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Twisted Pair Wire Model

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LAN_403

dude_500

Sat Feb 04 2012, 08:39AM

Registered Member #2288 Joined: Wed Aug 12 2009, 10:42PM
Location: Cambridge, MA
Posts: 179

I'm wondering what the inductive model for a twisted pair set looks like. Attached is a picture of what I think would be the two possibilities, but I'm not sure which it is.

In one sense it should be the first since they are wires traveling in the same direction, but at the same time they are technically wound in opposite directions (I think, it's hard to visualize even looking at it if that's actually true) making their actual winding inductance out of phase. Not sure which of these would dominate.

Mattski

Sat Feb 04 2012, 08:57AM

Registered Member #1792 Joined: Fri Oct 31 2008, 08:12PM
Location: University of California
Posts: 527

It would be the first way - for this purpose it doesn't matter much if the wires are twisted together or not, it only matters that they run in the same direction. If a current flows in one wire, a current will tend to flow in the opposite direction in the other wire so as to minimize the increase in magnetic field. Since a current flowing into L5's dot flows out of L4's dot, it is the first picture since this puts the currents in opposite directions.

Depending on what you're doing with the wire it may also be useful to consider a transmission line model with a number of series inductors with shunting capacitors in between.

Dr. Slack

Sat Feb 04 2012, 09:03AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Another way to look at it is the phaseing of the voltage that's generated by changing the flux linking both windings. As the flux changes, both wires pretty much take the same path, both will see the change with the same polarity, so will have have dots at the same end. This is easy to generalise to N conductors

radiotech

Sat Feb 04 2012, 09:05AM

Registered Member #2463 Joined: Wed Nov 11 2009, 03:49AM
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Posts: 1546

The twisted pair would the Second model, for the following reason:

The pair is a transmission line and the current flow on the top wire is
left to right, through the load and back to the source on the bottom
wire right to left. Therefore the impedance looking down the line is
resistive.

Whether its twisted or not, it is the same. The reason it is twisted is to
prevent external magnetic fields from inducing currents in the line.
-----------------------------
What I think you are asking is what happens when you wind a coil with
a twisted pair connecting the two wires in parallel. and the start and finish
of the winding being the ends of the pair. In this case the First model is
correct.

------------------------------

jpsmith123

Sat Feb 04 2012, 03:40PM

Registered Member #1321 Joined: Sat Feb 16 2008, 03:22AM
Location:
Posts: 843

It would be as shown in the first picture. There are several ways to visualize it. One way is to imagine the two wires bent into two parallel loops, for example, and apply say a positive voltage to one end of one wire, and then use Lenz' law to see which way an induced current would flow in the other loop.

Another way - which is what I think Dr. Slack is suggesting - is to imagine the two wires in proximity to yet another parallel wire, with alternating current flowing in it. And in this case the two wires would be indistinguishable from each other and the induced voltages would be essentially of the same magnitude and phase.

Dr. Slack

Sun Feb 05 2012, 08:06AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

#radiotech

There is no debate, the first diagram is correct. The only debate is about finding a way to visualise it, so that the model sits well with experience, is easy to remember and to apply to other similar scenarios

There are two rules for ideal (100% coupling, infinite inductance) transformers (which is what an ideal wire pair is)

a) all the dots have the same polarity, which generalises to all windings have the same volts per turn (because they share the same flux)
b) the algebraic sum of all currents into the dots is zero (strictly speaking only for equal numbers of turns, this generalises to the sum of all ampere turns is zero (because the flux tends to resist change)

Which is more convenient to use to understand the phasing of any given scenario if usually a matter of taste. To understand what happens when you've got a flyback, or are wrapping a few turns of a twisted pair around a core to make a common mode choke, you'll need both.

Steve Conner

Sun Feb 05 2012, 10:32AM

Registered Member #30 Joined: Fri Feb 03 2006, 10:52AM
Location: Glasgow, Scotland
Posts: 6706

Well guess what, I think both are true!

Reason: The twisted pair of wires has a common-mode inductance like in the left diagram. But it also has a leakage inductance between the two wires, since coupling isn't perfect.

Along with the capacitance between cores, this determines the impedance for signals in the differential mode.

Dr. Slack

Sun Feb 05 2012, 01:16PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

No excuse for my arrogance really, go into transformer / common mode choke / GDT mode of thought, and lose the other possibilities.

Once you've said common mode or differential mode to define the problem, the answer is as good as given. Common mode by definition uses both wires in the same polarity, differential uses them in opposite polarities.

If you are setting up a simulation where one or the other dominates, then use the dominating mode.

If both modes have a significant effect, then use both in series, with appropriate values. Perhaps the easiest model to use is a floating transmission line of an impedance to represent the characteristic impedance due to the distributed differential mode inductance and capacitance, in series with a common mode transformer with a suitable primary inductance which reflects whether the line pair is wrapped round a core.

In practice, it's easy to get large changes in common mode inductance by wrapping the pair round a core, but difficult to have much control over the differential mode, which is pretty much set by the wire diameter and insulation thickness. So it's easy to get the common mode to dominate. In my defence, I think it's that difference that skewed my take on the question.

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