (the image current on the outside of the braid) to the RFI currents measured on channels 1 and 2 (core and inside of the braid), correct? And even this leakage is common mode, right? Or does the 40dB refer to the differential RFI signal, i.e. the RFI you would actually measure as noise on the end of the coax cable?

 

[Twigg]

So 40dB is the ratio of the current of channel 3 (the image current on the outside of the braid) to the RFI currents measured on channels 1 and 2 (core and inside of the braid), correct? And even this leakage is common mode, right? Or does the 40dB refer to the differential RFI signal, i.e. the RFI you would actually measure as noise on the end of the coax cable?

Sorry, this wasn't my finest hour, clarity-wise. Let me try asking this again.

If I plug this cable into an impedance matched oscilloscope, and if I have 1mA of RFI current on the shielding, do I measure 10$\mu$A or do I measure 0A on the oscilloscope?

The reason I'm asking if I measure 0 is because I would think that the 1% leakage (40dB power ratio = 1% amplitude ratio) would be entirely common mode (current flowing in the same direction on the core and shielding), and so it wouldn't be seen on the oscilloscope since the oscilloscope looks for the differential mode (current flowing in opposite directions). Or does the 40dB "shielding efficiency" already take that into account? (In that case, I would expect to see the 10$\mu$A on the oscilloscope.)

 

[Baluncore]

An oscilloscope sees voltage, not current. If the oscilloscope input is terminated in 50 ohms, then it can convert the current to a voltage. But if you are at the end of the cable, you cannot see the voltages or currents flowing on the inside and outside of the braid.

Ok, so if I understand correctly, I should think of the RF cable as 3 channels:
1) the RF current on the core conductor
2) the opposing RF current on the inside of the braid
3) the image current on the outside of the braid that cancels all RFI fields inside the braid
Am I understanding this correctly?

Maybe not.
A channel is a circuit, so it must have a return path. A coaxial cable is actually two transmission lines with different dielectric, impedance and velocity factors.
1. The central conductor against the inside of the braid, with a low loss dielectric and well controlled impedance and velocity factor.
2. The outside of the braid, against the rest of the universe, with an air dielectric, with poorly controlled impedance, and a velocity closer to light.
Now you must think of the near and the far ends of the coaxial cable as being far apart and isolated from each other.

So 40dB is the ratio of the current of channel 3 (the image current on the outside of the braid) to the RFI currents measured on channels 1 and 2 (core and inside of the braid), correct? And even this leakage is common mode, right?

No.
There are only two information channels.
One signal is between the centre of the coaxial cable and the inside of the braid.
The other signal is the outside of the braid referenced to the near environment.
Those two circuits have a shared common ground terminal at the ends of the cable.
There is cross-talk of -40dB between the two signal circuits.

 

[Twigg]

An oscilloscope sees voltage, not current.

Sorry, yes, I was being lazy. You wouldn't measure 10$\mu$A with the oscilloscope, but 500$\mu$V (for 50 Ohm impedance).

Maybe not.
A channel is a circuit, so it must have a return path. A coaxial cable is actually two transmission lines with different dielectric, impedance and velocity factors.
1. The central conductor against the inside of the braid, with a low loss dielectric and well controlled impedance and velocity factor.
2. The outside of the braid, against the rest of the universe, with an air dielectric, with poorly controlled impedance, and a velocity closer to light.
Now you must think of the near and the far ends of the coaxial cable as being far apart and isolated from each other.

This was very helpful, thank you! So, just checking again if I understand this, if I plug one end of the cable into the 50ohm-terminated oscilloscope, and I have 1mA of RFI current on the outside of the shielding, then I measure 500$\mu$V on the 'scope due to cross-talk. However, if I connect the cable to the oscilloscope through a transformer, then I measure 0V from RFI because I've broken the RFI's return path, right? Why I think this is that the RFI current on the outside of the shielding doesn't return through the core, so there will be no magnetic flux induced in the transformer primary. Is that correct, or have I botched it again?

 

[alan123hk]

What does this "shielding effectiveness" mean? Does that mean that if there is RFI, there will be 40dB less pickup in the core than in the shielding?

Calculating or estimating the actual situation of the interference of external electromagnetic fields on the transmission line may be a complicated problem.

However, from a physics point of view, the basic concepts and principles of this so-called shielding effectiveness are relatively simple and easy to understand.

Simply put, shielding effectiveness is how much electromagnetic waves attenuate after passing through the shielding layer.

Shielding Theory​

https://learnemc.com/shielding-theory

Shielding Effectiveness Calculator​

https://cecas.clemson.edu/cvel/emc/calculators/SE_Calculator/index.html

 

[Twigg]

@berkeman I finally got around to doing the measurement you recommended in post #8. See below.

The blue (delayed) signal is the pulse train after it goes through the cable. Am I right to infer that the reflections are negligible?

After repeating my measurements with the square wave for 4 cables, I'm getting variations in velocity factor of about 2-3%, if anyone was curious.

 

[Baluncore]

Am I right to infer that the reflections are negligible?

Probably yes.
Your green received wave delayed by the one way transit time, T, looks good.
The slightly lower amplitude of the pink transmitted wave, for a period of 2T following an edge, appears to be due to the cable having a lower impedance than the signal generator or oscilloscope termination. The small reflection from the far end makes up the difference when it finally gets back to the start at 2T.

 

[Baluncore]

Here is an LTspice approximate simulation of the square wave test.
The signal generator is 50R series terminated into the cable.
The output is parallel terminated with 50R, 3R of which is dummy line-loss.
The manufacturer specifies the line as having an impedance of 50R ± 2R.
The line clearly has a lower than matched impedance.
So the lowest in-specification line impedance would be 48R.