Locating a cable fault — the Murray loop test as an alternative to TDR

The TDR guide covers how a time domain reflectometer determines the distance to a cable fault from the travel time of a reflected pulse — noting that a TDR does not always reliably see a fault with a relatively high transition resistance. The Murray loop test, a classic resistance-bridge technique related to the Wheatstone bridge, offers an alternative in that situation: instead of measuring a reflected pulse, the fault location is calculated from a resistance ratio.

The test setup

The Murray loop test requires, in addition to the faulty core, a healthy core of identical cross-section and length — for example an unused core in the same multicore cable, or a temporary test conductor of matching length pulled in alongside it. At the far end, the healthy core is bonded to the faulty core, forming a closed loop with a total length of 2L (out along the faulty core to the fault, then back along the remainder of the faulty core and the healthy core). At the test end, this loop is included in a bridge circuit with two adjustable resistance arms (P and Q), in series with a galvanometer/null detector.

The balance formula

By varying P and Q until the bridge is balanced (no deflection on the null detector), the distance to the fault follows from:

Lx = 2PL / (P + Q)

where Lx is the distance from the test end to the fault, L is the total (known) length of the cable, and P/Q are the resistance values of the two bridge arms at balance. Because the conductor resistance per unit length cancels out of the ratio, this calculation does not require exact knowledge of the resistivity of the conductor material — only the total cable length L and the balance ratio P/Q.

When this method succeeds where TDR falls short

Higher transition resistance of the fault — the Murray loop test works on the basis of a DC resistance measurement through the fault itself, and can therefore also locate faults that appear too "soft" for a TDR (which depends on a sufficiently sharp impedance mismatch).
Long cable runs where TDR resolution is limited — over long runs a small uncertainty in the TDR's assumed propagation velocity can produce a larger absolute error in the calculated distance; the Murray loop test is less sensitive to this, provided L is known accurately.

Limitations

The method requires a healthy core of identical cross-section and length to form the loop — for a single-core cable without a spare conductor, this method is not directly applicable without pulling in a temporary parallel test conductor. In addition, the fault must be conductive enough to allow a measurable current through the bridge: a fully open break (no conductive path at all) cannot be located with this method and requires a different technique (for example TDR, which gives a clear reflection precisely at an open break).

Practical relevance

When an initial TDR reading does not give a clear or consistent result for a cable fault — for example because of a high transition resistance at the fault — the Murray loop test can be used as a second, independent technique, provided a healthy core of matching cross-section and length is available. For multicore supply cables with an unused spare core this is often straightforward; for single-core cables a suitable test setup must first be arranged.

Common mistakes

Using a healthy core of a different cross-section or length — the balance formula assumes identical resistance per metre for both cores in the loop; a mismatch here introduces a systematic error into the calculated distance.
Applying the method to a fully open break — without any conductive path through the fault there is no current to balance the bridge; TDR is the more suitable technique here.
Estimating the total cable length L instead of measuring it or taking it from documentation — the accuracy of Lx is directly dependent on the accuracy of L.
Ignoring temperature effects on conductor resistance when there is a significant temperature difference between the healthy and the faulty core (for example when one core lies in the sun and the other in the shade) — this can affect the resistance ratio and therefore the calculated distance.