Power Supply of Wheatstone Bridges
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To obtain an output signal from a Wheatstone bridge as a result of the change in one or more sensors placed in its arms, we must supply the bridge with electric excitation. Whether voltage or current, dc 6r ac, this supply must be stable with time...
To obtain an output signal from a Wheatstone bridge as a result of the change in one or more sensors placed in its arms, we must supply the bridge with electric excitation. Whether voltage or current, dc 6r ac, this supply must be stable with time and temperature. This is due to a simple fact: When a resistive bridge is supplied by a dc voltage, for example, the output voltage is (Equation 3.31)
Now if while r remains constant, V undergoes a small change dV. Then we have
FIGURE 3.31 Measurement of average values by means of a resistance bridge. All sensors must have the same nominal resistance and sensitivitv.
which means that the output undergoes the same percent change. This may preclude, for example, the use of an ordinary power voltage supply with a O.lVol"C drift or that of some monolithic voltage regulators with thermal drifts in excess of lTol'C.
In applications where high precision is required, we must use high-quality acldc or dc/dc converteis or reference voltage generators like the ones used in multiplying DACs (digital-to-analog converters). Table 3.3 gives the sta- bility characteristics for several of these components.
Another factor to be considered is the maximal output current of the supply unit. Reference voltage generators used in ADCs and DACs, for example, source a maximal current lower than 20 mA and a voltage of + 10 V. Therefore they can be directly applied only to bridges having a 500-O or higher resistance. If larger voltage or current is needed then the supply output must be amplifled without degrading its stability. Figure 3.32 shows a circuit proposed for this application .
The need for a high stability for the supply voltage does not apply if the bridge output voltage is further processed by dividing it by the reference voltage. If the same voltage is used for supply and as a reference, then their possibl- drifts cancel. These kinds of measurements are called ratiometric.
This measurement principle can be applied, for example, when the pro- cessing circuitry includes an ADC because an ADC operates as a divider with digital output. Figure 3.33 shows that the inpur-voltage to the converter is compared with the reference voltage; that is, it is divided by it. If the voltage supply for the bridge were ac, the same method could be used, but the ac voltage would have to be rectified in order to yield the reference voltage. The voltage supply for the amplifier does not require high stability because the amplifier is able to reject its variations, as given by the specified PSRR (Power Supply Rejection Ratio).
Another supply-related problem arises when a low-resistance bridge is so far away that lead wire resistances can no longer be neglected. The problem does not arise if the bridge is supplied by a current instead of a voltage. But usually it is more cumbersome to have a low drift current source than a voltage source. For a voltage supply the solution relies on applying the four wire method shown in Figure 3.34.
It consists of applying the voltage with two wires and detecting the drop in voltage across the bridge using a different pair of wires; after amplification (G) the detected voltage is used to adjust the voltage output from the source by means of a high-gain amplifier (A). Note that this method does not avoid the drop in voltage along the supply lead wires but only yields the desired supply voltage across the bridge. Therefore the power supply will have to provide the bridge voltage plus the voltage drop along the wires. For the particular case of reference voltage generators that accept an error signal in the form of a current, it is possible to implement a circuit of this kind by using only three wires as shown in Figure 3.35 U).
A last consideration relative to bridge supplies concerns the choice ofa dc or ac signal for excitation. If a dc signal is used, then the thermoelectromo- tive effects (Section 6.1.1) appearing in junctions of dissimilar metals and amplifier drifts cause errors that restrict the physical layout of the circuit. An ac supply avoids thermoelectromotive effects but stray capacitances may cause bridge imbalance, Between a strain gage and the structure it is bonded on is a capacitance of approximately 100 pF. The impedance of stray capaci- tances has a more pronounced effect at high frequencies. But the supply frequency cannot be arbitrarily low if we measure dynamic variables as we will flnd in Chapter 5. Furthermore, if the measurement range includes both positive and negative values, we will require a phase-sensitive detector in order to know the sign of the bridge's outpirt signal. As a result an ac supply is not usually used, except in those applications where the available sensor favors that kind of supply or when we desire the low noise of ac amplifiers.
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