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<title>Murray loop bridge</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Murray loop bridge</span></span>

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<p>The <b>Murray loop bridge</b> is a <a href="Bridge_circuit" title="Bridge circuit">bridge circuit</a> used for locating faults in underground or underwater <a href="Electrical_cable" title="Electrical cable">cables</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> It has been used for more than 100 years<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> but is being replaced by the more precise <a href="Time-domain_reflectometer" title="Time-domain reflectometer">time-domain reflectometer</a>.

</p><p>One end of the faulted cable is connected through a pair of <a href="Resistor" title="Resistor">resistors</a> to the voltage source. Also a <a href="Null_detector" title="Null detector">null detector</a> is connected. The other end of the cable is shorted. The bridge is brought to balance by changing the values of <i>R<sub>B1</sub></i> and <i>R<sub>B2</sub></i>, which is achieved when:

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {R_{x}}{R_{g}+R_{y}}}={\frac {R_{B1}}{R_{B2}}}}">

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<annotation encoding="application/x-tex">{\displaystyle {\frac {R_{x}}{R_{g}+R_{y}}}={\frac {R_{B1}}{R_{B2}}}}</annotation>

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</math></span><img src="./33cc429bbf4a4037697eca00675101d6f5f126c4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.275ex; height:5.843ex;" alt="{\displaystyle {\frac {R_{x}}{R_{g}+R_{y}}}={\frac {R_{B1}}{R_{B2}}}}" loading="lazy"></span>

</p><p>which is equivalent to:

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{x}=(R_{g}+R_{y})\cdot {\frac {R_{B1}}{R_{B2}}}}">

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<annotation encoding="application/x-tex">{\displaystyle R_{x}=(R_{g}+R_{y})\cdot {\frac {R_{B1}}{R_{B2}}}}</annotation>

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</math></span><img src="./4ac07db1803f64b53bc94048c681e24d48d8c164.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:22.864ex; height:5.509ex;" alt="{\displaystyle R_{x}=(R_{g}+R_{y})\cdot {\frac {R_{B1}}{R_{B2}}}}" loading="lazy"></span>

</p><p>The value of resistance <i>R<sub>x</sub></i> is proportional the length <i>L<sub>x</sub></i>, thus the location of the fault can be calculated:

</p><p><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{x}=2\cdot L\cdot {\frac {R_{B1}}{R_{B1}+R_{B2}}}}">

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<annotation encoding="application/x-tex">{\displaystyle L_{x}=2\cdot L\cdot {\frac {R_{B1}}{R_{B1}+R_{B2}}}}</annotation>

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</math></span><img src="./ee063baeb481ef654f78ca6cf283482ec5e07d0f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.765ex; height:5.509ex;" alt="{\displaystyle L_{x}=2\cdot L\cdot {\frac {R_{B1}}{R_{B1}+R_{B2}}}}" loading="lazy"></span>

</p><p>where <i>L</i> is the total length of the cable under test - a value proportional to <i>R<sub>g</sub></i>.

</p><p>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.

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<div class="mw-heading mw-heading2"><h2 id="Varley_loop">Varley loop</h2></div>

<p>The similar Varley loop uses fixed resistors for RB1 and RB2, and inserts a variable resistor in the faulted leg. Test sets for cable testing can be connected for either bridge technique. If the fault resistance is high, the sensitivity of the Murray bridge is reduced and the Varley loop may be more suitable.

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<ul><li><a href="Fault_(power_engineering)" class="mw-redirect" title="Fault (power engineering)">Fault (power engineering)</a></li>

<li><a href="Time-domain_reflectometer" title="Time-domain reflectometer">Time-domain reflectometer</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20120217004355/http://sciencelinks.jp/j-east/article/200324/000020032403A0828577.php">"Science Links Japan | Development of Murray Loop Bridge for High Induced Voltage"</a>. <i>sciencelinks.jp</i>. Archived from <a rel="nofollow" class="external text" href="http://sciencelinks.jp/j-east/article/200324/000020032403A0828577.php">the original</a> on February 17, 2012.</cite></span>

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<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external free" href="https://www.jstage.jst.go.jp/article/ieejpes/123/11/123_11_1411/_pdf">https://www.jstage.jst.go.jp/article/ieejpes/123/11/123_11_1411/_pdf</a> Development of Murray Loop Bridge for High Induced Voltage (PDF) [2509K] (Japanese)</span>

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<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Latimer Clark, Robert Sabine <i>Electrical tables and formulæ: for use of telegraph inspectors and operators</i>, E. & F.N. Spon, 1871 pp. 41-44</span>

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</style><div id="Bridge_circuits79" style="font-size:114%;margin:0 4em"><a href="Bridge_circuit" title="Bridge circuit">Bridge circuits</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Resistance</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Kelvin_bridge" title="Kelvin bridge">Kelvin bridge</a></li>

<li><a href="Wheatstone_bridge" title="Wheatstone bridge">Wheatstone bridge</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Resistance–Capacitance</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Schering_bridge" title="Schering bridge">Schering bridge</a></li>

<li><a href="Wien_bridge" title="Wien bridge">Wien bridge</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Bridged_T_circuit" class="mw-redirect" title="Bridged T circuit">Bridged T circuit</a></li>

<li><a href="Carey_Foster_bridge" title="Carey Foster bridge">Carey Foster bridge</a></li>

<li><a href="Fontana_bridge" title="Fontana bridge">Fontana bridge</a></li>

<li><a href="Lattice_filter" class="mw-redirect" title="Lattice filter">Lattice filter</a></li>

<li><a href="Transformer_ratio_arm_bridge" title="Transformer ratio arm bridge">Transformer ratio arm bridge</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Inductance</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Maxwell_bridge" title="Maxwell bridge">Maxwell bridge</a></li>

<li><a href="Anderson's_bridge" title="Anderson's bridge">Anderson's bridge</a></li>

<li><a href="Hay's_bridge" title="Hay's bridge">Hay's bridge</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Diode_bridge" title="Diode bridge">Diode bridge</a></li>

<li><a href="H-bridge" title="H-bridge">H-bridge</a></li></ul>

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