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A Bridge is a mechanism that is use for measuring unknown values of passive elements in circuit. Generally a DC excited bridge use for resistance measurement (ie. Wheatstone bridge) and AC excited bridge (ie Schering Bridge) for reactive components like capacitor or inductor.

schematic

simulate this circuit – Schematic created using CircuitLab

In general use of bridge, whether DC or AC excited, to measure unknown component, one can vary one or two components values. When the bridge is balanced which means Va and Vb in schematic is equal; with proportion of components one can define the unknown value.

Almost any tutorial tells about balanced condition calculations. Of course they are voltage indepedent and with proportion of components one can easily calculate values.

Question is, in the case which we want to find unknown component value without balanced condition(unbalanced condition) of course with measured voltages of Va and Vb, how can we do that?

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    \$\begingroup\$ If presented with values for Va and Vb you cannot definitively know the answer. \$\endgroup\$
    – Andy aka
    Mar 10, 2014 at 12:18
  • \$\begingroup\$ In the balanced bridge Va and Vb are equal and its easy to find the answer but for the unbalanced it should be possible to solve provided you know Va, Vb and the phase relationship between them. But unless you know the phase relationship too its not possible as Andy has already pointed out. \$\endgroup\$ Mar 10, 2014 at 12:25

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When a bridge is balanced, you know that there is no voltage between Va and Vb, and as a consequence, there is no current flowing between them as well. This vastly simplifies the circuit analysis, making it easy to determine the unknown component(s) relative to the known ones.

For small values of imbalance, it is possible to linearize the analysis around the balance point, which retains some of the simplicity, but for large values of imbalance, you're forced to do the full analysis of the entire circuit. It can be done, but you've given up all the advantage of using a bridge in the first place. Other circuit topologies would actually be simpler to analyze.

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  • \$\begingroup\$ Do you have an examples about other circuit topologies you mentioned? \$\endgroup\$
    – cheour
    Mar 10, 2014 at 13:35
  • \$\begingroup\$ Sure. You just connect the unknown impedance in series with a known impedance, measure the magnitude and phase of the voltage at the junction (relative to the excitation) and solve for the unknown. \$\endgroup\$
    – Dave Tweed
    Mar 10, 2014 at 14:04
  • \$\begingroup\$ As a note for others, this document link describes well what you mentioned. \$\endgroup\$
    – cheour
    Mar 10, 2014 at 18:20

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