Measuring length of two wires inside copper with a TDR

Question

I have a cable as in the drawing.

The black parts are insulators and the brown parts are copper, so there is a big copper cable and inside are two smaller copper cables.

When the big copper cable is tied to ground I can use a time domain reflectometer (TDR) on the smaller cables to determine the length of the cable.

What happens if the big copper cable is in use with a current running through it that is 1000 times bigger than the current running through the two smaller copper cables? Will I still be able to determine the length with a TDR?

I think there shouldn't be a capacitance between the two smaller copper cables - but how am I then able to measure with it a TDR?

Answer 1

There is capacitance from each of the smaller conductors to the larger conductor, so there might be an effective capacitance between the smaller conductors equal to one-half of their capacitance to the larger conductor.

Of course, that does not imply that the capacitance to the larger conductor has no effect. Your statement that the larger conductor "has current going through it" is not enough information to judge how any signal on the larger conductor would influence the smaller conductors.

Answer 2

The effect of an AC or DC current in the large copper is a time-varying or constant magnetic field encompassing the little conductors. This field can in turn induce a current in the smaller conductors, in addition to any voltage induced through capacitive coupling.

A TDR length measurement, in general, is based on a measurement of reflections from the change in impedance (an open, or a short) at the end of the cable. It does not involve the direct measurement of capacitance or resistance of the cable.

In theory, the TDR does not have to be affected by such currents. And in practice, if you perform a "pedestrian" TDR measurement with a signal generator and a scope, you should be able to determine the length, or location of faults, regardless unrelated voltages or currents on the wire.

However, what happens may be specific to the TDR you are using: if the perceived change in impedance is affected by the induced currents or voltages due to the large conductor, then the algorithms internal to the TDR may be thrown off.

Knowing nothing more about your specific TDR device and the frequency of the current through the large conductor, it is unlikely we can provide a definitive answer.

However, you could provide more specific details (currents, frequency, type of wire, TDR model, more about the circumstances/application) and perhaps someone here has experienced a similar set-up.

Or, you could set up a mini experiment if you have a piece of that cable of known length, to determine whether the current affects the TDR processing by comparing the TDR's length measurement against the actual.

If, however, you are using a DMM to measure R and/or C and determine the length form it, then that's a different question.

Answer 3

If you attempt to measure the length of your cable by calculating the phase or group velocity of a signal based upon the RCLG parameters of the cable, you must take into consideration that the circuit is not the standard transmission line model

^{simulate this circuit – Schematic created using CircuitLab}

Instead, you have this:

^{simulate this circuit}

By symmetry, I would surmise that the RCLG parameters you want to use to calculate the phase or group velocity of a signal are those between one of the small conductors and the large conductor. The parameters between the two small conductors will different by a constant factor of either 2 (for the series elements) or \$\frac{1}{2}\$ (for the shunt elements)

These will not be the same as the RCLG parameters between the two small conductors if the large conductor were replaced by air or other insulating material.

Phase velocity (in the "flat phase velocity region") will still be

\$V_{\phi} = \frac{\displaystyle 1}{\displaystyle \sqrt{LC}}\$

but with the larger \$C\$ due to the more intimate relationship between the larger and smaller conductor, than between the two smaller conductors when separated by an insulator, and an \$L\$ that has probably changed also due to the different geometry.

In short, the RCLG parameters you should use are those of a coaxial cable consisting of one of the smaller conductors, its surrounding insulation, and the larger conductor, (or equivalently, those parameters adjusted by factors of 2 and \$\frac{1}{2}\$).