Characterizing High Impedance Cable?

[Andrew_K]

Hi All,

I am trying to characterize some specialty cable. It is NOT coax, which is making research on this topic very difficult for me. (I can only find things about transmission lines / coax)

As for the cable, it is about 10kOhm per foot. Each wire consists of a spiral of wire around a plastic core (for the high R).
There are 6 individual wires in the cable, separated by insulation only. There is no twisting of pairs. Differential measurements are taken from each pair.
This is great for DC, but there is unknown impedance at higher frequencies.

My end goal is to make a model of this wire for use in LT spice. I'm not sure if this can be considered a lossy Tline in terms of modeling, but R is per-length.

I do have measurements from a S21 measurement (high impedance active probe), as well as measurements from an impedance analyzer.

I have S21 mag and phase (from VNA), as well as Z mag/phase (from impedance analyzer). However, I'm not sure how to apply these for a model, other than using matlab tfest to get a transfer function.


Has anyone done similar?
Any recommendations on textbooks or app notes that would help me better understand this?

[Terry Bites]

Its likey going to bee seen as an open circuit by the vna.
Terminate the line with a known impedance and measure the Reflection Coefficient, Г.
You need a scope, a function generator and some basic algebra.
You want a load of the same order of magnitude.

See  Metamaterials - 2008 - Munk - Appendix C How to Measure the Characteristic Impedance and Attenuation of a Cable.pdf (91.41 kB - downloaded 65 times.)

[mag_therm]

If 10kOhm /ft it must be made of some resistive material ?

For a transmission line to form and energy to travel over wavelengths, the primary constants per length  have to be
jWL >> R
jWC >> G

if R >> jWL, the wire will just look like a resistor.

[Andrew_K]

It's like a super long wire wound resistor. Which makes me think it should be inductive.

There's definitely some complex impedance that I'm measuring

[gf]

Mybe this helps: https://www.edaboard.com/threads/extracting-rlgc-values-from-network-analyzer-s2p-files.168869/
( I don't feel able to assess the correctness of this information, though. )

[Benta]

Sounds like an ignition cable for a petrol engine spark plug.

[Andrew_K]

Its likey going to bee seen as an open circuit by the vna.
Terminate the line with a known impedance and measure the Reflection Coefficient, Г.
You need a scope, a function generator and some basic algebra.
You want a load of the same order of magnitude.

I ended up using an impedance analyzer to get the measurements. I did find a way to measure characteristic impedance with the short/open method.

Mybe this helps: https://www.edaboard.com/threads/extracting-rlgc-values-from-network-analyzer-s2p-files.168869/
( I don't feel able to assess the correctness of this information, though. )

Interesting! Unfortunately, I can't really get *full* 2-port measurements, as the impedance is not anywhere near 50 ohms.
And making a balun sounds painful.


That all being said, I do have the characteristic impedance and a few other parameters (Alpha, Beta).

Given that this is a lossy T-line, not a lossless one,
I'm really struggling to find equations where I could solve for the per-length C and L given what I have.

Maybe I need to take additional measurements...

[T3sl4co1l]

How much does it matter, anyway?  What are you using it for?

It sounds like the resistance will be so high, inductance is utterly negligible, and capacitance can be measured at low frequencies, and using a lossy (RC) t-line model should suffice.  And indeed, making a balun for that impedance is only going to work in a narrow bandwidth -- over which you probably won't be able to measure much inductive reactance.

Tim

[Bud]

There is no point to measure L because R will dominate in the impedance.

[gf]

That all being said, I do have the characteristic impedance and a few other parameters (Alpha, Beta).

A RLGC transmission line model is completely described by the parameters gamma(f) and Zc(f), where gamma(f) = alpha(f) + j * beta(f).
So it seems you have everything you need.
For a lossy TL, alpha is nonzero and Zc is not real, but complex.

If you need R,L,G,C instead of gamma and Zc, then I found a conversion here. If I'm not mistaken, this should be equivalent to

R(f) = real(gamma(f) * Zc(f));
L(f) = imag(gamma(f) * Zc(f)) / (2*pi*f);
G(f) = real(gamma(f) / Zc(f));
C(f) = imag(gamma(f) / Zc(f)) / (2*pi*f);

when numLines=1, i.e. for a single two-port transmission line.

[Andrew_K]

How much does it matter, anyway?  What are you using it for?

It sounds like the resistance will be so high, inductance is utterly negligible, and capacitance can be measured at low frequencies, and using a lossy (RC) t-line model should suffice.  And indeed, making a balun for that impedance is only going to work in a narrow bandwidth -- over which you probably won't be able to measure much inductive reactance.

Tim

I am trying to characterize this cable because the parasitics cause distortion. Changing the cable is a last resort, and might not even work.
If I can characterize it properly, and simulation reasonably matches, I can determine if compensation is feasible.
Some experimentation shows that compensation may work, but I'd rather not brute-force a design by trial-and-error on the bench if I can help it.

I'm not 100% positive that inductance would be negligible, since that is not the case for wire-wound resistors.

That all being said, I do have the characteristic impedance and a few other parameters (Alpha, Beta).

A RLGC transmission line model is completely described by the parameters gamma(f) and Zc(f), where gamma(f) = alpha(f) + j * beta(f).
So it seems you have everything you need.
For a lossy TL, alpha is nonzero and Zc is not real, but complex.

If you need R,L,G,C instead of gamma and Zc, then I found a conversion here. If I'm not mistaken, this should be equivalent to

R(f) = real(gamma(f) * Zc(f));
L(f) = imag(gamma(f) * Zc(f)) / (2*pi*f);
G(f) = real(gamma(f) / Zc(f));
C(f) = imag(gamma(f) / Zc(f)) / (2*pi*f);

when numLines=1, i.e. for a single two-port transmission line.

This looks promising, and this is what I was having trouble finding. Thank you very much!

[Stray Electron]

Sounds like an ignition cable for a petrol engine spark plug.

   That was my first thought too. But not with six conductors.  And with six conductors insulated from each other then it must be for some kind of low voltage service or it would arc over.

[mag_therm]

When all else fails you can calculate inductance L/metre directly, as you can see the spiral.

dia of spiral d [metre]
Area of spiral A [metre^2] = pi*(dia^2)/4
 Turns /metre can be counted

L/metre = 4*pi*1e-7 *(N^2) A/ 1    [Henry/metre]

Very sure you will find R/metre , which you already measured  is about 30000 Ohm/metre, will be >> | jW L |

As a <GUESS> ran <20 T/cm> = 200 T/m
spiral dia = <6mm> so A = 28.27e-6 m^2

L = 1.4 microHenry /metre
@ 1 MHz jWL = 8.79 Ohm/metre ........100 MHZ jWl= 879 Ohm/m     1000MHz jWL=8790 Ohm/m.....  but check my math

[T3sl4co1l]

I am trying to characterize this cable because the parasitics cause distortion. Changing the cable is a last resort, and might not even work.

Distort what?  And "distortion" in what sense?  To me, it's a linear element which therefore contributes no distortion, in the unqualified sense.

Tim

[mag_therm]

Sometimes the R and G primary constants were referred to as "parasitic transmission line losses"
I just saw reference to it in skin effect loss of microstrip lines.

The losses did cause distortion 100 years ago when thay were directly transmitting key pulses and baseband audio, because the distortion
was, in phase and attenuation,  frequency dependent. Telegrapher's Equation solves this.
Distortion like this was not such a problem when baseband was converted up on a carrier with relatively narrow bandwith.

Maybe this will arise again with the new  spread spectrum direct sequence modes. -high frequency data over a wide bandwidth.

[Andrew_K]

I am trying to characterize this cable because the parasitics cause distortion. Changing the cable is a last resort, and might not even work.

Distort what?  And "distortion" in what sense?  To me, it's a linear element which therefore contributes no distortion, in the unqualified sense.

Tim

If I put a pulse through the circuit, it looks like there was a LP filter applied to it. But modeling a simple 1st order filter does not match what is observed in the TD.
The frequency response also looks different.


Looking at my data, the phase of the Z0 changes dramatically with frequency. It makes some of the parameters- R' C' L' G', change rapidly - positive and negative, throughout the sweep. They do settle at high frequencies, but the values obtained don't give good results in Spice.


I'm thinking I may need to change my measurement procedure.

An impedance analyzer is 1-port only. VNAs are 2-port, but at Z0=50.

Is there any sort of 2-port network analyzer that is meant for high-impedance with other parameters? ABCD for example?

[Bud]

I'm not 100% positive that inductance would be negligible, since that is not the case for wire-wound resistors.

That is true for low Ohm resistors, up to couple hundred Ohm. But you have 10K resistance. It will swamp any inductive impedance.

[Andrew_K]

I'm not 100% positive that inductance would be negligible, since that is not the case for wire-wound resistors.

That is true for low Ohm resistors, up to couple hundred Ohm. But you have 10K resistance. It will swamp any inductive impedance.

You and Tim are probably correct, then.

Any suggestions on actually measuring this? The Open/Short method didn't seem to give good results.

Would I get a good measure of C given that it is so resistive?

[ejeffrey]

For a transmission line you need signal and return.  Are you using a separate return wire / plane or are some of the 6 wires used for the return?

[Andrew_K]

I used the open/closed method. I took two wires of a "pair". Measured across one "port", kept the other side of the cable open/short.

For reference, this is in section 5.9 of the impedance measurement handbook by Keysight.

I understand that this is technically a "balanced" cable, and I'm taking an imbalanced measurement. But I'm not sure how significant that is, given the impedance mismatch of the "UNKNOWN" ports would be very small w.r.t. the impedance of the cable being tested.

I looked at wide frequency baluns, but they're all 50 ohm impedance.


For reference, these are the measurements and obtained parameters.



And



The angle of the measured Z has a fairly large range. And it jumps by a significant amount, even when "settled". Units are degrees...

[T3sl4co1l]

Even if the cable has a large height above ground plane, it will still be in the vicinity of low 100s ohms, common mode.  That is, driving one line, alone or even with multiple remaining lines grounded, will end up with the common mode driving over GND, while the differential mode(s) within the cable decay more rapidly due to the higher capacitance between them.

So, you have a situation that varies with frequency and position/length.  High frequencies are absorbed quickly, so that only the nearest length behaves as a differential transmission line, and the remaining fraction of the input signal (which divides between the driven line and ground line(s) according to their relative impedances) follows the common mode path, which similarly decreases over distance, but should be slower than DM as mentioned, so you should observe two cutoff frequencies for DM and CM.  And since DM decays faster, you can measure the CM on any wire at the far end, driven or otherwise.

At low frequencies, at some point, DM will be perceptible at the far end, and CM will be less significant.  Obviously, at DC it's straight through, GND is GND and driven is driven.

A single pole RC should not give a good fit, but a chain of arbitrary length, with equal values of R and C, should give a good match with some adjustment.  It will diverge at high enough frequencies, as a lumped-element RC is only order N, while your cable is distributed, giving I think a cutoff probably something like exponential with frequency, the roll-off point depending on length.

Remember to model capacitance between wires in the cable, and from the cable (from each wire) to GND.  GND can be assumed ideal.  Set R from the DC measurement (resistance of the length, divided by the number of segments being modeled), and adjust the C's until the frequency response matches observation.

Your plots look rather noisy, which suggests using too long a length and too high a test frequency range.  s12 should be sufficient, or you can do a 4-port with ports 1 and 2 as +/- source and 3 and 4 as +/- load, measuring s13, s14, s23, s24.

Tim

[David Hess]

Are the conductors all wound in the same direction?  Delay line cable has wound conductors but they are wound in opposite directions.  I am thinking it might be low frequency delay line cable which is not going to behave sanely at frequencies above its cutoff.