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Ive been posed with a problem regarding calculating the characteristic impedance of a shielded twisted pair with a drain wire. While I understand how to calculate this for a "normal" shielded twisted pair, Im struggling to understand how (if at all) the drain wire would affect the answer.

Background:

The application is a particle detector, in which space for cabling is at an absolute premium. People are losing hair over trying to find spare millimeters to route the cables for the elements in their areas. There is also a lot of repitition of cables, so shaving a mm off one type of cable for instance, adds up to a not insignificant saving over the whole detector.

In the section I work in, we are connecting hundreds of internal chips to the outside world over a CAN bus each. Grounding and shielding requirements dictate that CANH and CANL for the CAN line are contained within a foil shielded twisted pair. Management have however requested that we insert a drain wire into this twisted pair as a current return path (please see a basic image below), as it saves on the insulation mass of routing it as a single wire. We have found a company willing to produce this cable for us, but before we purchase any samples (which i could perform time domain reflectometry on), ive been asked to calculate the characteristic impedance of it. For information, the CAN speed is 125kbps, so it is my understanding that we dont treat it as a transmission line.

Shielded twisted pair. Conductors in red, insulation orange and yellow, and shield in grey(conductors in red, foil shield in grey, and insulation in orange and yellow)

The equivelant cross section if a seperate wire is used (The equivelant cross section if a seperate wire is used)

From the following reference page of cable design equations, I can see that even a jacket on the outside of the shield (as I have) affects the impedance equation, but I have been unable to find any reference explaining mathematically how a drain wire would affect the equation. Anecdotaly I would imagine that the impedance of the shielding will be reduced due to a larger cross sectional area, but cant say much more than that. From my googling, I havent come across any instances of someone trying the same thing, and personally ive only ever used shielded twisted pairs without a drain wire. It may be that theres a good reason for this, in which case im happy to go back to management and tell them so, but im stumped. Can anyone point me in the right direction please?

Edit: Have added a sketch showing a rough idea of how this saves space compared to having the return line in a seperate wire.

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    \$\begingroup\$ "Management have however requested that we insert a drain wire into this twisted pair as a current return path" - this begs the question as to whether "management" are qualified to make this call and, if qualified, for what purpose is the drain wire (other than making an easy connection to the shield)? \$\endgroup\$ – Andy aka Oct 1 '19 at 12:20
  • \$\begingroup\$ Arguably, theyre not! And thats why I am more than prepared to go back and tell them no if theres a good reason, but I need to be able to justify it. \$\endgroup\$ – cstanto Oct 1 '19 at 12:30
  • \$\begingroup\$ The drain wire will be the ground connection to the asic that the CAN bus connects to. \$\endgroup\$ – cstanto Oct 1 '19 at 12:31
  • \$\begingroup\$ So ask them why they want it and get them to justify the cost for bespoke cable. \$\endgroup\$ – Andy aka Oct 1 '19 at 12:32
  • \$\begingroup\$ They want it as it saves space elsewhere for other cables. \$\endgroup\$ – cstanto Oct 1 '19 at 12:39

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