Wheatstone Bridge: Balance measurements

Wheatstone Bridge: Balance measurements

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On: 23 Jun, 2019

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Category: Sensors

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The Wheatstone bridge measurement method, shown in Figure 3.15, is based on a feedback system, either electric or manual, whose function is to adjust the value of a standard resistor until the current through the galvanometer or other null indicat...

The Wheatstone bridge measurement method, shown in Figure 3.15, is based on a feedback system, either electric or manual, whose function is to adjust the value of a standard resistor until the current through the galvanometer or other null indicator is zero. Once the balance condition has been achieved, we have

wheatstone bridge balance measurements 2.png

wheatstone bridge balance measurements 1.png

FIGURE 3.L5 Comparison measurement method for a Wheatstone bridge. The adjustment to reach balance can be performed manually or automatically.

That is, changes in R3 are directly proportional to the corresponding changes we have to produce in Ra in order for the bridge to be balanced. This measurement method can also be used as a polarity detector because the output is positive or negative depending on whether,r is greater or less than a given threshold.


The condition (3.28) is reached independent of the power supply voltage or current and its possible variations. It does not depend on the type of detector or its impedance. Even more, it does not need to be linear because it must only indicate the balance condition. From (3.28) we can also deduce that the supply and the detector can interchange their positions without affecting the measurement. Figure 3.16 shows an arrangement for eliminating the influence that the contact resistance in the adjustable arm has on the measurement.


If the sensor is placed far from the bridge, we must consider the presence of long lead wires whose resistance adds to the sensor resistance. Their

wheatstone bridge balance measurements 6.png

FIGURE 3.16 Wheatstone bridge arrangement to cancel the effect of contact resistance on the balance.

values can be very high if low temperature coefficient resistive conductors such as constantan and manganin are used. Conversely, if copper wires are
used because ofits higher conductivity, then temperature changes can result in important errors.


This problem can be solved by using the Siemens or three-wire method shown in Figure 3.17a. Wires I and 3 must be equal and be subjected to the
same thermal changes. The characteristics of wire 2 are not important as in the balance condition no current flows through the bridge central arm. The
relative error in the measurement of R3 is

wheatstone bridge balance measurements 3.png

Figure 3.17b shows an alternative circuit with the same objective. The error in this case is given by an expression similar to (3 .29). In both cases the

wheatstone bridge balance measurements 4.png

FIGURE 3.17 Siemens or three-wire method for measuring with a Wheatstone bridge when long leads are used.

wheatstone bridge balance measurements 5.png

FIGURE 3.18 Wheatstone bridge using the comparison method with automatic balance and digital output.

error decreases when R3 is large with respect to Rw.Figure 3.17c shows how to apply this method to several sensors without using more than a single set of three long wires.


The application of the null method to dynamic measurements depends on the availability of a fast enough automatic balancing system. Figure 3.18 shows such a method [3]. It is based on a digital-to-analog converter whose analog outputs are in the form of two complementary current sources. That is, in addition to a current corresponding to the digital input, it outputs another current corresponding to the complementary digital input. This way the sum of both currents is always a constant regardless of the digital input.


In Figure 3. 18 any imbalance of the bridge output exceeding the comparator threshold modifies the converter outputs, via the up-down counter, so
that one of them sinks the additional current necessary to keep the drop in voltage constant in both voltage dividers. At the same time the other converter output reduces the amount of current it sinks, thus contributing to the voltage balance which is reached independently of the sign of the change experienced by the sensor. The output of the system is then the digital word present at the input of the converter in order for the bridge to remain balanced.

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