Murray loop bridge

The Murray loop bridge is a bridge circuit used for locating faults in underground or underwater cables.^[1][2] It has been used for more than 100 years^[3] but is being replaced by the more precise Time-domain reflectometer.

One end of the faulted cable is connected through a pair of resistors to the voltage source. Also a null detector is connected. The other end of the cable is shorted. The bridge is brought to balance by changing the values of R_B1 and R_B2, which is achieved when:

${\displaystyle {\frac {R_{x}}{R_{g}+R_{y}}}={\frac {R_{B1}}{R_{B2}}}}$

which is equivalent to:

${\displaystyle R_{x}=(R_{g}+R_{y})\cdot {\frac {R_{B1}}{R_{B2}}}}$

The value of resistance R_x is proportional the length L_x, thus the location of the fault can be calculated:

${\displaystyle L_{x}=2\cdot L\cdot {\frac {R_{B1}}{R_{B1}+R_{B2}}}}$

where L is the total length of the cable under test - a value proportional to R_g.

The method assumes a single fault exists, of low resistance compared with the undamaged cable insulation resistance, and that the cable conductors have uniform resistance per unit length.