Impedance Measurement by a Resistive Bridge

The possibility of measuring an unknown impedance Z=R+jX by including it in one arm of a Wheatstone bridge, whose other arms are purely resistive, is examined. It is shown that by adjusting the variable resistance for minimum bridge output and measuring this output, one can calculate the magnitude ¿Z¿, the resistive part R, and the magnitude of the reactive part ¿X¿ of the unknown impedance. Using a fixed auxiliary capacitor whose reactance is less than 2¿X¿, the sign of the reactive part can also be determined. The sensitivity of the bridge decreases as the ratio ¿X¿/R increases; this can be remedied by adding a suitable series resistance to Z and/or by measuring the bridge output when its rate of variation with the adjustable resistance is maximum. An alternative method not involving voltage measurements, but requiring a suitable fixed, standard inductor or capacitor, has also been discussed. The theory involved in these measurements is pretty well within the reach of a sophomore student of electrical engineering and as such, this may constitute a simple, but interesting, laboratory exercise at that level.