## wire and coax impedance

• 0
I've come across something that I cannot find an explanation for although I have a theory. I am currently working on a coax design with a solid PTFE dielectric but using a NbTi wire (unplated) for the conductor. Through all of my calculations, I should be seeing 49.8 ohms. It's seems very basic, wire od, PTFE ID etc. However, when measuring the coax on a real time TDR, it is telling me it is 55 ohms. I've looked at it every which way I can think of and I'm clueless on why this is happening. PTFE is pure, and is properly cured. Could the resistance of the NbTi wire be causing issues with my TDR and artificially showing me an incorrect impedance? All other standard coax tested on the equipment tests the way it should. Thanks for any insight!
• 0
Yes, though Z0=sqrt( (R+jwL)/(G+jwC) ) so a high R will boost the impedance; it’s not artificial. You may have to increase C to compensate. Though I would expect R to be very frequency dependent. Can you sweep it on a VNA, and see what happens at very low frequency such as 300 kHz? You may see a spike in Z0 at very low frequency, which will be exasperated by the R since you are getting sort of a divide by zero.
• 0
Please provide dimensional information. Is relative mu (permeability) of NbTi equal to one? A non unity value would increase impedance. Here mu_r=1.22 would give the result you are seeing.
• 4
At some point I would like to capture the ipedance formula that takes into account mu... let me know where there is a good explanation of that.

The microwave office TXLine calculator does show some effect on Z0 when resistance increased, but not enough to explain a 10% shift.

Steve
• 0
Z= Zo x sqrt(mu_r/epsilon_r). Skin depth also decreases with increasing mu_r which in turn increases resistivity (rho= L/A and A decreases with mu_r).
• 4
Not sure I understand where this comes from

Z= Zo x sqrt(mu_r/epsilon_r)

But I'll try to give it some more thought!

Thanks
Steve
• 1
Now seems like a good time to point out that Electroless Nickel (such as in ENIG finishes) is not pure Ni but instead contains "high phosphorus content" typically around 10% P, this effectively makes the Electroless Nickel alloy non-magnetic with a relative permeability mu_r near 1. This is a common electrical simulation mistake where designers might assume electroless nickel has the same properties as pure nickel with a mu_r in the many hundreds.

Another side note, the bulk conductivity is also much worse than pure nickel...

I personally use mu_r of 3, and a resistivity of 60 uOhm-cm.
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